Hi folks!
Under the "Point Nine Recurring Equals One (or not)" topic discussions in the "Puzzling Questions" forum, I had spoken of 'giving' maths a more 'contextual' basis so as to make it MORE relevant, effective and robust for 'modeling reality'.
Judging by some of the responses, certain professional mathematicains and mathematics enthusiasts seemed to take umbrage when they heard that some of us 'on the outer' were not entirely 'satisfied' with the 'incomplete' status quo; and that some of us were even actively trying to improve mathematics from what it IS...to what it COULD BE...by simply looking again at it's 'foundations' and 'axioms' PER SE with a new 'perspective'.
Quoted just below is the latest reaction from one who is riled at the thought that some 'non-entity' (mathematics-wise, hehehe) has the gall and temerity to 'challenge' the maths status quo with which mathematical types/professionals are apparently quite 'satisfied' and 'content'. This reaction from NCN was even AFTER I pointed out to all that "Rome wasn't built in a day"....and neither was 'Mathematics'.
QUOTE (NoCleverName+Jul 10 2007, 09:36 AM)
Put up or shut up.
NCN's impatience has led him to make that 'retort'. His 'impatient challenge' I think makes an unfair demand, especially since MY work on 'Contextual Mathematics/Number Theory' has only been going for a few years VERY PART TIME...while the CURRENT status quo in maths/number theory has had CENTURIES and THOUSANDS OF MATHEMATICIANS to get to the current stage!
HOWEVER....Just to show him and everyone else that I have been merely criticising CONSTRUCTIVELY and with 'constructive alternatives' in mind, I will accede to NCN's request to "put up or shut up", hehehe!
I will here put ONE ITEM OF MANY within current mathematics/number theory that need 'sorting out' if maths/number theory is to ADVANCE and become IMMEDIATELY MORE RELEVANT.
Again, the following observation is but ONE of the perceived maths 'improvement areas' according to my 'contextual perspective' in the field.
In the reality context of observable phenomena, there is NO SUCH THING/POSSIBILITY as an 'abstract' NUMBER LINE.
ANY 'line' one cares to set out or draw is in reality IMMERSED in PROCESS and MOVEMENT...and as such is NOT an 'absolute' or 'defined' THING or DISTANCE etc.
So all the ZENO PARADOXES and 'progressive series' LIMITS and FUNCTIONS based on the IDEA that such a 'line' is COMPLETE AND STATIC from one 'end' to the 'other end' is in 'reality process context' FALLACIOUS from the outset.
Hence all those 'weird' things like Cantor's Set etc which come up with 'logical' BUT 'irrelevant in reality' results (like removing as many parts of a 'line' in a continuous process and STILL ending up with an 'INFINITE NUMBER OF POINTS' left on that 'line'.
One can see that the analysis of ANY 'line', WHEREVER OR HOWEVER OR WHENEVER IT IS 'DRAWN', and WHETHER PHYSICAL OR ABSTRACT, should allow for the 'contextual' fact that it is NOT 'stationary'. It is actually ALWAYS MOVING (in space-time? or whatever).
In other words, even as we 'LOOK' at and 'DISECT' a 'line' and make 'mathematical/number theory' observations about its 'properties', we are MISSING THE FACT that the 'line' we are analysing bears NO RELATION to the presumed stationary/absolute/finite 'distance/length' line we 'abstractly' and mistakenly 'see'.
Since the 'line' is actually tracing a PATH/TRAJECTORY THROUGH 'SPACETIME (or whatever), ANY so-called 1-DIMENSIONAL 'line' is actually a 2-DIMENSIONAL TIME/SPACE-dependent PLANE/MEMBRANE etc.
And THAT is ONE of the reasons why maths/number theory CURRENTLY gets all those weird results....because they are actually dealing with 'processes/functions that have LATERAL 'EXCURSION' 'properties/results' from the 'imagined' original 'LINEAR' construct.
Anyhow, NCN, I hope this shows that I (and everyone who is not satisfied with the maths status quo) aren't NECESSARILY as 'lazy' as you think.
Whether right or wrong, the above 'perspective' was arrived at through 'effort' beyond the 'accepted' orthodoxy 'pathway'...and as such involved a LOT more 'effort' than just UNQUESTIONINGLY and COMPLACENTLY 'following along with the crowd and the status quo'.
That's all the hints I can give you at this time, mateys!
The rest will have to wait until I have more time (oh what precious commodity!) to consider and incorporate the results of further stage results in our TOE efforts. Hopefully soon!
And now, mathematicians and non-mathematicians alike....GOOD DISCUSSING....and play nice, please.
Cheers all!
RC.
.
NCN's impatience has led him to make that 'retort'. His 'impatient challenge' I think makes an unfair demand, especially since MY work on 'Contextual Mathematics/Number Theory' has only been going for a few years VERY PART TIME...while the CURRENT status quo in maths/number theory has had CENTURIES and THOUSANDS OF MATHEMATICIANS to get to the current stage!
HOWEVER....Just to show him and everyone else that I have been merely criticising CONSTRUCTIVELY and with 'constructive alternatives' in mind, I will accede to NCN's request to "put up or shut up", hehehe!
I will here put ONE ITEM OF MANY within current mathematics/number theory that need 'sorting out' if maths/number theory is to ADVANCE and become IMMEDIATELY MORE RELEVANT.
Again, the following observation is but ONE of the perceived maths 'improvement areas' according to my 'contextual perspective' in the field.
In the reality context of observable phenomena, there is NO SUCH THING/POSSIBILITY as an 'abstract' NUMBER LINE.
ANY 'line' one cares to set out or draw is in reality IMMERSED in PROCESS and MOVEMENT...and as such is NOT an 'absolute' or 'defined' THING or DISTANCE etc.
So all the ZENO PARADOXES and 'progressive series' LIMITS and FUNCTIONS based on the IDEA that such a 'line' is COMPLETE AND STATIC from one 'end' to the 'other end' is in 'reality process context' FALLACIOUS from the outset.
Hence all those 'weird' things like Cantor's Set etc which come up with 'logical' BUT 'irrelevant in reality' results (like removing as many parts of a 'line' in a continuous process and STILL ending up with an 'INFINITE NUMBER OF POINTS' left on that 'line'.
One can see that the analysis of ANY 'line', WHEREVER OR HOWEVER OR WHENEVER IT IS 'DRAWN', and WHETHER PHYSICAL OR ABSTRACT, should allow for the 'contextual' fact that it is NOT 'stationary'. It is actually ALWAYS MOVING (in space-time? or whatever).
In other words, even as we 'LOOK' at and 'DISECT' a 'line' and make 'mathematical/number theory' observations about its 'properties', we are MISSING THE FACT that the 'line' we are analysing bears NO RELATION to the presumed stationary/absolute/finite 'distance/length' line we 'abstractly' and mistakenly 'see'.
Since the 'line' is actually tracing a PATH/TRAJECTORY THROUGH 'SPACETIME (or whatever), ANY so-called 1-DIMENSIONAL 'line' is actually a 2-DIMENSIONAL TIME/SPACE-dependent PLANE/MEMBRANE etc.
And THAT is ONE of the reasons why maths/number theory CURRENTLY gets all those weird results....because they are actually dealing with 'processes/functions that have LATERAL 'EXCURSION' 'properties/results' from the 'imagined' original 'LINEAR' construct.
Anyhow, NCN, I hope this shows that I (and everyone who is not satisfied with the maths status quo) aren't NECESSARILY as 'lazy' as you think.
Whether right or wrong, the above 'perspective' was arrived at through 'effort' beyond the 'accepted' orthodoxy 'pathway'...and as such involved a LOT more 'effort' than just UNQUESTIONINGLY and COMPLACENTLY 'following along with the crowd and the status quo'.
That's all the hints I can give you at this time, mateys!
The rest will have to wait until I have more time (oh what precious commodity!) to consider and incorporate the results of further stage results in our TOE efforts. Hopefully soon!
And now, mathematicians and non-mathematicians alike....GOOD DISCUSSING....and play nice, please.
Cheers all!
RC.
.
So you are going to are going to develop a ToE with the mathematical equivalent of counting on your fingers? Good luck with that.
Without generality and abstraction the math becomes too cumbersome to be usefull. I would need one theory to perform addition on apples and another for oranges. The beauty of math is that it works regardless of context.
Without generality and abstraction the math becomes too cumbersome to be usefull. I would need one theory to perform addition on apples and another for oranges. The beauty of math is that it works regardless of context.
QUOTE (Wulf+Jul 11 2007, 01:58 AM)
So you are going to are going to develop a ToE with the mathematical equivalent of counting on your fingers? Good luck with that.
Without generality and abstraction the math becomes too cumbersome to be usefull. I would need one theory to perform addition on apples and another for oranges. The beauty of math is that it works regardless of context.
Hi Wulf!
Thanks for your input, mate.
Can you explain how you got that from the hints I posted?
And can you point to the law that says maths would become "...too cumbersome..." with more 'context' as indicated?
In any case, would you prefer less cumbersome and less relevant; or more cumbersome and more relevant?hehehe.
And did you miss where I specifically said that THIS EXAMPLE was but ONE of the many items needing re-thinking across all the current mathematics?
Did you understand what the observations IMPLY for the current ABSTRACTION, STATIONARY and FINITE 'view' and 'practice' in 'number line' analysis and logics which my observations suggest 'may be' INADEQUATE AS THEY ARE...and so could do with some 'enhancing' because they give 'weird' and 'undefined' results?
Please elaborate if you have any specific 'counter-argument' to the observations/implications.
It would be very welcome by all here.
If you are indeed serious about mathematics and its future, please try to resist the temptation to 'knee-jerk' reactions, and take the time you require to calmly consider the implications before you respond further.
Cheers and thanks again mate!
RC.
.
Without generality and abstraction the math becomes too cumbersome to be usefull. I would need one theory to perform addition on apples and another for oranges. The beauty of math is that it works regardless of context.
Hi Wulf!
Thanks for your input, mate.
Can you explain how you got that from the hints I posted?
And can you point to the law that says maths would become "...too cumbersome..." with more 'context' as indicated?
In any case, would you prefer less cumbersome and less relevant; or more cumbersome and more relevant?hehehe.
And did you miss where I specifically said that THIS EXAMPLE was but ONE of the many items needing re-thinking across all the current mathematics?
Did you understand what the observations IMPLY for the current ABSTRACTION, STATIONARY and FINITE 'view' and 'practice' in 'number line' analysis and logics which my observations suggest 'may be' INADEQUATE AS THEY ARE...and so could do with some 'enhancing' because they give 'weird' and 'undefined' results?
Please elaborate if you have any specific 'counter-argument' to the observations/implications.
It would be very welcome by all here.
If you are indeed serious about mathematics and its future, please try to resist the temptation to 'knee-jerk' reactions, and take the time you require to calmly consider the implications before you respond further.
Cheers and thanks again mate!
RC.
.
QUOTE (RealityCheck+Jul 10 2007, 08:24 PM)
Hi Wulf!
Thanks for your input, mate.
Can you explain how you got that from the hints I posted?
And can you point to the law that says maths would become "...too cumbersome..." with more 'context' as indicated?
In any case, would you prefer less cumbersome and less relevant; or more cumbersome and more relevant?hehehe.
And did you miss ehere I specifically said that this EXAMPLE was but ONE of the many items needing re-thinking across all the current mathematics?
Did you understand what the observations IMPLY for the current ABSTRACTION, STATIONARY and FINITE 'view' and 'practice' in 'number line' analysis and logics which my observations suggest 'may be' INADEQUATE AS THEY ARE...and so could do with some 'enhancing' because they give 'weird' and 'undefined' results?
Please elaborate if you have any specific 'counter-argument' to the observed implications.
It would be very welcome by all here.
If you are indeed serious about mathematics and its future, please try to resist the temptation to 'knee-jerk' reactions, and take the time you require to calmly consider the implications before you respond further.
Cheers and thanks again mate!
RC.
.
QUOTE
Can you explain how you got that from the hints I posted?
Cramming atm, but I'll take a quick shot...
First of all let us look at the math being 'Finite'. Without infinity you can't even define counting. Since you can always count one higher than your currently defined set. This is a clear example of the importance of the concept of infinity.
QUOTE (->
| QUOTE |
| Can you explain how you got that from the hints I posted? |
Cramming atm, but I'll take a quick shot...
First of all let us look at the math being 'Finite'. Without infinity you can't even define counting. Since you can always count one higher than your currently defined set. This is a clear example of the importance of the concept of infinity.
Did you understand what the observations IMPLY for the current ABSTRACTION, STATIONARY and FINITE 'view' and 'practice' in 'number line' analysis and logics which my observations suggest 'may be' INADEQUATE AS THEY ARE...and so could do with some 'enhancing' because they give 'weird' and 'undefined' results?
Actually this implies that your understanding of math is inadequate as it is. You don't seem to understand the implications of your own reasoning even at the most fundamental levels.
Anyhow, I have work to do. I'm sure others will give you more details, but I doubt you will be able to understand them.
QUOTE (Wulf+Jul 11 2007, 02:51 AM)
Cramming atm, but I'll take a quick shot...
First of all let us look at the math being 'Finite'. Without infinity you can't even define counting. Since you can always count one higher than your currently defined set. This is a clear example of the importance of the concept of infinity.
Actually this implies that your understanding of math is inadequate as it is. You don't seem to understand the implications of your own reasoning even at the most fundamental levels.
Anyhow, I have work to do. I'm sure others will give you more details, but I doubt you will be able to understand them.
Hi Wulf!
The observations had to do with the conventional abstract 'number line' construct/analysis.
No more; no less.
What ever else you think I said is just that...your interpretation, mate!hehehe.
You seem to have somehow got it into your head that the concept of 'infinity' and 'counting' had something to do with what I observed per se.
They have not.
So please don't in your haste introduce/argue aspects irrelevant to what I have questioned HERE.
I merely point to the fact that NO PHYSICAL/ABSTRACT 'LINE CONSTRUCT' IS PROPERLY DEFINED or CORRECTLY ANALYSABLE UNLESS we RECOGNIZE AND ALLOW for the fact that no such line is EVER STATIC/FINITE in 'location/length' because all things have absolute/relative MOTION with respect to (spacetime? or) whatever the reality 'context' IS.
As such, the implication is that no analysis of ANY 'number line' PROPERTIES can be said to be COMPLETE without also considering the 'EXCURSION' across spacetime of the 'points' supposedly 'making up' that 'line' in any analysis/theory based on same.
Please try to comprehend what IS said and what is NOT said. Otherwise your input will miss the mark, hehehe!
Cheers and have fun "...Cramming atm..."!
RC.
.
QUOTE (RealityCheck+Jul 10 2007, 09:13 PM)
Hi Wulf!
The observations had to do with the conventional abstract 'number line' construct/analysis.
No more; no less.
What ever else you think I said is just that...your interpretation.
You seem to already got it into your head that the concept of 'infinity' and 'counting' have something to do with what I observed.
They have not.
So please don't in your haste introduce aspects I have NOT questioned HERE.
I merely point to the fact that NO PHYSICAL/ABSTRACT 'LINE CONSTRUCT' IS PROPERLY DEFINED or CORRECTLY ANALYSABLE UNLESS we RECOGNIZE AND ALLOW for the fact that no such line is EVER STATIC/FINITE in 'location/length' because all things have absolute/relative MOTION with respect to (spacetime? or) whatever the reality 'context' IS.
As such, the implication is that no analysis of ANY 'number line' PROPERTIES can be said to be COMPLETE without also considering the 'EXCURSION' across spacetime of the 'points' supposedly 'making up' that 'line' in any analysis/theory based on same.
Please try to comprehend what IS said and what is NOT said. Otherwise your input will miss the mark, hehehe!
Cheers and have fun "...Cramming atm..."!
RC.
.
I just used the simplest example that came to mind at first glance.
Lets try this in terms of your 'Finite' number line then, say I'm making measurements in km, and I am at the limit of precision of your line, the act of dropping down to cm for a calculation then converting back to km would lead to the loss of information. A finite representation is not scalable.
The reasonable responce to someone spotting serious flaws in your logic at a glance would be take a look and think a little. I'm not even a mathematician.
QUOTE (RealityCheck+Jul 10 2007, 09:21 PM)
In the reality context of observable phenomena, there is NO SUCH THING/POSSIBILITY as an 'abstract' NUMBER LINE.
Now, that is bizarre, RC! You don't see what is wrong with assuming that
Either the model *addresses* reality or it doesn't. If it does, then the model "is" reality. I am NOT saying that it's right because math books say so, of course (and I haven't read any lately anyway). If a means exists of reducing reality to its bare minimum so that it can be *addressed*, what that is supposed to mean to me is that the model is an infinitesimal of said reality thus its divisor, thus it has validity independent of the observer. The "observer" didn't quantize it... it was already like that when I got there
Similarly, (as far as *existence is concerned) if the abstract number line doesn't *exist*, what's to keep me from stating that my mind doesn't exist? That my worries are about nothing in particular? Take away the validity of the line number away and you have taken the validity of any theory of mind with it!javascript:emoticon(':(')
Either the model *addresses* reality or it doesn't. If it does, then the model "is" reality. I am NOT saying that it's right because math books say so, of course (and I haven't read any lately anyway). If a means exists of reducing reality to its bare minimum so that it can be *addressed*, what that is supposed to mean to me is that the model is an infinitesimal of said reality thus its divisor, thus it has validity independent of the observer. The "observer" didn't quantize it... it was already like that when I got there
Similarly, (as far as *existence is concerned) if the abstract number line doesn't *exist*, what's to keep me from stating that my mind doesn't exist? That my worries are about nothing in particular? Take away the validity of the line number away and you have taken the validity of any theory of mind with it!javascript:emoticon(':(')
ANY 'line' one cares to set out or draw is in reality IMMERSED in PROCESS and MOVEMENT...and as such is NOT an 'absolute' or 'defined' THING or DISTANCE etc.
Not so fast: are you saying that immersion in processing and movement has no presumed stationary/absolute/finite distance or length from my mind? That I am a part of the process of existence of that which is outside me? That the model does exist, does have validity, and that the fact that I am a part of it proves beyond a reasonable doubt that it exists independent of me? Finally, that strictly as a matter of immersion in processing and movement, that I am the center of all lines?
Aha! Thank you, I agree.
(Don't know what you are going to say but I agree!)
Hi Wulf! Why aren't you "...cramming atm..." instead of rashly replying here?hehehe.
Seriously, mate, you just HAVE to 'take a breath' and stick to the point.
What you just rattled off is mere 'convention' and 'bounded' perspective that has NOTHING to do with what is being observed in this topic.
One more time.....
Whatever 'line', or whatever conventional analysis IS being done on it, is NOT 'complete' in BASIS. See? No 'particular' CURRENT CONVENTIONAL AXIOMATIC argument as to what IS BEING DONE OR WHY has any bearing on the point that the 'line' construct ITSELF AS CURRENTLY 'defined' (and 'used/manipulated' by WHATEVER analytical system that CURRENTLY exists) is INADEQUATE AT BASIS.
All the things you are saying may or may not have relevance in what is NOW being 'done', but it has no bearing on what the observation implies regarding to the WHOLE BASIS for seeing that ANY 'line' construct AT ALL is NOT COMPLETE as it stands in definition/use NOW....simply because the 'axiomatic logics' of what is being done NOW has NOT allowed for the fact that the 'line' construct they based everything ON is NOT a COMPLETE/ADEQUATE ENOUGH 'construct' for current analyses and for what those analyses are expected to 'yield'....
.....which 'yield' is currently 'infested' with UNDEFINED and WEIRD 'things'.
Wouldn't it be nice to find out what all those 'undefined things' WERE? Have you no curiosity what they might IMPLY and and what might be accomplished if we 'treat' them so that they will no longer BE 'undefined'...and perhaps give us further information as to the underlying basis of reality in ALL contexts, and not just the 'already defined' ones?
Get "Cramming..." mate! This can wait until you have time to consider at leisure before 'knee-jerking' beside-the-point stuff into this discussion!hehehe.
And please try to keep in mind that THIS topic's observation/item is ONE among MANY OTHER parts of my 'contextual perspective' TOTALITY. Thanks.
Cheers!
RC.
.
One of the advantages of being willing to learn and puting thought into what I am learning is that I've developed a conceptual framework that allows me to quickly reason through things. There is nothing rash about my responses.
Do you need to sound out this sentence, or do you recognise the words without having to sound them out? Think a little.
Jya mata.
Hehehe. Give me 'slow' and 'complete' over 'quickly' and 'incomplete' anytime mate!
Still, for some people 'near enough' is apparently good enough if it gets them through the exams on the 'orthodoxy'.
Some other people 'try harder' even though they don't have to; because in some things, 'near enough' is NOT good enough, Wulf.
Can YOU read THAT and comprehend it OK with your 'quick reasoning'?
A reminder: Insults are NOT 'valid currency' in lieu of actual scientific debate on the point raised.
Cheers all!
RC.
.
That was meant to illustrate a point, not as an insult. Although I imagine it could be percieved that way if you caught your lips moving as you read it.
Hi StevenA! Was that ever raised in the 0.9r = 1 thread?
Perhaps AN, NCN et al can comment on your observations now?
Can you think of any 'contextual' terms/techniques that might 'enhance' those existing techniques/equations?
If not, maybe AlphaNumeric and NCN et al can help in this thread?
Gotta go for the rest of the day, folks. So....play nice!hehehe.
RC.
.
I believe I've made some comments along similar lines in that thread though likely not as directly about those specific discontinuities.
In terms of useful enhancements to integration and differentiation, I'd say an obvious one would be in frequency domain operations - like generating novel filter responses or Laplace transforms.
There's a stong disconnect between linear (additive) and exponential/logarithmic (multiplicative, which is linear on a logarithmic scale but this creates a 2 dimensional plane of values for numbers that has irreducible prime features) operations. Each is non-linear relative to the other and transformations between are the fundamental cause of complexity and we see this inherent in calculus as well. If we can remove this discontinuity then multiplication and addition could potentially be replaced by a single non-linear operation (my guess is we can take some clues from quantum mechanics here and use statistical values that represent both a number and a process simultaneous, much like irrational numbers, pi, e and .9r represent processes and not a specific numbers though they have arbitrarily accurate numeric approximations associated with them ... you could possibly unify data and algorithms by having each value represent both a range of numerical values as well as a range of algorithmic processes that both have statistical ranges and then you could swap numeric accuracy for computational efficiency just like you can compute pi to a variable number of digits ... you'd just be performing symbolic manipulation and expanding the result until the desired statistical reliability was achieved for a result ... sounds funky but it should be possible. There are already known algorithms that are stochastic and are faster than any known deterministic alternatives ... the price, as is seen physically in quantum mechanics, is that you can't ever be certain the result is 100% correct, but then again any computer running Windows isn't guaranteed to be 100% functional anyway
No, I'm entirely serious! 
)
As a simple example, take phi, the golden ratio. It's a simple ratio to generate and associated with many symbolic processes. If you avoid a numeric representation and instead retain an exact symbolic process (from a range of functionally identical processes) then theoretically you could calculate phi to any desired accuracy. But realistically we know we're only going to need to work with phi to some limited accuracy in the first place, so that also implies we don't need to use a process that generates phi exactly either. We could use an approximate process that generates an approximate result. So let's say we had some number like 1.617 (not exactly phi) and we wanted to efficiently multiply by this value approximately. If you iterate a fibonacci expansion for a limited number of terms you can find a value that's very close to 1.617 instead of phi. This could be seen as a tradeoff between numerical accuracy and computational efficiency (an extremely realistic form of tradeoff for real world computations). You could see this similar to physical particles with gaussian fields interacting with something similar to the Uncertainty Principle - each value is both a number and a process with probabilistic fields of interaction (though you can increase your equivalent sample size, or in this case computational resources, and generate an arbitrarily precise result given enough time).
I know most people won't recognize what the significance of this would be but you can go down the list of computational methods and find the same underlying problem of a two tiered system of representation and non-linear relationships between the two - AND-OR arrays in boolean or digital logic, sum of product terms in matrix multiplication, particle/wave duality in physics, or time/frequency domain operations and addition and multiplication giving rise to irreducibly prime relationships in mathematics. A single unified non-linear operation could allow for these two realms to be unified (and I believe gaussian/probabilistic fields are the key ... gaussians are transform invariant under Fourier and Lapace transforms, and as I showed even the code/data paradigm used in typical algorithms could be unifiable)
Now, that is bizarre, RC! You don't see what is wrong with assuming that
QUOTE
"the 'line' we are analysing bears NO RELATION to the presumed stationary/absolute/finite 'distance/length' line we 'abstractly' and mistakenly 'see'"?????
Either the model *addresses* reality or it doesn't. If it does, then the model "is" reality. I am NOT saying that it's right because math books say so, of course (and I haven't read any lately anyway). If a means exists of reducing reality to its bare minimum so that it can be *addressed*, what that is supposed to mean to me is that the model is an infinitesimal of said reality thus its divisor, thus it has validity independent of the observer. The "observer" didn't quantize it... it was already like that when I got there
Similarly, (as far as *existence is concerned) if the abstract number line doesn't *exist*, what's to keep me from stating that my mind doesn't exist? That my worries are about nothing in particular? Take away the validity of the line number away and you have taken the validity of any theory of mind with it!javascript:emoticon(':(')
QUOTE (->
| QUOTE |
| "the 'line' we are analysing bears NO RELATION to the presumed stationary/absolute/finite 'distance/length' line we 'abstractly' and mistakenly 'see'"????? |
Either the model *addresses* reality or it doesn't. If it does, then the model "is" reality. I am NOT saying that it's right because math books say so, of course (and I haven't read any lately anyway). If a means exists of reducing reality to its bare minimum so that it can be *addressed*, what that is supposed to mean to me is that the model is an infinitesimal of said reality thus its divisor, thus it has validity independent of the observer. The "observer" didn't quantize it... it was already like that when I got there
Similarly, (as far as *existence is concerned) if the abstract number line doesn't *exist*, what's to keep me from stating that my mind doesn't exist? That my worries are about nothing in particular? Take away the validity of the line number away and you have taken the validity of any theory of mind with it!javascript:emoticon(':(')
ANY 'line' one cares to set out or draw is in reality IMMERSED in PROCESS and MOVEMENT...and as such is NOT an 'absolute' or 'defined' THING or DISTANCE etc.
Not so fast: are you saying that immersion in processing and movement has no presumed stationary/absolute/finite distance or length from my mind? That I am a part of the process of existence of that which is outside me? That the model does exist, does have validity, and that the fact that I am a part of it proves beyond a reasonable doubt that it exists independent of me? Finally, that strictly as a matter of immersion in processing and movement, that I am the center of all lines?
Aha! Thank you, I agree.
(Don't know what you are going to say but I agree!)
QUOTE (Wulf+Jul 11 2007, 03:25 AM)
I just used the simplest example that came to mind at first glance.
Lets try this in terms of your 'Finite' number line then, say I'm making measurements in km, and I am at the limit of precision of your line, the act of dropping down to cm for a calculation then converting back to km would lead to the loss of information. A finite representation is not scalable.
Hi Wulf! Why aren't you "Cramming atm..." instead of rashly replying here?hehehe.
Seriously, mate, you just HAVE to 'take a breath' and stick to the point.
What you just rattled off is mere 'convention' and 'bounded' perspective that has NOTHING to do with what is being observed in this topic.
One more time.....
Whatever 'line', or whatever conventional analysis IS being done on it, is NOT 'complete' in BASIS. See?
No 'particular' CURRENT CONVENTIONAL AXIOMATIC argument as to what IS BEING DONE OR WHY has any bearing on the point that the 'line' construct ITSELF AS CURRENTLY 'defined' (and 'used/manipulated' by WHATEVER analytical system that CURRENTLY exists) is INADEQUATE AT BASIS.
All the things you are saying may or may not have relevance in what is NOW being 'done', but it has no bearing on what the observation implies regarding to the WHOLE BASIS for seeing that ANY 'line' construct AT ALL is NOT COMPLETE as it stands in definition/use NOW....simply because the 'axiomatic logics' of what is being done NOW has NOT allowed for the fact that the 'line' construct they based everything ON is NOT a COMPLETE/ADEQUATE ENOUGH 'construct' for current analyses and for what those analyses are expected to 'yield'....
.....which 'yield' is currently 'infested' with UNDEFINED and WEIRD 'things'.
Wouldn't it be nice to find out what all those 'undefined/weird things' WERE? Have you no curiosity what they might IMPLY and what might be accomplished if we 'treat' them in NEW/IMPROVED equations/constructs so that they will no longer BE 'undefined/weird'...and perhaps give us further information as to the underlying basis of reality in ALL contexts, and not just the 'already defined' ones?
Get "Cramming..." mate! This can wait until you have time to consider at leisure before 'knee-jerking' beside-the-point stuff into this discussion!hehehe.
And please try to keep in mind that THIS topic's observation/item is ONE among MANY OTHER parts of my 'contextual perspective' TOTALITY. Thanks.
Cheers!
RC.
.
Lets try this in terms of your 'Finite' number line then, say I'm making measurements in km, and I am at the limit of precision of your line, the act of dropping down to cm for a calculation then converting back to km would lead to the loss of information. A finite representation is not scalable.
Hi Wulf! Why aren't you "Cramming atm..." instead of rashly replying here?hehehe.
Seriously, mate, you just HAVE to 'take a breath' and stick to the point.
What you just rattled off is mere 'convention' and 'bounded' perspective that has NOTHING to do with what is being observed in this topic.
One more time.....
Whatever 'line', or whatever conventional analysis IS being done on it, is NOT 'complete' in BASIS. See?
No 'particular' CURRENT CONVENTIONAL AXIOMATIC argument as to what IS BEING DONE OR WHY has any bearing on the point that the 'line' construct ITSELF AS CURRENTLY 'defined' (and 'used/manipulated' by WHATEVER analytical system that CURRENTLY exists) is INADEQUATE AT BASIS.
All the things you are saying may or may not have relevance in what is NOW being 'done', but it has no bearing on what the observation implies regarding to the WHOLE BASIS for seeing that ANY 'line' construct AT ALL is NOT COMPLETE as it stands in definition/use NOW....simply because the 'axiomatic logics' of what is being done NOW has NOT allowed for the fact that the 'line' construct they based everything ON is NOT a COMPLETE/ADEQUATE ENOUGH 'construct' for current analyses and for what those analyses are expected to 'yield'....
.....which 'yield' is currently 'infested' with UNDEFINED and WEIRD 'things'.
Wouldn't it be nice to find out what all those 'undefined/weird things' WERE? Have you no curiosity what they might IMPLY and what might be accomplished if we 'treat' them in NEW/IMPROVED equations/constructs so that they will no longer BE 'undefined/weird'...and perhaps give us further information as to the underlying basis of reality in ALL contexts, and not just the 'already defined' ones?
Get "Cramming..." mate! This can wait until you have time to consider at leisure before 'knee-jerking' beside-the-point stuff into this discussion!hehehe.
And please try to keep in mind that THIS topic's observation/item is ONE among MANY OTHER parts of my 'contextual perspective' TOTALITY. Thanks.
Cheers!
RC.
.
QUOTE (RealityCheck+Jul 10 2007, 09:45 PM)
Hi Wulf! Why aren't you "...cramming atm..." instead of rashly replying here?hehehe.
Seriously, mate, you just HAVE to 'take a breath' and stick to the point.
What you just rattled off is mere 'convention' and 'bounded' perspective that has NOTHING to do with what is being observed in this topic.
One more time.....
Whatever 'line', or whatever conventional analysis IS being done on it, is NOT 'complete' in BASIS. See? No 'particular' CURRENT CONVENTIONAL AXIOMATIC argument as to what IS BEING DONE OR WHY has any bearing on the point that the 'line' construct ITSELF AS CURRENTLY 'defined' (and 'used/manipulated' by WHATEVER analytical system that CURRENTLY exists) is INADEQUATE AT BASIS.
All the things you are saying may or may not have relevance in what is NOW being 'done', but it has no bearing on what the observation implies regarding to the WHOLE BASIS for seeing that ANY 'line' construct AT ALL is NOT COMPLETE as it stands in definition/use NOW....simply because the 'axiomatic logics' of what is being done NOW has NOT allowed for the fact that the 'line' construct they based everything ON is NOT a COMPLETE/ADEQUATE ENOUGH 'construct' for current analyses and for what those analyses are expected to 'yield'....
.....which 'yield' is currently 'infested' with UNDEFINED and WEIRD 'things'.
Wouldn't it be nice to find out what all those 'undefined things' WERE? Have you no curiosity what they might IMPLY and and what might be accomplished if we 'treat' them so that they will no longer BE 'undefined'...and perhaps give us further information as to the underlying basis of reality in ALL contexts, and not just the 'already defined' ones?
Get "Cramming..." mate! This can wait until you have time to consider at leisure before 'knee-jerking' beside-the-point stuff into this discussion!hehehe.
And please try to keep in mind that THIS topic's observation/item is ONE among MANY OTHER parts of my 'contextual perspective' TOTALITY. Thanks.
Cheers!
RC.
.
One of the advantages of being willing to learn and puting thought into what I am learning is that I've developed a conceptual framework that allows me to quickly reason through things. There is nothing rash about my responses.
Do you need to sound out this sentence, or do you recognise the words without having to sound them out? Think a little.
Jya mata.
QUOTE (Wulf+Jul 11 2007, 04:04 AM)
One of the advantages of being willing to learn and puting thought into what I am learning is that I've developed a conceptual framework that allows me to quickly reason through things. There is nothing rash about my responses.
Do you need to sound out this sentence, or do you recognise the words without having to sound them out? Think a little.
Jya mata.
Hehehe. Give me 'slow' and 'complete' over 'quickly' but 'incomplete' anytime mate!
Still, for some people 'near enough' is apparently good enough if it gets them through the exams on the 'orthodoxy'.
Some other people 'try harder' even though they don't have to; because in some things, 'near enough' is NOT good enough, Wulf.
Can YOU read THAT and comprehend it OK with your 'quick reasoning'?
Cheers all!
RC.
.
Do you need to sound out this sentence, or do you recognise the words without having to sound them out? Think a little.
Jya mata.
Hehehe. Give me 'slow' and 'complete' over 'quickly' but 'incomplete' anytime mate!
Still, for some people 'near enough' is apparently good enough if it gets them through the exams on the 'orthodoxy'.
Some other people 'try harder' even though they don't have to; because in some things, 'near enough' is NOT good enough, Wulf.
Can YOU read THAT and comprehend it OK with your 'quick reasoning'?
Cheers all!
RC.
.
QUOTE (RealityCheck+Jul 10 2007, 10:15 PM)
Hehehe. Give me 'slow' and 'complete' over 'quickly' and 'incomplete' anytime mate!
Still, for some people 'near enough' is apparently good enough if it gets them through the exams on the 'orthodoxy'.
Some other people 'try harder' even though they don't have to; because in some things, 'near enough' is NOT good enough, Wulf.
Can YOU read THAT and comprehend it OK with your 'quick reasoning'?
A reminder: Insults are NOT 'valid currency' in lieu of actual scientific debate on the point raised.
Cheers all!
RC.
.
That was meant to illustrate a point, not as an insult. Although I imagine it could be percieved that way if you caught your lips moving as you read it.
QUOTE (Wulf+Jul 11 2007, 04:23 AM)
That was meant to illustrate a point, not as an insult. Although I imagine it could be percieved that way if you caught your lips moving as you read it.
Understood, mate! Sorry! I have gone back and removed that 'reminder'..
It would help if you made your points less 'cryptically', mate!hehehe
Can you now elaborate on the point you were trying to illustrate with the relevant sentence? Thanks.
RC.
.
Understood, mate! Sorry! I have gone back and removed that 'reminder'..
It would help if you made your points less 'cryptically', mate!hehehe
Can you now elaborate on the point you were trying to illustrate with the relevant sentence? Thanks.
RC.
.
QUOTE (Wulf+Jul 11 2007, 12:23 AM)
meant to illustrate a point, not as an insult.
You know what is reaaaaaly... point-illustrating?
To develop a ToE with the mathematical equivalent of counting on your fingers. Not that it would ever happen...
You know what is reaaaaaly... point-illustrating?
To develop a ToE with the mathematical equivalent of counting on your fingers. Not that it would ever happen...
One area that seems lacking in mathematics is the exception to polynomial integration (and this appears related to the .9!=1 discussion).
The formula derived by calculus for polynomial integration is http://hyperphysics.phy-astr.gsu.edu/hbase/intpol.html
integral(ax^n)=(ax^(n+1))/(n+1) + C
Except when n=-1, in which case it becomes:
integral(ax^-1)=a*ln(x) + C
What does this function approach for values of n that differ infinitesimally from n=-1? (Also, the rather arbitrary value for C can be a source of grief in that differentiation isn't entirely reversible without additional information being included)
Another one that deserves better scrutiny is the process of integration and differentiation themselves for fractional values. If we look at a Fourier Transform of a function that's undergone differentiation or integration we find the sinusoidal components have been rotated and filtered by discrete amounts. There are ways of interpolating between these 90 deg rotations that could give an ability to perform fractional integration and differentiation (it would be interesting to trace the evolution of something like an integration of 1/x into a logarithm by changing both the power of x used as well as the fractional integral used).
The formula derived by calculus for polynomial integration is http://hyperphysics.phy-astr.gsu.edu/hbase/intpol.html
integral(ax^n)=(ax^(n+1))/(n+1) + C
Except when n=-1, in which case it becomes:
integral(ax^-1)=a*ln(x) + C
What does this function approach for values of n that differ infinitesimally from n=-1? (Also, the rather arbitrary value for C can be a source of grief in that differentiation isn't entirely reversible without additional information being included)
Another one that deserves better scrutiny is the process of integration and differentiation themselves for fractional values. If we look at a Fourier Transform of a function that's undergone differentiation or integration we find the sinusoidal components have been rotated and filtered by discrete amounts. There are ways of interpolating between these 90 deg rotations that could give an ability to perform fractional integration and differentiation (it would be interesting to trace the evolution of something like an integration of 1/x into a logarithm by changing both the power of x used as well as the fractional integral used).
QUOTE (IAMoraes+Jul 11 2007, 04:38 AM)
You know what is reaaaaaly... point-illustrating?
To develop a ToE with the mathematical equivalent of counting on your fingers. Not that it would ever happen...
Hehehe. I read your longer post, IAM!
What a 'connection'! hehehe. Good sense of humour; does wonders for the spirit of the discussion, heh!
Thanks for your 'trust'....but don't stop questioning...even ME, mate!
Anyhow, the line does not exist AS DEFINED currently because it is not 'static' etc by virtue of MOTION and PROCESS (in 'spacetime?) in reality.....that is the salient point.
Oh, by the way, IAM, I will soon re-post those TOE thread stage-II questions for newcomers to the special Cosmology Project well before I post my own answer to same...so you will be given ample time to read them and give whatever input you think will 'answer' them!
Cheers!
RC.
.
To develop a ToE with the mathematical equivalent of counting on your fingers. Not that it would ever happen...
Hehehe. I read your longer post, IAM!
What a 'connection'! hehehe. Good sense of humour; does wonders for the spirit of the discussion, heh!
Thanks for your 'trust'....but don't stop questioning...even ME, mate!
Anyhow, the line does not exist AS DEFINED currently because it is not 'static' etc by virtue of MOTION and PROCESS (in 'spacetime?) in reality.....that is the salient point.
Oh, by the way, IAM, I will soon re-post those TOE thread stage-II questions for newcomers to the special Cosmology Project well before I post my own answer to same...so you will be given ample time to read them and give whatever input you think will 'answer' them!
Cheers!
RC.
.
QUOTE (StevenA+Jul 11 2007, 04:47 AM)
One area that seems lacking in mathematics is the exception to polynomial integration (and this appears related to the .9!=1 discussion).
The formula derived by calculus for polynomial integration is http://hyperphysics.phy-astr.gsu.edu/hbase/intpol.html
integral(ax^n)=(ax^(n+1))/(n+1) + C
Except when n=-1, in which case it becomes:
integral(ax^-1)=a*ln(x) + C
What does this function approach for values of n that differ infinitesimally from n=-1? (Also, the rather arbitrary value for C can be a source of grief in that differentiation isn't entirely reversible without additional information being included)
Another one that deserves better scrutiny is the process of integration and differentiation themselves for fractional values. If we look at a Fourier Transform of a function that's undergone differentiation or integration we find the sinusoidal components have been rotated and filtered by discrete amounts. There are ways of interpolating between these 90 deg rotations that could give an ability to perform fractional integration and differentiation (it would be interesting to trace the evolution of something like an integration of 1/x into a logarithm by changing both the power of x used as well as the fractional integral used).
Hi StevenA! Was that ever raised in the 0.9r = 1 thread?
Perhaps AN, NCN et al can comment on your observations now?
Can you think of any 'contextual' terms/techniques that might 'enhance' those existing techniques/equations?
If not, maybe AlphaNumeric and NCN et al can help in this thread?
Gotta go for the rest of the day, folks. So....play nice!hehehe.
RC.
.
The formula derived by calculus for polynomial integration is http://hyperphysics.phy-astr.gsu.edu/hbase/intpol.html
integral(ax^n)=(ax^(n+1))/(n+1) + C
Except when n=-1, in which case it becomes:
integral(ax^-1)=a*ln(x) + C
What does this function approach for values of n that differ infinitesimally from n=-1? (Also, the rather arbitrary value for C can be a source of grief in that differentiation isn't entirely reversible without additional information being included)
Another one that deserves better scrutiny is the process of integration and differentiation themselves for fractional values. If we look at a Fourier Transform of a function that's undergone differentiation or integration we find the sinusoidal components have been rotated and filtered by discrete amounts. There are ways of interpolating between these 90 deg rotations that could give an ability to perform fractional integration and differentiation (it would be interesting to trace the evolution of something like an integration of 1/x into a logarithm by changing both the power of x used as well as the fractional integral used).
Hi StevenA! Was that ever raised in the 0.9r = 1 thread?
Perhaps AN, NCN et al can comment on your observations now?
Can you think of any 'contextual' terms/techniques that might 'enhance' those existing techniques/equations?
If not, maybe AlphaNumeric and NCN et al can help in this thread?
Gotta go for the rest of the day, folks. So....play nice!hehehe.
RC.
.
QUOTE (RealityCheck+Jul 11 2007, 12:54 AM)
line does not exist AS DEFINED currently because it is not 'static' etc by virtue of MOTION and PROCESS (in 'spacetime?) in reality
Point taken. However, it doesn't exist because it doesn't have an address in space -it does, you just point at it-- but because it doesn't have an address in time. We don't know how to address time's infinity.
Point taken. However, it doesn't exist because it doesn't have an address in space -it does, you just point at it-- but because it doesn't have an address in time. We don't know how to address time's infinity.
QUOTE (IAMoraes+Jul 11 2007, 05:34 AM)
Point taken. However, it doesn't exist because it doesn't have an address in space -it does, you just point at it-- but because it doesn't have an address in time. We don't know how to address time's infinity.
Well spotted, IAM!
That is one of the aims of 'contextual' equations/analyses in reality....to make it POSSIBLE to handle NOT JUST 'infinities/singularities' (be these 'time' or' length/distance', mass etc) but also the WIDER IMPLICATIONS associated with ANY 'line construct' under 'mathematical/physical' study/system analysis regarding its 'numerical/real' or 'other' PROPERTIES.
In particular, we especially NEED to find some way of IDENTIFYING/QUANTIFYING all sorts of currently 'undefined/weird' results; and somehow EQUIP OUR EQUATIONS so that they may ' better inform' us about NOT ONLY the RATE OF CHANGE to/from such 'infinities/singularities'...but to hopefully also 'indicate/tell' WHERE AND IN WHAT 'PHYSICAL' STATES those infinities etc actually 'LIE' within the overall 'layer' and 'fundamental sublayer' CONTEXT in physical reality system PROCESSES/DYNAMICS.
Good work in highlighting that aspect, IAM!
See y'all tomorrow!
RC.
.
Well spotted, IAM!
That is one of the aims of 'contextual' equations/analyses in reality....to make it POSSIBLE to handle NOT JUST 'infinities/singularities' (be these 'time' or' length/distance', mass etc) but also the WIDER IMPLICATIONS associated with ANY 'line construct' under 'mathematical/physical' study/system analysis regarding its 'numerical/real' or 'other' PROPERTIES.
In particular, we especially NEED to find some way of IDENTIFYING/QUANTIFYING all sorts of currently 'undefined/weird' results; and somehow EQUIP OUR EQUATIONS so that they may ' better inform' us about NOT ONLY the RATE OF CHANGE to/from such 'infinities/singularities'...but to hopefully also 'indicate/tell' WHERE AND IN WHAT 'PHYSICAL' STATES those infinities etc actually 'LIE' within the overall 'layer' and 'fundamental sublayer' CONTEXT in physical reality system PROCESSES/DYNAMICS.
Good work in highlighting that aspect, IAM!
See y'all tomorrow!
RC.
.
QUOTE (RealityCheck+Jul 11 2007, 05:09 AM)
Hi StevenA! Was that ever raised in the 0.9r = 1 thread?
Perhaps AN, NCN et al can comment on your observations now?
Can you think of any 'contextual' terms/techniques that might 'enhance' those existing techniques/equations?
If not, maybe AlphaNumeric and NCN et al can help in this thread?
Gotta go for the rest of the day, folks. So....play nice!hehehe.
RC.
.
I believe I've made some comments along similar lines in that thread though likely not as directly about those specific discontinuities.
In terms of useful enhancements to integration and differentiation, I'd say an obvious one would be in frequency domain operations - like generating novel filter responses or Laplace transforms.
There's a stong disconnect between linear (additive) and exponential/logarithmic (multiplicative, which is linear on a logarithmic scale but this creates a 2 dimensional plane of values for numbers that has irreducible prime features) operations. Each is non-linear relative to the other and transformations between are the fundamental cause of complexity and we see this inherent in calculus as well. If we can remove this discontinuity then multiplication and addition could potentially be replaced by a single non-linear operation (my guess is we can take some clues from quantum mechanics here and use statistical values that represent both a number and a process simultaneous, much like irrational numbers, pi, e and .9r represent processes and not a specific numbers though they have arbitrarily accurate numeric approximations associated with them ... you could possibly unify data and algorithms by having each value represent both a range of numerical values as well as a range of algorithmic processes that both have statistical ranges and then you could swap numeric accuracy for computational efficiency just like you can compute pi to a variable number of digits ... you'd just be performing symbolic manipulation and expanding the result until the desired statistical reliability was achieved for a result ... sounds funky but it should be possible. There are already known algorithms that are stochastic and are faster than any known deterministic alternatives ... the price, as is seen physically in quantum mechanics, is that you can't ever be certain the result is 100% correct, but then again any computer running Windows isn't guaranteed to be 100% functional anyway
No, I'm entirely serious! )As a simple example, take phi, the golden ratio. It's a simple ratio to generate and associated with many symbolic processes. If you avoid a numeric representation and instead retain an exact symbolic process (from a range of functionally identical processes) then theoretically you could calculate phi to any desired accuracy. But realistically we know we're only going to need to work with phi to some limited accuracy in the first place, so that also implies we don't need to use a process that generates phi exactly either. We could use an approximate process that generates an approximate result. So let's say we had some number like 1.617 (not exactly phi) and we wanted to efficiently multiply by this value approximately. If you iterate a fibonacci expansion for a limited number of terms you can find a value that's very close to 1.617 instead of phi. This could be seen as a tradeoff between numerical accuracy and computational efficiency (an extremely realistic form of tradeoff for real world computations). You could see this similar to physical particles with gaussian fields interacting with something similar to the Uncertainty Principle - each value is both a number and a process with probabilistic fields of interaction (though you can increase your equivalent sample size, or in this case computational resources, and generate an arbitrarily precise result given enough time).
I know most people won't recognize what the significance of this would be but you can go down the list of computational methods and find the same underlying problem of a two tiered system of representation and non-linear relationships between the two - AND-OR arrays in boolean or digital logic, sum of product terms in matrix multiplication, particle/wave duality in physics, or time/frequency domain operations and addition and multiplication giving rise to irreducibly prime relationships in mathematics. A single unified non-linear operation could allow for these two realms to be unified (and I believe gaussian/probabilistic fields are the key ... gaussians are transform invariant under Fourier and Lapace transforms, and as I showed even the code/data paradigm used in typical algorithms could be unifiable)
QUOTE (StevenA+Jul 11 2007, 05:47 AM)
The formula derived by calculus for polynomial integration is http://hyperphysics.phy-astr.gsu.edu/hbase/intpol.html
integral(ax^n)=(ax^(n+1))/(n+1) + C
Except when n=-1, in which case it becomes:
integral(ax^-1)=a*ln(x) + C
What does this function approach for values of n that differ infinitesimally from n=-1? (Also, the rather arbitrary value for C can be a source of grief in that differentiation isn't entirely reversible without additional information being included)
Do you not think anyone has noticed that before? It's fairly straight forward to see why when you consider what functions tend to at their limits of 0 and infinity and how you'd expect to be able to bound discrete summations.
Int ( x^n ) is (x^n+1)/(n+1) except at n=-1 because that is the cross over point. For n<-1, the function's decay rate is high enough to give a convergence integral. For n>=-1, it's not.
Radii of convergence, regions of convergence, Stokes lines, discontinuities, Riemann-Hilbert Problems. These are all tools developed to investigate such things.
You say "We should be investigating these things!" when we have! Those things I just mentioned are all over 100 years old! But you continue to work on the notion of "If I don't know it, it doesn't exist".
This thread is just another illustration of how cranks and nuts rather than hours giving excuses about why they haven't spent minutes reading books. But avoiding work is more enjoyable than doing work, right?
integral(ax^n)=(ax^(n+1))/(n+1) + C
Except when n=-1, in which case it becomes:
integral(ax^-1)=a*ln(x) + C
What does this function approach for values of n that differ infinitesimally from n=-1? (Also, the rather arbitrary value for C can be a source of grief in that differentiation isn't entirely reversible without additional information being included)
Do you not think anyone has noticed that before? It's fairly straight forward to see why when you consider what functions tend to at their limits of 0 and infinity and how you'd expect to be able to bound discrete summations.
Int ( x^n ) is (x^n+1)/(n+1) except at n=-1 because that is the cross over point. For n<-1, the function's decay rate is high enough to give a convergence integral. For n>=-1, it's not.
Radii of convergence, regions of convergence, Stokes lines, discontinuities, Riemann-Hilbert Problems. These are all tools developed to investigate such things.
You say "We should be investigating these things!" when we have! Those things I just mentioned are all over 100 years old! But you continue to work on the notion of "If I don't know it, it doesn't exist".
This thread is just another illustration of how cranks and nuts rather than hours giving excuses about why they haven't spent minutes reading books. But avoiding work is more enjoyable than doing work, right?
I am not knowledgeable so much about mathematics as self-evident independent of any world but i do have some questions in regard to reality. Linear anything seems to describe only few percent of reality. And linear is what we like to model with. Be it linear progression or amplification...Keep it simple cause reality is simple. I don't believe anymore that reality is simple. Its beyond weirdest. I always find it hard to believe that any mathematical construct actually describes reality as it is. I do however believe in approximations. The question is of course why do approximations work so accurately. This is the main trick. What is accurately enough not to be questioned by us anymore? For example -it works and thats it. Why all these new theories then? Any exception proves that model is not absolutely correct. In describing reality you have to be precise down to the last bit. And it seems there is nothing to get a hold of in quantum realms except approximations.
You cannot just neglect things when considering reality. For example the sensitivity of "macro appearance" on "stability" of micro world is so large that not a single event can be neglected. But who would find that worth pursuing? We cannot even predict weather patterns few days ahead correctly. Its an approximation. Butterfly effect still rules the planet and like followers of god there are followers of "final order". Its very much history repeating in every aspect of our knowledge. You have practical mathematicians, religious mathematicians...Difference between them could be that religious ask why and practical ask how. Skeptics don't go into either direction, they question everything and are concluding there is nothing for them except something which is undefinable. And finally it doesn't make a difference who is right or wrong. What everybody seeked was just the truth and nothing else. It is a group effort basically. Everyone builds on previous and so on. Imagine everybody starting from beginning by themselves. Seeking of truth whatever it is, is a group effort. It shouldn't get personal whatsoever. If it gets personal then we have unnecessary complexity which slows down the effort. There is no hurry and we got plenty of time. We have to be sure we didn't miss anything out. There is only one way and its not individualism. It is however interesting that in meaningless reality or religious one things stay the same. Everybody is equally meaningless or equally meaningful in front of the truth.
You cannot just neglect things when considering reality. For example the sensitivity of "macro appearance" on "stability" of micro world is so large that not a single event can be neglected. But who would find that worth pursuing? We cannot even predict weather patterns few days ahead correctly. Its an approximation. Butterfly effect still rules the planet and like followers of god there are followers of "final order". Its very much history repeating in every aspect of our knowledge. You have practical mathematicians, religious mathematicians...Difference between them could be that religious ask why and practical ask how. Skeptics don't go into either direction, they question everything and are concluding there is nothing for them except something which is undefinable. And finally it doesn't make a difference who is right or wrong. What everybody seeked was just the truth and nothing else. It is a group effort basically. Everyone builds on previous and so on. Imagine everybody starting from beginning by themselves. Seeking of truth whatever it is, is a group effort. It shouldn't get personal whatsoever. If it gets personal then we have unnecessary complexity which slows down the effort. There is no hurry and we got plenty of time. We have to be sure we didn't miss anything out. There is only one way and its not individualism. It is however interesting that in meaningless reality or religious one things stay the same. Everybody is equally meaningless or equally meaningful in front of the truth.
Hi all,
Welcome back RC; I hope your health remains strong!
StevenA Posted on Today at 6:28 AM
There's a stong disconnect between linear (additive) and exponential/logarithmic (multiplicative, which is linear on a logarithmic scale but this creates a 2 dimensional plane of values for numbers that has irreducible prime features) operations. Each is non-linear relative to the other and transformations between are the fundamental cause of complexity and we see this inherent in calculus as well. If we can remove this discontinuity then multiplication and addition could potentially be replaced by a single non-linear operation (my guess is we can take some clues from quantum mechanics here and use statistical values that represent both a number and a process simultaneous, much like irrational numbers, pi, e and .9r represent processes and not a specific numbers though they have arbitrarily accurate numeric approximations associated with them ...
There's nothing like measuring a "rate with a rate". We come up with "infinities/singularities" because of our style of approach. As Majkl mentioned, we prefer to deal with "linear" representations, of part of a non-linear phenomenon.
When you do this "piece-meal", you have broken a chain, and you are measuring something "as if" it were a "new One". This compartmentalization works with "logic", but not so well with a "physical" math. When you create a new "One", you shift the "zero point" as well. I'm not trying to be cryptic here; I am just saying that "ground states" of energy should NOT all have their own separate "existence", and start from "zero". We need the common background term, from which to establish/quantify a relative "zero-point field".
Well, that goes in the other direction as well. Think about statistics, and large numbers. I believe (if I remember right), that about "8 digits out" gives us a "fuzzy" approximation, because it CAN NOT be "accurate" to an arbitrary number of digits.
This worked well for Planck, and has been leading in a "fuzzy" way ever since. There is NO other reason that h has any meaning, or functionality in QM. When you give an "answer" that has -34 digits, and you are only working with "12 digit accuracy", you don't see the difference. Right answers; wrong reasons.
In the world of "inverse" symmetry, you can't measure an integer with an integer. Right now, we just deal with the irrationals in a "limited" sense. If we start with an integer, we get an irrational anyway.
IE. take any visible frequency, divide by c , and you get an irrational wavelength.
Can anyone "approximate" what the wavelength would be, WITHOUT using our "constant" of c ? In other words, actually perform TWO measurements independently, whose product = c , without "seeding" the logic by using the answer ahead of time.
This is the value of my "system".
regards,
T.Roc
Welcome back RC; I hope your health remains strong!
QUOTE
RealityCheck Posted on Today at 5:53 AM
In particular, we especially NEED to find some way of IDENTIFYING/QUANTIFYING all sorts of currently 'undefined/weird' results; and somehow EQUIP OUR EQUATIONS so that they may ' better inform' us about NOT ONLY the RATE OF CHANGE to/from such 'infinities/singularities' ..
In particular, we especially NEED to find some way of IDENTIFYING/QUANTIFYING all sorts of currently 'undefined/weird' results; and somehow EQUIP OUR EQUATIONS so that they may ' better inform' us about NOT ONLY the RATE OF CHANGE to/from such 'infinities/singularities' ..
QUOTE (->
| QUOTE |
| RealityCheck Posted on Today at 5:53 AM In particular, we especially NEED to find some way of IDENTIFYING/QUANTIFYING all sorts of currently 'undefined/weird' results; and somehow EQUIP OUR EQUATIONS so that they may ' better inform' us about NOT ONLY the RATE OF CHANGE to/from such 'infinities/singularities' .. |
StevenA Posted on Today at 6:28 AM
There's a stong disconnect between linear (additive) and exponential/logarithmic (multiplicative, which is linear on a logarithmic scale but this creates a 2 dimensional plane of values for numbers that has irreducible prime features) operations. Each is non-linear relative to the other and transformations between are the fundamental cause of complexity and we see this inherent in calculus as well. If we can remove this discontinuity then multiplication and addition could potentially be replaced by a single non-linear operation (my guess is we can take some clues from quantum mechanics here and use statistical values that represent both a number and a process simultaneous, much like irrational numbers, pi, e and .9r represent processes and not a specific numbers though they have arbitrarily accurate numeric approximations associated with them ...
There's nothing like measuring a "rate with a rate". We come up with "infinities/singularities" because of our style of approach. As Majkl mentioned, we prefer to deal with "linear" representations, of part of a non-linear phenomenon.
When you do this "piece-meal", you have broken a chain, and you are measuring something "as if" it were a "new One". This compartmentalization works with "logic", but not so well with a "physical" math. When you create a new "One", you shift the "zero point" as well. I'm not trying to be cryptic here; I am just saying that "ground states" of energy should NOT all have their own separate "existence", and start from "zero". We need the common background term, from which to establish/quantify a relative "zero-point field".
QUOTE
StevenA Posted on Today at 6:28 AM
But realistically we know we're only going to need to work with phi to some limited accuracy in the first place, so that also implies we don't need to use a process that generates phi exactly either. We could use an approximate process that generates an approximate result.
But realistically we know we're only going to need to work with phi to some limited accuracy in the first place, so that also implies we don't need to use a process that generates phi exactly either. We could use an approximate process that generates an approximate result.
Well, that goes in the other direction as well. Think about statistics, and large numbers. I believe (if I remember right), that about "8 digits out" gives us a "fuzzy" approximation, because it CAN NOT be "accurate" to an arbitrary number of digits.
This worked well for Planck, and has been leading in a "fuzzy" way ever since. There is NO other reason that h has any meaning, or functionality in QM. When you give an "answer" that has -34 digits, and you are only working with "12 digit accuracy", you don't see the difference. Right answers; wrong reasons.
In the world of "inverse" symmetry, you can't measure an integer with an integer. Right now, we just deal with the irrationals in a "limited" sense. If we start with an integer, we get an irrational anyway.
IE. take any visible frequency, divide by c , and you get an irrational wavelength.
Can anyone "approximate" what the wavelength would be, WITHOUT using our "constant" of c ? In other words, actually perform TWO measurements independently, whose product = c , without "seeding" the logic by using the answer ahead of time.
This is the value of my "system".
regards,
T.Roc
QUOTE (TRoc+Jul 11 2007, 08:59 AM)
... without "seeding" the logic by using the answer ahead of time.
I can't seem to get this point across to certain people. It's like getting from 1 to 0 or vice versa, without knowing the other ahead of time. It can't be done. It doesn't seem important to them.
If you're headed in a direction and don't know the destination, how can you even begin? Every step will be the same step and not one of them will get you there, because you don't know where "there" is. Well, I suppose you could say you could begin by taking one step, but there's no way to calculate the step. Technically, you'd stay right where you are.
Everything actually stays right where it is, but we're always seeing the answer ahead of time, and the answer isn't actually the answer.
I never leave the house when I drive to the store, but I keep up my car insurance anyway.
I can't seem to get this point across to certain people. It's like getting from 1 to 0 or vice versa, without knowing the other ahead of time. It can't be done. It doesn't seem important to them.
If you're headed in a direction and don't know the destination, how can you even begin? Every step will be the same step and not one of them will get you there, because you don't know where "there" is. Well, I suppose you could say you could begin by taking one step, but there's no way to calculate the step. Technically, you'd stay right where you are.
Everything actually stays right where it is, but we're always seeing the answer ahead of time, and the answer isn't actually the answer.
I never leave the house when I drive to the store, but I keep up my car insurance anyway.
QUOTE (TRoc+Jul 11 2007, 11:59 AM)
There's nothing like measuring a "rate with a rate". We come up with "infinities/singularities" because of our style of approach. As Majkl mentioned, we prefer to deal with "linear" representations, of part of a non-linear phenomenon.
When you do this "piece-meal", you have broken a chain, and you are measuring something "as if" it were a "new One". This compartmentalization works with "logic", but not so well with a "physical" math. When you create a new "One", you shift the "zero point" as well. I'm not trying to be cryptic here; I am just saying that "ground states" of energy should NOT all have their own separate "existence", and start from "zero". We need the common background term, from which to establish/quantify a relative "zero-point field".
You can't simultaneously want the ground state of "energy" to be zero and not explain where the future energy is going to come from.
However, since you are measuring a "rate with a rate", and since Steven mentioned phi, and since phi is directly related to a spiral, and since you need a new "one" that works well with logic and physical reality...
... then you can't treat each new "one" as an entity without an angle.
The easiest way to do that would be, say, to give an angle of zero to (x+y), then another to (x*y) by adding either 90 or 45 degrees to the equation, then another to (x to the y'th), by adding either another 90 or 22 1/2 degrees. (to the descriptions! Not to the equation's inputs and outputs. Otherwise the established/quantified "zero-point field" would be input/output (i.e., data) and not establishing nor quantifying much.)
By the time the ground state of "energy" gets to be "zero" all the "energy" will have migrated to its own description. That is why everyone wants a tiny little equation that will explain the universe.
This is faking it, of course. Only a number to the power of infinity actually turns 90 degrees. But it may provide more of a smooth transition between straight lines and curved lines:
The formula derived by calculus for polynomial integration is http://hyperphysics.phy-astr.gsu.edu/hbase/intpol.html
integral(ax^n)=(ax^(n+1))/(n+1) + C
Except when n=-1, in which case it becomes:
integral(ax^-1)=a*ln(x) + C
What does this function approach for values of n that differ infinitesimally from n=-1? (Also, the rather arbitrary value for C can be a source of grief in that differentiation isn't entirely reversible without additional information being included)
As soon as I learn what an integral is you will hear the fireworks, the loud music, the beer pops, the urps and burps
Meanwhile, an integral is procedurally -thus mathematically- wrong if each one of their iterations doesn't take into consideration the computational angle of the equation itself.
The "equations themselves", being descriptions, are stored in space and matter, thus they turn in time. A "rate with a rate" equation can only describe matter in movement by being a fractal part, an infinitesimal part, of that which it describes: the description is part of the *mass* of that which is described.
When you do this "piece-meal", you have broken a chain, and you are measuring something "as if" it were a "new One". This compartmentalization works with "logic", but not so well with a "physical" math. When you create a new "One", you shift the "zero point" as well. I'm not trying to be cryptic here; I am just saying that "ground states" of energy should NOT all have their own separate "existence", and start from "zero". We need the common background term, from which to establish/quantify a relative "zero-point field".
You can't simultaneously want the ground state of "energy" to be zero and not explain where the future energy is going to come from.
However, since you are measuring a "rate with a rate", and since Steven mentioned phi, and since phi is directly related to a spiral, and since you need a new "one" that works well with logic and physical reality...
... then you can't treat each new "one" as an entity without an angle.
The easiest way to do that would be, say, to give an angle of zero to (x+y), then another to (x*y) by adding either 90 or 45 degrees to the equation, then another to (x to the y'th), by adding either another 90 or 22 1/2 degrees. (to the descriptions! Not to the equation's inputs and outputs. Otherwise the established/quantified "zero-point field" would be input/output (i.e., data) and not establishing nor quantifying much.)
By the time the ground state of "energy" gets to be "zero" all the "energy" will have migrated to its own description. That is why everyone wants a tiny little equation that will explain the universe.
This is faking it, of course. Only a number to the power of infinity actually turns 90 degrees. But it may provide more of a smooth transition between straight lines and curved lines:
QUOTE (StevenA @ Jul 11 2007+ 05:47 AM)
The formula derived by calculus for polynomial integration is http://hyperphysics.phy-astr.gsu.edu/hbase/intpol.html
integral(ax^n)=(ax^(n+1))/(n+1) + C
Except when n=-1, in which case it becomes:
integral(ax^-1)=a*ln(x) + C
What does this function approach for values of n that differ infinitesimally from n=-1? (Also, the rather arbitrary value for C can be a source of grief in that differentiation isn't entirely reversible without additional information being included)
As soon as I learn what an integral is you will hear the fireworks, the loud music, the beer pops, the urps and burps
Meanwhile, an integral is procedurally -thus mathematically- wrong if each one of their iterations doesn't take into consideration the computational angle of the equation itself.
The "equations themselves", being descriptions, are stored in space and matter, thus they turn in time. A "rate with a rate" equation can only describe matter in movement by being a fractal part, an infinitesimal part, of that which it describes: the description is part of the *mass* of that which is described.
.
Hi AlphaNumeric!
Regarding yours and others “current axiomatic understandings” that view zero as “a real number” and as “the only infinitessimal” etc. etc, as indicated in following abstract of one of posts your in the “Simple Proof That .9r!=1” thread.....
Hi AlphaNumeric!
Regarding yours and others “current axiomatic understandings” that view zero as “a real number” and as “the only infinitessimal” etc. etc, as indicated in following abstract of one of posts your in the “Simple Proof That .9r!=1” thread.....
QUOTE (AlphaNumeric to StevenA+Jan 15 2008, 07:24 AM)
...
...
"An arbitrarily small Real number" equates to an infinitesimal. It doesn't. It's still a Real number. Infinitesimals aren't. They are defined to be smaller than any Real number. So by definition you cannot construct them from Reals because any number you construct from Reals is a Real number!
I would very much like and appreciate your and others input to a certain conversation between myself and NoCleverName on this aspect of 'zero' in the “Point Nine Recurring Equals One (or not)” Thread.
For the time being I’d like everyone to bring in and treat ONLY those aspects relevant to the CURRENT Axioms and consistent definitions from those axioms as to ZERO supposedly being “a rational number” and "only infinitesimal" etc.
The series of exchanges in my relevant conversation with NoCleverName began with the quote immediately below. Please, BEFORE participating, and in order to avoid the usual misunderstandings and knee-jerk reactions and distracting 'sideshows/feuds' already afflicting many otherwise illuminating discussions in too many other topics/threads, I would ask all intending participants in THIS present discussion to first PLEASE read carefully and properly comprehend the CRUX of THIS particular conversation, and only then restrict as much as possible your (constructive) inputs to addressing ONLY the requested AXIOMATIX and DEFINITIONAL aspects regarding ZERO’s CURRENT TREATMENT as “ a rational number”.
Here goes with my relevant conversation so far with NoCleverName:
...
"An arbitrarily small Real number" equates to an infinitesimal. It doesn't. It's still a Real number. Infinitesimals aren't. They are defined to be smaller than any Real number. So by definition you cannot construct them from Reals because any number you construct from Reals is a Real number!
I would very much like and appreciate your and others input to a certain conversation between myself and NoCleverName on this aspect of 'zero' in the “Point Nine Recurring Equals One (or not)” Thread.
For the time being I’d like everyone to bring in and treat ONLY those aspects relevant to the CURRENT Axioms and consistent definitions from those axioms as to ZERO supposedly being “a rational number” and "only infinitesimal" etc.
The series of exchanges in my relevant conversation with NoCleverName began with the quote immediately below. Please, BEFORE participating, and in order to avoid the usual misunderstandings and knee-jerk reactions and distracting 'sideshows/feuds' already afflicting many otherwise illuminating discussions in too many other topics/threads, I would ask all intending participants in THIS present discussion to first PLEASE read carefully and properly comprehend the CRUX of THIS particular conversation, and only then restrict as much as possible your (constructive) inputs to addressing ONLY the requested AXIOMATIX and DEFINITIONAL aspects regarding ZERO’s CURRENT TREATMENT as “ a rational number”.
Here goes with my relevant conversation so far with NoCleverName:
QUOTE (NoCleverName to NeoDevin+Jan 10 2008, 06:18 PM)
...
....I claim it is a rational number (in this case zero).
Hi guys.
Just curious. If "0" is not ON the "abstract number" LINE construct, then how can it BE a "number" per se rather than a mere symbol for the number STRING notation convention indicating "absence of number" in a position IN a "notational STRING" rather than ON the "number LINE"?
Cheers.
RC.
.
....I claim it is a rational number (in this case zero).
QUOTE (RealityCheck to NoCleverName AND NeoDevin+Jan 11 2008, 12:09 AM)
Hi guys.
Just curious. If "0" is not ON the "abstract number" LINE construct, then how can it BE a "number" per se rather than a mere symbol for the number STRING notation convention indicating "absence of number" in a position IN a "notational STRING" rather than ON the "number LINE"?
Cheers.
RC.
.
QUOTE (NoCleverName to me+Jan 11 2008, 12:37 AM)
Of course zero is on the number line. This isn't even worth the time to argue about.
"Real"ly? hehehe.
Then why is it 'undefined' when using that 'number' as in 0/0?
Obviously some 'axiomatic ad hocness' is required to 'bring' the "0" onto ANY number line as a UNIQUE and DEFINED 'number' which then unfortunately STILL behaves/results as UNDEFINED in operations using that ad hocly 'defined' number '0'.
I like discussing it. Perhaps you don't consider it worthy of doing so. Sigh. Never mind. There are plenty of others who do. hehehe.
Left to, itself, "0" would not BE a number at all....let alone on any number line UNIQUELY DEFINED in all cases.
It would be valid as a symbolic placeholder (in a number STRING) and also as a BOUNDARY CONDITION/VALUE real-point/number TRANSITION/BRIDGING state/value between CONTRA-BALANCED 'lines'/continuums/actions etc.
Cheers for a while until I get back to these main forum discussions once more!
RC.
.
QUOTE (RealityCheck to NCN+Jan 11 2008, 02:15 AM)
"Real"ly? hehehe.
Then why is it 'undefined' when using that 'number' as in 0/0?
Obviously some 'axiomatic ad hocness' is required to 'bring' the "0" onto ANY number line as a UNIQUE and DEFINED 'number' which then unfortunately STILL behaves/results as UNDEFINED in operations using that ad hocly 'defined' number '0'.
I like discussing it. Perhaps you don't consider it worthy of doing so. Sigh. Never mind. There are plenty of others who do. hehehe.
Left to, itself, "0" would not BE a number at all....let alone on any number line UNIQUELY DEFINED in all cases.
It would be valid as a symbolic placeholder (in a number STRING) and also as a BOUNDARY CONDITION/VALUE real-point/number TRANSITION/BRIDGING state/value between CONTRA-BALANCED 'lines'/continuums/actions etc.
Cheers for a while until I get back to these main forum discussions once more!
RC.
.
QUOTE (NoCleverName to me+Jan 11 2008, 02:20 AM)
The only reason why 0 is mentioned is to define the concept of "starting point". Without "starting point" it isn't obvious how to measure anything, is it? Do not try to embellish such a simple concept with philosophical claptrap.
Hi again, NCN!
BTW, I just added to my last post for the sake of completeness etc.
And yeah, I understand what you say about needing a 'staring point' from which all else 'springs'.
BUT what IS the 'nature' of that staring point in reality/abstract?
It is a BOUNDARY CONDITION/STATE in a NON-EXISTENT/DISCONTINUOUS "OUTSIDE" of the 'continuum' under study....and/OR it actually IS some FIRST non-ZERO point for TWO OR MORE 'interconnecting continuums' that have NO 'outside' discontinuities' conveniently IGNORED by axiomatic elimination, hehehe.
Anyhow, a starting point is NOT the FIRST POINT unless it IS A POINT that is consistent with the behaviour of all other points on the line....and then we come to the UNDEFINED 0/0...and we see that YOUR idea of '0' is neither a starting POINT (since the next-lower 'point' is NOT ON the 'line')....OR it is ON the line and IS NOT ACTUALLY 'ZERO' as you treat it.
That is the DICHOTOMY that is introduced by the existing 'starting point' AXIOM using the NEBULOUS '0' concept/number as you do. It's OK for while you remain within ythe current AXIOMATIC BOUNADIES...but it cannot be used INDEPENDENTLY IN ALL CASES OUTSIDE THAT CONVENIENTLY axiomatically=bounded construct.
Tha's all I'm pointing out...and trying to explore the implications/consequences 'contextually' in a way that SIDESTEPS THE NECESSITY for axiomatic ad hocness in order to avoid inconsistencies within the currently 'defined' system.
I and others are working OUTSIDE current cinstructs....that is the whole point of these discussions, I think.
I and others ENJOY 'mucking about'....who knows what SERENDIPITY will bring from the most 'unlikely' DABBLER in the 'unknown', hehehe.
Nothing personal in our 'dabbling' and 'babbling', hehehe. So no hard feelings all round, I hope!
Cheers again!
RC.
.
QUOTE (RealityCheck to NCN+Jan 11 2008, 02:36 AM)
Hi again, NCN!
BTW, I just added to my last post for the sake of completeness etc.
And yeah, I understand what you say about needing a 'staring point' from which all else 'springs'.
BUT what IS the 'nature' of that staring point in reality/abstract?
It is a BOUNDARY CONDITION/STATE in a NON-EXISTENT/DISCONTINUOUS "OUTSIDE" of the 'continuum' under study....and/OR it actually IS some FIRST non-ZERO point for TWO OR MORE 'interconnecting continuums' that have NO 'outside' discontinuities' conveniently IGNORED by axiomatic elimination, hehehe.
Anyhow, a starting point is NOT the FIRST POINT unless it IS A POINT that is consistent with the behaviour of all other points on the line....and then we come to the UNDEFINED 0/0...and we see that YOUR idea of '0' is neither a starting POINT (since the next-lower 'point' is NOT ON the 'line')....OR it is ON the line and IS NOT ACTUALLY 'ZERO' as you treat it.
That is the DICHOTOMY that is introduced by the existing 'starting point' AXIOM using the NEBULOUS '0' concept/number as you do. It's OK for while you remain within ythe current AXIOMATIC BOUNADIES...but it cannot be used INDEPENDENTLY IN ALL CASES OUTSIDE THAT CONVENIENTLY axiomatically=bounded construct.
Tha's all I'm pointing out...and trying to explore the implications/consequences 'contextually' in a way that SIDESTEPS THE NECESSITY for axiomatic ad hocness in order to avoid inconsistencies within the currently 'defined' system.
I and others are working OUTSIDE current cinstructs....that is the whole point of these discussions, I think.
I and others ENJOY 'mucking about'....who knows what SERENDIPITY will bring from the most 'unlikely' DABBLER in the 'unknown', hehehe.
Nothing personal in our 'dabbling' and 'babbling', hehehe. So no hard feelings all round, I hope!
Cheers again!
RC.
.
QUOTE (NoCleverName to me+Jan 11 2008, 02:40 AM)
Zero. It's just a simple, innocent starting point. "Nothing" more, "nothing" less. 
Hi again, NCN!
BTW, I just added to my last post for the sake of completeness etc.
And yeah, I understand what you say about needing a 'statring point' from which all else 'springs'.
BUT what IS the 'nature' of that starting point in reality/abstract?
It is a BOUNDARY CONDITION/STATE in a NON-EXISTENT/DISCONTINUOUS "OUTSIDE" of the 'continuum' under study....and/OR it actually IS some FIRST non-ZERO point for TWO OR MORE 'interconnecting continuums' that have NO 'outside' discontinuities' conveniently IGNORED by axiomatic elimination, hehehe.
Anyhow, a starting point is NOT the FIRST POINT unless it IS A POINT that is consistent with the behaviour of all other points on the line....and then we come to the UNDEFINED 0/0...and we see that YOUR idea of '0' is neither a starting POINT (since the next-lower 'point' is NOT ON the 'line')....OR it is ON the line and IS NOT ACTUALLY 'ZERO' as you treat it.
That is the DICHOTOMY that is introduced by the existing 'starting point' AXIOM using the NEBULOUS '0' concept/number as you do. It's OK for while you remain within ythe current AXIOMATIC BOUNADIES...but it cannot be used INDEPENDENTLY IN ALL CASES OUTSIDE THAT CONVENIENTLY axiomatically=bounded construct.
Tha's all I'm pointing out...and trying to explore the implications/consequences 'contextually' in a way that SIDESTEPS THE NECESSITY for axiomatic ad hocness in order to avoid inconsistencies within the currently 'defined' system.
I and others are working OUTSIDE current cinstructs....that is the whole point of these discussions, I think.
I and others ENJOY 'mucking about'....who knows what SERENDIPITY will bring from the most 'unlikely' DABBLER in the 'unknown', hehehe.
Nothing personal in our 'dabbling' and 'babbling', hehehe. So no hard feelings all round, I hope!
Cheers again!
RC.
.
QUOTE (RealityCheck to NCN+Jan 11 2008, 02:36 AM)
Hi again, NCN!
BTW, I just added to my last post for the sake of completeness etc.
And yeah, I understand what you say about needing a 'statring point' from which all else 'springs'.
BUT what IS the 'nature' of that starting point in reality/abstract?
It is a BOUNDARY CONDITION/STATE in a NON-EXISTENT/DISCONTINUOUS "OUTSIDE" of the 'continuum' under study....and/OR it actually IS some FIRST non-ZERO point for TWO OR MORE 'interconnecting continuums' that have NO 'outside' discontinuities' conveniently IGNORED by axiomatic elimination, hehehe.
Anyhow, a starting point is NOT the FIRST POINT unless it IS A POINT that is consistent with the behaviour of all other points on the line....and then we come to the UNDEFINED 0/0...and we see that YOUR idea of '0' is neither a starting POINT (since the next-lower 'point' is NOT ON the 'line')....OR it is ON the line and IS NOT ACTUALLY 'ZERO' as you treat it.
That is the DICHOTOMY that is introduced by the existing 'starting point' AXIOM using the NEBULOUS '0' concept/number as you do. It's OK for while you remain within ythe current AXIOMATIC BOUNADIES...but it cannot be used INDEPENDENTLY IN ALL CASES OUTSIDE THAT CONVENIENTLY axiomatically=bounded construct.
Tha's all I'm pointing out...and trying to explore the implications/consequences 'contextually' in a way that SIDESTEPS THE NECESSITY for axiomatic ad hocness in order to avoid inconsistencies within the currently 'defined' system.
I and others are working OUTSIDE current cinstructs....that is the whole point of these discussions, I think.
I and others ENJOY 'mucking about'....who knows what SERENDIPITY will bring from the most 'unlikely' DABBLER in the 'unknown', hehehe.
Nothing personal in our 'dabbling' and 'babbling', hehehe. So no hard feelings all round, I hope!
Cheers again!
RC.
.
QUOTE (NoCleverName to me +Jan 11 2008, 02:40 AM)
Zero. It's just a simple, innocent starting point. "Nothing" more, "nothing" less.
Think about what you just said.
If zero is a starting point that 'exists', then it is the GROUND STATE 'point' from which you RELATIVELY go on to construct/measure things form as the ORIGIN STATE/POINT.
In which case you are IPSO FACTO treating ZERO and the whole NUMBER LINE 'relatively' to begin with.
So there is NO ABSOLUTE starting point that is NOTHING....rather it is the FIRST SOMETHING/NUMBER that you AXIOMATICALLY relegated to 'nothingness' simply because of a RELATIVITY AD HOC 'definition' for STARTING POINT.
In which case, if zero IS merely a starting GROUND STATE VALUE 'someting', then 0/0 would BE "1" in the same 'AXIOMATIC RELATIVITY LINE CONSTRUCT/MANIPULATIONS.
That is, relative nothing "ground state something" starting value/point divided by another axiomatically identical relative nothing "ground state something" starting value/point, would be a "starting something" divided by a "starting something"...which would be "1"....and NOT 'undefined'.
See?
If "0" IS something relegated RELATIVELY to 'undefined' nothingness for 0/0, then of course 0/0 is 'undefined'.
BUT, if it is ABSOLUTELY 'something at the start', then it is actually 'something' that makes 0/0 DEFINED as "1".
More "philosophical claptrap" for your delectation, mate! hehehe.
PS:...And it was 'philosophical claptrap' (but 'incompletely' done, obviously) which 'gave' you the current AXIOMS in the first place...which axioms are obviously also 'incomplete'. Philosophical claptrap must be 'completely' done by a new generation od 'philosophical claptrappers' if we are to have 'complete' axioms/mathematics.
Cheers.
RC.
.
QUOTE (RealityCheck to NCN+Jan 11 2008, 02:51 AM)
Think about what you just said.
If zero is a starting point that 'exists', then it is the GROUND STATE 'point' from which you RELATIVELY go on to construct/measure things form as the ORIGIN STATE/POINT.
In which case you are IPSO FACTO treating ZERO and the whole NUMBER LINE 'relatively' to begin with.
So there is NO ABSOLUTE starting point that is NOTHING....rather it is the FIRST SOMETHING/NUMBER that you AXIOMATICALLY relegated to 'nothingness' simply because of a RELATIVITY AD HOC 'definition' for STARTING POINT.
In which case, if zero IS merely a starting GROUND STATE VALUE 'someting', then 0/0 would BE "1" in the same 'AXIOMATIC RELATIVITY LINE CONSTRUCT/MANIPULATIONS.
That is, relative nothing "ground state something" starting value/point divided by another axiomatically identical relative nothing "ground state something" starting value/point, would be a "starting something" divided by a "starting something"...which would be "1"....and NOT 'undefined'.
See?
If "0" IS something relegated RELATIVELY to 'undefined' nothingness for 0/0, then of course 0/0 is 'undefined'.
BUT, if it is ABSOLUTELY 'something at the start', then it is actually 'something' that makes 0/0 DEFINED as "1".
More "philosophical claptrap" for your delectation, mate! hehehe.
PS:...And it was 'philosophical claptrap' (but 'incompletely' done, obviously) which 'gave' you the current AXIOMS in the first place...which axioms are obviously also 'incomplete'. Philosophical claptrap must be 'completely' done by a new generation od 'philosophical claptrappers' if we are to have 'complete' axioms/mathematics.
Cheers.
RC.
.
QUOTE (NoCleverName to me+Jan 11 2008, 03:55 AM)
Nice try, RC ... but you're wasting your time here beating on poor old zero. Besides, since simple transformations can move zero to where ever you want it ... and other numbers over zero, it's hard to see why it should be singled out.
So 'transformations' are still RELATIVE manipulations based on RELATIVE axioms/definitions of the RELATIVE 'something' that will STILL be 'a starting something' 'relabelled' and RELATIVELY 'relegated' to NOTHINGNESS simply for the convenience of that RELATIVE construction from a RELATIVE 'definition' etc etc etc.
See?
There is no getting away ABSOLUTELY from 'philosophical claptrap' unless you have some ABSOLUTE NOTHINGNESS 'point' that IS 'on' ANY number line uniquely defined as a definite ABSOLUTE starting something Value/Point of 'origin'....instead of a BOUNDARY COMPOUND/SUPERPOSITION STATE/VALUE as I described earlier.
I appreciate where you're 'coming from', really I do....but that ZERO NUMBER 'starting point' is not definable as a VALID NUMBER....UNLESS it is actually a starting "something"; in which case, that something NUMBER "0" divided by that same something NUMBER "0" is then "1"...and not "undefined" as currently 'derived' from the INCOMPLETE 'philosophical claptrap' that has "0" defined BOTH as a RELATIVE STARTING "SOMETHING" point/number, AND also a NOTHING 'ORIGIN' concept that is ABSOLUTELY not on the line at all. No wonder the inconsistencies and undefined 'derivations/definitions'.
Cheers all!
.RC.
.
And that is where that conversation between me and NCN stands at this time.
I again hereby invite the open participation of any and all constructive intellects of whatever persuasions, schools of thought, lay/professional standing, gender and personal beliefs. It doesn’t matter as long as you are a GENUINE ‘explorer’ of the concrete/abstract world around you! hehehe.
IMPORTANT NOTE to all intending participents: Please try to FORGET all past “FEUDS” you may have had with whomever. All I desire HERE is for the conversation to BEGIN “CLEAN” and PROCEED “WITHOUT RANCOUR” and REMAIN RELEVANT ONLY to “AXIOMATIC/DEFINITIONAL” aspects of ZERO....and no ‘muddying’ extraneous sideshows and feuds. We are NOT here to take ‘potshots’ at ANYONE OR ANYTHING.....we are here to PROPERLY and LEGITIMATELY and SOBERLY and RESPECTFULLY re-examine the status quo axiomatis and definitional “understandings” regarding ‘zero’....and see where that re-examination leads. OK? PLEASE!.....check all “old vitriol" and "personal baggage” at the door before entering! hehehe.
PS: I find myself very short of time at the moment, so I’ll be back in THIS thread in a few days to see how the (hopefully polite and constructive) conversation and axiomatic/definitional re-examination is going. Cheers all!
Thankyou, AlphaNumeric, everyone. Good luck and good thinking, all!
Your friend in Science (both mathematical and physical),
RealityCkeck.
.
QUOTE (RealityCheck to NCN+Jan 11 2008, 04:48 AM)
So 'transformations' are still RELATIVE manipulations based on RELATIVE axioms/definitions of the RELATIVE 'something' that will STILL be 'a starting something' 'relabelled' and RELATIVELY 'relegated' to NOTHINGNESS simply for the convenience of that RELATIVE construction from a RELATIVE 'definition' etc etc etc.
See?
There is no getting away ABSOLUTELY from 'philosophical claptrap' unless you have some ABSOLUTE NOTHINGNESS 'point' that IS 'on' ANY number line uniquely defined as a definite ABSOLUTE starting something Value/Point of 'origin'....instead of a BOUNDARY COMPOUND/SUPERPOSITION STATE/VALUE as I described earlier.
I appreciate where you're 'coming from', really I do....but that ZERO NUMBER 'starting point' is not definable as a VALID NUMBER....UNLESS it is actually a starting "something"; in which case, that something NUMBER "0" divided by that same something NUMBER "0" is then "1"...and not "undefined" as currently 'derived' from the INCOMPLETE 'philosophical claptrap' that has "0" defined BOTH as a RELATIVE STARTING "SOMETHING" point/number, AND also a NOTHING 'ORIGIN' concept that is ABSOLUTELY not on the line at all. No wonder the inconsistencies and undefined 'derivations/definitions'.
Cheers all!
.RC.
.
And that is where that conversation between me and NCN stands at this time.
I again hereby invite the open participation of any and all constructive intellects of whatever persuasions, schools of thought, lay/professional standing, gender and personal beliefs. It doesn’t matter as long as you are a GENUINE ‘explorer’ of the concrete/abstract world around you! hehehe.
IMPORTANT NOTE to all intending participents: Please try to FORGET all past “FEUDS” you may have had with whomever. All I desire HERE is for the conversation to BEGIN “CLEAN” and PROCEED “WITHOUT RANCOUR” and REMAIN RELEVANT ONLY to “AXIOMATIC/DEFINITIONAL” aspects of ZERO....and no ‘muddying’ extraneous sideshows and feuds. We are NOT here to take ‘potshots’ at ANYONE OR ANYTHING.....we are here to PROPERLY and LEGITIMATELY and SOBERLY and RESPECTFULLY re-examine the status quo axiomatis and definitional “understandings” regarding ‘zero’....and see where that re-examination leads. OK? PLEASE!.....check all “old vitriol" and "personal baggage” at the door before entering! hehehe.
PS: I find myself very short of time at the moment, so I’ll be back in THIS thread in a few days to see how the (hopefully polite and constructive) conversation and axiomatic/definitional re-examination is going. Cheers all!
Thankyou, AlphaNumeric, everyone. Good luck and good thinking, all!
Your friend in Science (both mathematical and physical),
RealityCkeck.
.
Thanks for bumping this thread and I so have some things to add now:
1. The concept of 'infinity' is underspecified and indeterminant. Only a single unbounded, variable quantity should be used when computing limits (and it would appear natural to associate this with the time over which a process has occured).
If we define infinity and 0 to be:
infinity=n
0=1/n
and then allow for all irrational numbers to be defined by a single variable term n->infinity, to determine precision, then we no longer have indeterminism involved in statements like 0/0=1 of 0^0~=1-log(infinity)/infinity or infinity^2>infinity or infinity-infinity=0 etc.
And we can simply denote many irrational values as, for example e=(1+0)^infinity.
An additive 0, if necessary to describe for some reason (there are an infinite number of possible 0s we could add to an equation and so an addition of 0 isn't necessary or useful), we could construct is a cancellation of equal and opposing polarity terms such as 0-0 or x-x etc.
2. Irrational numbers have no specific precision (truly irrationals and likely even integers could be seen in the same context). A number line is dynamic and context dependent and consists of an ordering of elements at any particular moment and for example, the computation of 2+5=7 implicitly constructs the numberline:
0<1<2<5<7
(The numbers 0 and 1 I included because of their implicit necessity in both constructing 2 and 5 as (1+1) and (1+1+1+1+1) and the number 0 is also implicitly required in order that we can detect equality and inequality, because this is determined by whether or not x-y=0, in which case x=y, though we could remove 1 and define it as 0/0)
Numbers only have a meaning relative to other numbers and more fundamentally to the units by which numbers are constructed.
A more fundamental representation of "Real" numbers in this context could be seen as a range of possible solutions, which actually requires 2 dimensions to specify as either a minimum and maximum value or a central value with a tolerance, that are ordered numerically, with a fundamental representation as two rings, representing positive and negative quantities respectively and an implicit detached zero point for determining equality between these.
If we define +0, +1 and +infinity as starting points of a line segment (though we can define +1 to be either the geometric mean or the product of +0 and +infinity), then we have a positive number line ordered as:
+0<+1<+infinity
If we apply a reciprocal operation, this becomes the same as reversing the order of a set:
+1/+infinity<+1/+1=+1<+/+0
If we negate the original values, we again invert the ordering of this set and get:
-infinity<-1<-0
If we append these two, positive and negative line segments together, and place an element Z to indicate the additive identity for zero, we get:
-infinity<-1<-0<Z<+0<+1<+infinity
A potential problem arises though when an additive operation crosses from the positive line to the negative line as we have the potential inclusion of Z as an element and, for example +1-(+1) would not necessarily equal +0 or -0, but instead the additive zero, Z.
But at least the context in which a multiplicative 0 or infinite value occurs is deterministic by this system and as points are added and manipulated to this number line, a specific solution could be seen as arising from various reversals and shifts of segments of numbers along this axis and for some computation resulting in an approximation of pi, we could see the total context of a computation as, for example:
-(infinity^2)<-infinity<-1<-0<Z<+0<+1<+3<+3.1<pi<+3.2<+10<log(+infinity)<+infinity
And in this case pi is defined not as a single number but an ordered pairing of {3.1,3.2}, or alternately it might be a pairing of a current estimate and an iteration number etc.
3. A finite number is actually a number and not a variable. The statement "x is finite" is inaccurate, just as the statement that "all elements of 1,2,3,... are numbers" is inaccurate as '...' isn't a number and this implies that a recursive definition that an infinite sequence is a number.
And taken as a limit, there is no specific number that terminates the sequences 1,2,3,... and neither does a specific number terminate the sequence 1/1,1/2,1/3,.... The diferences in one case are infinite and in the other case the differences are infinitesimal.
4. An informationally compressive mapping from a set of possible solutions convey some quantity of information to an alternate mapping that doesn't convey identical information is not invertible and can't be considered an equality or provable identity, but instead a possible approximation or isolated solution from other elements and if a set is infinite, then any finite result would automatically not be an identity.
1. The concept of 'infinity' is underspecified and indeterminant. Only a single unbounded, variable quantity should be used when computing limits (and it would appear natural to associate this with the time over which a process has occured).
If we define infinity and 0 to be:
infinity=n
0=1/n
and then allow for all irrational numbers to be defined by a single variable term n->infinity, to determine precision, then we no longer have indeterminism involved in statements like 0/0=1 of 0^0~=1-log(infinity)/infinity or infinity^2>infinity or infinity-infinity=0 etc.
And we can simply denote many irrational values as, for example e=(1+0)^infinity.
An additive 0, if necessary to describe for some reason (there are an infinite number of possible 0s we could add to an equation and so an addition of 0 isn't necessary or useful), we could construct is a cancellation of equal and opposing polarity terms such as 0-0 or x-x etc.
2. Irrational numbers have no specific precision (truly irrationals and likely even integers could be seen in the same context). A number line is dynamic and context dependent and consists of an ordering of elements at any particular moment and for example, the computation of 2+5=7 implicitly constructs the numberline:
0<1<2<5<7
(The numbers 0 and 1 I included because of their implicit necessity in both constructing 2 and 5 as (1+1) and (1+1+1+1+1) and the number 0 is also implicitly required in order that we can detect equality and inequality, because this is determined by whether or not x-y=0, in which case x=y, though we could remove 1 and define it as 0/0)
Numbers only have a meaning relative to other numbers and more fundamentally to the units by which numbers are constructed.
A more fundamental representation of "Real" numbers in this context could be seen as a range of possible solutions, which actually requires 2 dimensions to specify as either a minimum and maximum value or a central value with a tolerance, that are ordered numerically, with a fundamental representation as two rings, representing positive and negative quantities respectively and an implicit detached zero point for determining equality between these.
If we define +0, +1 and +infinity as starting points of a line segment (though we can define +1 to be either the geometric mean or the product of +0 and +infinity), then we have a positive number line ordered as:
+0<+1<+infinity
If we apply a reciprocal operation, this becomes the same as reversing the order of a set:
+1/+infinity<+1/+1=+1<+/+0
If we negate the original values, we again invert the ordering of this set and get:
-infinity<-1<-0
If we append these two, positive and negative line segments together, and place an element Z to indicate the additive identity for zero, we get:
-infinity<-1<-0<Z<+0<+1<+infinity
A potential problem arises though when an additive operation crosses from the positive line to the negative line as we have the potential inclusion of Z as an element and, for example +1-(+1) would not necessarily equal +0 or -0, but instead the additive zero, Z.
But at least the context in which a multiplicative 0 or infinite value occurs is deterministic by this system and as points are added and manipulated to this number line, a specific solution could be seen as arising from various reversals and shifts of segments of numbers along this axis and for some computation resulting in an approximation of pi, we could see the total context of a computation as, for example:
-(infinity^2)<-infinity<-1<-0<Z<+0<+1<+3<+3.1<pi<+3.2<+10<log(+infinity)<+infinity
And in this case pi is defined not as a single number but an ordered pairing of {3.1,3.2}, or alternately it might be a pairing of a current estimate and an iteration number etc.
3. A finite number is actually a number and not a variable. The statement "x is finite" is inaccurate, just as the statement that "all elements of 1,2,3,... are numbers" is inaccurate as '...' isn't a number and this implies that a recursive definition that an infinite sequence is a number.
And taken as a limit, there is no specific number that terminates the sequences 1,2,3,... and neither does a specific number terminate the sequence 1/1,1/2,1/3,.... The diferences in one case are infinite and in the other case the differences are infinitesimal.
4. An informationally compressive mapping from a set of possible solutions convey some quantity of information to an alternate mapping that doesn't convey identical information is not invertible and can't be considered an equality or provable identity, but instead a possible approximation or isolated solution from other elements and if a set is infinite, then any finite result would automatically not be an identity.
QUOTE (StevenA+Jan 15 2008, 07:36 PM)
Thanks for bumping this thread and I so have some things to add now:
1. The concept of 'infinity' is underspecified and indeterminant. Only a single unbounded, variable quantity should be used when computing limits (and it would appear natural to associate this with the time over which a process has occured).
If we define infinity and 0 to be:
infinity=n
0=1/n
and then allow for all irrational numbers to be defined by a single variable term n->infinity, to determine precision, then we no longer have indeterminism involved in statements like 0/0=1 of 0^0~=1-log(infinity)/infinity or infinity^2>infinity or infinity-infinity=0 etc.
And we can simply denote many irrational values as, for example e=(1+0)^infinity.
An additive 0, if necessary to describe for some reason (there are an infinite number of possible 0s we could add to an equation and so an addition of 0 isn't necessary or useful), we could construct is a cancellation of equal and opposing polarity terms such as 0-0 or x-x etc.
2. Irrational numbers have no specific precision (truly irrationals and likely even integers could be seen in the same context). A number line is dynamic and context dependent and consists of an ordering of elements at any particular moment and for example, the computation of 2+5=7 implicitly constructs the numberline:
0<1<2<5<7
(The numbers 0 and 1 I included because of their implicit necessity in both constructing 2 and 5 as (1+1) and (1+1+1+1+1) and the number 0 is also implicitly required in order that we can detect equality and inequality, because this is determined by whether or not x-y=0, in which case x=y, though we could remove 1 and define it as 0/0)
Numbers only have a meaning relative to other numbers and more fundamentally to the units by which numbers are constructed.
A more fundamental representation of "Real" numbers in this context could be seen as a range of possible solutions, which actually requires 2 dimensions to specify as either a minimum and maximum value or a central value with a tolerance, that are ordered numerically, with a fundamental representation as two rings, representing positive and negative quantities respectively and an implicit detached zero point for determining equality between these.
If we define +0, +1 and +infinity as starting points of a line segment (though we can define +1 to be either the geometric mean or the product of +0 and +infinity), then we have a positive number line ordered as:
+0<+1<+infinity
If we apply a reciprocal operation, this becomes the same as reversing the order of a set:
+1/+infinity<+1/+1=+1<+/+0
If we negate the original values, we again invert the ordering of this set and get:
-infinity<-1<-0
If we append these two, positive and negative line segments together, and place an element Z to indicate the additive identity for zero, we get:
-infinity<-1<-0<Z<+0<+1<+infinity
A potential problem arises though when an additive operation crosses from the positive line to the negative line as we have the potential inclusion of Z as an element and, for example +1-(+1) would not necessarily equal +0 or -0, but instead the additive zero, Z.
But at least the context in which a multiplicative 0 or infinite value occurs is deterministic by this system and as points are added and manipulated to this number line, a specific solution could be seen as arising from various reversals and shifts of segments of numbers along this axis and for some computation resulting in an approximation of pi, we could see the total context of a computation as, for example:
-(infinity^2)<-infinity<-1<-0<Z<+0<+1<+3<+3.1<pi<+3.2<+10<log(+infinity)<+infinity
And in this case pi is defined not as a single number but an ordered pairing of {3.1,3.2}, or alternately it might be a pairing of a current estimate and an iteration number etc.
3. A finite number is actually a number and not a variable. The statement "x is finite" is inaccurate, just as the statement that "all elements of 1,2,3,... are numbers" is inaccurate as '...' isn't a number and this implies that a recursive definition that an infinite sequence is a number.
And taken as a limit, there is no specific number that terminates the sequences 1,2,3,... and neither does a specific number terminate the sequence 1/1,1/2,1/3,.... The diferences in one case are infinite and in the other case the differences are infinitesimal.
4. An informationally compressive mapping from a set of possible solutions convey some quantity of information to an alternate mapping that doesn't convey identical information is not invertible and can't be considered an equality or provable identity, but instead a possible approximation or isolated solution from other elements and if a set is infinite, then any finite result would automatically not be an identity.
Infinity is a concept, not a number. You're treating infinity as a number, which caters to the answers you seek, but does not hold valid for all statements.
For example, in your post, you define 0 as equal to 1/n, when it should be a limit. The same thing holds true for defining n as infinity, by which I mean that you should be treating it as a limit.
Again, you make the same mistake assuming 0/0=1. Granted, 0=0*1 is true, but using your convoluted logic, you could say that since 0=0*2, then 0/0=2. All of a sudden, 1=2 which is not true. Thus, you cannot do that. Now, Euler also had a problem with the infinitely large and small, but he addressed this issue many a times in Opera Omnia. Clearly you've never read it, but then again, most math professors haven't either.
We run into the same problem here, where you define e=(1+0)^infinity. In reality, e=limit((1+1/n)^n) n->infinity. Now, 1/e=limit((1-1/n)^n) n->infinity. If 1/n according to you equals 0, then (1+0)^infinity and (1-0)^infinity should be the same, when in reality they aren't.
Another major mistake you've committed is treating a line segment as a line. Line segments have finite length, but are constituted of infinite points (i.e. your line segment may start at 0 and end at 2, but 0<0.000...0001<0.000...0002<2). Lines, however, are of infinite length. Infinity can never exist on a line segment.
I'll leave it to AlphaNumeric (or someone else from the "forum mafia") to butcher the rest.
1. The concept of 'infinity' is underspecified and indeterminant. Only a single unbounded, variable quantity should be used when computing limits (and it would appear natural to associate this with the time over which a process has occured).
If we define infinity and 0 to be:
infinity=n
0=1/n
and then allow for all irrational numbers to be defined by a single variable term n->infinity, to determine precision, then we no longer have indeterminism involved in statements like 0/0=1 of 0^0~=1-log(infinity)/infinity or infinity^2>infinity or infinity-infinity=0 etc.
And we can simply denote many irrational values as, for example e=(1+0)^infinity.
An additive 0, if necessary to describe for some reason (there are an infinite number of possible 0s we could add to an equation and so an addition of 0 isn't necessary or useful), we could construct is a cancellation of equal and opposing polarity terms such as 0-0 or x-x etc.
2. Irrational numbers have no specific precision (truly irrationals and likely even integers could be seen in the same context). A number line is dynamic and context dependent and consists of an ordering of elements at any particular moment and for example, the computation of 2+5=7 implicitly constructs the numberline:
0<1<2<5<7
(The numbers 0 and 1 I included because of their implicit necessity in both constructing 2 and 5 as (1+1) and (1+1+1+1+1) and the number 0 is also implicitly required in order that we can detect equality and inequality, because this is determined by whether or not x-y=0, in which case x=y, though we could remove 1 and define it as 0/0)
Numbers only have a meaning relative to other numbers and more fundamentally to the units by which numbers are constructed.
A more fundamental representation of "Real" numbers in this context could be seen as a range of possible solutions, which actually requires 2 dimensions to specify as either a minimum and maximum value or a central value with a tolerance, that are ordered numerically, with a fundamental representation as two rings, representing positive and negative quantities respectively and an implicit detached zero point for determining equality between these.
If we define +0, +1 and +infinity as starting points of a line segment (though we can define +1 to be either the geometric mean or the product of +0 and +infinity), then we have a positive number line ordered as:
+0<+1<+infinity
If we apply a reciprocal operation, this becomes the same as reversing the order of a set:
+1/+infinity<+1/+1=+1<+/+0
If we negate the original values, we again invert the ordering of this set and get:
-infinity<-1<-0
If we append these two, positive and negative line segments together, and place an element Z to indicate the additive identity for zero, we get:
-infinity<-1<-0<Z<+0<+1<+infinity
A potential problem arises though when an additive operation crosses from the positive line to the negative line as we have the potential inclusion of Z as an element and, for example +1-(+1) would not necessarily equal +0 or -0, but instead the additive zero, Z.
But at least the context in which a multiplicative 0 or infinite value occurs is deterministic by this system and as points are added and manipulated to this number line, a specific solution could be seen as arising from various reversals and shifts of segments of numbers along this axis and for some computation resulting in an approximation of pi, we could see the total context of a computation as, for example:
-(infinity^2)<-infinity<-1<-0<Z<+0<+1<+3<+3.1<pi<+3.2<+10<log(+infinity)<+infinity
And in this case pi is defined not as a single number but an ordered pairing of {3.1,3.2}, or alternately it might be a pairing of a current estimate and an iteration number etc.
3. A finite number is actually a number and not a variable. The statement "x is finite" is inaccurate, just as the statement that "all elements of 1,2,3,... are numbers" is inaccurate as '...' isn't a number and this implies that a recursive definition that an infinite sequence is a number.
And taken as a limit, there is no specific number that terminates the sequences 1,2,3,... and neither does a specific number terminate the sequence 1/1,1/2,1/3,.... The diferences in one case are infinite and in the other case the differences are infinitesimal.
4. An informationally compressive mapping from a set of possible solutions convey some quantity of information to an alternate mapping that doesn't convey identical information is not invertible and can't be considered an equality or provable identity, but instead a possible approximation or isolated solution from other elements and if a set is infinite, then any finite result would automatically not be an identity.
Infinity is a concept, not a number. You're treating infinity as a number, which caters to the answers you seek, but does not hold valid for all statements.
For example, in your post, you define 0 as equal to 1/n, when it should be a limit. The same thing holds true for defining n as infinity, by which I mean that you should be treating it as a limit.
Again, you make the same mistake assuming 0/0=1. Granted, 0=0*1 is true, but using your convoluted logic, you could say that since 0=0*2, then 0/0=2. All of a sudden, 1=2 which is not true. Thus, you cannot do that. Now, Euler also had a problem with the infinitely large and small, but he addressed this issue many a times in Opera Omnia. Clearly you've never read it, but then again, most math professors haven't either.
We run into the same problem here, where you define e=(1+0)^infinity. In reality, e=limit((1+1/n)^n) n->infinity. Now, 1/e=limit((1-1/n)^n) n->infinity. If 1/n according to you equals 0, then (1+0)^infinity and (1-0)^infinity should be the same, when in reality they aren't.
Another major mistake you've committed is treating a line segment as a line. Line segments have finite length, but are constituted of infinite points (i.e. your line segment may start at 0 and end at 2, but 0<0.000...0001<0.000...0002<2). Lines, however, are of infinite length. Infinity can never exist on a line segment.
I'll leave it to AlphaNumeric (or someone else from the "forum mafia") to butcher the rest.
QUOTE (Guest00+Jan 15 2008, 05:44 PM)
Infinity is a concept, not a number. You're treating infinity as a number, which caters to the answers you seek, but does not hold valid for all statements.
For example, in your post, you define 0 as equal to 1/n, when it should be a limit. The same thing holds true for defining n as infinity, by which I mean that you should be treating it as a limit.
Again, you make the same mistake assuming 0/0=1. Granted, 0=0*1 is true, but using your convoluted logic, you could say that since 0=0*2, then 0/0=2. All of a sudden, 1=2 which is not true. Thus, you cannot do that. Now, Euler also had a problem with the infinitely large and small, but he addressed this issue many a times in Opera Omnia. Clearly you've never read it, but then again, most math professors haven't either.
We run into the same problem here, where you define e=(1+0)^infinity. In reality, e=limit((1+1/n)^n) n->infinity. Now, 1/e=limit((1-1/n)^n) n->infinity. If 1/n according to you equals 0, then (1+0)^infinity and (1-0)^infinity should be the same, when in reality they aren't.
Another major mistake you've committed is treating a line segment as a line. Line segments have finite length, but are constituted of infinite points (i.e. your line segment may start at 0 and end at 2, but 0<0.000...0001<0.000...0002<2). Lines, however, are of infinite length. Infinity can never exist on a line segment.
I'll leave it to AlphaNumeric (or someone else from the "forum mafia") to butcher the rest.
Please leave the thread if you don't have anything to add to it.
For example, in your post, you define 0 as equal to 1/n, when it should be a limit. The same thing holds true for defining n as infinity, by which I mean that you should be treating it as a limit.
Again, you make the same mistake assuming 0/0=1. Granted, 0=0*1 is true, but using your convoluted logic, you could say that since 0=0*2, then 0/0=2. All of a sudden, 1=2 which is not true. Thus, you cannot do that. Now, Euler also had a problem with the infinitely large and small, but he addressed this issue many a times in Opera Omnia. Clearly you've never read it, but then again, most math professors haven't either.
We run into the same problem here, where you define e=(1+0)^infinity. In reality, e=limit((1+1/n)^n) n->infinity. Now, 1/e=limit((1-1/n)^n) n->infinity. If 1/n according to you equals 0, then (1+0)^infinity and (1-0)^infinity should be the same, when in reality they aren't.
Another major mistake you've committed is treating a line segment as a line. Line segments have finite length, but are constituted of infinite points (i.e. your line segment may start at 0 and end at 2, but 0<0.000...0001<0.000...0002<2). Lines, however, are of infinite length. Infinity can never exist on a line segment.
I'll leave it to AlphaNumeric (or someone else from the "forum mafia") to butcher the rest.
Please leave the thread if you don't have anything to add to it.
QUOTE (NoCleverName to NeoDevin @ Jan 10 2008+ 06:18 PM)
....I claim it is a rational number (in this case zero).
QUOTE (Someone+)
No, it isn't
QUOTE (SomeoneElse+)
Is too
QUOTE (APerson+)
Esteemed lame horse, no it isn't
QUOTE (AnotherPerson+)
Venerable diseased dog, it is too
QUOTE (DistinguishedGentleman+)
My solution is right, all others are wrong or my name isn't Ivan
Uh, I didn't really say that. Everybody is right.
Uh, I didn't really say that. Everybody is right.
QUOTE (RealityCheck to NoCleverName AND NeoDevin @ Jan 11 2008+ 12:09 AM)
If "0" is not ON the "abstract number" LINE construct, then how can it BE a "number" per se rather than a mere symbol for the number STRING notation convention indicating "absence of number" in a position IN a "notational STRING" rather than ON the "number LINE"?
QUOTE (NoCleverName to me @ Jan 11 2008+ 12:37 AM)
Of course zero is on the number line.
Then why is it 'undefined' when using that 'number' as in 0/0?
(...)Left to, itself, "0" would not BE a number at all....let alone on any number line UNIQUELY DEFINED in all cases.
I will stop here because as far as I can tell, you --RC-- were the only one who got an answer that agrees with what I know. It's not that 0/0 would not be a number, since it would, and it's not that it wouldn't be on the number line, because it would. Steven favors 0/0=1, whereas I favor 0/0= zero turned out of space. I can have my answer, he can have his 1, those who want can have their decidable or undecidable number, those who want it can have their line number, you can have your non-number, but there is only one method of definitely synthesizing all of those into a single answer: if zero divided by zero is solemnly declared to be both a place and a set of instructions in time. It is a position and a time.
It is very much like the redness of red: "Where did you see it? Show it to me and I will go check it and if that redness of red is really red I will tell you!"
I have seen the "redness of red" of 0/0. Trying to give it a "result" without telling you what I was doing at the time I saw that redness is outside the scope of my communicational ability. 0/0 doesn't fall out of the sky on top of people's heads, it comes in with a whole context. That context is the verb: what sort of equation caused it? Where was it going? Show it to me and I will confirm it or not.
One can't show me the redness of red --as one can't show me any result of 0/0-- without a checkable context to give it substance. Every single time thought ended up with a problem that ended in 0/0 it went around it. Computers are programmed around it.
A set of *unread* instructions is as a "momentum", say a "magnetic momentum" frozen in time: where was the equation that ended up with 0/0 coming from? It is that context that will have to know what to do with it. Examples would be:
1-... ...3/-3=-1, 2/-2=-2, 1/-1=-1, 0/0=1, 1/1=1, 2/2=1, 3/3=3... ...
2-... ...and since every n/1 equals 1, all n/0 must equal 0... ...
3-... ...and since n*0 equals 0, all n/0 equals n... ...
4-... ...and since n^infinity= n 90 degrees out of space, then 0/0 is no exception... ...
5-... ...if zero IS merely a starting GROUND STATE VALUE 'something', then 0/0 would BE "1" in the same 'AXIOMATIC RELATIVITY LINE CONSTRUCT/MANIPULATIONS... ...
The question is: does it have a use? This is philosophical pragmatism, I am aware... don't have much use for it...
In all cases, the instability was caused by the **operation** of division... the operation is unstable, and this instability will remain showing up in all systems you set up to handle it. When the numbers are unending, you will have to take a decision after each and every digit comes out of the operation, a conditionally-random walk... the "science of last digits" is the most sophisticatedly predictive superscience that doesn't exist. I know that because if all random walks are ready-made and previously written with numbers in the fabric of space, they collapse into the fabric of the atom.
A set of instructions can be taken apart piece by piece. The set of instructions of division takes as its last operation the last digit of a number, the one that upholds the unit quantity. Ignoring it, that is, rounding the unit quantity, destroys the information that it contains so much that it is impossible to recover the number's original numberiness because the numberiness of a number is spread over all of its digits. All of the truth of a number is spread over the totality of its expression, no matter what language and/or numeric base you use. It's a superimposition. A rounded-off number leaves you with the problem of monaditis, a most unpleasant disease of the nerves acquired by watching people discuss why fried rounded-off monads are so melted
QUOTE (RealityCheck to NCN @ Jan 11 2008+ 02:15 AM)
Then why is it 'undefined' when using that 'number' as in 0/0?
(...)Left to, itself, "0" would not BE a number at all....let alone on any number line UNIQUELY DEFINED in all cases.
I will stop here because as far as I can tell, you --RC-- were the only one who got an answer that agrees with what I know. It's not that 0/0 would not be a number, since it would, and it's not that it wouldn't be on the number line, because it would. Steven favors 0/0=1, whereas I favor 0/0= zero turned out of space. I can have my answer, he can have his 1, those who want can have their decidable or undecidable number, those who want it can have their line number, you can have your non-number, but there is only one method of definitely synthesizing all of those into a single answer: if zero divided by zero is solemnly declared to be both a place and a set of instructions in time. It is a position and a time.
It is very much like the redness of red: "Where did you see it? Show it to me and I will go check it and if that redness of red is really red I will tell you!"
I have seen the "redness of red" of 0/0. Trying to give it a "result" without telling you what I was doing at the time I saw that redness is outside the scope of my communicational ability. 0/0 doesn't fall out of the sky on top of people's heads, it comes in with a whole context. That context is the verb: what sort of equation caused it? Where was it going? Show it to me and I will confirm it or not.
One can't show me the redness of red --as one can't show me any result of 0/0-- without a checkable context to give it substance. Every single time thought ended up with a problem that ended in 0/0 it went around it. Computers are programmed around it.
A set of *unread* instructions is as a "momentum", say a "magnetic momentum" frozen in time: where was the equation that ended up with 0/0 coming from? It is that context that will have to know what to do with it. Examples would be:
1-... ...3/-3=-1, 2/-2=-2, 1/-1=-1, 0/0=1, 1/1=1, 2/2=1, 3/3=3... ...
2-... ...and since every n/1 equals 1, all n/0 must equal 0... ...
3-... ...and since n*0 equals 0, all n/0 equals n... ...
4-... ...and since n^infinity= n 90 degrees out of space, then 0/0 is no exception... ...
5-... ...if zero IS merely a starting GROUND STATE VALUE 'something', then 0/0 would BE "1" in the same 'AXIOMATIC RELATIVITY LINE CONSTRUCT/MANIPULATIONS... ...
The question is: does it have a use? This is philosophical pragmatism, I am aware... don't have much use for it...
In all cases, the instability was caused by the **operation** of division... the operation is unstable, and this instability will remain showing up in all systems you set up to handle it. When the numbers are unending, you will have to take a decision after each and every digit comes out of the operation, a conditionally-random walk... the "science of last digits" is the most sophisticatedly predictive superscience that doesn't exist. I know that because if all random walks are ready-made and previously written with numbers in the fabric of space, they collapse into the fabric of the atom.
A set of instructions can be taken apart piece by piece. The set of instructions of division takes as its last operation the last digit of a number, the one that upholds the unit quantity. Ignoring it, that is, rounding the unit quantity, destroys the information that it contains so much that it is impossible to recover the number's original numberiness because the numberiness of a number is spread over all of its digits. All of the truth of a number is spread over the totality of its expression, no matter what language and/or numeric base you use. It's a superimposition. A rounded-off number leaves you with the problem of monaditis, a most unpleasant disease of the nerves acquired by watching people discuss why fried rounded-off monads are so melted
QUOTE (RC+)
Obviously some 'axiomatic ad hocness' is required to 'bring' the "0" onto ANY number line as a UNIQUE and DEFINED 'number' which then unfortunately STILL behaves/results as UNDEFINED in operations using that ad hocly 'defined' number '0'
What is the verb? A verb that encompasses a superimposition from which all meanings could possibly be derived IS the completest-possible definition of the circumstances that lead into that superimposition It is the best Chaitinly information algorithm that represents itself. There is and there can be no off-rounding, no corner-cutting... UNLESS you have a use for it. What is the degree of zoom you need?
If "infinitesimal is a photon", and "infinitesimal is the verb", it is evident that you would be "thusly" led:
1 is a photon, thus
11 is a photon, thus
1
11
101
1111
is a photon, thus
1
11
101
1111
10001
111111
1010101
11011011
101000101
1111111111
...
is a photon, and so on.
(Tangentially: are you all sure you can't see why this
http://zms.desy.de/news/newsnbsp/2004nbsp/.../index_eng.html
is screamingly funny? I was in stiches!)
Those are pre-written conclusions that you have no way of avoiding. Since it is all superimposed and what changes my zoom level, I might as well change the word "photon" above for the word "electron", or "atom", "number", "infinity", "infinitesimal", "pixel", etc., and this leaves me speaking a language of my own --so much so that I seem to have changed the subject-- but there is not and there can not exist any difference... everything started from the primordial infinitesimal... or is it infinity?
A meaning collapse, you mean, when all values are equally right and equally wrong. Agreed.
A meaning collapse, you mean, when all values are equally right and equally wrong. Agreed.
The only reason why 0 is mentioned is to define the concept of "starting point". Without "starting point" it isn't obvious how to measure anything, is it?
You can have your starting point only as long as it is subjected to having uses other than the ones intended: "starting point" in time or in space or in organization or in execution or in placement or in quantity? All of the above? It collapsed then. That is the nature of a starting point, it means all things because nothing else can have meaning without it and its "numberiness" is spread over what it started.
But wait, there is more, you get a free Ginsu Peeler. There is a long additional "right answer".
6--... ...if zero-as-a-unit-of-thought can turn in space then it has a "thickness" and that thickness is exactly, no more and no less, but exactly, the same length as the "unit of thought" that led you to it (be it an actual thought or number, atom, infinitesimal, infinity, AIT algorithm, whatever). This is another way of saying that infinitesimal and infinity have the same prime code length OR Chaitin program length. This thickness has its own numberiness, which is accessed when the turn happens. 0/0 as the end of a computational process of turning will give you as Yet Another Right Answer the infinitesimal PLACE resting on an infinitesimal length, and in order to check the redness of that red you will have to go there and check if it is a 1 or a 0 that is at the position you want along that length.
The smallest-possible code (instruction code for an instruction set, algorithm for Chaitin-ly compression, or prime code for a number) for the biggest-possible meaning can not be lossy or the numberiness of a number/thought/infinity/instruction would be lost--meaning wouldn't be salvageable through algorithmic decompression, the equation would make the "wrong" sort of mistakes -not the right mistakes such as ours in this thread-, the atom wouldn't hold, the infinity would be embraceable, the computer wouldn't add. The bit length of the infinitesimal is the same as the bit length of infinity because both are numerically equivalent, but not formally. The form (1010101010...) is not the form (110110110110...) even though they are both infinite-bitted. But both are collapsible into integer lengths.
The integer length bits are what is missing from any meaningful discussion of 0/0 and other singularities. If they are not recovered, the process is lossy. "recovery" is easier said than done, unfortunately.
Each and every bit of the "universe" or "equation" that led us to 0/0 has to be recoverable. So that if the "universe" you have at hand is a superimposition, the operation will have to specify each and every bit so that the result is right.
I thought people would see at a glance, because it is so obvious to me, that prime code wrapped around Sack's spiral is supposed to be a series of numbers in an irrational language we don't yet know, and that they are probably sines and cosines of integers. All of a family of irrationals already written in a number table. When Steven says
he is unwillingly exchanging a limited numeric accuracy for the accuracy of a form in space, which T.Roc answered with
he is unwillingly exchanging a limited numeric accuracy for the accuracy of a form in space, which T.Roc answered with
about "8 digits out" gives us a "fuzzy" approximation, because it CAN NOT be "accurate" to an arbitrary number of digits.
This worked well for Planck, and has been leading in a "fuzzy" way ever since. There is NO other reason that h has any meaning, or functionality in QM. When you give an "answer" that has -34 digits, and you are only working with "12 digit accuracy", you don't see the difference. Right answers; wrong reasons.
Which only leads me back to the same thing I already think: all answers will collapse into understanding, even if they turn out to be only a cheat-sheet of previously-written "unreadable" numbers.
Whatever your "unit of thought" is, all meanings stand spread, superimposed over it, screaming to be heard. Sometimes I wish they'd shut up.
So what? What use is an observable number line in reality? What possible use do I have for infinite points between any two points "in observable reality".
There is no linear anything in reality. Everything we do that is linear is but a weak local approximation of the non-linear process it is modeling.
Mathematics is a modeling and simulation language. To the extent you input the variables and algorithms, it can calculate reality to arbitrary accuracies.
Sorry, I consider your conclusion to be trivial, obvious, and of no apparent value.
So what? What use is an observable number line in reality? What possible use do I have for infinite points between any two points "in observable reality".
There is no linear anything in reality. Everything we do that is linear is but a weak local approximation of the non-linear process it is modeling.
Mathematics is a modeling and simulation language. To the extent you input the variables and algorithms, it can calculate reality to arbitrary accuracies.
Sorry, I consider your conclusion to be trivial, obvious, and of no apparent value.
One can see that the analysis of ANY 'line', WHEREVER OR HOWEVER OR WHENEVER IT IS 'DRAWN', and WHETHER PHYSICAL OR ABSTRACT, should allow for the 'contextual' fact that it is NOT 'stationary'. It is actually ALWAYS MOVING (in space-time? or whatever).
Why? If you want to model a line in reality, have at it. You can use all sorts of techniques to quantify the errors, the motion. But, what is it going to tell you? That it isn't perfect!! Whoopee!! We already knew that.
What is the verb?
A verb that encompasses a superimposition from which all meanings could possibly be derived IS the completest-possible definition of the circumstances that lead into that superimposition It is the best Chaitinly information algorithm that represents itself. There is and there can be no off-rounding, no corner-cutting... UNLESS you have a use for it. What is the degree of zoom you need?If "infinitesimal is a photon", and "infinitesimal is the verb", it is evident that you would be "thusly" led:
1 is a photon, thus
11 is a photon, thus
1
11
101
1111
is a photon, thus
1
11
101
1111
10001
111111
1010101
11011011
101000101
1111111111
...
is a photon, and so on.
(Tangentially: are you all sure you can't see why this
http://zms.desy.de/news/newsnbsp/2004nbsp/.../index_eng.html
is screamingly funny? I was in stiches!)
Those are pre-written conclusions that you have no way of avoiding. Since it is all superimposed and what changes my zoom level, I might as well change the word "photon" above for the word "electron", or "atom", "number", "infinity", "infinitesimal", "pixel", etc., and this leaves me speaking a language of my own --so much so that I seem to have changed the subject-- but there is not and there can not exist any difference... everything started from the primordial infinitesimal... or is it infinity?
QUOTE
It would be valid as a symbolic placeholder (in a number STRING) and also as a BOUNDARY CONDITION/VALUE real-point/number TRANSITION/BRIDGING state/value between CONTRA-BALANCED 'lines'/continuums/actions etc.
A meaning collapse, you mean, when all values are equally right and equally wrong. Agreed.
QUOTE (->
| QUOTE |
| It would be valid as a symbolic placeholder (in a number STRING) and also as a BOUNDARY CONDITION/VALUE real-point/number TRANSITION/BRIDGING state/value between CONTRA-BALANCED 'lines'/continuums/actions etc. |
A meaning collapse, you mean, when all values are equally right and equally wrong. Agreed.
The only reason why 0 is mentioned is to define the concept of "starting point". Without "starting point" it isn't obvious how to measure anything, is it?
You can have your starting point only as long as it is subjected to having uses other than the ones intended: "starting point" in time or in space or in organization or in execution or in placement or in quantity? All of the above? It collapsed then. That is the nature of a starting point, it means all things because nothing else can have meaning without it and its "numberiness" is spread over what it started.
But wait, there is more, you get a free Ginsu Peeler. There is a long additional "right answer".
6--... ...if zero-as-a-unit-of-thought can turn in space then it has a "thickness" and that thickness is exactly, no more and no less, but exactly, the same length as the "unit of thought" that led you to it (be it an actual thought or number, atom, infinitesimal, infinity, AIT algorithm, whatever). This is another way of saying that infinitesimal and infinity have the same prime code length OR Chaitin program length. This thickness has its own numberiness, which is accessed when the turn happens. 0/0 as the end of a computational process of turning will give you as Yet Another Right Answer the infinitesimal PLACE resting on an infinitesimal length, and in order to check the redness of that red you will have to go there and check if it is a 1 or a 0 that is at the position you want along that length.
The smallest-possible code (instruction code for an instruction set, algorithm for Chaitin-ly compression, or prime code for a number) for the biggest-possible meaning can not be lossy or the numberiness of a number/thought/infinity/instruction would be lost--meaning wouldn't be salvageable through algorithmic decompression, the equation would make the "wrong" sort of mistakes -not the right mistakes such as ours in this thread-, the atom wouldn't hold, the infinity would be embraceable, the computer wouldn't add. The bit length of the infinitesimal is the same as the bit length of infinity because both are numerically equivalent, but not formally. The form (1010101010...) is not the form (110110110110...) even though they are both infinite-bitted. But both are collapsible into integer lengths.
The integer length bits are what is missing from any meaningful discussion of 0/0 and other singularities. If they are not recovered, the process is lossy. "recovery" is easier said than done, unfortunately.
Each and every bit of the "universe" or "equation" that led us to 0/0 has to be recoverable. So that if the "universe" you have at hand is a superimposition, the operation will have to specify each and every bit so that the result is right.
I thought people would see at a glance, because it is so obvious to me, that prime code wrapped around Sack's spiral is supposed to be a series of numbers in an irrational language we don't yet know, and that they are probably sines and cosines of integers. All of a family of irrationals already written in a number table. When Steven says
QUOTE
But realistically we know we're only going to need to work with phi to some limited accuracy in the first place, so that also implies we don't need to use a process that generates phi exactly either. We could use an approximate process that generates an approximate result.
he is unwillingly exchanging a limited numeric accuracy for the accuracy of a form in space, which T.Roc answered with
QUOTE (->
| QUOTE |
| But realistically we know we're only going to need to work with phi to some limited accuracy in the first place, so that also implies we don't need to use a process that generates phi exactly either. We could use an approximate process that generates an approximate result. |
he is unwillingly exchanging a limited numeric accuracy for the accuracy of a form in space, which T.Roc answered with
about "8 digits out" gives us a "fuzzy" approximation, because it CAN NOT be "accurate" to an arbitrary number of digits.
This worked well for Planck, and has been leading in a "fuzzy" way ever since. There is NO other reason that h has any meaning, or functionality in QM. When you give an "answer" that has -34 digits, and you are only working with "12 digit accuracy", you don't see the difference. Right answers; wrong reasons.
Which only leads me back to the same thing I already think: all answers will collapse into understanding, even if they turn out to be only a cheat-sheet of previously-written "unreadable" numbers.
Whatever your "unit of thought" is, all meanings stand spread, superimposed over it, screaming to be heard. Sometimes I wish they'd shut up.
QUOTE (RC+ in the opening post)
[COLOR=blue]Since the 'line' is actually tracing a PATH/TRAJECTORY THROUGH 'SPACETIME (or whatever), ANY so-called 1-DIMENSIONAL 'line' is actually a 2-DIMENSIONAL TIME/SPACE-dependent PLANE/MEMBRANE etc.[/COLOR=blue]
But 2-dimensional does NOT describe it! If zero turned out of space still leaves information behind exactly BECAUSE if it were really nothing it wouldn't be turning, then that information is infinitesimal. It would have to be 1 + an infinitesimal, 1 + 2 infinitesimals, 1 + 3 infinitesimals, and so on... That is what would make infinitesimals collapse into what we already know. And we will collapse them.
But 2-dimensional does NOT describe it! If zero turned out of space still leaves information behind exactly BECAUSE if it were really nothing it wouldn't be turning, then that information is infinitesimal. It would have to be 1 + an infinitesimal, 1 + 2 infinitesimals, 1 + 3 infinitesimals, and so on... That is what would make infinitesimals collapse into what we already know. And we will collapse them.
QUOTE
In the reality context of observable phenomena, there is NO SUCH THING/POSSIBILITY as an 'abstract' NUMBER LINE.
So what? What use is an observable number line in reality? What possible use do I have for infinite points between any two points "in observable reality".
There is no linear anything in reality. Everything we do that is linear is but a weak local approximation of the non-linear process it is modeling.
Mathematics is a modeling and simulation language. To the extent you input the variables and algorithms, it can calculate reality to arbitrary accuracies.
Sorry, I consider your conclusion to be trivial, obvious, and of no apparent value.
QUOTE (->
| QUOTE |
| In the reality context of observable phenomena, there is NO SUCH THING/POSSIBILITY as an 'abstract' NUMBER LINE. |
So what? What use is an observable number line in reality? What possible use do I have for infinite points between any two points "in observable reality".
There is no linear anything in reality. Everything we do that is linear is but a weak local approximation of the non-linear process it is modeling.
Mathematics is a modeling and simulation language. To the extent you input the variables and algorithms, it can calculate reality to arbitrary accuracies.
Sorry, I consider your conclusion to be trivial, obvious, and of no apparent value.
One can see that the analysis of ANY 'line', WHEREVER OR HOWEVER OR WHENEVER IT IS 'DRAWN', and WHETHER PHYSICAL OR ABSTRACT, should allow for the 'contextual' fact that it is NOT 'stationary'. It is actually ALWAYS MOVING (in space-time? or whatever).
Why? If you want to model a line in reality, have at it. You can use all sorts of techniques to quantify the errors, the motion. But, what is it going to tell you? That it isn't perfect!! Whoopee!! We already knew that.
QUOTE (meBigGuy+Jan 16 2008, 07:15 AM)
There is no linear anything in reality. Everything we do that is linear is but a weak local approximation of the non-linear process it is modeling.
Mathematics is a modeling and simulation language. To the extent you input the variables and algorithms, it can calculate reality to arbitrary accuracies.
There was nothing non-trivial in it, it was dripping with trivial, and RC was saying that before you!
If he is immersed in process and movement and you are modeling and simulating language, and he says there is no such thing as an abstract number line and you say there is no linear in anything, is it supposed to be cuter or more valid when you say it? Do you also really think your hair is sooooo good?
As for "arbitrary accuracy", it ain't getting within ten miles of me without being stoned -- "0.9r=1?" is beneath me and I will never do it unless I can change it into a mirror because my hair too is really sooooo good...
(Hey, what can I tell you? I am green with envy because of BDW!)
The thread is supposed to be a search for some sort of quantization in the distance between mathematics and real:
If he is immersed in process and movement and you are modeling and simulating language, and he says there is no such thing as an abstract number line and you say there is no linear in anything, is it supposed to be cuter or more valid when you say it? Do you also really think your hair is sooooo good?
As for "arbitrary accuracy", it ain't getting within ten miles of me without being stoned -- "0.9r=1?" is beneath me and I will never do it unless I can change it into a mirror because my hair too is really sooooo good...
(Hey, what can I tell you? I am green with envy because of BDW!)
The thread is supposed to be a search for some sort of quantization in the distance between mathematics and real:
Hence all those 'weird' things like Cantor's Set etc which come up with 'logical' BUT 'irrelevant in reality' results (like removing as many parts of a 'line' in a continuous process and STILL ending up with an 'INFINITE NUMBER OF POINTS' left on that 'line'.
One can see that the analysis of ANY 'line', WHEREVER OR HOWEVER OR WHENEVER IT IS 'DRAWN', and WHETHER PHYSICAL OR ABSTRACT, should allow for the 'contextual' fact that it is NOT 'stationary'. It is actually ALWAYS MOVING (in space-time? or whatever).
In other words, even as we 'LOOK' at and 'DISECT' a 'line' and make 'mathematical/number theory' observations about its 'properties', we are MISSING THE FACT that the 'line' we are analysing bears NO RELATION to the presumed stationary/absolute/finite 'distance/length' line we 'abstractly' and mistakenly 'see'.
Since the 'line' is actually tracing a PATH/TRAJECTORY THROUGH 'SPACETIME (or whatever), ANY so-called 1-DIMENSIONAL 'line' is actually a 2-DIMENSIONAL TIME/SPACE-dependent PLANE/MEMBRANE etc.
And THAT is ONE of the reasons why maths/number theory CURRENTLY gets all those weird results....because they are actually dealing with 'processes/functions that have LATERAL 'EXCURSION' 'properties/results' from the 'imagined' original 'LINEAR' construct.
Mathematics is a modeling and simulation language. To the extent you input the variables and algorithms, it can calculate reality to arbitrary accuracies.
There was nothing non-trivial in it, it was dripping with trivial, and RC was saying that before you!
QUOTE
In the reality context of observable phenomena, there is NO SUCH THING/POSSIBILITY as an 'abstract' NUMBER LINE.
ANY 'line' one cares to set out or draw is in reality IMMERSED in PROCESS and MOVEMENT...and as such is NOT an 'absolute' or 'defined' THING or DISTANCE etc.
So all the ZENO PARADOXES and 'progressive series' LIMITS and FUNCTIONS based on the IDEA that such a 'line' is COMPLETE AND STATIC from one 'end' to the 'other end' is in 'reality process context' FALLACIOUS from the outset.
Hence all those 'weird' things like Cantor's Set etc which come up with 'logical' BUT 'irrelevant in reality' results (like removing as many parts of a 'line' in a continuous process and STILL ending up with an 'INFINITE NUMBER OF POINTS' left on that 'line'.
ANY 'line' one cares to set out or draw is in reality IMMERSED in PROCESS and MOVEMENT...and as such is NOT an 'absolute' or 'defined' THING or DISTANCE etc.
So all the ZENO PARADOXES and 'progressive series' LIMITS and FUNCTIONS based on the IDEA that such a 'line' is COMPLETE AND STATIC from one 'end' to the 'other end' is in 'reality process context' FALLACIOUS from the outset.
Hence all those 'weird' things like Cantor's Set etc which come up with 'logical' BUT 'irrelevant in reality' results (like removing as many parts of a 'line' in a continuous process and STILL ending up with an 'INFINITE NUMBER OF POINTS' left on that 'line'.
If he is immersed in process and movement and you are modeling and simulating language, and he says there is no such thing as an abstract number line and you say there is no linear in anything, is it supposed to be cuter or more valid when you say it? Do you also really think your hair is sooooo good?
As for "arbitrary accuracy", it ain't getting within ten miles of me without being stoned -- "0.9r=1?" is beneath me and I will never do it unless I can change it into a mirror because my hair too is really sooooo good...
(Hey, what can I tell you? I am green with envy because of BDW!)
The thread is supposed to be a search for some sort of quantization in the distance between mathematics and real:
QUOTE (->
| QUOTE |
| In the reality context of observable phenomena, there is NO SUCH THING/POSSIBILITY as an 'abstract' NUMBER LINE. ANY 'line' one cares to set out or draw is in reality IMMERSED in PROCESS and MOVEMENT...and as such is NOT an 'absolute' or 'defined' THING or DISTANCE etc. So all the ZENO PARADOXES and 'progressive series' LIMITS and FUNCTIONS based on the IDEA that such a 'line' is COMPLETE AND STATIC from one 'end' to the 'other end' is in 'reality process context' FALLACIOUS from the outset. Hence all those 'weird' things like Cantor's Set etc which come up with 'logical' BUT 'irrelevant in reality' results (like removing as many parts of a 'line' in a continuous process and STILL ending up with an 'INFINITE NUMBER OF POINTS' left on that 'line'. |
If he is immersed in process and movement and you are modeling and simulating language, and he says there is no such thing as an abstract number line and you say there is no linear in anything, is it supposed to be cuter or more valid when you say it? Do you also really think your hair is sooooo good?
As for "arbitrary accuracy", it ain't getting within ten miles of me without being stoned -- "0.9r=1?" is beneath me and I will never do it unless I can change it into a mirror because my hair too is really sooooo good...
(Hey, what can I tell you? I am green with envy because of BDW!)
The thread is supposed to be a search for some sort of quantization in the distance between mathematics and real:
Hence all those 'weird' things like Cantor's Set etc which come up with 'logical' BUT 'irrelevant in reality' results (like removing as many parts of a 'line' in a continuous process and STILL ending up with an 'INFINITE NUMBER OF POINTS' left on that 'line'.
One can see that the analysis of ANY 'line', WHEREVER OR HOWEVER OR WHENEVER IT IS 'DRAWN', and WHETHER PHYSICAL OR ABSTRACT, should allow for the 'contextual' fact that it is NOT 'stationary'. It is actually ALWAYS MOVING (in space-time? or whatever).
In other words, even as we 'LOOK' at and 'DISECT' a 'line' and make 'mathematical/number theory' observations about its 'properties', we are MISSING THE FACT that the 'line' we are analysing bears NO RELATION to the presumed stationary/absolute/finite 'distance/length' line we 'abstractly' and mistakenly 'see'.
Since the 'line' is actually tracing a PATH/TRAJECTORY THROUGH 'SPACETIME (or whatever), ANY so-called 1-DIMENSIONAL 'line' is actually a 2-DIMENSIONAL TIME/SPACE-dependent PLANE/MEMBRANE etc.
And THAT is ONE of the reasons why maths/number theory CURRENTLY gets all those weird results....because they are actually dealing with 'processes/functions that have LATERAL 'EXCURSION' 'properties/results' from the 'imagined' original 'LINEAR' construct.
Ivan
This surely has to be worth reading since You have made such long post about what= a 0. I will do it just have some lunch to get energy
By the way, in Sanskrit 0 is "shuna", which in Latvian ( that is my language, one of 2 closest relatives to Sanskrit, the closest being Lithuanian language ) means CELL.
I was thinking about 0 again in terms of derivatives between scales of infinitesimals:
1) if 2 functions has a ratio 0/0 in some point in some scale and this uncertainty for many functions can be resolved up by taking FIRST derivative = going one scale down -> and that ratio of derivatives could lead to any finite value with any sign, meaning that each of derivatives would be of finite value with some sign->
Which means that in a case of 2 n times differentiable functions which remain 0 until nth differentiation, , there are n-1 dimensions or parameters how these 2 zeroes can be infinitely different, and with every differentiation we get closer to the last finite difference in some dimension or split like finite/0 = infinity or 0/finite=0
However, when we have infinitely differentiable function giving 0 at the same point , we will only after performing infinite amount of differentiations get to scale where both zeroes will be perfectly identical as all differences will be eliminated, 0/0=finite in that last scale. (I do not know if there are such functions).
So, as a result we will get a scale where both 0 - oes will be identical. This 1 identical 0 should be absolute 0.
If we start from it now and integrate upwards, what properties comes first in mind that could split such a identical to itself 0 into 2 infinitely different ones?
Too many
Not good idea.
This surely has to be worth reading since You have made such long post about what= a 0. I will do it just have some lunch to get energy
By the way, in Sanskrit 0 is "shuna", which in Latvian ( that is my language, one of 2 closest relatives to Sanskrit, the closest being Lithuanian language ) means CELL.
I was thinking about 0 again in terms of derivatives between scales of infinitesimals:
1) if 2 functions has a ratio 0/0 in some point in some scale and this uncertainty for many functions can be resolved up by taking FIRST derivative = going one scale down -> and that ratio of derivatives could lead to any finite value with any sign, meaning that each of derivatives would be of finite value with some sign->
Which means that in a case of 2 n times differentiable functions which remain 0 until nth differentiation, , there are n-1 dimensions or parameters how these 2 zeroes can be infinitely different, and with every differentiation we get closer to the last finite difference in some dimension or split like finite/0 = infinity or 0/finite=0
However, when we have infinitely differentiable function giving 0 at the same point , we will only after performing infinite amount of differentiations get to scale where both zeroes will be perfectly identical as all differences will be eliminated, 0/0=finite in that last scale. (I do not know if there are such functions).
So, as a result we will get a scale where both 0 - oes will be identical. This 1 identical 0 should be absolute 0.
If we start from it now and integrate upwards, what properties comes first in mind that could split such a identical to itself 0 into 2 infinitely different ones?
Too many
Not good idea.
Not to break the specific "flow" of the discussion, but in the spirit of the thread...
A brief note on the...
Psychologically Relevant Contextual Naming of Numbers as "Variables"
=============================================
An Example:
(provisionally...) 111 in "Kolo Math"
= eka
Naming Derivation:
1) In numerology, 111 is considered an "Angel Number" and is related to the concept of phases and cycles and "gateways" of cosmic nature or otherwise. I believe an underlying mathematical basis can be given to at least partly explain this psychic tendency, but will save that discussion for another time...
2a) e == energy
2b) Ka == 1 of 5 parts of the Soul, according to Egyptian Mythology, representing life force. See:
http://en.wikipedia.org/wiki/Egyptian_soul
3) eka is Sanskrit for the word "One"
4) 111 == the atomic number of "Eka Gold," otherwise known as Roentgenium (Gold is element 112), See: http://www.3rd1000.com/elements/Roentgenium.htm
Now, let's stop there and get to the point:
Let's say you're learning the periodic table. Who the holy heck hey is going to remember "Roentgenium," much less be able to spell it or speak it? Even those who scoff at the notion of naming conventions that evidence any hint of humanity... heavens forbid we make things EASY or FUN in the sciences... well, I'd lay a dollar to a dime that the average physicist or mathematician on this board who reads this post is now far more likely to remember "eka" than Roentgenium.
And I'd up the ante on that to a C-note to a penny on retention capacity when it comes to the average Joe or Jane who finds this post via Google and... voila... now knows what Roentgenium is, as well as a bit more about the number 111.
Best,
Raphie
More about the Number 111
http://home.earthlink.net/~mrob/pub/math/numbers-8.html
= 1 * 10^2 + 1 * 10^1 + 1* 10^0
= 7 in base II
= 3*37
P.S. Hard to say, if "Roentgenium" is a step forward or back from "Unununium," which is the name it replaced :-)
http://en.wikipedia.org/wiki/Roentgenium
A brief note on the...
Psychologically Relevant Contextual Naming of Numbers as "Variables"
=============================================
An Example:
(provisionally...) 111 in "Kolo Math"
= eka
Naming Derivation:
1) In numerology, 111 is considered an "Angel Number" and is related to the concept of phases and cycles and "gateways" of cosmic nature or otherwise. I believe an underlying mathematical basis can be given to at least partly explain this psychic tendency, but will save that discussion for another time...
2a) e == energy
2b) Ka == 1 of 5 parts of the Soul, according to Egyptian Mythology, representing life force. See:
http://en.wikipedia.org/wiki/Egyptian_soul
3) eka is Sanskrit for the word "One"
4) 111 == the atomic number of "Eka Gold," otherwise known as Roentgenium (Gold is element 112), See: http://www.3rd1000.com/elements/Roentgenium.htm
Now, let's stop there and get to the point:
Let's say you're learning the periodic table. Who the holy heck hey is going to remember "Roentgenium," much less be able to spell it or speak it? Even those who scoff at the notion of naming conventions that evidence any hint of humanity... heavens forbid we make things EASY or FUN in the sciences... well, I'd lay a dollar to a dime that the average physicist or mathematician on this board who reads this post is now far more likely to remember "eka" than Roentgenium.
And I'd up the ante on that to a C-note to a penny on retention capacity when it comes to the average Joe or Jane who finds this post via Google and... voila... now knows what Roentgenium is, as well as a bit more about the number 111.
Best,
Raphie
More about the Number 111
http://home.earthlink.net/~mrob/pub/math/numbers-8.html
= 1 * 10^2 + 1 * 10^1 + 1* 10^0
= 7 in base II
= 3*37
P.S. Hard to say, if "Roentgenium" is a step forward or back from "Unununium," which is the name it replaced :-)
http://en.wikipedia.org/wiki/Roentgenium
Putting all the big words aside, did RC say on the first page that you can't use regular math to counter anything he says because it is incomplete in his opinion?
QUOTE (nabiul+Jan 17 2008, 12:37 AM)
Putting all the big words aside, did RC say on the first page that you can't use regular math to counter anything he says because it is incomplete in his opinion?
Mathematics is not just incomplete in RC's opinion...
Gödel's incompleteness theorems
http://en.wikipedia.org/wiki/Gödel's_i...eteness_theorem
Best,
Raphie
Mathematics is not just incomplete in RC's opinion...
Gödel's incompleteness theorems
http://en.wikipedia.org/wiki/Gödel's_i...eteness_theorem
Best,
Raphie
Well the fact of the matter is that it will never be complete because we can't know what were missing, but there are certains levels of completeness that are acceptable for doing certain types of calculations.
Any ways on the subject of math not reflecting reality, 1+1=2 in reality would mean that 1 object with the exact same mass/volume/subatomic particles with correct electron alignment as another object would have properties that are double the original in quantity when you combine them. Well this doesn't reflect reality all the time according to my highschool level education in physics, when two atomic/sub atomic particles fuse together, there is a decrease in net energy and an increase in mass in relation to the mass equivalence formula (e=mc^2), which appears to be conversion between two different dimensions. So 1+1=2 is 'incomplete', but most people would instead say inadequete for this situation.
Correct me if I got something wrong, my knowledge is limited.
Any ways on the subject of math not reflecting reality, 1+1=2 in reality would mean that 1 object with the exact same mass/volume/subatomic particles with correct electron alignment as another object would have properties that are double the original in quantity when you combine them. Well this doesn't reflect reality all the time according to my highschool level education in physics, when two atomic/sub atomic particles fuse together, there is a decrease in net energy and an increase in mass in relation to the mass equivalence formula (e=mc^2), which appears to be conversion between two different dimensions. So 1+1=2 is 'incomplete', but most people would instead say inadequete for this situation.
Correct me if I got something wrong, my knowledge is limited.
Naibul,
You may find the below article from THE INTERNET ENCYCLOPEDIA OF SCIENCE of interest...
excerpt from...
--------------------
Riemann and curved space
Riemann... put on a firm footing the type of non-Euclidean geometry that Gauss had hinted at, the kind known as elliptic geometry, in which there are no parallel lines and in which the angles of a triangle always add up to more than 180 degrees. He also generalized the notion of the shortest distance between two points. In Euclidean geometry this is simply a straight line. But step out of Euclid’s domain and the quickest way to get from A to B involves a change of tack. The easiest way to grasp this idea is to think about traveling on Earth’s surface, which isn’t flat but (roughly) spherical – a special case of Riemann’s elliptic geometry. To take a ship on the shortest route between two ports you sail, wherever possible, along an arc of a great circle – the circle that goes all the way around the Earth and on which both ports lie. Any such minimum-length path on a surface, the special case of which on a plane is a straight line, is called a geodesic, meaning “Earth divider”.
In Euclidean geometry, the shortest distance between two points can be found using Pythagoras’s theorem. What Riemann discovered was a more powerful, general form of Pythagoras’s theorem that works on curved surfaces, even when the curvature is in more than two dimensions and varies from one place to another. In this looking-glass world of curved space, the familiar idea of distance is replaced by the broader concept of something called a metric, from the Greek for “measure,” while curvature is similarly described by a more elaborate mathematical object. Gauss had found that the curvature in the neighborhood of a point of a specified two-dimensional geometry is given by a single number: the Gaussian curvature. Riemann showed that six numbers are needed to describe the curvature of a three-dimensional space at a given point, and that 20 numbers at each point are required for a four-dimensional geometry: the 20 independent components of the so-called Riemann curvature tensor.
In his famous lecture of 1854, Riemann emphasized, as Gauss had done, that the truth about the space we live in can’t be found by poring over 2,000-year-old books of Greek geometry. It has to come from physical experience. He pointed out that space could be highly irregular at very small distances and yet appear smooth on an everyday level. At very great distances, he also noted, a large-scale curvature of space might show up, perhaps even bending the universe into a closed system like a gigantic ball.
MORE AT...
http://www.daviddarling.info/encyclopedia/R/Riemann.html
===================================================
Best,
Raphie
P.S. I might add... Einstein gets the credit, but without Riemann there would be no "Einstein" as certainly as that without Galileo there would be no "Riemann." :-)
You may find the below article from THE INTERNET ENCYCLOPEDIA OF SCIENCE of interest...
excerpt from...
--------------------
Riemann and curved space
Riemann... put on a firm footing the type of non-Euclidean geometry that Gauss had hinted at, the kind known as elliptic geometry, in which there are no parallel lines and in which the angles of a triangle always add up to more than 180 degrees. He also generalized the notion of the shortest distance between two points. In Euclidean geometry this is simply a straight line. But step out of Euclid’s domain and the quickest way to get from A to B involves a change of tack. The easiest way to grasp this idea is to think about traveling on Earth’s surface, which isn’t flat but (roughly) spherical – a special case of Riemann’s elliptic geometry. To take a ship on the shortest route between two ports you sail, wherever possible, along an arc of a great circle – the circle that goes all the way around the Earth and on which both ports lie. Any such minimum-length path on a surface, the special case of which on a plane is a straight line, is called a geodesic, meaning “Earth divider”.
In Euclidean geometry, the shortest distance between two points can be found using Pythagoras’s theorem. What Riemann discovered was a more powerful, general form of Pythagoras’s theorem that works on curved surfaces, even when the curvature is in more than two dimensions and varies from one place to another. In this looking-glass world of curved space, the familiar idea of distance is replaced by the broader concept of something called a metric, from the Greek for “measure,” while curvature is similarly described by a more elaborate mathematical object. Gauss had found that the curvature in the neighborhood of a point of a specified two-dimensional geometry is given by a single number: the Gaussian curvature. Riemann showed that six numbers are needed to describe the curvature of a three-dimensional space at a given point, and that 20 numbers at each point are required for a four-dimensional geometry: the 20 independent components of the so-called Riemann curvature tensor.
In his famous lecture of 1854, Riemann emphasized, as Gauss had done, that the truth about the space we live in can’t be found by poring over 2,000-year-old books of Greek geometry. It has to come from physical experience. He pointed out that space could be highly irregular at very small distances and yet appear smooth on an everyday level. At very great distances, he also noted, a large-scale curvature of space might show up, perhaps even bending the universe into a closed system like a gigantic ball.
MORE AT...
http://www.daviddarling.info/encyclopedia/R/Riemann.html
===================================================
Best,
Raphie
P.S. I might add... Einstein gets the credit, but without Riemann there would be no "Einstein" as certainly as that without Galileo there would be no "Riemann." :-)
A very simple example of the cyclical nature of the natural numbers involving digit addition and reduction to the digital root...
n^2 = x; digit addition = root
==================
1^2 = 1; 1
2^2 = 4; 4
3^2 = 9; 9
4^2 = 16; 6 + 1 = 7
5^2 = 25; 2 + 5 = 7
6^2 = 36; 3 + 6 = 9
7^2 = 49; 4 + 9 = 13; 1 + 3 = 4
8^2 = 64; 6 + 4 = 10; 1 + 0 = 1
9^2 = 81; 8 + 1 = 9;
10^2 = 100; 1 + 0 + 0 = 1
11^2 = 121; 1 + 2 + 1 = 4
12^2 = 144; 1 + 4 + 4 = 9
13^2 = 169; 1 + 6 + 9 = 16; 1 + 6 = 7
14^2 = 196; 1 + 9 + 6 = 16; 1 + 6 = 7
15^2 = 225; 2 + 2 + 5 = 9
16^2 = 256; 2 + 5 + 6 = 13; 1 + 3 = 4
16^2 = 289; 2 + 8 + 9 = 19; 1 + 0 = 1
17^2 = 324; 3 + 2 + 4 = 9
19^2 = 361; 3 + 6 + 1 = 10; 1 + 0 = 1
20^2 = 400; 4 + 0 + 0 = 4
The pattern:
1, 4, 9, 7, 7, 9, 4, 1 + 9 +++ 1, 4, 9, 7, 7, 9, 4, 1 + 9 +++ 1, 4, 9, 7, 7, 9, 4, 1 + 9....
From here to infinity. Now map against the counting numbers...
DIGITAL ROOT
1, 4, 9, 7, 7, 9, 4, 1 ++ 9 ++ \\01//, 04, 09, 07, 07, 09, 04, 01 ++ 09 ++ 01, \\04//, 09, 07, 07, 09, 04, 01 ++ 09 ++ 01, 04, \\09//, 07....
COUNTING NUMBER
1, 2, 3, 4, 5, 6, 7, 8 ++ 9 ++ \\10//, 11, 12, 13, 14, 15, 16, 17 ++ 18 ++ 19, \\20//, 21, 22, 23, 24, 25, 26 ++ 27 ++ 28, 29, \\30//....
See the palindromic nature of the cycle at the digital root level with that 9 almost as if a "period" marking the end of each cycle?
See how the numbers go "out of alignment" by one "step" per cycle?
03 "cycles" equals 27th counting number
10 "cycles" equals 90th counting number
The correspondence between n and the associated digital root...
10 --> 1
20 --> 4
30 --> 9
40 --> 7
50 --> 7
60 --> 9
70 --> 4
80 --> 1
++++++
90 --> 9
++++++
Start again at 91, 181, 271, 361, and so on...
Now, call me silly for suggesting there may be anything "circular" about our "linear" natural number line, but the periodicity of that cycle sure does bear an awful striking resemblance to the degrees of a CIRCLE (= 360)/4...
Best,
Raphie
=================================
=================================
P.S.
91 = the 13th Triangular Number = 7 * 13, the 4th and 6th primes (skipping 11). 7 and 13 also generate Mersenne primes when inserted into the equation 2^n - 1 as exponents. 2^7 - 1 = 127; 2^13 - 1 = 8191. "Conveniently," in a "Contextual" frame of mind, where 16,114 equals the 18th "tone" of the Golden Scale (Fib 2,5)...
16114*(phi^30 + phi^-30) - 100*8191 + (127 + 1)
= 29,979,245,800
= 100 * the speed of light * s/m
Meaningful?
Maybe yes, maybe no. One, after all, can make numbers do anything. For instance...
Let...
a = 111
b = (495*496)*11 = 2700720
... where 495 equals the 3 digit Kaprekar Constant and 496 the 3rd perfect number. Then...
(111^2 + (2*111) + ((2700720)*111)) + 5
= 299,792,458
= c * s/m
= a^2 + 2a + ab + 5
= a ( a + 2 + b ) + 5
= c * s/m
[Observation: 2, 5 are the first two "tones" of the Golden Scale (Fib 2, 5), while 02700720 is a palindromic number, as is 111]
related post...
------------------
RELATIONSHIP BETWEEN 5040 (7!), Sigma (1 through 100), 496 and 495
http://forum.physorg.com/index.php?showtop...ndpost&p=297404
n^2 = x; digit addition = root
==================
1^2 = 1; 1
2^2 = 4; 4
3^2 = 9; 9
4^2 = 16; 6 + 1 = 7
5^2 = 25; 2 + 5 = 7
6^2 = 36; 3 + 6 = 9
7^2 = 49; 4 + 9 = 13; 1 + 3 = 4
8^2 = 64; 6 + 4 = 10; 1 + 0 = 1
9^2 = 81; 8 + 1 = 9;
10^2 = 100; 1 + 0 + 0 = 1
11^2 = 121; 1 + 2 + 1 = 4
12^2 = 144; 1 + 4 + 4 = 9
13^2 = 169; 1 + 6 + 9 = 16; 1 + 6 = 7
14^2 = 196; 1 + 9 + 6 = 16; 1 + 6 = 7
15^2 = 225; 2 + 2 + 5 = 9
16^2 = 256; 2 + 5 + 6 = 13; 1 + 3 = 4
16^2 = 289; 2 + 8 + 9 = 19; 1 + 0 = 1
17^2 = 324; 3 + 2 + 4 = 9
19^2 = 361; 3 + 6 + 1 = 10; 1 + 0 = 1
20^2 = 400; 4 + 0 + 0 = 4
The pattern:
1, 4, 9, 7, 7, 9, 4, 1 + 9 +++ 1, 4, 9, 7, 7, 9, 4, 1 + 9 +++ 1, 4, 9, 7, 7, 9, 4, 1 + 9....
From here to infinity. Now map against the counting numbers...
DIGITAL ROOT
1, 4, 9, 7, 7, 9, 4, 1 ++ 9 ++ \\01//, 04, 09, 07, 07, 09, 04, 01 ++ 09 ++ 01, \\04//, 09, 07, 07, 09, 04, 01 ++ 09 ++ 01, 04, \\09//, 07....
COUNTING NUMBER
1, 2, 3, 4, 5, 6, 7, 8 ++ 9 ++ \\10//, 11, 12, 13, 14, 15, 16, 17 ++ 18 ++ 19, \\20//, 21, 22, 23, 24, 25, 26 ++ 27 ++ 28, 29, \\30//....
See the palindromic nature of the cycle at the digital root level with that 9 almost as if a "period" marking the end of each cycle?
See how the numbers go "out of alignment" by one "step" per cycle?
03 "cycles" equals 27th counting number
10 "cycles" equals 90th counting number
The correspondence between n and the associated digital root...
10 --> 1
20 --> 4
30 --> 9
40 --> 7
50 --> 7
60 --> 9
70 --> 4
80 --> 1
++++++
90 --> 9
++++++
Start again at 91, 181, 271, 361, and so on...
Now, call me silly for suggesting there may be anything "circular" about our "linear" natural number line, but the periodicity of that cycle sure does bear an awful striking resemblance to the degrees of a CIRCLE (= 360)/4...
Best,
Raphie
=================================
=================================
P.S.
91 = the 13th Triangular Number = 7 * 13, the 4th and 6th primes (skipping 11). 7 and 13 also generate Mersenne primes when inserted into the equation 2^n - 1 as exponents. 2^7 - 1 = 127; 2^13 - 1 = 8191. "Conveniently," in a "Contextual" frame of mind, where 16,114 equals the 18th "tone" of the Golden Scale (Fib 2,5)...
16114*(phi^30 + phi^-30) - 100*8191 + (127 + 1)
= 29,979,245,800
= 100 * the speed of light * s/m
Meaningful?
Maybe yes, maybe no. One, after all, can make numbers do anything. For instance...
Let...
a = 111
b = (495*496)*11 = 2700720
... where 495 equals the 3 digit Kaprekar Constant and 496 the 3rd perfect number. Then...
(111^2 + (2*111) + ((2700720)*111)) + 5
= 299,792,458
= c * s/m
= a^2 + 2a + ab + 5
= a ( a + 2 + b ) + 5
= c * s/m
[Observation: 2, 5 are the first two "tones" of the Golden Scale (Fib 2, 5), while 02700720 is a palindromic number, as is 111]
related post...
------------------
RELATIONSHIP BETWEEN 5040 (7!), Sigma (1 through 100), 496 and 495
http://forum.physorg.com/index.php?showtop...ndpost&p=297404
QUOTE (Raphie Frank+Jan 16 2008, 10:32 PM)
n^2 = x; digit addition = root
==================
1^2 = 1; 1
2^2 = 4; 4
3^2 = 9; 9
4^2 = 16; 6 + 1 = 7
5^2 = 25; 2 + 5 = 7
6^2 = 36; 3 + 6 = 9
7^2 = 49; 4 + 9 = 13; 1 + 3 = 4
8^2 = 64; 6 + 4 = 10; 1 + 0 = 1
9^2 = 81; 8 + 1 = 9;
10^2 = 100; 1 + 0 + 0 = 1
11^2 = 121; 1 + 2 + 1 = 4
12^2 = 144; 1 + 4 + 4 = 9
13^2 = 169; 1 + 6 + 9 = 16; 1 + 6 = 7
14^2 = 196; 1 + 9 + 6 = 16; 1 + 6 = 7
15^2 = 225; 2 + 2 + 5 = 9
16^2 = 256; 2 + 5 + 6 = 13; 1 + 3 = 4
16^2 = 289; 2 + 8 + 9 = 19; 1 + 0 = 1
17^2 = 324; 3 + 2 + 4 = 9
19^2 = 361; 3 + 6 + 1 = 10; 1 + 0 = 1
20^2 = 400; 4 + 0 + 0 = 4
The pattern:
1, 4, 9, 7, 7, 9, 4, 1 + 9 +++ 1, 4, 9, 7, 7, 9, 4, 1 + 9 +++ 1, 4, 9, 7, 7, 9, 4, 1 + 9....
Well, yes, it is a logical circle. Here is the same thing in base 9:
1^2 = 1; 1
2^2 = 4; 4
3^2 = 10; 1
4^2 = 17; 1 + 7 = 8
5^2 = 27; 2 + 7 = 10; 1
6^2 = 40; 4
7^2 = 54; 5 + 4 = 10; 1
8^2 = 71; 7 + 1 = 8; 8
9^2 = 100; 1
10^2 = 121; 1 + 2 + 1 = 4
11^2 = 144; 1 + 4 + 4 = 10; 1
12^2 = 170; 1 + 7 + 0 = 8
13^2 = 207; 2 + 7 = 10; 1
For a cycle of (1, 4, 1, 8) but... I don't really see what you are trying to say, Ralphie: that at each repetition of the cycle you went around full circle? Are you wondering if it is possible to model infinitesimal behavior with that?!
That would be *something*, very refreshing too, but it has to be cross-base, afaict.
I did base 9 on the other curiosity you sent in the other day with the subtraction of two differently-ordered sets of digits. I did find a few cycles, but I would have to plot them in a significant number of bases in order to prove that the thing is following fractal rules.
==================
1^2 = 1; 1
2^2 = 4; 4
3^2 = 9; 9
4^2 = 16; 6 + 1 = 7
5^2 = 25; 2 + 5 = 7
6^2 = 36; 3 + 6 = 9
7^2 = 49; 4 + 9 = 13; 1 + 3 = 4
8^2 = 64; 6 + 4 = 10; 1 + 0 = 1
9^2 = 81; 8 + 1 = 9;
10^2 = 100; 1 + 0 + 0 = 1
11^2 = 121; 1 + 2 + 1 = 4
12^2 = 144; 1 + 4 + 4 = 9
13^2 = 169; 1 + 6 + 9 = 16; 1 + 6 = 7
14^2 = 196; 1 + 9 + 6 = 16; 1 + 6 = 7
15^2 = 225; 2 + 2 + 5 = 9
16^2 = 256; 2 + 5 + 6 = 13; 1 + 3 = 4
16^2 = 289; 2 + 8 + 9 = 19; 1 + 0 = 1
17^2 = 324; 3 + 2 + 4 = 9
19^2 = 361; 3 + 6 + 1 = 10; 1 + 0 = 1
20^2 = 400; 4 + 0 + 0 = 4
The pattern:
1, 4, 9, 7, 7, 9, 4, 1 + 9 +++ 1, 4, 9, 7, 7, 9, 4, 1 + 9 +++ 1, 4, 9, 7, 7, 9, 4, 1 + 9....
Well, yes, it is a logical circle. Here is the same thing in base 9:
1^2 = 1; 1
2^2 = 4; 4
3^2 = 10; 1
4^2 = 17; 1 + 7 = 8
5^2 = 27; 2 + 7 = 10; 1
6^2 = 40; 4
7^2 = 54; 5 + 4 = 10; 1
8^2 = 71; 7 + 1 = 8; 8
9^2 = 100; 1
10^2 = 121; 1 + 2 + 1 = 4
11^2 = 144; 1 + 4 + 4 = 10; 1
12^2 = 170; 1 + 7 + 0 = 8
13^2 = 207; 2 + 7 = 10; 1
For a cycle of (1, 4, 1, 8) but... I don't really see what you are trying to say, Ralphie: that at each repetition of the cycle you went around full circle? Are you wondering if it is possible to model infinitesimal behavior with that?!
That would be *something*, very refreshing too, but it has to be cross-base, afaict.
I did base 9 on the other curiosity you sent in the other day with the subtraction of two differently-ordered sets of digits. I did find a few cycles, but I would have to plot them in a significant number of bases in order to prove that the thing is following fractal rules.
Dear Ivan,
I don't have the time at the moment to full out explain. It would take a book, frankly, but the bottom line is this:
I have been attempting to "callibrate" the number system by setting positional (i.e. nth number in a given progression) "reference frames" in a CONSISTENT manner as one might "white balance" a video camera and I have been triangulating between Base II, powers of phi, various scales of the Fibonacci Series, powers of 10 & 2, as well as Kaprekar Numbers, prime numbers and more....
I have been setting variables and "constants", such as these ones from what I call the "Shen Set" composed of what I call Ra Numbers, Ma'at Numbers and Thoth Numbers...
Mersenne Number Constant
M_c = 7 = (2^n)-1; n = 3
"Balance" Number Constant
B_c = 4 = 2^(n-1); n = 3
Perfect Number Constant
P_c = 28 = M_c*B_c; n = 3
K_c = 495 = Kaprekar Constant (3 digit)
K_c4 = 6174 = Kaprekar Constant (4 digit)
I = sqrt 11
k-log (x) = k = 0180 = rad*1/pi
p-log (x) = 'p = 5040 = rad*P_c/pi (= 7!)
where rad = 1 radian = 180/pi (standard math convention)
... and so on and my primary "targets," so to speak, that which I have been using to "sharpen focus" -- again as one might with a video camera or an old style SLR, wherein you zoom in on the detail, set focus and then zoom back out again and the entire frame is sharp -- are alpha (the fine structure constant) and the speed of light.
By and large, when I find relations such as...
(7^3*k)/10 = K_c4
(7^3*180)/10 = 6174
or, using...
(7^3*k*I^2)
then...
(7^3*180*11)/1372 = 495 = K_c3
(7^3*180*11)/110 = 6174 = K_c4
... or the constructions for alpha and the speed of light I have been posting, it is the numbers "doing the work," not me. It would be one thing if I were creating "weird," far out variables, but I am not. I am using the most basic of basic number progressions like the Mersenne Numbers and Perfect Numbers and phi^30 and phi^31 (based on the midway point between 0 (= 1-1) and 61 (= 60+1), 60, of course being 1/6*360 (=K) and a number I am well familiar with based on my work as a film electrician... (i.e. 60 cycles/second)
Irrespective of whether these relationships I am finding are significant specifically with regards to the physical world, the EASE with which I am finding them, I believe, IS significant as is the fact that I am finding them by applying the below basic principles (there are more...), cut and pasted from the thread...
The Fine Structure Constant As Fractal Construct?
http://forum.physorg.com/index.php?showtop...ndpost&p=285139
===========================================================
A FEW GUIDING HYPOTHESES/ASSUMPTIONS REGARDING THE BELOW "NUMEROLOGICALLY" DERIVED "PHYSIO-THEORETICAL" APPROXIMATIONS FOR ALPHA:
1) In order to bridge the very large with the very small, one must incorporate the "progression" (i.e. evolution).
2) Dimensionless Constants, by definition, must have dimensionless Equivalents
3) All truly "Fundamental" Constants are dimensionless by definition. They only seem to be not so RELATIVE to our "somewhat" arbitrarily chosen units of measurement, but...
4) IF the Laws of physics apply to ALL things in the known Universe, including human patterns of perception and organization on all levels from the individual psyche to the world collective, and including a progressive component THROUGH TIME, then such laws apply also to the development and evolution of our units of measure. In theory, then, such measurements approach, but never reach some optimal "mean" (golden or otherwise).
5) Pure mathematics alone can be used to describe the workings and underlying structure of the Cosmos, which does not exclude the need for Empirical experimentation and verification, as there are infinite possible mathematical structures from which to choose, not all of which can accurately describe at least THIS Universe.
6) Phi, the Golden Ratio, represents the Universal Constant of progression through space/time in a resistanceless environment. Viswanath's Constant, on the other hand, represents a state of maximum entropy/equlibrium. ( About Viswanath's Constant for the uninitiated: http://en.wikipedia.org/wiki/Viswanath's_constant )
===========================================================
Over the last few days I have come up with the best short description I can:
-----------------
Kolo Math
-----------------
Node & Network Math for the Age of Information
aka "Tuning Number Strings in C-Flat"
... and pretty much have the "starter set" of number variables I am working with down on paper. When I can I will type them up and post them, but without the derivations, many worked out visually, it might seem like so much gobbledygook. :-)
For the record, yes, I believe there are applications in theoretical physics for what I am doing, specifically with regards to to spin networks and n-dimensional spheres, both of which I am still learning about.
But I won't be able to do it alone... My discipline-specific knowledge base is not yet there.
Best,
Raphie
I don't have the time at the moment to full out explain. It would take a book, frankly, but the bottom line is this:
I have been attempting to "callibrate" the number system by setting positional (i.e. nth number in a given progression) "reference frames" in a CONSISTENT manner as one might "white balance" a video camera and I have been triangulating between Base II, powers of phi, various scales of the Fibonacci Series, powers of 10 & 2, as well as Kaprekar Numbers, prime numbers and more....
I have been setting variables and "constants", such as these ones from what I call the "Shen Set" composed of what I call Ra Numbers, Ma'at Numbers and Thoth Numbers...
Mersenne Number Constant
M_c = 7 = (2^n)-1; n = 3
"Balance" Number Constant
B_c = 4 = 2^(n-1); n = 3
Perfect Number Constant
P_c = 28 = M_c*B_c; n = 3
K_c = 495 = Kaprekar Constant (3 digit)
K_c4 = 6174 = Kaprekar Constant (4 digit)
I = sqrt 11
k-log (x) = k = 0180 = rad*1/pi
p-log (x) = 'p = 5040 = rad*P_c/pi (= 7!)
where rad = 1 radian = 180/pi (standard math convention)
... and so on and my primary "targets," so to speak, that which I have been using to "sharpen focus" -- again as one might with a video camera or an old style SLR, wherein you zoom in on the detail, set focus and then zoom back out again and the entire frame is sharp -- are alpha (the fine structure constant) and the speed of light.
By and large, when I find relations such as...
(7^3*k)/10 = K_c4
(7^3*180)/10 = 6174
or, using...
(7^3*k*I^2)
then...
(7^3*180*11)/1372 = 495 = K_c3
(7^3*180*11)/110 = 6174 = K_c4
... or the constructions for alpha and the speed of light I have been posting, it is the numbers "doing the work," not me. It would be one thing if I were creating "weird," far out variables, but I am not. I am using the most basic of basic number progressions like the Mersenne Numbers and Perfect Numbers and phi^30 and phi^31 (based on the midway point between 0 (= 1-1) and 61 (= 60+1), 60, of course being 1/6*360 (=K) and a number I am well familiar with based on my work as a film electrician... (i.e. 60 cycles/second)
Irrespective of whether these relationships I am finding are significant specifically with regards to the physical world, the EASE with which I am finding them, I believe, IS significant as is the fact that I am finding them by applying the below basic principles (there are more...), cut and pasted from the thread...
The Fine Structure Constant As Fractal Construct?
http://forum.physorg.com/index.php?showtop...ndpost&p=285139
===========================================================
A FEW GUIDING HYPOTHESES/ASSUMPTIONS REGARDING THE BELOW "NUMEROLOGICALLY" DERIVED "PHYSIO-THEORETICAL" APPROXIMATIONS FOR ALPHA:
1) In order to bridge the very large with the very small, one must incorporate the "progression" (i.e. evolution).
2) Dimensionless Constants, by definition, must have dimensionless Equivalents
3) All truly "Fundamental" Constants are dimensionless by definition. They only seem to be not so RELATIVE to our "somewhat" arbitrarily chosen units of measurement, but...
4) IF the Laws of physics apply to ALL things in the known Universe, including human patterns of perception and organization on all levels from the individual psyche to the world collective, and including a progressive component THROUGH TIME, then such laws apply also to the development and evolution of our units of measure. In theory, then, such measurements approach, but never reach some optimal "mean" (golden or otherwise).
5) Pure mathematics alone can be used to describe the workings and underlying structure of the Cosmos, which does not exclude the need for Empirical experimentation and verification, as there are infinite possible mathematical structures from which to choose, not all of which can accurately describe at least THIS Universe.
6) Phi, the Golden Ratio, represents the Universal Constant of progression through space/time in a resistanceless environment. Viswanath's Constant, on the other hand, represents a state of maximum entropy/equlibrium. ( About Viswanath's Constant for the uninitiated: http://en.wikipedia.org/wiki/Viswanath's_constant )
===========================================================
Over the last few days I have come up with the best short description I can:
-----------------
Kolo Math
-----------------
Node & Network Math for the Age of Information
aka "Tuning Number Strings in C-Flat"
... and pretty much have the "starter set" of number variables I am working with down on paper. When I can I will type them up and post them, but without the derivations, many worked out visually, it might seem like so much gobbledygook. :-)
For the record, yes, I believe there are applications in theoretical physics for what I am doing, specifically with regards to to spin networks and n-dimensional spheres, both of which I am still learning about.
But I won't be able to do it alone... My discipline-specific knowledge base is not yet there.
Best,
Raphie
related to the previous post...
http://forum.physorg.com/index.php?showtop...ndpost&p=303078
"KOLO MATH" NUMBER VARIABLES...
~~~~~~~~~~~~
CLARIFICATION
~~~~~~~~~~~~
1 k-log (x) = 180
1 p-log (x) = 5040
where...
1 p-log = 1 radian * pi = 180
1 k-log = 1 radian * 28*pi = 5040
1 radian = 180/pi ~ 57.2957795... (standard math convention)
1 "kolo" = 180
1 "plato" = 5040 = 7!
NOTE:
1 K-log = 360
1 P-Log = 30,240 (= 6*7! or 10!/5!)
~~~~~~~~~~~~
ERRATUM
~~~~~~~~~~~~
(111^2 + (2*111) + ((2700720)*111)) - 5
= 299,792,458
= c * s/m
NOT
(111^2 + (2*111) + ((2700720)*111)) + 5
----------------------------
Best,
Raphie
http://forum.physorg.com/index.php?showtop...ndpost&p=303078
"KOLO MATH" NUMBER VARIABLES...
~~~~~~~~~~~~
CLARIFICATION
~~~~~~~~~~~~
1 k-log (x) = 180
1 p-log (x) = 5040
where...
1 p-log = 1 radian * pi = 180
1 k-log = 1 radian * 28*pi = 5040
1 radian = 180/pi ~ 57.2957795... (standard math convention)
1 "kolo" = 180
1 "plato" = 5040 = 7!
NOTE:
1 K-log = 360
1 P-Log = 30,240 (= 6*7! or 10!/5!)
~~~~~~~~~~~~
ERRATUM
~~~~~~~~~~~~
(111^2 + (2*111) + ((2700720)*111)) - 5
= 299,792,458
= c * s/m
NOT
(111^2 + (2*111) + ((2700720)*111)) + 5
----------------------------
Best,
Raphie
QUOTE (Raphie Frank+Jan 17 2008, 04:58 AM)
A FEW GUIDING HYPOTHESES/ASSUMPTIONS REGARDING THE BELOW "NUMEROLOGICALLY" DERIVED "PHYSIO-THEORETICAL" APPROXIMATIONS FOR ALPHA:
1) In order to bridge the very large with the very small, one must incorporate the "progression" (i.e. evolution).
2) Dimensionless Constants, by definition, must have dimensionless Equivalents
3) All truly "Fundamental" Constants are dimensionless by definition. They only seem to be not so RELATIVE to our "somewhat" arbitrarily chosen units of measurement, but...
4) IF the Laws of physics apply to ALL things in the known Universe, including human patterns of perception and organization on all levels from the individual psyche to the world collective, and including a progressive component THROUGH TIME, then such laws apply also to the development and evolution of our units of measure. In theory, then, such measurements approach, but never reach some optimal "mean" (golden or otherwise).
5) Pure mathematics alone can be used to describe the workings and underlying structure of the Cosmos, which does not exclude the need for Empirical experimentation and verification, as there are infinite possible mathematical structures from which to choose, not all of which can accurately describe at least THIS Universe.
hej Raphie
To those 5 I absolutely agree.
I would also add that names for universal constants are not freely chozen, but resonates with their role in Universe.
1) In order to bridge the very large with the very small, one must incorporate the "progression" (i.e. evolution).
2) Dimensionless Constants, by definition, must have dimensionless Equivalents
3) All truly "Fundamental" Constants are dimensionless by definition. They only seem to be not so RELATIVE to our "somewhat" arbitrarily chosen units of measurement, but...
4) IF the Laws of physics apply to ALL things in the known Universe, including human patterns of perception and organization on all levels from the individual psyche to the world collective, and including a progressive component THROUGH TIME, then such laws apply also to the development and evolution of our units of measure. In theory, then, such measurements approach, but never reach some optimal "mean" (golden or otherwise).
5) Pure mathematics alone can be used to describe the workings and underlying structure of the Cosmos, which does not exclude the need for Empirical experimentation and verification, as there are infinite possible mathematical structures from which to choose, not all of which can accurately describe at least THIS Universe.
hej Raphie
To those 5 I absolutely agree.
I would also add that names for universal constants are not freely chozen, but resonates with their role in Universe.
Dear Ivars,
In the interests of "cross-pollination," please do offer a critique for #6. Perhaps we can find a middle ground. I have noted with interest your postings on e^(pi/2).
Ramanujan, by the way, had a very interesting formula tying together e, pi and phi, which I just came across last night. I will post it, but do not have it in front of me at the moment. But it involves an e^(2*pi/5) multiplier.
Best,
Raphie
P.S. @ Ivan. Thank you for posting the Base 9 Correspondence related to the digital roots of the squares of counting numbers. Could you expand on what you meant by "cross-base."? TIA.
In the interests of "cross-pollination," please do offer a critique for #6. Perhaps we can find a middle ground. I have noted with interest your postings on e^(pi/2).
Ramanujan, by the way, had a very interesting formula tying together e, pi and phi, which I just came across last night. I will post it, but do not have it in front of me at the moment. But it involves an e^(2*pi/5) multiplier.
Best,
Raphie
P.S. @ Ivan. Thank you for posting the Base 9 Correspondence related to the digital roots of the squares of counting numbers. Could you expand on what you meant by "cross-base."? TIA.
Hej Raphie,
I just have not yet got to golden ratio so I have no idea about it. I know the answer will come from continuous fractions but I have not found their place either.
While with i, e^(pi/2) and tetration I have been more successful.
I use Your first five statements often to check some ideas or get new directions. It is like part of the strategy. But I do not play with numbers anymore. I look for origin. Or origen. After that, the real play will begin.
The idea is , and basic part of strategy is that mathematics has a clear structure which we are able to find, but have not. Ramanujan, Euler, I think were closest to having intuitive idea about it, or even perhaps had simple model which they applied consistently, producing monstrous amounts of correct results easily.
So in essence, it is simple, this structure, but has so many fast multiplying projections that seeing it is a difficult task. Maya.
I just have not yet got to golden ratio so I have no idea about it. I know the answer will come from continuous fractions but I have not found their place either.
While with i, e^(pi/2) and tetration I have been more successful.
I use Your first five statements often to check some ideas or get new directions. It is like part of the strategy. But I do not play with numbers anymore. I look for origin. Or origen. After that, the real play will begin.
The idea is , and basic part of strategy is that mathematics has a clear structure which we are able to find, but have not. Ramanujan, Euler, I think were closest to having intuitive idea about it, or even perhaps had simple model which they applied consistently, producing monstrous amounts of correct results easily.
So in essence, it is simple, this structure, but has so many fast multiplying projections that seeing it is a difficult task. Maya.
EXPONENTS FOR MERSENNE PRIMES
&
MULTIPLICATIVE & SUBTRACTIVE FORMULATIONS FOR (EVEN) PERFECT NUMBERS
Mersenne Numbers follow form...
2^(n - 1)
... and construct (Even) Perfect Numbers of the form...
==========================
A.
MULTIPLICATIVE (Even) PERFECT NUMBER CONSTRUCTION
2^(n - 1)*((2^n) - 1) = y
ex.
n = 3
y = 4 * 7 = 28
=========================
B.
SUBTRACTIVE (Even) PERFECT NUMBER CONSTRUCTION
2^(2x+1) - 2^(x) = y'
ex.
n = 3
x = n -1 = 2
y' = 32 - 4 = 28
=====================================
Multiplicative Construction
-------------------------------
n =
(first 31)
2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091
(remaining 13 known)
756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657
Via Wikipedia: http://en.wikipedia.org/wiki/Perfect_number
=====================================
Subtractive Construction
-------------------------------
x = (n - 1)
(first 31)
1, 2, 4, 6, 12, 16, 18, 30, 60, 88, 106, 126, 520, 606, 1278, 2202, 2280, 3216, 4252, 4422, 9688, 9940, 11212, 19936, 21700, 23208, 44496, 86242, 110502, 132048, 216090
(remaining 13 known)
756838, 859432, 1257786, 1398268, 2976220, 3021376, 6972592, 13466916, 20996010, 24036582, 25964950, 30402456, 32582656
&
MULTIPLICATIVE & SUBTRACTIVE FORMULATIONS FOR (EVEN) PERFECT NUMBERS
Mersenne Numbers follow form...
2^(n - 1)
... and construct (Even) Perfect Numbers of the form...
==========================
A.
MULTIPLICATIVE (Even) PERFECT NUMBER CONSTRUCTION
2^(n - 1)*((2^n) - 1) = y
ex.
n = 3
y = 4 * 7 = 28
=========================
B.
SUBTRACTIVE (Even) PERFECT NUMBER CONSTRUCTION
2^(2x+1) - 2^(x) = y'
ex.
n = 3
x = n -1 = 2
y' = 32 - 4 = 28
=====================================
Multiplicative Construction
-------------------------------
n =
(first 31)
2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091
(remaining 13 known)
756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657
Via Wikipedia: http://en.wikipedia.org/wiki/Perfect_number
=====================================
Subtractive Construction
-------------------------------
x = (n - 1)
(first 31)
1, 2, 4, 6, 12, 16, 18, 30, 60, 88, 106, 126, 520, 606, 1278, 2202, 2280, 3216, 4252, 4422, 9688, 9940, 11212, 19936, 21700, 23208, 44496, 86242, 110502, 132048, 216090
(remaining 13 known)
756838, 859432, 1257786, 1398268, 2976220, 3021376, 6972592, 13466916, 20996010, 24036582, 25964950, 30402456, 32582656
.
Hi Raphie Frank, IAM, Ivars et al.
Just posted to say this: Raphie, you definitely are NOT 'silly' in your suggestions/mathematics re 'cyclic number line'! Repeat: NOT! hehehe.
I am short of time for now, but hope to (any day now) add further supporting observations to your own suggestions and mathematical-explorations of this aspect of 'line'.
Well observed, all!
RC.
.
Hi Raphie Frank, IAM, Ivars et al.
Just posted to say this: Raphie, you definitely are NOT 'silly' in your suggestions/mathematics re 'cyclic number line'! Repeat: NOT! hehehe.
I am short of time for now, but hope to (any day now) add further supporting observations to your own suggestions and mathematical-explorations of this aspect of 'line'.
Well observed, all!
RC.
.
QUOTE (Ivars+Jan 17 2008, 07:26 PM)
I use Your first five statements often to check some ideas or get new directions. It is like part of the strategy.
Here is another statement for you:
7) Numbers can be thought of as having position and orientation as well as value RELATIVE to a given point of reference.
Thus, the value of the "relative zero" which I wish was my coinage, but Liebniz beat me to it. :-)
Best,
Raphie
Here is another statement for you:
7) Numbers can be thought of as having position and orientation as well as value RELATIVE to a given point of reference.
Thus, the value of the "relative zero" which I wish was my coinage, but Liebniz beat me to it. :-)
Best,
Raphie
hej RC
Is not it so that Godel's theorem breaks down at infinities, meaning that if You develop logic and right symbols how to handle infinity/infinitesimals SUCH mathematics would be complete?
I think that is possible. See how easily Euler manipulated infinities, no mistakes, few basic simple rules. Just to extend on that.
Today I had the odd feeling that the beginning of processes what we observe today lays, in fact, in the future. Meaning that we kind of have to reverse the way we look at things naturally as well.
For example, in case of divergent series, we should be starting not from first term, but from where the series diverge to. One place we can do it is tetration. In summation or products I have not yet found the idea how to get to the other end before the start. Where is that end?
In infinite tetration, You just put the brackets starting from the end of series - calculate from the right - and it works. For divergent power towers, You take analytic continuation and get back from complex plane to reals easily.
Ivars
Is not it so that Godel's theorem breaks down at infinities, meaning that if You develop logic and right symbols how to handle infinity/infinitesimals SUCH mathematics would be complete?
I think that is possible. See how easily Euler manipulated infinities, no mistakes, few basic simple rules. Just to extend on that.
Today I had the odd feeling that the beginning of processes what we observe today lays, in fact, in the future. Meaning that we kind of have to reverse the way we look at things naturally as well.
For example, in case of divergent series, we should be starting not from first term, but from where the series diverge to. One place we can do it is tetration. In summation or products I have not yet found the idea how to get to the other end before the start. Where is that end?
In infinite tetration, You just put the brackets starting from the end of series - calculate from the right - and it works. For divergent power towers, You take analytic continuation and get back from complex plane to reals easily.
Ivars
QUOTE (Raphie Frank+Jan 17 2008, 07:48 PM)
Here is another statement for you:
7) Numbers can be thought of as having position and orientation as well as value RELATIVE to a given point of reference.
Thus, the value of the "relative zero" which I wish was my coinage, but Liebniz beat me to it. :-)
Best,
Raphie
hej Raphie
Sure. There is an absolute point of reference, where there are no numbers, (may be absolute 0), then there are scales on which numbers differ as they are built up.
all infinitesimals of order > dx (dx^2 etc) are smaller than dx in one scale. So infinitesimal area is smaller than lenght, volume smaller than area etc.
For example, 2 is not the same in different scales relative to that absolute scale.
Do not ask me what i mean exactly, but we will find out.
7) Numbers can be thought of as having position and orientation as well as value RELATIVE to a given point of reference.
Thus, the value of the "relative zero" which I wish was my coinage, but Liebniz beat me to it. :-)
Best,
Raphie
hej Raphie
Sure. There is an absolute point of reference, where there are no numbers, (may be absolute 0), then there are scales on which numbers differ as they are built up.
all infinitesimals of order > dx (dx^2 etc) are smaller than dx in one scale. So infinitesimal area is smaller than lenght, volume smaller than area etc.
For example, 2 is not the same in different scales relative to that absolute scale.
Do not ask me what i mean exactly, but we will find out.
Ivars,
If you stay with just Euclid (not non-Euclidean & GR) a different perspective using an a pentagon then a pentagram begins to take shape around it (tunnels one way, tower the other, moving in & out to infinity).
The is a mystery in this concept, each diagonal divides which ever diagonal it crosses into a Golden Ratio. I believe that Euclid defined it as (please check on this)
Example:
1/x = x/(1-x)
I think it is quiet a step for the use of algebra, using a letter for an unknown number (quantity) but when the n is lifted you see the hidden number.
Sure you know the rest, like the golden mean 2:3, 3:5, 5:8, 8:13,...as better approximations.
dawn
If this is incorrect Raphie Frank I would like to hear your perspective. That is my understanding (sure my memory does not serve me well on this) I really would love to see the corrections needed, in hope of helping us both.
If you stay with just Euclid (not non-Euclidean & GR) a different perspective using an a pentagon then a pentagram begins to take shape around it (tunnels one way, tower the other, moving in & out to infinity).
The is a mystery in this concept, each diagonal divides which ever diagonal it crosses into a Golden Ratio. I believe that Euclid defined it as (please check on this)
QUOTE
As the whole line is to the greater segment, so the greater is to the less.
This was a huge step just dealing with algebra.Example:
1/x = x/(1-x)
I think it is quiet a step for the use of algebra, using a letter for an unknown number (quantity) but when the n is lifted you see the hidden number.
Sure you know the rest, like the golden mean 2:3, 3:5, 5:8, 8:13,...as better approximations.
dawn
If this is incorrect Raphie Frank I would like to hear your perspective. That is my understanding (sure my memory does not serve me well on this) I really would love to see the corrections needed, in hope of helping us both.
OFF-TOPIC
In the feedback section Euler calls me a "complete idiot."
That's fine Euler. Think what you wish. I have been called far worse names.
Others can decide for themselves.
Best,
Raphie
P.S. I care far more about the respect of people like the ones who work here:
(/edit)
Swandivedigital announces Website launch for The Shubert Foundation
Easy-to-use, universally accessible site brings respected Foundation into the Information Age
http://www.swandive.com/about/releases/press_072303.php3
===========
and here...
===========
Swandivedigital Announces Launch of Redesigned Markle Foundation Website
http://www.swandive.com/about/releases/press_052804.php3
About the Markle Foundation
Emerging information and communication technologies possess enormous potential to improve people's lives. The Markle Foundation works to realize this potential and to accelerate the use of these technologies to address critical public needs...
excerpt
---------------
...added swandivedigital Senior Producer, Raphie Frank, "The Markle Foundation's own research has indicated that over 60% of all Internet users consider 'library' as the defining metaphor for the Internet. In other words, people go online predominantly to find information. That the Foundation charged us with helping them make their own information accessible online was a task that we were proud to be associated with. It's a bit like being an architect and having another architect ask you to design their house."
In the feedback section Euler calls me a "complete idiot."
That's fine Euler. Think what you wish. I have been called far worse names.
Others can decide for themselves.
Best,
Raphie
P.S. I care far more about the respect of people like the ones who work here:
(/edit)
Swandivedigital announces Website launch for The Shubert Foundation
Easy-to-use, universally accessible site brings respected Foundation into the Information Age
http://www.swandive.com/about/releases/press_072303.php3
===========
and here...
===========
Swandivedigital Announces Launch of Redesigned Markle Foundation Website
http://www.swandive.com/about/releases/press_052804.php3
About the Markle Foundation
Emerging information and communication technologies possess enormous potential to improve people's lives. The Markle Foundation works to realize this potential and to accelerate the use of these technologies to address critical public needs...
excerpt
---------------
...added swandivedigital Senior Producer, Raphie Frank, "The Markle Foundation's own research has indicated that over 60% of all Internet users consider 'library' as the defining metaphor for the Internet. In other words, people go online predominantly to find information. That the Foundation charged us with helping them make their own information accessible online was a task that we were proud to be associated with. It's a bit like being an architect and having another architect ask you to design their house."
QUOTE (Ivars+Jan 17 2008, 07:53 PM)
hej RC
Is not it so that Godel's theorem breaks down at infinities, meaning that if You develop logic and right symbols how to handle infinity/infinitesimals SUCH mathematics would be complete?
I think that is possible. See how easily Euler manipulated infinities, no mistakes, few basic simple rules. Just to extend on that.
Today I had the odd feeling that the beginning of processes what we observe today lays, in fact, in the future. Meaning that we kind of have to reverse the way we look at things naturally as well.
For example, in case of divergent series, we should be starting not from first term, but from where the series diverge to. One place we can do it is tetration. In summation or products I have not yet found the idea how to get to the other end before the start. Where is that end?
In infinite tetration, You just put the brackets starting from the end of series - calculate from the right - and it works. For divergent power towers, You take analytic continuation and get back from complex plane to reals easily.
Ivars
Hi Ivars.
That should be (and effectively IS, hehehe) the aim of all NEW mathematician 'explores' of the AXIOMATIC 'frontiers'.....the explores in THIS place being not only yourself, but also StevenA, Precursor, IAMoraes, Raphie Frank, Bloy, myself et al.
The CURRENT ORTHODOXY axiomatic mathematics is in the capable hands of hands of orthodox mathematicians perfectly suited to extend the CURRENT orthodoxy axiomatic mathematics.....and that 'techincal extension' Of the 'status quo' is admirable and useful. No question.....because it's ALL WE HAVE at the moment, after hundreds of years and millions of manhours spent on the INEVITABLY "INCOMPLETENESS" of the mathematics based on PATENTLY "INCOMPLETE" AXIOMS. hehehe.
So let's leave the current INCOMPLETENESS TECHNICIANS tinker with the current incompleteness maths and apply it accordingly and as best they can to the current batch of THEMSELVES obviously 'incomplete' PHYSICAL theories.....which theories must thereby perforce REMAIN always 'incomplete' as long as ONLY the current 'incomplete mathematics' is all that is available for 'consequently incomplete' modeling' of all the so far 'incomplete' physical theories. hehehe
In return, we shall humbly ask that those same conventional mathematics/physics 'technicians' leave US new breed of mathematics/physics explorers to get on to do all the necessary 'explorations' into all the 'possibilities-for-completeness' to be found in the NEW and DANGEROUS world of MORE 'COMPLETE' AXIOMS! hehehe.
Does that resonate with your own and other 'explorers' perpective looking into that new world of 'completeness possibilities, Ivars? hehehe.
Cheers all explorers in ANY field of scientific human endeavour!
RC.
Is not it so that Godel's theorem breaks down at infinities, meaning that if You develop logic and right symbols how to handle infinity/infinitesimals SUCH mathematics would be complete?
I think that is possible. See how easily Euler manipulated infinities, no mistakes, few basic simple rules. Just to extend on that.
Today I had the odd feeling that the beginning of processes what we observe today lays, in fact, in the future. Meaning that we kind of have to reverse the way we look at things naturally as well.
For example, in case of divergent series, we should be starting not from first term, but from where the series diverge to. One place we can do it is tetration. In summation or products I have not yet found the idea how to get to the other end before the start. Where is that end?
In infinite tetration, You just put the brackets starting from the end of series - calculate from the right - and it works. For divergent power towers, You take analytic continuation and get back from complex plane to reals easily.
Ivars
Hi Ivars.
That should be (and effectively IS, hehehe) the aim of all NEW mathematician 'explores' of the AXIOMATIC 'frontiers'.....the explores in THIS place being not only yourself, but also StevenA, Precursor, IAMoraes, Raphie Frank, Bloy, myself et al.
The CURRENT ORTHODOXY axiomatic mathematics is in the capable hands of hands of orthodox mathematicians perfectly suited to extend the CURRENT orthodoxy axiomatic mathematics.....and that 'techincal extension' Of the 'status quo' is admirable and useful. No question.....because it's ALL WE HAVE at the moment, after hundreds of years and millions of manhours spent on the INEVITABLY "INCOMPLETENESS" of the mathematics based on PATENTLY "INCOMPLETE" AXIOMS. hehehe.
So let's leave the current INCOMPLETENESS TECHNICIANS tinker with the current incompleteness maths and apply it accordingly and as best they can to the current batch of THEMSELVES obviously 'incomplete' PHYSICAL theories.....which theories must thereby perforce REMAIN always 'incomplete' as long as ONLY the current 'incomplete mathematics' is all that is available for 'consequently incomplete' modeling' of all the so far 'incomplete' physical theories. hehehe
In return, we shall humbly ask that those same conventional mathematics/physics 'technicians' leave US new breed of mathematics/physics explorers to get on to do all the necessary 'explorations' into all the 'possibilities-for-completeness' to be found in the NEW and DANGEROUS world of MORE 'COMPLETE' AXIOMS! hehehe.
Does that resonate with your own and other 'explorers' perpective looking into that new world of 'completeness possibilities, Ivars? hehehe.
Cheers all explorers in ANY field of scientific human endeavour!
RC.
QUOTE (Raphie Frank+Jan 17 2008, 08:12 PM)
In the feedback section Euler calls me a "complete idiot."
That's fine Euler. Think what you wish. I have been called far worse names.
Others can decide for themselves.
Best,
Raphie
P.S. I care far more about the respect of people like the ones who work here:
Swandivedigital Announces Launch of Redesigned Markle Foundation Website
http://www.swandive.com/about/releases/press_052804.php3
About the Markle Foundation
Emerging information and communication technologies possess enormous potential to improve people's lives. The Markle Foundation works to realize this potential and to accelerate the use of these technologies to address critical public needs...
and here...
Swandivedigital announces Website launch for The Shubert Foundation
Easy-to-use, universally accessible site brings respected Foundation into the Information Age
http://www.swandive.com/about/releases/press_072303.php3
Ignore that one and others like it, Raphie.
For our 'ersatz' "Euler" is a disgrace to the name and the memory of the real Euler.
And our ersatz "Euler" comes across as a frightened fossil wrapped in the static incomplete mathematics which he and his kind would wish to inflict on humanity forevermore....simply because he and they have NO IMAGINATION and/or COURAGE to explore further than what past giants have accomplished....and whom "ersatz Euler" DISRESPECTS thereby the legacy of those giants' OWN IMAGINATION and INDOMITABLE COURAGE and SPIRIT OF EXPLORATION into the UNKNOWN.
Don't let frightened rabbits caught in the headlights of ADVANCEMENT drag you into their frightened and terminal 'burrows' of ABDICATION and DEFEATIST MINDSET. Courage is not their forte; obviously.
Leave them to the miserable self-inflicted fate of their own making/choosing....we explorers who respect the memory/work of past giants in the field have other fish to fry.....COMPLETENESS OR BUST!
I am proud to be collaborating with such valiant explorer types as those here. Every indomitable one of you. Kudos.
RC.
.
That's fine Euler. Think what you wish. I have been called far worse names.
Others can decide for themselves.
Best,
Raphie
P.S. I care far more about the respect of people like the ones who work here:
Swandivedigital Announces Launch of Redesigned Markle Foundation Website
http://www.swandive.com/about/releases/press_052804.php3
About the Markle Foundation
Emerging information and communication technologies possess enormous potential to improve people's lives. The Markle Foundation works to realize this potential and to accelerate the use of these technologies to address critical public needs...
and here...
Swandivedigital announces Website launch for The Shubert Foundation
Easy-to-use, universally accessible site brings respected Foundation into the Information Age
http://www.swandive.com/about/releases/press_072303.php3
Ignore that one and others like it, Raphie.
For our 'ersatz' "Euler" is a disgrace to the name and the memory of the real Euler.
And our ersatz "Euler" comes across as a frightened fossil wrapped in the static incomplete mathematics which he and his kind would wish to inflict on humanity forevermore....simply because he and they have NO IMAGINATION and/or COURAGE to explore further than what past giants have accomplished....and whom "ersatz Euler" DISRESPECTS thereby the legacy of those giants' OWN IMAGINATION and INDOMITABLE COURAGE and SPIRIT OF EXPLORATION into the UNKNOWN.
Don't let frightened rabbits caught in the headlights of ADVANCEMENT drag you into their frightened and terminal 'burrows' of ABDICATION and DEFEATIST MINDSET. Courage is not their forte; obviously.
Leave them to the miserable self-inflicted fate of their own making/choosing....we explorers who respect the memory/work of past giants in the field have other fish to fry.....COMPLETENESS OR BUST!
I am proud to be collaborating with such valiant explorer types as those here. Every indomitable one of you. Kudos.
RC.
.
QUOTE (RealityCheck+Jan 17 2008, 08:19 PM)
In return, we shall humbly ask that those same conventional mathematics/physics 'technicians' leave US new breed of mathematics/physics explorers to get on to do all the necessary 'explorations' into all the 'possibilities-for-completeness' to be found in the NEW and DANGEROUS world of MORE 'COMPLETE' AXIOMS! hehehe.
Does that resonate with your own and other 'explorers' perpective looking into that new world of 'completeness possibilities, Ivars? hehehe.
hej RC
Sure. There is no problem with physics actually, only mathematics.
On a fundamental level, we shall split the continuous and discrete math to where they belong.
My opinion is that continuous math works only below quantum level, and discrete certainly above. If so, than there is not big problem ( theoretically) to unite gravity equations as such (if they are considered to be truly continuous-which the need for imaginary time seems to imply) and quantum physics- You just have to describe the point where continuous mathematics naturally creates discrete structures which becomes first physically accessible structures and strangely enough, possesses spin h, transports information in first SQ layer with speed c, etc.
So in sense it is a well defined thing with well known properties -this scale. Also from entropy point of view- obviously discrete structures appear when the infinitesimals get so complex that the negative entropy coming from absolute 0 level is not enough to build the next level of sub quantum structures- meaning that in first SQ level entropy created by movement of those SQ particles reduces negative entropy available to such extent than what is available is not enough to build yet another layer, complexity scale of SQ infinitesimals- and they get real, discrete.
Of course inability to handle infinitesimals, infinities and divergences logically is the reason why not physics, but mathematics is totally disjointed. Physics just follows- as does other applications of mathematics.
To get funds and support You either need exact results or sponsors.
Does that resonate with your own and other 'explorers' perpective looking into that new world of 'completeness possibilities, Ivars? hehehe.
hej RC
Sure. There is no problem with physics actually, only mathematics.
On a fundamental level, we shall split the continuous and discrete math to where they belong.
My opinion is that continuous math works only below quantum level, and discrete certainly above. If so, than there is not big problem ( theoretically) to unite gravity equations as such (if they are considered to be truly continuous-which the need for imaginary time seems to imply) and quantum physics- You just have to describe the point where continuous mathematics naturally creates discrete structures which becomes first physically accessible structures and strangely enough, possesses spin h, transports information in first SQ layer with speed c, etc.
So in sense it is a well defined thing with well known properties -this scale. Also from entropy point of view- obviously discrete structures appear when the infinitesimals get so complex that the negative entropy coming from absolute 0 level is not enough to build the next level of sub quantum structures- meaning that in first SQ level entropy created by movement of those SQ particles reduces negative entropy available to such extent than what is available is not enough to build yet another layer, complexity scale of SQ infinitesimals- and they get real, discrete.
Of course inability to handle infinitesimals, infinities and divergences logically is the reason why not physics, but mathematics is totally disjointed. Physics just follows- as does other applications of mathematics.
To get funds and support You either need exact results or sponsors.
QUOTE (RealityCheck+Jan 17 2008, 08:31 PM)
Don't let frightened rabbits caught in the headlights of ADVANCEMENT drag you into their frightened and terminal ABDICATION and DEFEATIST mindset...
OFF-TOPIC
Dear RC,
"Attacks" such as Euler's -- and "attack" is a very apt word choice in this instance -- do not off-put me, but I feel obligated to air out in the light such banalities. Such attacks are corrosive to the spirit of innovation. Full stop.
Best,
Raphie
P.S. Not everyone out there has the confidence you or I do. People such as Ivan and Ivars and you and I, etc. make it easier for others to come forward. In the grand sense, we need to get all minds "on deck" to confront the challenges of the 21st Century. And if not me, if not you, then who? The other guy? In social psychology there is a specific term for the phenomena: "DIFFUSION OF RESPONSIBILITY."
A related post from the Laissez Faire Libel Thread...
========================
Mo. City Outlaws Internet Harassment
========================
excerpt...
DARDENNE PRAIRIE, Mo. (AP) — City officials unanimously passed a measure making online harassment a crime, days after learning that a 13-year-old girl killed herself last year after receiving cruel messages on the Internet...
MORE: http://forum.physorg.com/index.php?showtop...ndpost&p=285450
OFF-TOPIC
Dear RC,
"Attacks" such as Euler's -- and "attack" is a very apt word choice in this instance -- do not off-put me, but I feel obligated to air out in the light such banalities. Such attacks are corrosive to the spirit of innovation. Full stop.
Best,
Raphie
P.S. Not everyone out there has the confidence you or I do. People such as Ivan and Ivars and you and I, etc. make it easier for others to come forward. In the grand sense, we need to get all minds "on deck" to confront the challenges of the 21st Century. And if not me, if not you, then who? The other guy? In social psychology there is a specific term for the phenomena: "DIFFUSION OF RESPONSIBILITY."
A related post from the Laissez Faire Libel Thread...
========================
Mo. City Outlaws Internet Harassment
========================
excerpt...
DARDENNE PRAIRIE, Mo. (AP) — City officials unanimously passed a measure making online harassment a crime, days after learning that a 13-year-old girl killed herself last year after receiving cruel messages on the Internet...
MORE: http://forum.physorg.com/index.php?showtop...ndpost&p=285450
QUOTE (Ivars+Jan 17 2008, 08:38 PM)
hej RC
Sure. There is no problem with physics actually, only mathematics.
On a fundamental level, we shall split the continuous and discrete math to where they belong.
My opinion is that continuous math works only below quantum level, and discrete certainly above. If so, than there is not big problem ( theoretically) to unite gravity equations as such (if they are considered to be truly continuous-which the need for imaginary time seems to imply) and quantum physics- You just have to describe the point where continuous mathematics naturally creates discrete structures which becomes first physically accessible structures and strangely enough, possesses spin h, transports information in first SQ layer with speed c, etc.
So in sense it is a well defined thing with well known properties -this scale. Also from entropy point of view- obviously discrete structures appear when the infinitesimals get so complex that the negative entropy coming from absolute 0 level is not enough to build the next level of sub quantum structures- meaning that in first SQ level entropy created by movement of those SQ particles reduces negative entropy available to such extent than what is available is not enough to build yet another layer, complexity scale of SQ infinitesimals- and they get real, discrete.
Of course inability to handle infinitesimals, infinities and divergences logically is the reason why not physics, but mathematics is totally disjointed. Physics just follows- as does other applications of mathematics.
To get funds and support You either need exact results or sponsors.
You have identified 'where it's at' there, Ivars. hehehe.
And I will be posting something in a couple of days in the TOE/Cosmology special project SUB-forum that will, I really feel, will give you and other explores here some novel 'objects/concepts' to really get your 'mathematical teeth' into; and that I hope will provide some solid 'purchase' for your and others' new and exciting 'mathematical footings' in bridging the present 'incompleteness gap' between 'absolute contiguous' and 'relative discreteness' mathematical treatments of the reality!
Cheers!
RC.
.
Sure. There is no problem with physics actually, only mathematics.
On a fundamental level, we shall split the continuous and discrete math to where they belong.
My opinion is that continuous math works only below quantum level, and discrete certainly above. If so, than there is not big problem ( theoretically) to unite gravity equations as such (if they are considered to be truly continuous-which the need for imaginary time seems to imply) and quantum physics- You just have to describe the point where continuous mathematics naturally creates discrete structures which becomes first physically accessible structures and strangely enough, possesses spin h, transports information in first SQ layer with speed c, etc.
So in sense it is a well defined thing with well known properties -this scale. Also from entropy point of view- obviously discrete structures appear when the infinitesimals get so complex that the negative entropy coming from absolute 0 level is not enough to build the next level of sub quantum structures- meaning that in first SQ level entropy created by movement of those SQ particles reduces negative entropy available to such extent than what is available is not enough to build yet another layer, complexity scale of SQ infinitesimals- and they get real, discrete.
Of course inability to handle infinitesimals, infinities and divergences logically is the reason why not physics, but mathematics is totally disjointed. Physics just follows- as does other applications of mathematics.
To get funds and support You either need exact results or sponsors.
You have identified 'where it's at' there, Ivars. hehehe.
And I will be posting something in a couple of days in the TOE/Cosmology special project SUB-forum that will, I really feel, will give you and other explores here some novel 'objects/concepts' to really get your 'mathematical teeth' into; and that I hope will provide some solid 'purchase' for your and others' new and exciting 'mathematical footings' in bridging the present 'incompleteness gap' between 'absolute contiguous' and 'relative discreteness' mathematical treatments of the reality!
Cheers!
RC.
.
QUOTE (Raphie Frank+Jan 17 2008, 08:44 PM)
OFF-TOPIC
Dear RC,
"Attacks" such as Euler's -- and "attack" is a very apt word choice in this instance -- do not off-put me, but I feel obligated to air out in the light such banalities. Such attacks are corrosive to the spirit of innovation. Full stop.
Best,
Raphie
P.S. Not everyone out there has the confidence you or I do. People such as Ivan and Ivars and you and I, etc. make it easier for others to come forward. In the grand sense, we need to get all minds "on deck" to confront the challenges of the 21st Century. And if not me, if not you, then who? The other guy? In social psychology there is a specific term for the phenomena: "DIFFUSION OF RESPONSIBILITY."
Hehehe. Very apt descriptive terms: all such "ersatz thinkers" are DIFFUSIONISTS; as opposed to we FUSIONISTS! I like it! hehehe.
Yeah, all 'followers' and no 'leaders' among the lot in the current 'orthodoxical breed', hey?
Never mind....the explorers are in town! and here they will stay until......"completeness or bust"! hey? hehehe.
Cheers all!
RC.
.
Dear RC,
"Attacks" such as Euler's -- and "attack" is a very apt word choice in this instance -- do not off-put me, but I feel obligated to air out in the light such banalities. Such attacks are corrosive to the spirit of innovation. Full stop.
Best,
Raphie
P.S. Not everyone out there has the confidence you or I do. People such as Ivan and Ivars and you and I, etc. make it easier for others to come forward. In the grand sense, we need to get all minds "on deck" to confront the challenges of the 21st Century. And if not me, if not you, then who? The other guy? In social psychology there is a specific term for the phenomena: "DIFFUSION OF RESPONSIBILITY."
Hehehe. Very apt descriptive terms: all such "ersatz thinkers" are DIFFUSIONISTS; as opposed to we FUSIONISTS! I like it! hehehe.
Yeah, all 'followers' and no 'leaders' among the lot in the current 'orthodoxical breed', hey?
Never mind....the explorers are in town! and here they will stay until......"completeness or bust"! hey? hehehe.
Cheers all!
RC.
.
QUOTE (Raphie Frank+Jan 17 2008, 08:44 PM)
...
...
A related post from the Laissez Faire Libel Thread...
========================
Mo. City Outlaws Internet Harassment
========================
excerpt...
DARDENNE PRAIRIE, Mo. (AP) — City officials unanimously passed a measure making online harassment a crime, days after learning that a 13-year-old girl killed herself last year after receiving cruel messages on the Internet...
MORE: http://forum.physorg.com/index.php?showtop...ndpost&p=285450
About ruddy time too!
But do you think the sociopathic DIFFUSIONISTS are capable of comprehending and 'internalising' the implications for themselves and their victims?
RC.
.
...
A related post from the Laissez Faire Libel Thread...
========================
Mo. City Outlaws Internet Harassment
========================
excerpt...
DARDENNE PRAIRIE, Mo. (AP) — City officials unanimously passed a measure making online harassment a crime, days after learning that a 13-year-old girl killed herself last year after receiving cruel messages on the Internet...
MORE: http://forum.physorg.com/index.php?showtop...ndpost&p=285450
About ruddy time too!
But do you think the sociopathic DIFFUSIONISTS are capable of comprehending and 'internalising' the implications for themselves and their victims?
RC.
.
@ RC -- You can use terms such as "sociopath," but I don't recommend it. It is lowering oneself to the level of the opposition. Kind of like saying torture is all right because the other guys do it too. Last I checked, water was the way to put out a fire most times, though not always... :-)
====================================================
Dear Dawn,
Let me simply supplement your thoughts on the Golden Ratio, or rather the Fibonacci-type ("F-type") series. One of the greatest aspects of all F-type series is that they are "pre-callibrated" progressions.
And what do I mean by "pre-callibrated"?
Well, basically, if you find a relationship that applies to just two consecutive pairs of numbers in the series, it applies to ALL number pairs in the progression (i.e. the "system"). That's a basic axiom, although I have not read it anywhere, perhaps because it is so "obvious."
By way of example...
CASE I
------------
Fib Series equals, beginning with index number (i = 0):
F_(i) = 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144
===================
IDENTITY
F_(i-1)^2 + F_(i)^2 = F_(2i-1)
===================
i = 4
3^2 + 5^2 = 9 + 25 = 34 = F_(2*4 -1) = F_7
i = 5
5^2 + 8^2 = 25 + 64 = 89 = F_(2*5 -1) = F_9
The relationship applies always and EXACTLY. Here's another one:
CASE II
------------
Lucas Series equals, beginning with index number (i = 0):
L_(i) = 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322
=====================
IDENTITY
L_i^2 = L_(2i) + 2*(-1)^(n-1)
=====================
i = 4
L_i^2 = 7^2 = 49 = L_(2*4) + 2*(-1)^(4-1) = L_8 + 2*(-1)^(3) = 49 -2 = 47
i = 5
L_i^2 = 11^2 = 121 = L_(2*5) + 2*(-1)^(5-1) = L_10 + 2*(-1)^(4) = 121 + 2 = 123
The principle applies for basically any two number pairs, EVEN ACROSS SERIES...
CASE III
------------
Lucas Series equals, beginning with index number (i = 0):
L_(i) = 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322
Fib Series equals, beginning with index number (i = 0):
F_(i) = 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144
===================
IDENTITY
F_i * L_i = F_(2i)
===================
i = 4
F_i * L_i = 7*3 = 21 = F_(2*4) = F_8
i = 5
F_i * L_i = 11*5 = 55 = F_(2*5) = F_10
===================
Now, though I derived these identities myself, they are not new. They have been known for hundreds of years. BUT. I still derived them myself, meaning, in a sense, that when you work with these progressions, basically anyone can be a Euler or a Ramanujan.
My twist? (or one of them...)
I am setting relations via Fibonacci and then seeing how they relate to non-Fibonacci Progressions. The results have been rather intriguing to say the least. Here is a link to one such relationship:
PERFECT NUMBER / LUCAS CORRESPONDENCE
http://forum.physorg.com/index.php?showtop...ndpost&p=301248
Best,
Raphie
====================================================
Dear Dawn,
Let me simply supplement your thoughts on the Golden Ratio, or rather the Fibonacci-type ("F-type") series. One of the greatest aspects of all F-type series is that they are "pre-callibrated" progressions.
And what do I mean by "pre-callibrated"?
Well, basically, if you find a relationship that applies to just two consecutive pairs of numbers in the series, it applies to ALL number pairs in the progression (i.e. the "system"). That's a basic axiom, although I have not read it anywhere, perhaps because it is so "obvious."
By way of example...
CASE I
------------
Fib Series equals, beginning with index number (i = 0):
F_(i) = 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144
===================
IDENTITY
F_(i-1)^2 + F_(i)^2 = F_(2i-1)
===================
i = 4
3^2 + 5^2 = 9 + 25 = 34 = F_(2*4 -1) = F_7
i = 5
5^2 + 8^2 = 25 + 64 = 89 = F_(2*5 -1) = F_9
The relationship applies always and EXACTLY. Here's another one:
CASE II
------------
Lucas Series equals, beginning with index number (i = 0):
L_(i) = 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322
=====================
IDENTITY
L_i^2 = L_(2i) + 2*(-1)^(n-1)
=====================
i = 4
L_i^2 = 7^2 = 49 = L_(2*4) + 2*(-1)^(4-1) = L_8 + 2*(-1)^(3) = 49 -2 = 47
i = 5
L_i^2 = 11^2 = 121 = L_(2*5) + 2*(-1)^(5-1) = L_10 + 2*(-1)^(4) = 121 + 2 = 123
The principle applies for basically any two number pairs, EVEN ACROSS SERIES...
CASE III
------------
Lucas Series equals, beginning with index number (i = 0):
L_(i) = 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322
Fib Series equals, beginning with index number (i = 0):
F_(i) = 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144
===================
IDENTITY
F_i * L_i = F_(2i)
===================
i = 4
F_i * L_i = 7*3 = 21 = F_(2*4) = F_8
i = 5
F_i * L_i = 11*5 = 55 = F_(2*5) = F_10
===================
Now, though I derived these identities myself, they are not new. They have been known for hundreds of years. BUT. I still derived them myself, meaning, in a sense, that when you work with these progressions, basically anyone can be a Euler or a Ramanujan.
My twist? (or one of them...)
I am setting relations via Fibonacci and then seeing how they relate to non-Fibonacci Progressions. The results have been rather intriguing to say the least. Here is a link to one such relationship:
PERFECT NUMBER / LUCAS CORRESPONDENCE
http://forum.physorg.com/index.php?showtop...ndpost&p=301248
Best,
Raphie
QUOTE (Raphie Frank+Jan 17 2008, 03:00 PM)
P.S. @ Ivan. Thank you for posting the Base 9 Correspondence related to the digital roots of the squares of counting numbers. Could you expand on what you meant by "cross-base."? TIA.
I know that if something is fractal it will repeat itself, so that if there is a series of numbers that don't repeat and progress in a particular manner, either they are fractal or they are random. If they are random, fine, I don't do "random". If they follow a rule that can be stated as a mathematical rule and there is a chance they are fractal, the first thing I want to check is whether the rule only applies to one base or not, like the digit-addition you introduced a few threads --years!-- ago. I thought it was fabulous, but the first thing that came to mind was the obvious to my way of thinking: if you have results for bases above 2 for the digital addition, for instance, calculated for different number of digits in that base, all of that would go on one single coordinate, the first line of the graph. You would have to remember that this coordinate is plotted on logarithmic space, which is easy to do because if you try to plot those numbers where they are supposed to be you will be out of screen and memory long before you end. Then you would plot all results for base 4 on the next horizontal, then the next, etc...
If you end up with a fractal, which I am sure you will in that case, then you will have discovered an "intuitive" way of predicting with certainty a thing or two about the set of instructions and/or equations and/or their **future** results --the ones you are too lazy to plot... Not That I Would Ever Ever Do It, Mind You!
Edit: here is one that may or may not crash, but is really exciting... we know that Sierpinski's triangle is a fractal AND we know from (x logically ANDed with y) that its code increases by 1 at every coordinate AND we know that ordered integers lengths wrapped around Sack's spiral (it's just a log spiral, I think) form a seven-legged spiral... what else would we know about Sierpinski's triangle if we wrapped its code around a log spiral?)
I know that if something is fractal it will repeat itself, so that if there is a series of numbers that don't repeat and progress in a particular manner, either they are fractal or they are random. If they are random, fine, I don't do "random". If they follow a rule that can be stated as a mathematical rule and there is a chance they are fractal, the first thing I want to check is whether the rule only applies to one base or not, like the digit-addition you introduced a few threads --years!-- ago. I thought it was fabulous, but the first thing that came to mind was the obvious to my way of thinking: if you have results for bases above 2 for the digital addition, for instance, calculated for different number of digits in that base, all of that would go on one single coordinate, the first line of the graph. You would have to remember that this coordinate is plotted on logarithmic space, which is easy to do because if you try to plot those numbers where they are supposed to be you will be out of screen and memory long before you end. Then you would plot all results for base 4 on the next horizontal, then the next, etc...
If you end up with a fractal, which I am sure you will in that case, then you will have discovered an "intuitive" way of predicting with certainty a thing or two about the set of instructions and/or equations and/or their **future** results --the ones you are too lazy to plot... Not That I Would Ever Ever Do It, Mind You!
Edit: here is one that may or may not crash, but is really exciting... we know that Sierpinski's triangle is a fractal AND we know from (x logically ANDed with y) that its code increases by 1 at every coordinate AND we know that ordered integers lengths wrapped around Sack's spiral (it's just a log spiral, I think) form a seven-legged spiral... what else would we know about Sierpinski's triangle if we wrapped its code around a log spiral?)
Raphie Frank, all,
Thank you for your time, did not mean for you to go to such trouble. When sailing or just rock climbing (warm weather) G.H.Hardy- A Mathematician's Apology, I am sure you have the book it keeps me honest along with others that causes me to hide under a book for a few weeks.
Remember he was the one who said,
Now my head is beginning to spin thinking about the G-ratio..
dawn
Thank you for your time, did not mean for you to go to such trouble. When sailing or just rock climbing (warm weather) G.H.Hardy- A Mathematician's Apology, I am sure you have the book it keeps me honest along with others that causes me to hide under a book for a few weeks.
Remember he was the one who said,
QUOTE
"Beauty is the first test"
it really deals with many expressions like, π, √2, phi (the golden ratio = 1.61803399), e (could not find the imaginary # symbol) & pi. Just suggested it in case what you are working on might become stressful.Now my head is beginning to spin thinking about the G-ratio..
dawn
OFF-TOPIC
========
It occurs to me that one way to fight against the negative feedback of the cranks, because it is they that are far more the "cranks" than such as RC or Ivan, is that if you like the work someone is doing, then give that person positive feedback.
As I said, water, not fire.
Best,
Raphie
P.S. And make it something POSITIVE about that person, rather than simply as an anti-spam statement. Protect AND build at the same time.
P.P.S. "Why did you build that?" they said to the architect. He replied "Because it wasn't there."
P.P.S. @ Dawn. You're welcome. :-)
========
It occurs to me that one way to fight against the negative feedback of the cranks, because it is they that are far more the "cranks" than such as RC or Ivan, is that if you like the work someone is doing, then give that person positive feedback.
As I said, water, not fire.
Best,
Raphie
P.S. And make it something POSITIVE about that person, rather than simply as an anti-spam statement. Protect AND build at the same time.
P.P.S. "Why did you build that?" they said to the architect. He replied "Because it wasn't there."
P.P.S. @ Dawn. You're welcome. :-)
QUOTE (IAMoraes+Jan 17 2008, 10:06 PM)
I know that if something is fractal it will repeat itself, so that if there is a series of numbers that don't repeat and progress in a particular manner, either they are fractal or they are random. If they are random, fine, I don't do "random". If they follow a rule that can be stated as a mathematical rule and there is a chance they are fractal, the first thing I want to check is whether the rule only applies to one base or not, like the digit-addition you introduced a few threads --years!-- ago. I thought it was fabulous, but the first thing that came to mind was the obvious to my way of thinking: if you have results for bases above 2 for the digital addition, for instance, calculated for different number of digits in that base, all of that would go on one single coordinate, the first line of the graph. You would have to remember that this coordinate is plotted on logarithmic space, which is easy to do because if you try to plot those numbers where they are supposed to be you will be out of screen and memory long before you end. Then you would plot all results for base 4 on the next horizontal, then the next, etc...
FRACTAL - BASIC DEFINITION
Particularly with regards to the "cross-base" issue that Ivan mentions, note the different classifications, especially the "quasi-self-similar" fractal-type, which I can imagine as having relevance with regards to quasi-crystals, a REAL WORLD phenomena, deemed impossible until the 1980's, not unrelated to the Golden Ratio...
"Cut and pasted" from Wikipedia
=====================================
FRACTAL
A fractal is generally "a rough or fragmented geometric shape that can be subdivided into parts, each of which is (at least approximately) a reduced-size copy of the whole,"[1] a property called self-similarity. The term was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured."
A fractal often has the following features:
-- It has a fine structure at arbitrarily small scales.
-- It is too irregular to be easily described in traditional Euclidean geometric language.
-- It is self-similar (at least approximately or stochastically).
-- It has a Hausdorff dimension which is greater than its topological dimension (although this -- requirement is not met by space-filling curves such as the Hilbert curve).
It has a simple and recursive definition.[2]
Because they appear similar at all levels of magnification, fractals are often considered to be infinitely complex (in informal terms). Natural objects that approximate fractals to a degree include clouds, mountain ranges, lightning bolts, coastlines, and snow flakes. However, not all self-similar objects are fractals—for example, the real line (a straight Euclidean line) is formally self-similar but fails to have other fractal characteristics.
=====================================
-----------------
Classification
-----------------
Fractals can also be classified according to their self-similarity. There are three types of self-similarity found in fractals:
-- Exact self-similarity — This is the strongest type of self-similarity; the fractal appears identical at different scales. Fractals defined by iterated function systems often display exact self-similarity.
-- Quasi-self-similarity — This is a loose form of self-similarity; the fractal appears approximately (but not exactly) identical at different scales. Quasi-self-similar fractals contain small copies of the entire fractal in distorted and degenerate forms. Fractals defined by recurrence relations are usually quasi-self-similar but not exactly self-similar.
-- Statistical self-similarity — This is the weakest type of self-similarity; the fractal has numerical or statistical measures which are preserved across scales. Most reasonable definitions of "fractal" trivially imply some form of statistical self-similarity. (Fractal dimension itself is a numerical measure which is preserved across scales.) Random fractals are examples of fractals which are statistically self-similar, but neither exactly nor quasi-self-similar.
http://en.wikipedia.org/wiki/Fractal
Phoenix de Julia
http://en.wikipedia.org/wiki/Image:Phoenix%28Julia%29.gif
SELF SIMILARITY
In mathematics, a self-similar object is exactly or approximately similar to a part of itself, e.g., the whole has the same shape as one or more of the parts. Many objects in the real world, such as coastlines, are statistically self-similar: parts of them show the same statistical properties at many scales[1]. Self-similarity is a typical property of fractals.
Scale invariance is an exact form of self-similarity where at any magnification there is a smaller piece of the object that is similar to the whole. For instance, a side of the Koch snowflake is both symmetrical and scale-invariant; it can be continually magnified 3x without changing shape.
http://en.wikipedia.org/wiki/Self-similarity
THE HAUSDORFF DIMENSION
In mathematics, the Hausdorff dimension (also known as the Hausdorff-Besicovitch dimension) is an extended non-negative real number associated to any metric space. It was introduced in 1918 by the mathematician Felix Hausdorff. Many of the technical developments used to compute the Hausdorff dimension for highly irregular sets were obtained by Abram Samoilovitch Besicovitch.
Less frequently it is also called the capacity dimension or fractal dimension (the latter is somewhat misleading as there are many other choices of definition).
http://en.wikipedia.org/wiki/Hausdorff_dimension
FRACTAL - BASIC DEFINITION
Particularly with regards to the "cross-base" issue that Ivan mentions, note the different classifications, especially the "quasi-self-similar" fractal-type, which I can imagine as having relevance with regards to quasi-crystals, a REAL WORLD phenomena, deemed impossible until the 1980's, not unrelated to the Golden Ratio...
"Cut and pasted" from Wikipedia
=====================================
FRACTAL
A fractal is generally "a rough or fragmented geometric shape that can be subdivided into parts, each of which is (at least approximately) a reduced-size copy of the whole,"[1] a property called self-similarity. The term was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured."
A fractal often has the following features:
-- It has a fine structure at arbitrarily small scales.
-- It is too irregular to be easily described in traditional Euclidean geometric language.
-- It is self-similar (at least approximately or stochastically).
-- It has a Hausdorff dimension which is greater than its topological dimension (although this -- requirement is not met by space-filling curves such as the Hilbert curve).
It has a simple and recursive definition.[2]
Because they appear similar at all levels of magnification, fractals are often considered to be infinitely complex (in informal terms). Natural objects that approximate fractals to a degree include clouds, mountain ranges, lightning bolts, coastlines, and snow flakes. However, not all self-similar objects are fractals—for example, the real line (a straight Euclidean line) is formally self-similar but fails to have other fractal characteristics.
=====================================
-----------------
Classification
-----------------
Fractals can also be classified according to their self-similarity. There are three types of self-similarity found in fractals:
-- Exact self-similarity — This is the strongest type of self-similarity; the fractal appears identical at different scales. Fractals defined by iterated function systems often display exact self-similarity.
-- Quasi-self-similarity — This is a loose form of self-similarity; the fractal appears approximately (but not exactly) identical at different scales. Quasi-self-similar fractals contain small copies of the entire fractal in distorted and degenerate forms. Fractals defined by recurrence relations are usually quasi-self-similar but not exactly self-similar.
-- Statistical self-similarity — This is the weakest type of self-similarity; the fractal has numerical or statistical measures which are preserved across scales. Most reasonable definitions of "fractal" trivially imply some form of statistical self-similarity. (Fractal dimension itself is a numerical measure which is preserved across scales.) Random fractals are examples of fractals which are statistically self-similar, but neither exactly nor quasi-self-similar.
http://en.wikipedia.org/wiki/Fractal
Phoenix de Julia
http://en.wikipedia.org/wiki/Image:Phoenix%28Julia%29.gif
SELF SIMILARITY
In mathematics, a self-similar object is exactly or approximately similar to a part of itself, e.g., the whole has the same shape as one or more of the parts. Many objects in the real world, such as coastlines, are statistically self-similar: parts of them show the same statistical properties at many scales[1]. Self-similarity is a typical property of fractals.
Scale invariance is an exact form of self-similarity where at any magnification there is a smaller piece of the object that is similar to the whole. For instance, a side of the Koch snowflake is both symmetrical and scale-invariant; it can be continually magnified 3x without changing shape.
http://en.wikipedia.org/wiki/Self-similarity
THE HAUSDORFF DIMENSION
In mathematics, the Hausdorff dimension (also known as the Hausdorff-Besicovitch dimension) is an extended non-negative real number associated to any metric space. It was introduced in 1918 by the mathematician Felix Hausdorff. Many of the technical developments used to compute the Hausdorff dimension for highly irregular sets were obtained by Abram Samoilovitch Besicovitch.
Less frequently it is also called the capacity dimension or fractal dimension (the latter is somewhat misleading as there are many other choices of definition).
http://en.wikipedia.org/wiki/Hausdorff_dimension
I'm going to go out on a limb here: you guys don't know much mathematics, do you?
Dear Euler,
I'm going to go out on a limb here and imagine that you have more than the emotional maturity of a five year old. So please do show us this side of yourself, okay?
:-)
Best,
Raphie
P.S. Plato and Archimedes didn't have a clue what a derivative was. Nor either the Mayans who created a calendar far more accurate than our own. It's called OBSERVATION, Euler, Try it some time :-)
I'm going to go out on a limb here and imagine that you have more than the emotional maturity of a five year old. So please do show us this side of yourself, okay?
:-)
Best,
Raphie
P.S. Plato and Archimedes didn't have a clue what a derivative was. Nor either the Mayans who created a calendar far more accurate than our own. It's called OBSERVATION, Euler, Try it some time :-)
QUOTE (Raphie Frank+Jan 17 2008, 10:59 PM)
So please do show us this side of yourself, okay?
I'll stop taking the piss, when you guys learn some mathematics...
I'll stop taking the piss, when you guys learn some mathematics...
QUOTE (Raphie Frank+Jan 17 2008, 09:34 PM)
@ RC -- You can use terms such as "sociopath," but I don't recommend it. It is lowering oneself to the level of the opposition. Kind of like saying torture is all right because the other guys do it too. Last I checked, water was the way to put out a fire most times, though not always... :-)
...
......
Best,
Raphie
True. Please disregard my 'inadvertant stooping' to their level.
Thanks for the heads up, Raphie Frank!
Respects from this and your other friends in AXIOMATIC EXPLORATION into mathematics territory,
RC.
.
...
......
Best,
Raphie
True. Please disregard my 'inadvertant stooping' to their level.
Thanks for the heads up, Raphie Frank!
Respects from this and your other friends in AXIOMATIC EXPLORATION into mathematics territory,
RC.
.
QUOTE (Euler+Jan 17 2008, 11:04 PM)
I'll stop taking the piss, when you guys learn some mathematics...
Euler, look, I've no desire whatsoever to fight back and forth with you. There's room enough here on this forum for both of us. It takes a village and all that?
:-)
Best,
Raphie
Euler, look, I've no desire whatsoever to fight back and forth with you. There's room enough here on this forum for both of us. It takes a village and all that?
:-)
Best,
Raphie
QUOTE (Raphie Frank+Jan 17 2008, 11:59 PM)
P.S. Plato and Archimedes didn't have a clue what a derivative was. Nor either the Mayans who created a calendar far more accurate than our own. It's called OBSERVATION, Euler, Try it some time :-)
The Mayan Calender isn't more accurate than ours. Can you cite evidence?
Also, Plato and Archimedes didn't know about derivatives but they were exceptionally well read and greatly valided the notion of evidence and learning from the works of others. Most cranks here don't. They 'discuss' but they are only interested in talking about their own ideas, not in the actual exchange of information.
The famous Greeks learnt all they could about an area they were interested in. Cranks here don't.
So your examples are mute and infact go against you.
The Mayan Calender isn't more accurate than ours. Can you cite evidence?
Also, Plato and Archimedes didn't know about derivatives but they were exceptionally well read and greatly valided the notion of evidence and learning from the works of others. Most cranks here don't. They 'discuss' but they are only interested in talking about their own ideas, not in the actual exchange of information.
The famous Greeks learnt all they could about an area they were interested in. Cranks here don't.
So your examples are mute and infact go against you.
QUOTE (Euler+Jan 17 2008, 11:04 PM)
I'll stop taking the piss, when you guys learn some mathematics...
What's it to YOU, bub?
People here are primarily making axiomatic explorations INTO mathematics COMPLETENESS possibilities rather than merely 'doing' current 'incomplete mathematics' like you may be confining yourself to through your own lack of get-up-and-go (and other things).
If ever we need an 'incomplete' diffusionist in this thread, we'll call you.
Don't call us; we'll call you.
Bye bub.
.
.
What's it to YOU, bub?
People here are primarily making axiomatic explorations INTO mathematics COMPLETENESS possibilities rather than merely 'doing' current 'incomplete mathematics' like you may be confining yourself to through your own lack of get-up-and-go (and other things).
If ever we need an 'incomplete' diffusionist in this thread, we'll call you.
Don't call us; we'll call you.
Bye bub.
.
.
QUOTE (RealityCheck+Jan 17 2008, 11:12 PM)
People here are primarily making axiomatic explorations INTO mathematics COMPLETENESS...
No, people here are talking rubbish. The fact that you don't realise you're talking rubbish doesn't change the fact of the matter. You guys wouldn't even pass a high school exam on the subject!
No, people here are talking rubbish. The fact that you don't realise you're talking rubbish doesn't change the fact of the matter. You guys wouldn't even pass a high school exam on the subject!
QUOTE (Euler+Jan 17 2008, 11:17 PM)
No, people here are talking rubbish. The fact that you don't realise you're talking rubbish doesn't change the fact of the matter. You guys wouldn't even pass a high school exam on the subject!
My post said "...axiomatic explorations INTO mathematics COMPLETENESS possibilities...".
How on Earth are you going to ever get anything straight and 'complete' if you can't see ALL the 'context'?
When we need a diffusionist 'incompleteness' proponent/expert, we'll call you.
Don't call us; we'll call you.
OK, bub?
.
.
My post said "...axiomatic explorations INTO mathematics COMPLETENESS possibilities...".
How on Earth are you going to ever get anything straight and 'complete' if you can't see ALL the 'context'?
When we need a diffusionist 'incompleteness' proponent/expert, we'll call you.
Don't call us; we'll call you.
OK, bub?
.
.
Look Alphanumeric. I know Euler is a friend of yours, so I don't take umbrage, but I'm not exactly unwell read myself, truth be told and, no, I will not get into a "Have you read this or that" debate. :-)
As for the Mayan calendar, It's not as if I just make (/edit) such things up and post them, but I will grant you that it all depends on one's reference points, as always. In other words the issue of accuracy is RELATIVE.
==================================================
Robert D. Peden
MEngSc. BE. ( Melbourne University ) ARMTC TTTC. Formerly Principal Lecturer in the School of Sciences, Deakin University, Australia.
Foreword
The Mayan Ritual year of 260 days was successful for one major reason - after a cycle lasting 59 Ritual years, the tropical year and the Ritual year lock together in step. A period of 59 by 260 days equals a period of 42 tropical years, of 365.242 days.
Key excerpt...
The Long Count is a lunar calendar with an accuracy of 0.8 days in 100 years.
The Accounting year of 364 days might be considered a Venus Calendar with an accuracy of 0.3 days in 100 years.
http://spiderorchid.com/mesoamerica/mesoamerica.htm
==================================================
Care to tell me the accuracy of the Gregorian Calendar if one does not correct every four years by adding in an extra day?
Or do I have to do all the work on that too?
:-)
Best,
Raphie
P.S. I thought you handled that recent attack within the confines of this forum very well. My compliments.
P.P.S. Actually I do "make things up," and post them but those are called "ideas," and "hypotheses" not "facts."
As for the Mayan calendar, It's not as if I just make (/edit) such things up and post them, but I will grant you that it all depends on one's reference points, as always. In other words the issue of accuracy is RELATIVE.
==================================================
Robert D. Peden
MEngSc. BE. ( Melbourne University ) ARMTC TTTC. Formerly Principal Lecturer in the School of Sciences, Deakin University, Australia.
Foreword
The Mayan Ritual year of 260 days was successful for one major reason - after a cycle lasting 59 Ritual years, the tropical year and the Ritual year lock together in step. A period of 59 by 260 days equals a period of 42 tropical years, of 365.242 days.
Key excerpt...
The Long Count is a lunar calendar with an accuracy of 0.8 days in 100 years.
The Accounting year of 364 days might be considered a Venus Calendar with an accuracy of 0.3 days in 100 years.
http://spiderorchid.com/mesoamerica/mesoamerica.htm
==================================================
Care to tell me the accuracy of the Gregorian Calendar if one does not correct every four years by adding in an extra day?
Or do I have to do all the work on that too?
:-)
Best,
Raphie
P.S. I thought you handled that recent attack within the confines of this forum very well. My compliments.
P.P.S. Actually I do "make things up," and post them but those are called "ideas," and "hypotheses" not "facts."
QUOTE (RealityCheck+Jan 17 2008, 11:22 PM)
My post said "...axiomatic explorations INTO mathematics COMPLETENESS possibilities...".
Your post was full of dribble. You don't know any mathematics and this screams through in your posts. Do you agree that you wouldn't pass a high school exam in the subject?
Your post was full of dribble. You don't know any mathematics and this screams through in your posts. Do you agree that you wouldn't pass a high school exam in the subject?
QUOTE (Raphie Frank+Jan 17 2008, 11:24 PM)
... but I'm not exactly unwell read myself, truth be told ...
I beg to differ. I am willing to bet you can't answer a question from a high school maths exam. Would you like me to provide you with such a question?
I beg to differ. I am willing to bet you can't answer a question from a high school maths exam. Would you like me to provide you with such a question?
QUOTE (Euler+Jan 17 2008, 11:26 PM)
Your post was full of dribble. You don't know any mathematics and this screams through in your posts. Do you agree that you wouldn't pass a high school exam in the subject?
Like I already told you, we'll be sure to call you if ever we need an 'incomplete mathematics' proponent/expert to teach us how 'incomplete' mathematics should be 'done'.
Happy, bub?
But don't call us; we'll call you.
.
.
Like I already told you, we'll be sure to call you if ever we need an 'incomplete mathematics' proponent/expert to teach us how 'incomplete' mathematics should be 'done'.
Happy, bub?
But don't call us; we'll call you.
.
.
QUOTE (RealityCheck+Jan 17 2008, 11:31 PM)
We'll be sure to call you...
Did you miss this question:
Did you miss this question:
QUOTE (Euler+)
Do you agree that you wouldn't pass a high school exam in the subject?
Do tell.
Do tell.
QUOTE (Euler+Jan 17 2008, 11:33 PM)
Did you miss this question:
QUOTE (Euler+)
Do you agree that you wouldn't pass a high school exam in the subject?
Do tell.
What subject is that?....'incomplete' mathematics?
Not interested in 'incompleteness' of any sort, bub.
THIS thread is NOT concerned with your or anyone else's personal need to 'validate' yourself in your 'incomplete' understandings.
Is 'incomplete' comprehension forevermore a 'preferred' state for you?
Don't call us...*sigh*...we'll call you.
.
.
Do tell.
What subject is that?....'incomplete' mathematics?
Not interested in 'incompleteness' of any sort, bub.
THIS thread is NOT concerned with your or anyone else's personal need to 'validate' yourself in your 'incomplete' understandings.
Is 'incomplete' comprehension forevermore a 'preferred' state for you?
Don't call us...*sigh*...we'll call you.
.
.
So you're willing to admit that school children know and understand more mathematics than you?
QUOTE (Euler+Jan 17 2008, 11:40 PM)
So you're willing to admit that school children know and understand more mathematics than you?
Disinterested in 'incompleteness' grade of school children like yourself.
Come back when you grow up and want the 'complete' grown-up understanding.
.
Disinterested in 'incompleteness' grade of school children like yourself.
Come back when you grow up and want the 'complete' grown-up understanding.
.
QUOTE (RealityCheck+Jan 17 2008, 11:42 PM)
Disinterested in 'incompleteness' grade of school children like yourself.
So you're willing to admit that school children know and understand more mathematics than you?
So you're willing to admit that school children know and understand more mathematics than you?
QUOTE (Euler+Jan 17 2008, 11:43 PM)
So you're willing to admit that school children know and understand more mathematics than you?
Like I said: Come back when you grow up; and want the 'complete' grown-up understanding..
.
Like I said: Come back when you grow up; and want the 'complete' grown-up understanding..
.
CONTEXTUAL ANALOGY (#1)
----------------------------------
FACT:
In the United States, there are two primary factions on the issue of abortion:
Pro-Choice and Pro-Life.
QUESTION:
Are those who are Pro-Choice, then Anti-Life? Or those who are Pro-Life then Anti-Choice?
---------------------------------------------------------------------------------------
After all, it would be a "logical" inference, even if one dependent upon
the manner in which the debate has been FRAMED...
...BY THE OPPOSITION.
Bottom Line?
To come to any logical conclusion whatsoever on the issue based on any
framing "designed" to a priori discredit the opponent would not be
very logical at all.
It's all a question of which aspect of a given phenomena one
CHOOSES to focus on, a choice I might add, can only be made by
the living, most of whom I would suggest are very PRO-LIFE, at
least their own...
---------------------------------------------------------------------------------------
Best,
Raphie
P.S. I have a position on this specific issue, but assiduously avoided making mention of it in order that the LOGIC may not be lost to those on either side of the issue.
P.P.S. By way of a second example in terms of the "framing" of issues I could post rather substantive information regarding "stalking behaviors" and legal definitions of "harrassment" to this thread, but this would not be very constructive at the moment...
----------------------------------
FACT:
In the United States, there are two primary factions on the issue of abortion:
Pro-Choice and Pro-Life.
QUESTION:
Are those who are Pro-Choice, then Anti-Life? Or those who are Pro-Life then Anti-Choice?
---------------------------------------------------------------------------------------
After all, it would be a "logical" inference, even if one dependent upon
the manner in which the debate has been FRAMED...
...BY THE OPPOSITION.
Bottom Line?
To come to any logical conclusion whatsoever on the issue based on any
framing "designed" to a priori discredit the opponent would not be
very logical at all.
It's all a question of which aspect of a given phenomena one
CHOOSES to focus on, a choice I might add, can only be made by
the living, most of whom I would suggest are very PRO-LIFE, at
least their own...
---------------------------------------------------------------------------------------
Best,
Raphie
P.S. I have a position on this specific issue, but assiduously avoided making mention of it in order that the LOGIC may not be lost to those on either side of the issue.
P.P.S. By way of a second example in terms of the "framing" of issues I could post rather substantive information regarding "stalking behaviors" and legal definitions of "harrassment" to this thread, but this would not be very constructive at the moment...
ABOUT THE MAYAN CALENDAR
Hi hehehe,
How about you start learning about the Gaussian normal curve, it models reality very well actually.
Cheers
Darren
Thanks for that insight, mate. Cheers!
RC.
.
QUOTE (Raphie Frank+Jan 17 2008, 11:24 PM)
====
Robert D. Peden
MEngSc. BE. ( Melbourne University ) ARMTC TTTC. Formerly Principal Lecturer in the School of Sciences, Deakin University, Australia.
Foreword
The Mayan Ritual year of 260 days was successful for one major reason - after a cycle lasting 59 Ritual years, the tropical year and the Ritual year lock together in step. A period of 59 by 260 days equals a period of 42 tropical years, of 365.242 days.
Key excerpt...
The Long Count is a lunar calendar with an accuracy of 0.8 days in 100 years.
The Accounting year of 364 days might be considered a Venus Calendar with an accuracy of 0.3 days in 100 years.
http://spiderorchid.com/mesoamerica/mesoamerica.htm
To answer the question:
==========================================
What is the accuracy of the Gregorian Calendar if one does not correct every four years by adding in an extra day... assuming the accuracy of the calculation referred to above.
==========================================
Here is a ROUGH, not exact, approximation...
100 years/25 "leap days" /century = 25 days/century
100 years/.8 "leap days" /century = .8 days/century
25 / .8 = 31.25
One could make the case, then, that the Mayan calendar is 31.25 times more "accurate" than the Gregorian Calendar.
The average length of a month each calendar year?
365 / 12 = 30.4166667
One can not help but muse upon the concept, not unrelated to ideas brought up by Charles Seife in "Zero: Biography of a Dangerous Idea" of just how accurate our calendar might be were we to have a day ZERO each month, but did not because ZERO was considered "evil."
377 / 12 = 31.4166667
(377 / 12) - 31.25 = 0.166666667 = 1/6 day/century variance
For the record...
375/12 = 31.25
In other words, add in 5 days for every 6 months and we would be in alignment (roughly speaking, of course...) with the Mayan Long Count Calendar, but that, of course, wouldn't make much sense because we would then be out of alignment with the seasons here on earth.
In other words...
RELATIVELY speaking, the Gregorian Calendar makes far more sense in Western culture than the Mayan calendar because it is USEFUL to us. It gives us a "clock" by which to seed our crops and sow our harvests.
But... let us not forget the lessons of Copernicus: We are not the center of the Universe and our Western notions of "usefulness" do not necessarily apply to peoples the world over.
The Mayans, you can't help but wonder if they were not the "Italians" of their Day and Age in their part of the world, always dreaming and looking to the stars, poetically speaking, living life at the speed of phi and falling into sky...
===========================================
CONTEXTUAL PHOTO
photo "Falling Into Sky" by Giampaolo Macorig (Italy)
http://www.flickr.com/photos/gmacorig/270122318/
===========================================
Best,
Raphie
P.S. With regards to the following statement:
"The Accounting year of 364 days might be considered a Venus Calendar with an accuracy of 0.3 days in 100 years."
25 / .3 = 83.3333333 days/century = 100 - 16.666666...7
Robert D. Peden
MEngSc. BE. ( Melbourne University ) ARMTC TTTC. Formerly Principal Lecturer in the School of Sciences, Deakin University, Australia.
Foreword
The Mayan Ritual year of 260 days was successful for one major reason - after a cycle lasting 59 Ritual years, the tropical year and the Ritual year lock together in step. A period of 59 by 260 days equals a period of 42 tropical years, of 365.242 days.
Key excerpt...
The Long Count is a lunar calendar with an accuracy of 0.8 days in 100 years.
The Accounting year of 364 days might be considered a Venus Calendar with an accuracy of 0.3 days in 100 years.
http://spiderorchid.com/mesoamerica/mesoamerica.htm
To answer the question:
==========================================
What is the accuracy of the Gregorian Calendar if one does not correct every four years by adding in an extra day... assuming the accuracy of the calculation referred to above.
==========================================
Here is a ROUGH, not exact, approximation...
100 years/25 "leap days" /century = 25 days/century
100 years/.8 "leap days" /century = .8 days/century
25 / .8 = 31.25
One could make the case, then, that the Mayan calendar is 31.25 times more "accurate" than the Gregorian Calendar.
The average length of a month each calendar year?
365 / 12 = 30.4166667
One can not help but muse upon the concept, not unrelated to ideas brought up by Charles Seife in "Zero: Biography of a Dangerous Idea" of just how accurate our calendar might be were we to have a day ZERO each month, but did not because ZERO was considered "evil."
377 / 12 = 31.4166667
(377 / 12) - 31.25 = 0.166666667 = 1/6 day/century variance
For the record...
375/12 = 31.25
In other words, add in 5 days for every 6 months and we would be in alignment (roughly speaking, of course...) with the Mayan Long Count Calendar, but that, of course, wouldn't make much sense because we would then be out of alignment with the seasons here on earth.
In other words...
RELATIVELY speaking, the Gregorian Calendar makes far more sense in Western culture than the Mayan calendar because it is USEFUL to us. It gives us a "clock" by which to seed our crops and sow our harvests.
But... let us not forget the lessons of Copernicus: We are not the center of the Universe and our Western notions of "usefulness" do not necessarily apply to peoples the world over.
The Mayans, you can't help but wonder if they were not the "Italians" of their Day and Age in their part of the world, always dreaming and looking to the stars, poetically speaking, living life at the speed of phi and falling into sky...
===========================================
CONTEXTUAL PHOTO
photo "Falling Into Sky" by Giampaolo Macorig (Italy)
http://www.flickr.com/photos/gmacorig/270122318/
===========================================
Best,
Raphie
P.S. With regards to the following statement:
"The Accounting year of 364 days might be considered a Venus Calendar with an accuracy of 0.3 days in 100 years."
25 / .3 = 83.3333333 days/century = 100 - 16.666666...7
OFF-TOPIC...
I feel rather privileged, actually. It's as if I've been specifically targeted or something...
==========================
Alpha Posted: Today at 2:03 AM
Negative Feedback Massacre - Part 1
Cecil P Abstract Posted: Yesterday at 9:40 PM
Negative Neg generator test #2
Euler Posted: Yesterday at 7:51 PM
Negative Complete idiot.
N O M Posted: Yesterday at 9:04 AM
Negative Neg generator - test 1
==========================
Wowza. This is almost like COORDINATED...
I feel rather privileged, actually. It's as if I've been specifically targeted or something...
==========================
Alpha Posted: Today at 2:03 AM
Negative Feedback Massacre - Part 1
Cecil P Abstract Posted: Yesterday at 9:40 PM
Negative Neg generator test #2
Euler Posted: Yesterday at 7:51 PM
Negative Complete idiot.
N O M Posted: Yesterday at 9:04 AM
Negative Neg generator - test 1
==========================
Wowza. This is almost like COORDINATED...
QUOTE (Raphie Frank+Jan 18 2008, 02:08 AM)
OFF-TOPIC...
I feel rather privileged, actually. It's as if I've been specifically targeted or something...
==========================
Alpha Posted: Today at 2:03 AM
Negative Feedback Massacre - Part 1
Cecil P Abstract Posted: Yesterday at 9:40 PM
Negative Neg generator test #2
Euler Posted: Yesterday at 7:51 PM
Negative Complete idiot.
N O M Posted: Yesterday at 9:04 AM
Negative Neg generator - test 1
==========================
Wowza. This is almost like COORDINATED...
Hi Raphie Frank.
Yeah; silly, wasn't it?
That 'co-ordinated nonsense' was just the usual 'pack-playtime' noises emanating from the diffusionist kindergarten centre operating next door. hehehe.
PS: Catch y'all tomorrow!
..
.
I feel rather privileged, actually. It's as if I've been specifically targeted or something...
==========================
Alpha Posted: Today at 2:03 AM
Negative Feedback Massacre - Part 1
Cecil P Abstract Posted: Yesterday at 9:40 PM
Negative Neg generator test #2
Euler Posted: Yesterday at 7:51 PM
Negative Complete idiot.
N O M Posted: Yesterday at 9:04 AM
Negative Neg generator - test 1
==========================
Wowza. This is almost like COORDINATED...
Hi Raphie Frank.
Yeah; silly, wasn't it?
That 'co-ordinated nonsense' was just the usual 'pack-playtime' noises emanating from the diffusionist kindergarten centre operating next door. hehehe.
PS: Catch y'all tomorrow!
..
.
QUOTE (Raphie Frank+Jan 18 2008, 01:15 AM)
"The Accounting year of 364 days might be considered a Venus Calendar with an accuracy of 0.3 days in 100 years."
25 / .3 = 83.3333333 days/century = 100 - 16.666666...7
CONTEXTUAL/"TANTEXTUAL" LEARNING...
With regards to:
25 / .3 = 83.3333333 days/century
83.3333... = 1000/12
100 - 83.3333333 = 16.66666...7 = 50/3
A Google search for...
-------------------------
1.666666 physics
-------------------------
... as opposed to 16.66666, since most expressions in physics are of form n.x * 10^y yields the following on Page 1:
=========================================
Wave, Sound, and Music
http://universe-review.ca/R12-03-wave.htm
One of the most characteristic features of the quantum theory is the wave-particle duality, i.e., the ability of matter or light quanta to demonstrate the wave-like property of interference (such as standing wave), and yet to appear subsequently in the form of localizable particles, even after such interference has taken place. Atomic and molecular theory depends on the computation of probability wave. Elementary particle theory starts from a field equation. The concepts of standing wave and fourier superposition are fundamental to quantum theory. Therefore in addition to its application to natural phenomena, an understanding of wave is one of the pre-requisites for the studying of modern physics...
=========================================
It's actually a very interesting and informative web page with accessible mathematics. The following, in particular, captured my interest...
=========================================
Mathemetically, the displacement u of the wave in three dimensional space is expressed by the differential equation:
where x, y, z are the spatial coordinates, t is the time, and v is the propagation velocity of the wave (referring to a certain phase) in the medium; it is also known as the phase velocity. For wave motion in one dimension, e.g., along the x axis, the 2nd and 3rd terms in Eq.(4a) vanish; the solution for u at any point x and any time t is expressed by the sine function:
u = A sin(kx -wt)
where w = 2
v, k = 2/
Best,
Raphie
=========================================
=========================================
P.S. Tantextual = "Contextual Tangent"
P.P.S. From the above cited link, 1.66666.... corresponds with a major sixth in music.
Note : A
Syllable: La
Consonant Interval: Major sixth
Ratio: 5/3
Decimal: 1.666666
E-T Interval (n)/(¢): n = 9 / 900
E-T Scale, 2n/12: 1.681793
Difference/(in ¢): -0.015127 / -15.6
Table 01 depicts the consonant intervals (sometimes referred to as "harmonic tuning" or "Just Scale") in rational number with the corresponding decimal and the "equal temperament" (E-T) scale for comparison. The difference is shown in the last column...
For example, the difference of frequency in cents between minor third and the E-T interval (with n=3) is (see Table 01):
¢ = (1200/ln(2)) x ln(1.2/1.189207) = 15.6
or the minor third can be expressed in cents by: ¢ = (1200/ln(2)) x ln(1.2/1.0) = 315.6
http://universe-review.ca/R12-03-wave.htm
---------------------------------------------------------------
That difference in cents, it so happens: -0.015127, is the 20th note of the Lucas series 15,127*10^-6*-1, 15,127 being a number I mentioned the other day (but mistakenly referred to as the 22nd Fibonacci number):
PERFECT NUMBER / LUCAS CORRESPONDENCE
http://forum.physorg.com/index.php?showtop...ndpost&p=301248
Also related, a concept kindly brought to my attention by MeBigGuy:
TWELFTH ROOT OF TWO
http://en.wikipedia.org/wiki/Twelfth_root_of_two
25 / .3 = 83.3333333 days/century = 100 - 16.666666...7
CONTEXTUAL/"TANTEXTUAL" LEARNING...
With regards to:
25 / .3 = 83.3333333 days/century
83.3333... = 1000/12
100 - 83.3333333 = 16.66666...7 = 50/3
A Google search for...
-------------------------
1.666666 physics
-------------------------
... as opposed to 16.66666, since most expressions in physics are of form n.x * 10^y yields the following on Page 1:
=========================================
Wave, Sound, and Music
http://universe-review.ca/R12-03-wave.htm
One of the most characteristic features of the quantum theory is the wave-particle duality, i.e., the ability of matter or light quanta to demonstrate the wave-like property of interference (such as standing wave), and yet to appear subsequently in the form of localizable particles, even after such interference has taken place. Atomic and molecular theory depends on the computation of probability wave. Elementary particle theory starts from a field equation. The concepts of standing wave and fourier superposition are fundamental to quantum theory. Therefore in addition to its application to natural phenomena, an understanding of wave is one of the pre-requisites for the studying of modern physics...
=========================================
It's actually a very interesting and informative web page with accessible mathematics. The following, in particular, captured my interest...
=========================================
Mathemetically, the displacement u of the wave in three dimensional space is expressed by the differential equation:
where x, y, z are the spatial coordinates, t is the time, and v is the propagation velocity of the wave (referring to a certain phase) in the medium; it is also known as the phase velocity. For wave motion in one dimension, e.g., along the x axis, the 2nd and 3rd terms in Eq.(4a) vanish; the solution for u at any point x and any time t is expressed by the sine function:
u = A sin(kx -wt)
where w = 2
v, k = 2/Best,
Raphie
=========================================
=========================================
P.S. Tantextual = "Contextual Tangent"
P.P.S. From the above cited link, 1.66666.... corresponds with a major sixth in music.
Note : A
Syllable: La
Consonant Interval: Major sixth
Ratio: 5/3
Decimal: 1.666666
E-T Interval (n)/(¢): n = 9 / 900
E-T Scale, 2n/12: 1.681793
Difference/(in ¢): -0.015127 / -15.6
Table 01 depicts the consonant intervals (sometimes referred to as "harmonic tuning" or "Just Scale") in rational number with the corresponding decimal and the "equal temperament" (E-T) scale for comparison. The difference is shown in the last column...
For example, the difference of frequency in cents between minor third and the E-T interval (with n=3) is (see Table 01):
¢ = (1200/ln(2)) x ln(1.2/1.189207) = 15.6
or the minor third can be expressed in cents by: ¢ = (1200/ln(2)) x ln(1.2/1.0) = 315.6
http://universe-review.ca/R12-03-wave.htm
---------------------------------------------------------------
That difference in cents, it so happens: -0.015127, is the 20th note of the Lucas series 15,127*10^-6*-1, 15,127 being a number I mentioned the other day (but mistakenly referred to as the 22nd Fibonacci number):
PERFECT NUMBER / LUCAS CORRESPONDENCE
http://forum.physorg.com/index.php?showtop...ndpost&p=301248
Also related, a concept kindly brought to my attention by MeBigGuy:
TWELFTH ROOT OF TWO
http://en.wikipedia.org/wiki/Twelfth_root_of_two
QUOTE (RealityCheck+Jul 11 2007, 01:21 AM)
.
Hi folks!
Under the "Point Nine Recurring Equals One (or not)" topic discussions in the "Puzzling Questions" forum, I had spoken of 'giving' maths a more 'contextual' basis so as to make it MORE relevant, effective and robust for 'modeling reality'.
Hi hehehe,
How about you start learning about the Gaussian normal curve, it models reality very well actually.
Cheers
Darren
Hi folks!
Under the "Point Nine Recurring Equals One (or not)" topic discussions in the "Puzzling Questions" forum, I had spoken of 'giving' maths a more 'contextual' basis so as to make it MORE relevant, effective and robust for 'modeling reality'.
Hi hehehe,
How about you start learning about the Gaussian normal curve, it models reality very well actually.
Cheers
Darren
QUOTE (Darren+Jan 18 2008, 02:46 AM)
Hi hehehe,
How about you start learning about the Gaussian normal curve, it models reality very well actually.
Cheers
Darren
Thanks for that insight, mate. Cheers!
RC.
.
QUOTE (Raphie Frank+Jan 17 2008, 10:37 PM)
Wave, Sound, and Music
http://universe-review.ca/R12-03-wave.htm
http://universe-review.ca/R12-03-wave.htm
QUOTE (Raphie Frank+Jan 18 2008, 01:15 AM)
The average length of a month each calendar year?
365 / 12 = 30.4166667
One can not help but muse upon the concept, not unrelated to ideas brought up by Charles Seife in "Zero: Biography of a Dangerous Idea" of just how accurate our calendar might be were we to have a day ZERO each month, but did not because ZERO was considered "evil."
KOLO MATH PHYSICAL CONSTANT NUMBER FUN
Given that I have been toying with phi^30 and phi^31, I couldn't resist having a little number "fun" with "Kolo Math" and that 30.4166667 ratio. Purely number juggling here... but not a whole lot of variables were required to get a pretty close approximation on more or less the first try...
Let...
c' = speed of light * s/m
O'^y = phi^30.4166667 + phi^-30.4166667 = 2273565.12
v = Viswanath's Constant = 1.13198824
-----------------------------
Z = unknown
.1*c'/O'^y - 10*v = Z
Z = (.1*c*s/m/(phi^30.4166667) - 10*1.13198824 = 1.866124693...
A = (sqrt 3 + 2)/2 = cos 30 degrees + 2*sin 30 degrees = 1.8660254
Z/A = 1.00005321
A/Z = 0.99994679
Interesting to me, at least in part, if only because of previous formulas I have derived for the fine structure constant using Viswanath's constant and sqrt 3 + 1
2006 Co-Data Value for Alpha
@ = 0.0072973525680 ± 0.0000000000240
@^-1 = 137.03599910810831
@' = Exploratory Value for Alpha # 1
-------------------------------------
@'^-1 = (1 / ((.1 * (e^((i * phi)^2))) + ((1 + sqrt(3)) / (10^6)) + (7.030001 / (10^9)))) - (1.13198824 / (10^8)) - (1 / ((phi^2) * (10^10)))
= 137.035999108108367
MORE HERE:
http://forum.physorg.com/index.php?showtop...ndpost&p=297745
Best,
Raphie
P.S. The actual exponent required to "balance" phi to c ~
100*phi^30.9914054974 = c + 0.00270366669
365 / 12 = 30.4166667
One can not help but muse upon the concept, not unrelated to ideas brought up by Charles Seife in "Zero: Biography of a Dangerous Idea" of just how accurate our calendar might be were we to have a day ZERO each month, but did not because ZERO was considered "evil."
KOLO MATH PHYSICAL CONSTANT NUMBER FUN
Given that I have been toying with phi^30 and phi^31, I couldn't resist having a little number "fun" with "Kolo Math" and that 30.4166667 ratio. Purely number juggling here... but not a whole lot of variables were required to get a pretty close approximation on more or less the first try...
Let...
c' = speed of light * s/m
O'^y = phi^30.4166667 + phi^-30.4166667 = 2273565.12
v = Viswanath's Constant = 1.13198824
-----------------------------
Z = unknown
.1*c'/O'^y - 10*v = Z
Z = (.1*c*s/m/(phi^30.4166667) - 10*1.13198824 = 1.866124693...
A = (sqrt 3 + 2)/2 = cos 30 degrees + 2*sin 30 degrees = 1.8660254
Z/A = 1.00005321
A/Z = 0.99994679
Interesting to me, at least in part, if only because of previous formulas I have derived for the fine structure constant using Viswanath's constant and sqrt 3 + 1
2006 Co-Data Value for Alpha
@ = 0.0072973525680 ± 0.0000000000240
@^-1 = 137.03599910810831
@' = Exploratory Value for Alpha # 1
-------------------------------------
@'^-1 = (1 / ((.1 * (e^((i * phi)^2))) + ((1 + sqrt(3)) / (10^6)) + (7.030001 / (10^9)))) - (1.13198824 / (10^8)) - (1 / ((phi^2) * (10^10)))
= 137.035999108108367
MORE HERE:
http://forum.physorg.com/index.php?showtop...ndpost&p=297745
Best,
Raphie
P.S. The actual exponent required to "balance" phi to c ~
100*phi^30.9914054974 = c + 0.00270366669
QUOTE (dawn+Jan 17 2008, 08:10 PM)
Ivars,
If you stay with just Euclid (not non-Euclidean & GR) a different perspective using an a pentagon then a pentagram begins to take shape around it (tunnels one way, tower the other, moving in & out to infinity).
The is a mystery in this concept, each diagonal divides which ever diagonal it crosses into a Golden Ratio. I believe that Euclid defined it as (please check on this) This was a huge step just dealing with algebra.
Example:
1/x = x/(1-x)
hej dawn
It is like a star inside and outside pentagon( if You continue the edges until they meat) rotating by 72 degrees with each next step and dissappearing into infinity; See, every person has its star.
what is between those 72 degree rotations involving phi?
I wander if
1/x = x/(1-x)
1/x^2=1/(1-x)
can not be used to analyze some of the divergent series based on
1/(1-x) = 1+x+x^2+x^3 .............
So we can replace 1-x with 1/x^2 in case x=phi
so 1/(1-phi)= 1/phi^2 = 1+phi+pi^2+phi^3 + ..........
Since phi >1 this diverges. But since we are looking for where the star disappears into infinity, divergence should not be a problem, but a thing to look into.
Asin this divergent series we have phi^2, its natural to assume that 1/phi will have 2 series representation which will be positive and negative roots of 1/phi^2. Which may have the relation to either direction of rotation (while coming out from infinity = divergent place where the series starts.)
I have to look into Euler to see if there is a way to find these series for 1/phi, -1/phi from the series given above. He had a lot of formulas for dealing with series and continuous fractions.
I should also look if infinite tetration of phi h (phi) which is divergent- if it leads to any meaningful complex number.
Ivars
If you stay with just Euclid (not non-Euclidean & GR) a different perspective using an a pentagon then a pentagram begins to take shape around it (tunnels one way, tower the other, moving in & out to infinity).
The is a mystery in this concept, each diagonal divides which ever diagonal it crosses into a Golden Ratio. I believe that Euclid defined it as (please check on this) This was a huge step just dealing with algebra.
Example:
1/x = x/(1-x)
hej dawn
It is like a star inside and outside pentagon( if You continue the edges until they meat) rotating by 72 degrees with each next step and dissappearing into infinity; See, every person has its star.
what is between those 72 degree rotations involving phi?
I wander if
1/x = x/(1-x)
1/x^2=1/(1-x)
can not be used to analyze some of the divergent series based on
1/(1-x) = 1+x+x^2+x^3 .............
So we can replace 1-x with 1/x^2 in case x=phi
so 1/(1-phi)= 1/phi^2 = 1+phi+pi^2+phi^3 + ..........
Since phi >1 this diverges. But since we are looking for where the star disappears into infinity, divergence should not be a problem, but a thing to look into.
Asin this divergent series we have phi^2, its natural to assume that 1/phi will have 2 series representation which will be positive and negative roots of 1/phi^2. Which may have the relation to either direction of rotation (while coming out from infinity = divergent place where the series starts.)
I have to look into Euler to see if there is a way to find these series for 1/phi, -1/phi from the series given above. He had a lot of formulas for dealing with series and continuous fractions.
I should also look if infinite tetration of phi h (phi) which is divergent- if it leads to any meaningful complex number.
Ivars
Well, so far nothing special from tetration related to phi, but I found this:
Hello,
I tried to find h(z) = h((I/2)^(2/I)) = h( exp(pi)/exp(-I*2*ln2)
ln ( exp*pi/exp(-I*2*ln2)) = pi+ I*2*ln2
-ln(z) = - pi- I*2*ln2
so as W(-pi-I*2*ln2) = ln2 - I*(pi/2)
Than h(z) = (ln2-I*(pi/2))/ (-pi - i*2*ln2)
This can be braught to :
h(z) = 0.5*I ( i guess with plus sign, not sure)
now, since I/2 = sin (I*ln(phi)) than
h((i/2)^(2/i)) = sin(I*ln(phi))
so Arcsin(h(I/2^(2/I)) = I*ln(phi)
phi= -I*e^Arcsin(h(I/2)^(2/I))
so taking a self root of I/2 can be related to phi in this way.
I think it is possible to continue with I/3, I/4 etc in the same way.
is this well known, if there is no mistake?
Hello,
I tried to find h(z) = h((I/2)^(2/I)) = h( exp(pi)/exp(-I*2*ln2)
ln ( exp*pi/exp(-I*2*ln2)) = pi+ I*2*ln2
-ln(z) = - pi- I*2*ln2
so as W(-pi-I*2*ln2) = ln2 - I*(pi/2)
Than h(z) = (ln2-I*(pi/2))/ (-pi - i*2*ln2)
This can be braught to :
h(z) = 0.5*I ( i guess with plus sign, not sure)
now, since I/2 = sin (I*ln(phi)) than
h((i/2)^(2/i)) = sin(I*ln(phi))
so Arcsin(h(I/2^(2/I)) = I*ln(phi)
phi= -I*e^Arcsin(h(I/2)^(2/I))
so taking a self root of I/2 can be related to phi in this way.
I think it is possible to continue with I/3, I/4 etc in the same way.
is this well known, if there is no mistake?
Hello,
And this is the interpretation of previous finding:
so taking a self root of I/2 can be related to phi in this way.
It is of course just trivial transformations, but if we think about starting from i as one symbol close to infinity we can see that splitting it in 2 and than tetrating back leads to an imginary arc and imaginary angle from which in exponent and divided again by the same I leads to phi.
The exponent there makes thing difficult to visualize - in which dimension is it turned?
However, it is obvious that You can not get connection between i and phi without adding one more 2, so in that sense, phi means( as in old times ) that any division in 2 halves of an ideal line will lead to phi. So phi somehow appears with the first differentiation of smallest scale? Meaning that division in the smallest scale is harmonious, but as we backtetrate from it, and involve reals in the path, or, phi gets deformed and harmony is not perfect.
The star moves away from its target.
And this is the interpretation of previous finding:
so taking a self root of I/2 can be related to phi in this way.
It is of course just trivial transformations, but if we think about starting from i as one symbol close to infinity we can see that splitting it in 2 and than tetrating back leads to an imginary arc and imaginary angle from which in exponent and divided again by the same I leads to phi.
The exponent there makes thing difficult to visualize - in which dimension is it turned?
However, it is obvious that You can not get connection between i and phi without adding one more 2, so in that sense, phi means( as in old times ) that any division in 2 halves of an ideal line will lead to phi. So phi somehow appears with the first differentiation of smallest scale? Meaning that division in the smallest scale is harmonious, but as we backtetrate from it, and involve reals in the path, or, phi gets deformed and harmony is not perfect.
The star moves away from its target.
A few rather "trivial" identities, but ones that are good to know, thus perhaps not so trivial...
Let...
Phi = 1.61803399...
phi = 0.61803399...
===========================
2*cos (pi/5)
= 1.61803399
= Phi
sqrt 1.25
= sqrt 5/2
= 1.1803399...
= Phi - 1/2; phi + 1/2
sqrt .8
= 2/sqrt 5
= 1/1.1803399...
= 0.894427191...
= 1/(Phi - 1/2); 1/(phi + 1/2)
sqrt 3/2
= 0.866025404...
= 1/2 * Phi
2 / sqrt 3
= 1.15470054...
= 1/(1/2 * Phi)
= 2*phi
===========================
2 * (cos 30 degrees + sin 30 degrees)
2 * (cos 60 degrees + sin 60 degrees)
= 2.73205081...
= sqrt 3 + 1
2 * ((e^((i * pi) / 3)) + (e^((i * pi) / 6)))
= 2.73205081... + 2.73205081... i
= (sqrt 3 + 1) + (sqrt 3 + 1)*i
===========================
Best,
Raphie
Let...
Phi = 1.61803399...
phi = 0.61803399...
===========================
2*cos (pi/5)
= 1.61803399
= Phi
sqrt 1.25
= sqrt 5/2
= 1.1803399...
= Phi - 1/2; phi + 1/2
sqrt .8
= 2/sqrt 5
= 1/1.1803399...
= 0.894427191...
= 1/(Phi - 1/2); 1/(phi + 1/2)
sqrt 3/2
= 0.866025404...
= 1/2 * Phi
2 / sqrt 3
= 1.15470054...
= 1/(1/2 * Phi)
= 2*phi
===========================
2 * (cos 30 degrees + sin 30 degrees)
2 * (cos 60 degrees + sin 60 degrees)
= 2.73205081...
= sqrt 3 + 1
2 * ((e^((i * pi) / 3)) + (e^((i * pi) / 6)))
= 2.73205081... + 2.73205081... i
= (sqrt 3 + 1) + (sqrt 3 + 1)*i
===========================
Best,
Raphie
QUOTE (Ivars+Jan 18 2008, 11:36 AM)
However, it is obvious that You can not get connection between i and phi without adding one more 2, so in that sense, phi means( as in old times ) that any division in 2 halves of an ideal line will lead to phi.
"any division in 2 halves"
That, Ivars, is the clause of that statement I would emphasize.
Best,
Raphie
"any division in 2 halves"
That, Ivars, is the clause of that statement I would emphasize.
Best,
Raphie
A couple naming conventions I will personally adopt consequence of discussions upon this thread...
LOGICAL CIRCLE -- (courtesy Ivan)
IDEAL LINE -- (courtesy Ivars)
@ Ivan and Ivars
Please do feel free to expand upon those concepts both for me and for others who this way might pass through.
Best,
Raphie
LOGICAL CIRCLE -- (courtesy Ivan)
IDEAL LINE -- (courtesy Ivars)
@ Ivan and Ivars
Please do feel free to expand upon those concepts both for me and for others who this way might pass through.
Best,
Raphie
ABOUT E8
==================================
Image and Text from Centripetal Notion
http://centripetalnotion.com/2007/03/22/22:31:00/
==================================
E8
This is a 2-dimensional projection of E8, a 248-dimensional object seen here simplified into only 8-dimensions to help preserve sanity. Essentially, if I understand it correctly, it’s like a 2-D shadow of a 248-D sphere, an object so symmetrical you could theoretically rotate it in any direction in up to 248 dimensions and it still appear the same. Talk about a stick in the mud. It took 18 mathematicians four years to produce the calculation for this object, its formula weighing in at 60 gigabytes. The computation was announced at MIT by David Vogan this Monday, the 19th of March, 2007.
==================================
Text from American Institute of Mathematics
http://www.aimath.org/E8/
==================================
Mathematicians Map E8
Mathematicians have mapped the inner workings of one of the most complicated structures ever studied: the object known as the exceptional Lie group E8. This achievement is significant both as an advance in basic knowledge and because of the many connections between E8 and other areas, including string theory and geometry. The magnitude of the calculation is staggering: the answer, if written out in tiny print, would cover an area the size of Manhattan. Mathematicians are known for their solitary work style, but the assault on E8 is part of a large project bringing together 18 mathematicians from the U.S. and Europe for an intensive four-year collaboration.
"This is exciting," said Peter Sarnak, Eugene Higgins Professor of Mathematics at Princeton University (not affiliated with the project). "Understanding and classifying the representations of Lie Groups has been critical to understanding phenomena in many different areas of mathematics and science including algebra, geometry, number theory, Physics and Chemistry. This project will be valuable for future mathematicians and scientists."
==================================
Image and Text from Wikipedia
http://en.wikipedia.org/wiki/E8_(mathematics)
==================================
E8
In mathematics, E8 is the name given to a family of closely related structures. In particular, it is the name of some exceptional simple Lie algebras as well as that of the associated simple Lie groups. It is also the name given to the corresponding root system, root lattice, and Weyl/Coxeter group, and to some finite simple Chevalley groups. E8 was formulated between the years of 1888 and 1890 by Wilhelm Killing.
The designation E8 comes from Wilhelm Killing and Élie Cartan's classification of the complex simple Lie algebras, which fall into four infinite families labeled An, Bn, Cn, Dn, and five exceptional cases labeled E6, E7, E8, F4, and G2. The E8 algebra is the largest and most complicated of these exceptional cases, and is often the last case of various theorems to be proved.
RELATED BLOG POST:
==================================
Image by Film Gaffer Sean Sheridan; Text by Raphie Frank
Image URL: http://flickr.com/photos/srsheridan/1601524449/
==================================
Toward an EXCEPTIONAL Simple Theory Of Everything :: Celestial Chiaroscuro
excerpt
-----------
As such, in my view at least, the string theory community would do itself a service to embrace the possibility, not of the “miraculous” break through coming via the Standard Model alone, but via what Progressive Physicist David Bohm termed the implicate order (i.e. hidden or “enfolded”) that Lisi’s theory suggests.
In other words, it’s not this or that, but this and that because this is that. Not just the light and the dark — what artists might call the “positive and negative space” — but also the underlying order that threads them both together in celestial chiaroscuro.
MORE: http://raphie.wordpress.com/2007/11/24/tow...olemys-revenge/
--------------------------------------------------------------------------
RELATED THREAD:
An Exceptionally Simple Theory Of Everything?, a new paper by Garrett Lisi
http://forum.physorg.com/index.php?showtopic=19183
==========================================
All fields of the standard model and gravity are unified as an E8 principal bundle connection. A non-compact real form of the E8 Lie algebra has G2 and F4 subalgebras which break down to strong su(3), electroweak su(2) x u(1), gravitational so(3,1), the frame-Higgs, and three generations of fermions related by triality. The interactions and dynamics of these 1-form and Grassmann valued parts of an E8 superconnection are described by the curvature and action over a four dimensional base manifold.
(Submitted on 6 Nov 2007 to ArXiv)
Download Paper: http://arxiv.org/abs/0711.0770
Best,
Raphie
-- As proudly and completely "idiotically" yours as a Boston Red Sock
SEE RELATED FEEDBACK: http://forum.physorg.com/index.php?act=feedback&mid=17285
P.S. This post will be cross-posted to the thread:
An Exceptionally Simple Theory Of Everything?, a new paper by Garrett Lisi
http://forum.physorg.com/index.php?showtopic=19183
Please pardon the redundancy in advance.
==================================
Image and Text from Centripetal Notion
http://centripetalnotion.com/2007/03/22/22:31:00/
==================================
E8
This is a 2-dimensional projection of E8, a 248-dimensional object seen here simplified into only 8-dimensions to help preserve sanity. Essentially, if I understand it correctly, it’s like a 2-D shadow of a 248-D sphere, an object so symmetrical you could theoretically rotate it in any direction in up to 248 dimensions and it still appear the same. Talk about a stick in the mud. It took 18 mathematicians four years to produce the calculation for this object, its formula weighing in at 60 gigabytes. The computation was announced at MIT by David Vogan this Monday, the 19th of March, 2007.
==================================
Text from American Institute of Mathematics
http://www.aimath.org/E8/
==================================
Mathematicians Map E8
Mathematicians have mapped the inner workings of one of the most complicated structures ever studied: the object known as the exceptional Lie group E8. This achievement is significant both as an advance in basic knowledge and because of the many connections between E8 and other areas, including string theory and geometry. The magnitude of the calculation is staggering: the answer, if written out in tiny print, would cover an area the size of Manhattan. Mathematicians are known for their solitary work style, but the assault on E8 is part of a large project bringing together 18 mathematicians from the U.S. and Europe for an intensive four-year collaboration.
"This is exciting," said Peter Sarnak, Eugene Higgins Professor of Mathematics at Princeton University (not affiliated with the project). "Understanding and classifying the representations of Lie Groups has been critical to understanding phenomena in many different areas of mathematics and science including algebra, geometry, number theory, Physics and Chemistry. This project will be valuable for future mathematicians and scientists."
==================================
Image and Text from Wikipedia
http://en.wikipedia.org/wiki/E8_(mathematics)
==================================
E8
In mathematics, E8 is the name given to a family of closely related structures. In particular, it is the name of some exceptional simple Lie algebras as well as that of the associated simple Lie groups. It is also the name given to the corresponding root system, root lattice, and Weyl/Coxeter group, and to some finite simple Chevalley groups. E8 was formulated between the years of 1888 and 1890 by Wilhelm Killing.
The designation E8 comes from Wilhelm Killing and Élie Cartan's classification of the complex simple Lie algebras, which fall into four infinite families labeled An, Bn, Cn, Dn, and five exceptional cases labeled E6, E7, E8, F4, and G2. The E8 algebra is the largest and most complicated of these exceptional cases, and is often the last case of various theorems to be proved.
RELATED BLOG POST:
==================================
Image by Film Gaffer Sean Sheridan; Text by Raphie Frank
Image URL: http://flickr.com/photos/srsheridan/1601524449/
==================================
Toward an EXCEPTIONAL Simple Theory Of Everything :: Celestial Chiaroscuro
excerpt
-----------
As such, in my view at least, the string theory community would do itself a service to embrace the possibility, not of the “miraculous” break through coming via the Standard Model alone, but via what Progressive Physicist David Bohm termed the implicate order (i.e. hidden or “enfolded”) that Lisi’s theory suggests.
In other words, it’s not this or that, but this and that because this is that. Not just the light and the dark — what artists might call the “positive and negative space” — but also the underlying order that threads them both together in celestial chiaroscuro.
MORE: http://raphie.wordpress.com/2007/11/24/tow...olemys-revenge/
--------------------------------------------------------------------------
RELATED THREAD:
An Exceptionally Simple Theory Of Everything?, a new paper by Garrett Lisi
http://forum.physorg.com/index.php?showtopic=19183
==========================================
All fields of the standard model and gravity are unified as an E8 principal bundle connection. A non-compact real form of the E8 Lie algebra has G2 and F4 subalgebras which break down to strong su(3), electroweak su(2) x u(1), gravitational so(3,1), the frame-Higgs, and three generations of fermions related by triality. The interactions and dynamics of these 1-form and Grassmann valued parts of an E8 superconnection are described by the curvature and action over a four dimensional base manifold.
(Submitted on 6 Nov 2007 to ArXiv)
Download Paper: http://arxiv.org/abs/0711.0770
Best,
Raphie
-- As proudly and completely "idiotically" yours as a Boston Red Sock
SEE RELATED FEEDBACK: http://forum.physorg.com/index.php?act=feedback&mid=17285
P.S. This post will be cross-posted to the thread:
An Exceptionally Simple Theory Of Everything?, a new paper by Garrett Lisi
http://forum.physorg.com/index.php?showtopic=19183
Please pardon the redundancy in advance.
THE GAUSSIAN "NORMAL" DISTRIBUTION :: CONTEXTUAL POST
Hi hehehe,
How about you start learning about the Gaussian normal curve, it models reality very well actually.
Cheers
Darren
Richard (RIP) and Shane @ The Levee
Photo by Raphie Frank from...
Ghost Writers in the Sky
http://boojummy.blogs.friendster.com/snipe..._writers_i.html
@ Darren
Indeed the Gaussian Curve does "model reality" quite well, MOST OF THE TIME and the rules that guide the underlying order of the "system" we call SOCIETY wherever that society may be -- our rules and regulations and so on -- are in large part guided by that distribution.
But there's a little problem, one I even have a name for:
STATISTICAL DISCRIMINATION
Societies, most of them anyway, are structured around Utilitarian principles. In other words: The good of the many supercedes the good of the few, or is supposed to (which is rather debatable often in practice).
QUESTION:
What happens to those at the far end of the range" To those more than three standard deviations from the mean?
SEE: Are We Failing Our Geniuses?
http://www.time.com/time/magazine/article/...1653653,00.html
Time Magazine: August 16, 2007
I will tell you:
They get, quite simply, "screwed" and many, at least, opt out of the "system" because the system does not work for them. I would quite gladly put the minds that pass through the Verb Cafe here in Williamsburg, Brooklyn on any given day up against many of the leading academics in a public debate on issues of public policy and am confident that, at least on a level playing field, the intellectuals and artists I know would very easily hold their own, if not come out ahead... at least in the court of public opinion.
Moreover, however, and far more seriously from a societal standpoint, there are more and more out there for whom the current "rules" do not work because the way we are learning and living and working in the INFORMATION/DIGITAL/GLOBALIZED AGE is changing faster than our institutions are changing around us. This is not hypothesis, but pretty much near a societal "fact."
Not to be political, but to anecdotally underscore the point in non-partisan manner, the image of that woman telling G.W. Bush that she was working three jobs at some town meeting comes to mind. Dubya's reply? Something along the lines of:
"Now that's what I call an American."
Three jobs? Just to support a family? Is that what it means to be an American in the 21st Century? Good gosh. If so, I want no part of that. The notion is far too Upton Sinclair ("The Jungle") for me...
Another example? 8 years ago or so I was doing some temp work (at the WTC complex, it so happens...). The same jobs that paid me over $20/hour then now pay $10/hour.
My point?
Our Gaussian Distribution Curves, I would contend, are NOT modeling reality very well at the moment and we are rather in serious need of some RE-CALLIBRATION of the Gaussian distributions that guide our current social policies in order to account for the accelerated social evolution that accompanies increased flow of information and mobility in a globalized networked society. But in order to properly recallibrate, one needs FULL, not FOOL information, meaning one needs to know as many of the relevant variables involved.
One can not account for the uncounted (in Sociology they call such people "Hidden Populations"), whether those uncounted be votes or people and there are many, many, many uncounted out there. In my part of the world I know many of them by name, some of whom don't make it, such as Richard in that photo up there above.
The Gaussian Distribution failed him as it fails far too many.
Best,
Raphie
THE GAUSSIAN "NORMAL" DISTRIBUTION
aka "The Bell Curve"
via Wikipedia
http://en.wikipedia.org/wiki/Normal_distribution
The normal distribution, also called the Gaussian distribution, is an important family of continuous probability distributions, applicable in many fields. Each member of the family may be defined by two parameters, location and scale: the mean ("average", ?) and variance ("variability", ?2), respectively. The standard normal distribution is the normal distribution with a mean of zero and a variance of one (the green curves in the plots to the right). Carl Friedrich Gauss became associated with this set of distributions when he analyzed astronomical data using them [1], and defined the equation of its probability density function. It is often called the bell curve because the graph of its probability density resembles a bell.
The importance of the normal distribution as a model of quantitative phenomena in the natural and behavioral sciences is due to the central limit theorem. Many psychological measurements and physical phenomena (like noise) can be approximated well by the normal distribution. While the mechanisms underlying these phenomena are often unknown, the use of the normal model can be theoretically justified by assuming that many small, independent effects are additively contributing to each observation.
The normal distribution also arises in many areas of statistics. For example, the sampling distribution of the sample mean is approximately normal, even if the distribution of the population from which the sample is taken is not normal. In addition, the normal distribution maximizes information entropy among all distributions with known mean and variance, which makes it the natural choice of underlying distribution for data summarized in terms of sample mean and variance. The normal distribution is the most widely used family of distributions in statistics and many statistical tests are based on the assumption of normality. In probability theory, normal distributions arise as the limiting distributions of several continuous and discrete families of distributions.
QUOTE (Darren+Jan 18 2008, 02:46 AM)
Hi hehehe,
How about you start learning about the Gaussian normal curve, it models reality very well actually.
Cheers
Darren
Richard (RIP) and Shane @ The Levee
Photo by Raphie Frank from...
Ghost Writers in the Sky
http://boojummy.blogs.friendster.com/snipe..._writers_i.html
@ Darren
Indeed the Gaussian Curve does "model reality" quite well, MOST OF THE TIME and the rules that guide the underlying order of the "system" we call SOCIETY wherever that society may be -- our rules and regulations and so on -- are in large part guided by that distribution.
But there's a little problem, one I even have a name for:
STATISTICAL DISCRIMINATION
Societies, most of them anyway, are structured around Utilitarian principles. In other words: The good of the many supercedes the good of the few, or is supposed to (which is rather debatable often in practice).
QUESTION:
What happens to those at the far end of the range" To those more than three standard deviations from the mean?
SEE: Are We Failing Our Geniuses?
http://www.time.com/time/magazine/article/...1653653,00.html
Time Magazine: August 16, 2007
I will tell you:
They get, quite simply, "screwed" and many, at least, opt out of the "system" because the system does not work for them. I would quite gladly put the minds that pass through the Verb Cafe here in Williamsburg, Brooklyn on any given day up against many of the leading academics in a public debate on issues of public policy and am confident that, at least on a level playing field, the intellectuals and artists I know would very easily hold their own, if not come out ahead... at least in the court of public opinion.
Moreover, however, and far more seriously from a societal standpoint, there are more and more out there for whom the current "rules" do not work because the way we are learning and living and working in the INFORMATION/DIGITAL/GLOBALIZED AGE is changing faster than our institutions are changing around us. This is not hypothesis, but pretty much near a societal "fact."
Not to be political, but to anecdotally underscore the point in non-partisan manner, the image of that woman telling G.W. Bush that she was working three jobs at some town meeting comes to mind. Dubya's reply? Something along the lines of:
"Now that's what I call an American."
Three jobs? Just to support a family? Is that what it means to be an American in the 21st Century? Good gosh. If so, I want no part of that. The notion is far too Upton Sinclair ("The Jungle") for me...
Another example? 8 years ago or so I was doing some temp work (at the WTC complex, it so happens...). The same jobs that paid me over $20/hour then now pay $10/hour.
My point?
Our Gaussian Distribution Curves, I would contend, are NOT modeling reality very well at the moment and we are rather in serious need of some RE-CALLIBRATION of the Gaussian distributions that guide our current social policies in order to account for the accelerated social evolution that accompanies increased flow of information and mobility in a globalized networked society. But in order to properly recallibrate, one needs FULL, not FOOL information, meaning one needs to know as many of the relevant variables involved.
One can not account for the uncounted (in Sociology they call such people "Hidden Populations"), whether those uncounted be votes or people and there are many, many, many uncounted out there. In my part of the world I know many of them by name, some of whom don't make it, such as Richard in that photo up there above.
The Gaussian Distribution failed him as it fails far too many.
Best,
Raphie
THE GAUSSIAN "NORMAL" DISTRIBUTION
aka "The Bell Curve"
via Wikipedia
http://en.wikipedia.org/wiki/Normal_distribution
The normal distribution, also called the Gaussian distribution, is an important family of continuous probability distributions, applicable in many fields. Each member of the family may be defined by two parameters, location and scale: the mean ("average", ?) and variance ("variability", ?2), respectively. The standard normal distribution is the normal distribution with a mean of zero and a variance of one (the green curves in the plots to the right). Carl Friedrich Gauss became associated with this set of distributions when he analyzed astronomical data using them [1], and defined the equation of its probability density function. It is often called the bell curve because the graph of its probability density resembles a bell.
The importance of the normal distribution as a model of quantitative phenomena in the natural and behavioral sciences is due to the central limit theorem. Many psychological measurements and physical phenomena (like noise) can be approximated well by the normal distribution. While the mechanisms underlying these phenomena are often unknown, the use of the normal model can be theoretically justified by assuming that many small, independent effects are additively contributing to each observation.
The normal distribution also arises in many areas of statistics. For example, the sampling distribution of the sample mean is approximately normal, even if the distribution of the population from which the sample is taken is not normal. In addition, the normal distribution maximizes information entropy among all distributions with known mean and variance, which makes it the natural choice of underlying distribution for data summarized in terms of sample mean and variance. The normal distribution is the most widely used family of distributions in statistics and many statistical tests are based on the assumption of normality. In probability theory, normal distributions arise as the limiting distributions of several continuous and discrete families of distributions.
We spend our time looking for complicated questions to simple answers.
Once we find the complicated questions we have already forgoten the simple answer.
So then the complicated question becomes our simple answer.
There are problems with maths that suggest logic as a whole is flawed. Idk how many "scientists" are ready to deal with this fact.
Once we find the complicated questions we have already forgoten the simple answer.
So then the complicated question becomes our simple answer.
There are problems with maths that suggest logic as a whole is flawed. Idk how many "scientists" are ready to deal with this fact.
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