I started to read Cantors "Contributions to the founding of the theory of transfinite numbers" . It is rather heavy, I hope I have understood correctly that his "aggregates" are todays "sets".
Anyway, after first diagonal reading one idea is clear:
Cardinals (including transfinite) are numbers that can be applied to sets not taking into account any ordering that might be imposed on set in broadest sense;
Ordinals (including transfinite) are numbers that are related to set taking into account simple ( but in principle any) ordering.
Now what is interesting, is that in Ordinal arithmetic neither summation , nor multiplication is commutative, while for triples of Ordinals associative property in summation holds. etc.
What that means is that the result of operations performed with ordinals DEPENDS on the order ( or path ) how they are performed.
Without further explanations, it is quite obvious to me, that time, being ordered set
(see e.g Time Calculus) must have the same property ( as long as we consider domains where time is infinitely faster (e.g. speed is w in Cantor notation) than our discrete time- results depend on path.
So , to summarize, in general principle of least action in physics must be derivable from the fact that Time is an ordered set. There has to exist certain order of operations in Time which is preferred by Nature to all others, and this order has to be possible to find from Cantors approach to numbers plus understanding that the physical finite time we measure is not the only time has to be accounted for.
Since all classical physics can be derived from not more than second derivative of time, for principle of least action, only 2 scales of time are important .
That is a starting point, just to envision the solution to why principle of least action works.
The triples mentioned above may help to explain why, whatever path is taken, results are always projected in 3D mathematical space ( this I am not so sure of).
It's like StevenA posting. Only even more ignorant! 
Dear Ivars,
I did a quick search for "time is an ordered set" and came across the following...
A Spatio-Temporal Extended Event Language for Tracking Epi-
demic Spread from Outbreak Reports
http://ftp.informatik.rwth-aachen.de/Publi...102/chaudet.pdf
by Hervé Chaudet
Faculté de Médecine de Marseille, Laboratoire d’informatique médicale (herve.chaudet@medecine.univ-mrs.fr)
I only skimmed it, but here are a couple excerpts you might find interesting...
excerpt 1
-----------------
Time stamps. Time is a concept that cannot be easily
represented,16 and several suggestions have been
proposed for natural language processing.17,18,19 Our
aim is to represent temporal entities in a convenient
manner for inducing the times and ordering of events.
In our ontology, time is an ordered set (T,A) where
elements of T are Shahar’s time stamps,20 which are
issued from time expressions encountered in the
narratives and can be placed on a time axis (e.g. “16
September 2002”). Formally, this choice allows using
event name for time specification, as proposed in the
New Event Calculus...
excerpt 2
-----------------
Spatiotemporal relations. Following Hazarika and
Cohn’s mereotopological theory of space-time,24,25
spatiotemporal relations between objects can be rep-
resented with binary relations based on the notion of
connection. Two entities are spatially connected (sp-
connected) if they share at least a spatial point,
though not necessarily simultaneously (e.g. Zaïre that
has been renamed as Congo Démocratique). Tempo-
ral connection (t-connected) of two time intervals is
defined by the existence of at least a common tempo-
ral point, though not necessarily at the same place.
Finally two entities are spatiotemporally connected
(st-connected) if the closures of these entities share at
least a spatiotemporal point. This ?-connected(x,y)
primitive, where ? ? {st, sp, t}, allows defining a set
of 10 others mereotopological relations that consti-
tutes the basis of a qualitative representation lan-
guage (Table 2).
=================================
At the very least, someone out there is conducting scientific research related to at least a part of what you are thinking about.
Here are some more papers by Chaudet:
http://lib.bioinfo.pl/auth:Chaudet,H
And here is a link about "Event Calculus" that may perhaps stir some thought on your end.
http://en.wikipedia.org/wiki/Event_calculus
Best,
Raphie
I did a quick search for "time is an ordered set" and came across the following...
A Spatio-Temporal Extended Event Language for Tracking Epi-
demic Spread from Outbreak Reports
http://ftp.informatik.rwth-aachen.de/Publi...102/chaudet.pdf
by Hervé Chaudet
Faculté de Médecine de Marseille, Laboratoire d’informatique médicale (herve.chaudet@medecine.univ-mrs.fr)
I only skimmed it, but here are a couple excerpts you might find interesting...
excerpt 1
-----------------
Time stamps. Time is a concept that cannot be easily
represented,16 and several suggestions have been
proposed for natural language processing.17,18,19 Our
aim is to represent temporal entities in a convenient
manner for inducing the times and ordering of events.
In our ontology, time is an ordered set (T,A) where
elements of T are Shahar’s time stamps,20 which are
issued from time expressions encountered in the
narratives and can be placed on a time axis (e.g. “16
September 2002”). Formally, this choice allows using
event name for time specification, as proposed in the
New Event Calculus...
excerpt 2
-----------------
Spatiotemporal relations. Following Hazarika and
Cohn’s mereotopological theory of space-time,24,25
spatiotemporal relations between objects can be rep-
resented with binary relations based on the notion of
connection. Two entities are spatially connected (sp-
connected) if they share at least a spatial point,
though not necessarily simultaneously (e.g. Zaïre that
has been renamed as Congo Démocratique). Tempo-
ral connection (t-connected) of two time intervals is
defined by the existence of at least a common tempo-
ral point, though not necessarily at the same place.
Finally two entities are spatiotemporally connected
(st-connected) if the closures of these entities share at
least a spatiotemporal point. This ?-connected(x,y)
primitive, where ? ? {st, sp, t}, allows defining a set
of 10 others mereotopological relations that consti-
tutes the basis of a qualitative representation lan-
guage (Table 2).
=================================
At the very least, someone out there is conducting scientific research related to at least a part of what you are thinking about.
Here are some more papers by Chaudet:
http://lib.bioinfo.pl/auth:Chaudet,H
And here is a link about "Event Calculus" that may perhaps stir some thought on your end.
http://en.wikipedia.org/wiki/Event_calculus
Best,
Raphie
QUOTE (Ivars+May 18 2008, 02:06 PM)
Anyway, after first diagonal reading one idea is clear:
Cardinals (including transfinite) are numbers that can be applied to sets not taking into account any ordering that might be imposed on set in broadest sense;
Ordinals (including transfinite) are numbers that are related to set taking into account simple ( but in principle any) ordering.
Now what is interesting, is that in Ordinal arithmetic neither summation , nor multiplication is commutative, while for triples of Ordinals associative property in summation holds. etc.
What that means is that the result of operations performed with ordinals DEPENDS on the order ( or path ) how they are performed.
Without further explanations, it is quite obvious to me, that time, being ordered set (see e.g Time Calculus) must have the same property ( as long as we consider domains where time is infinitely faster (e.g. speed is w in Cantor notation) than our discrete time- results depend on path.
So , to summarize, in general principle of least action in physics must be derivable from the fact that Time is an ordered set. There has to exist certain order of operations in Time which is preferred by Nature to all others, and this order has to be possible to find from Cantors approach to numbers plus understanding that the physical finite time we measure is not the only time has to be accounted for.
But if
Does that mean then that there is still the definition of "any ordering" to be disposed of?
"Any ordering" simply doesn't fly with me, it's methodologically quite fuzzy. If distribution is "normal" in such randomness, then that normalcy itself is addressable as a true representation of a set of infinitely "random" and infinitely "disorganized" infinite numbers.
Even if you derive your "randomness" from a radioactive tick, even then that "randomness" is addressable only as a representative of its source, that is, the radioactive material.
(This gets increasingly "Foundation" and Asimovish. I don't quite think I can explain my thoughts on it!)
You don't address your thoughts to me, but to specific actions that I have taken, or words I have said, or actions that came from me. "You son of a b**ch" doesn't address me, it addresses particular action, verb, or state that has belonged in my past, and that you don't approve of.
I am not addressable, my history is.
I also address your addressing as your state of mind at a particular moment, the moment you address me, so that I have no access to the problem itself that you are addressing but instead address myself to your thought.
So that if there is a "method" and it produces true "randomness", then that "randomness" that is produced is a measure of a subset of all things random. The method itself is a series of instructions in an infinite series of instructions. But if by action or instruction you already addressed the randomness that you are using to prove something about randomness, then if you have had access to *true* randomness through said method, then you can't possibly have said something about all randomness, because the method says more about itself than about all randomness. The method for randomness collapses into a not-so-random series of instructions, therefore into an integer -philosophically speaking, of course. Now a subset of all-randomness that addresses a subset of all-randomness is left looking like an integer that addresses its multiples..
I knew I wasn't going to be able to develop it but it was worth a try: there was something wrong with Cantor's initial assumptions and I have tried for years to rationalize what it is...
If you have a **method** to produce an infinite series of random numbers in order to prove that there exists something beyond and above them, you have not expanded infinitely -or added an extension to- the universe. You just added a single bit to the known universe. A single bit of empty space.
That single bit of empty space comes from the next coordinate of the prime graph being the previous diagonal plus the bit zero at the end. Reviewing:
...>primordial start at nothing, second coordinate is a series of plain 1's
...l..>the third diagonal is 1, 0
...l..l..>the fourth diagonal is 1,1,0
...l././...>the fifth diagonal is 1,0,1,0
../././..//the sixth diagonal is 1,1,1,1,0 ... ... ...and so on...
.0000000000...primordial start at "nothing at all times"
.1111111111...second coordinate is a series of plain 1's, a "something through time"
.1010101010...the third coordinate is 1, 0
.1101101101...the fourth coordinate is 1,1,0
.1010101010...the fifth coordinate is 1,0,1,0
.1111011110...the sixth coordinate is 1,1,1,1,0 ... ... ... and so on...
You asked in another thread about what "energy" is supposed to be, and according to this "logic" (even though you can arrive at the same conclusion from a number of different directions) "energy" is the plain release of a space that has no owner. That would be why a dynamo rotates: because the space becomes available. According to another logic that is reducible to this one through a series of tortuous thought connections, the "energy" is the "carry bit" of arithmetic, and through an even more crooked series of connections, "energy" would be a little circle. So "energy" is not "mass" as much as it is the rearranging of mass so that it moves forward by a single bit. By this reasoning, mass could increase forever as it approaches the speed of light and still it would simultaneously have the exact same value as always because the increase only happens through the "time is an ordered set" aspect. It's time's relationship to matter that changes.
Does that mean then that there is still the definition of "any ordering" to be disposed of?
"Any ordering" simply doesn't fly with me, it's methodologically quite fuzzy. If distribution is "normal" in such randomness, then that normalcy itself is addressable as a true representation of a set of infinitely "random" and infinitely "disorganized" infinite numbers.
Even if you derive your "randomness" from a radioactive tick, even then that "randomness" is addressable only as a representative of its source, that is, the radioactive material.
(This gets increasingly "Foundation" and Asimovish. I don't quite think I can explain my thoughts on it!)
You don't address your thoughts to me, but to specific actions that I have taken, or words I have said, or actions that came from me. "You son of a b**ch" doesn't address me, it addresses particular action, verb, or state that has belonged in my past, and that you don't approve of.
I am not addressable, my history is.
I also address your addressing as your state of mind at a particular moment, the moment you address me, so that I have no access to the problem itself that you are addressing but instead address myself to your thought.
So that if there is a "method" and it produces true "randomness", then that "randomness" that is produced is a measure of a subset of all things random. The method itself is a series of instructions in an infinite series of instructions. But if by action or instruction you already addressed the randomness that you are using to prove something about randomness, then if you have had access to *true* randomness through said method, then you can't possibly have said something about all randomness, because the method says more about itself than about all randomness. The method for randomness collapses into a not-so-random series of instructions, therefore into an integer -philosophically speaking, of course. Now a subset of all-randomness that addresses a subset of all-randomness is left looking like an integer that addresses its multiples..
I knew I wasn't going to be able to develop it but it was worth a try: there was something wrong with Cantor's initial assumptions and I have tried for years to rationalize what it is...
If you have a **method** to produce an infinite series of random numbers in order to prove that there exists something beyond and above them, you have not expanded infinitely -or added an extension to- the universe. You just added a single bit to the known universe. A single bit of empty space.
That single bit of empty space comes from the next coordinate of the prime graph being the previous diagonal plus the bit zero at the end. Reviewing:
...>primordial start at nothing, second coordinate is a series of plain 1's
...l..>the third diagonal is 1, 0
...l..l..>the fourth diagonal is 1,1,0
...l././...>the fifth diagonal is 1,0,1,0
../././..//the sixth diagonal is 1,1,1,1,0 ... ... ...and so on...
.0000000000...primordial start at "nothing at all times"
.1111111111...second coordinate is a series of plain 1's, a "something through time"
.1010101010...the third coordinate is 1, 0
.1101101101...the fourth coordinate is 1,1,0
.1010101010...the fifth coordinate is 1,0,1,0
.1111011110...the sixth coordinate is 1,1,1,1,0 ... ... ... and so on...
You asked in another thread about what "energy" is supposed to be, and according to this "logic" (even though you can arrive at the same conclusion from a number of different directions) "energy" is the plain release of a space that has no owner. That would be why a dynamo rotates: because the space becomes available. According to another logic that is reducible to this one through a series of tortuous thought connections, the "energy" is the "carry bit" of arithmetic, and through an even more crooked series of connections, "energy" would be a little circle. So "energy" is not "mass" as much as it is the rearranging of mass so that it moves forward by a single bit. By this reasoning, mass could increase forever as it approaches the speed of light and still it would simultaneously have the exact same value as always because the increase only happens through the "time is an ordered set" aspect. It's time's relationship to matter that changes.
The triples mentioned above may help to explain why, whatever path is taken, results are always projected in 3D mathematical space ( this I am not so sure of).
"Results are always projected in 3D" (though I am equally not so sure of either) because the manipulation of 2d "mass/energy" (where both "d"s represents a dimension of 3 sub-dimensions each) releases space that belongs to neither one of the dimensions you were dealing with. The epidemiological research that Raphie linked seems to acknowledge as much though it doesn't explicitly recognize it, but unfortunately I didn't understand much of the work itself.
"energy" is the plain release of a space that has no owner.
hej IAM
Happy to hear from You again. Yes, I have finally reached sets and philosophy because I want to find out how COMPLETELY random release of infinitesimal space dimension is possible. Out of potential space via interaction with imaginary time.
We can always imagine/find randomness of various degrees, sub normal distribution in space relaeases as next infinitesimal dimension is released in some relation to the state of all previous or other releases, but I am looking for origin, for totally random release.
Your idea about energy is EXCELLENT and clear. I think that quotation above deserves to be cut in stone, You know
Raphie, Thanks for links. I for sure want to understand Cantor etc. to see where we may be able to extend the theory to the last step- pure chaos, pure energy, totally disconnected chaotic space dimensionalites getting available at will Normally distributed in their appearance ( or perhaps, not normally? have to think- normal distribution ) . It is just one step that is missing. And we know we have to be looking at imaginary unit, 0, pi and e. So its getting warm.
Ivan- genial- now I understand more of what you have been saying earlier. Simple sentence like this!
Cardinals (including transfinite) are numbers that can be applied to sets not taking into account any ordering that might be imposed on set in broadest sense;
Ordinals (including transfinite) are numbers that are related to set taking into account simple ( but in principle any) ordering.
Now what is interesting, is that in Ordinal arithmetic neither summation , nor multiplication is commutative, while for triples of Ordinals associative property in summation holds. etc.
What that means is that the result of operations performed with ordinals DEPENDS on the order ( or path ) how they are performed.
Without further explanations, it is quite obvious to me, that time, being ordered set (see e.g Time Calculus) must have the same property ( as long as we consider domains where time is infinitely faster (e.g. speed is w in Cantor notation) than our discrete time- results depend on path.
So , to summarize, in general principle of least action in physics must be derivable from the fact that Time is an ordered set. There has to exist certain order of operations in Time which is preferred by Nature to all others, and this order has to be possible to find from Cantors approach to numbers plus understanding that the physical finite time we measure is not the only time has to be accounted for.
But if
QUOTE
"Cardinals (including transfinite) are numbers that can be applied to sets not taking into account any ordering that might be imposed on set in broadest sense"
Does that mean then that there is still the definition of "any ordering" to be disposed of?
"Any ordering" simply doesn't fly with me, it's methodologically quite fuzzy. If distribution is "normal" in such randomness, then that normalcy itself is addressable as a true representation of a set of infinitely "random" and infinitely "disorganized" infinite numbers.
Even if you derive your "randomness" from a radioactive tick, even then that "randomness" is addressable only as a representative of its source, that is, the radioactive material.
(This gets increasingly "Foundation" and Asimovish. I don't quite think I can explain my thoughts on it!)
You don't address your thoughts to me, but to specific actions that I have taken, or words I have said, or actions that came from me. "You son of a b**ch" doesn't address me, it addresses particular action, verb, or state that has belonged in my past, and that you don't approve of.
I am not addressable, my history is.
I also address your addressing as your state of mind at a particular moment, the moment you address me, so that I have no access to the problem itself that you are addressing but instead address myself to your thought.
So that if there is a "method" and it produces true "randomness", then that "randomness" that is produced is a measure of a subset of all things random. The method itself is a series of instructions in an infinite series of instructions. But if by action or instruction you already addressed the randomness that you are using to prove something about randomness, then if you have had access to *true* randomness through said method, then you can't possibly have said something about all randomness, because the method says more about itself than about all randomness. The method for randomness collapses into a not-so-random series of instructions, therefore into an integer -philosophically speaking, of course. Now a subset of all-randomness that addresses a subset of all-randomness is left looking like an integer that addresses its multiples..
I knew I wasn't going to be able to develop it but it was worth a try: there was something wrong with Cantor's initial assumptions and I have tried for years to rationalize what it is...
If you have a **method** to produce an infinite series of random numbers in order to prove that there exists something beyond and above them, you have not expanded infinitely -or added an extension to- the universe. You just added a single bit to the known universe. A single bit of empty space.
That single bit of empty space comes from the next coordinate of the prime graph being the previous diagonal plus the bit zero at the end. Reviewing:
...>primordial start at nothing, second coordinate is a series of plain 1's
...l..>the third diagonal is 1, 0
...l..l..>the fourth diagonal is 1,1,0
...l././...>the fifth diagonal is 1,0,1,0
../././..//the sixth diagonal is 1,1,1,1,0 ... ... ...and so on...
.0000000000...primordial start at "nothing at all times"
.1111111111...second coordinate is a series of plain 1's, a "something through time"
.1010101010...the third coordinate is 1, 0
.1101101101...the fourth coordinate is 1,1,0
.1010101010...the fifth coordinate is 1,0,1,0
.1111011110...the sixth coordinate is 1,1,1,1,0 ... ... ... and so on...
You asked in another thread about what "energy" is supposed to be, and according to this "logic" (even though you can arrive at the same conclusion from a number of different directions) "energy" is the plain release of a space that has no owner. That would be why a dynamo rotates: because the space becomes available. According to another logic that is reducible to this one through a series of tortuous thought connections, the "energy" is the "carry bit" of arithmetic, and through an even more crooked series of connections, "energy" would be a little circle. So "energy" is not "mass" as much as it is the rearranging of mass so that it moves forward by a single bit. By this reasoning, mass could increase forever as it approaches the speed of light and still it would simultaneously have the exact same value as always because the increase only happens through the "time is an ordered set" aspect. It's time's relationship to matter that changes.
QUOTE (->
| QUOTE |
| "Cardinals (including transfinite) are numbers that can be applied to sets not taking into account any ordering that might be imposed on set in broadest sense" |
Does that mean then that there is still the definition of "any ordering" to be disposed of?
"Any ordering" simply doesn't fly with me, it's methodologically quite fuzzy. If distribution is "normal" in such randomness, then that normalcy itself is addressable as a true representation of a set of infinitely "random" and infinitely "disorganized" infinite numbers.
Even if you derive your "randomness" from a radioactive tick, even then that "randomness" is addressable only as a representative of its source, that is, the radioactive material.
(This gets increasingly "Foundation" and Asimovish. I don't quite think I can explain my thoughts on it!)
You don't address your thoughts to me, but to specific actions that I have taken, or words I have said, or actions that came from me. "You son of a b**ch" doesn't address me, it addresses particular action, verb, or state that has belonged in my past, and that you don't approve of.
I am not addressable, my history is.
I also address your addressing as your state of mind at a particular moment, the moment you address me, so that I have no access to the problem itself that you are addressing but instead address myself to your thought.
So that if there is a "method" and it produces true "randomness", then that "randomness" that is produced is a measure of a subset of all things random. The method itself is a series of instructions in an infinite series of instructions. But if by action or instruction you already addressed the randomness that you are using to prove something about randomness, then if you have had access to *true* randomness through said method, then you can't possibly have said something about all randomness, because the method says more about itself than about all randomness. The method for randomness collapses into a not-so-random series of instructions, therefore into an integer -philosophically speaking, of course. Now a subset of all-randomness that addresses a subset of all-randomness is left looking like an integer that addresses its multiples..
I knew I wasn't going to be able to develop it but it was worth a try: there was something wrong with Cantor's initial assumptions and I have tried for years to rationalize what it is...
If you have a **method** to produce an infinite series of random numbers in order to prove that there exists something beyond and above them, you have not expanded infinitely -or added an extension to- the universe. You just added a single bit to the known universe. A single bit of empty space.
That single bit of empty space comes from the next coordinate of the prime graph being the previous diagonal plus the bit zero at the end. Reviewing:
...>primordial start at nothing, second coordinate is a series of plain 1's
...l..>the third diagonal is 1, 0
...l..l..>the fourth diagonal is 1,1,0
...l././...>the fifth diagonal is 1,0,1,0
../././..//the sixth diagonal is 1,1,1,1,0 ... ... ...and so on...
.0000000000...primordial start at "nothing at all times"
.1111111111...second coordinate is a series of plain 1's, a "something through time"
.1010101010...the third coordinate is 1, 0
.1101101101...the fourth coordinate is 1,1,0
.1010101010...the fifth coordinate is 1,0,1,0
.1111011110...the sixth coordinate is 1,1,1,1,0 ... ... ... and so on...
You asked in another thread about what "energy" is supposed to be, and according to this "logic" (even though you can arrive at the same conclusion from a number of different directions) "energy" is the plain release of a space that has no owner. That would be why a dynamo rotates: because the space becomes available. According to another logic that is reducible to this one through a series of tortuous thought connections, the "energy" is the "carry bit" of arithmetic, and through an even more crooked series of connections, "energy" would be a little circle. So "energy" is not "mass" as much as it is the rearranging of mass so that it moves forward by a single bit. By this reasoning, mass could increase forever as it approaches the speed of light and still it would simultaneously have the exact same value as always because the increase only happens through the "time is an ordered set" aspect. It's time's relationship to matter that changes.
The triples mentioned above may help to explain why, whatever path is taken, results are always projected in 3D mathematical space ( this I am not so sure of).
"Results are always projected in 3D" (though I am equally not so sure of either) because the manipulation of 2d "mass/energy" (where both "d"s represents a dimension of 3 sub-dimensions each) releases space that belongs to neither one of the dimensions you were dealing with. The epidemiological research that Raphie linked seems to acknowledge as much though it doesn't explicitly recognize it, but unfortunately I didn't understand much of the work itself.
QUOTE (Yma Sumac+)
like StevenA posting. Only even more ignorant!
No, that would be me. But let me guess: your students ganged up on you and you got a wedgie and bloody nose again? What did your daddy say?
NO. I am NOT talking about physics. This is philosophy, get it?
No, that would be me. But let me guess: your students ganged up on you and you got a wedgie and bloody nose again? What did your daddy say?
NO. I am NOT talking about physics. This is philosophy, get it?
QUOTE (IAMoraes+May 19 2008, 04:33 AM)
"energy" is the plain release of a space that has no owner.
hej IAM
Happy to hear from You again. Yes, I have finally reached sets and philosophy because I want to find out how COMPLETELY random release of infinitesimal space dimension is possible. Out of potential space via interaction with imaginary time.
We can always imagine/find randomness of various degrees, sub normal distribution in space relaeases as next infinitesimal dimension is released in some relation to the state of all previous or other releases, but I am looking for origin, for totally random release.
Your idea about energy is EXCELLENT and clear. I think that quotation above deserves to be cut in stone, You know
Raphie, Thanks for links. I for sure want to understand Cantor etc. to see where we may be able to extend the theory to the last step- pure chaos, pure energy, totally disconnected chaotic space dimensionalites getting available at will Normally distributed in their appearance ( or perhaps, not normally? have to think- normal distribution ) . It is just one step that is missing. And we know we have to be looking at imaginary unit, 0, pi and e. So its getting warm.
Ivan- genial- now I understand more of what you have been saying earlier. Simple sentence like this!
In this formulation, classical principle of least action becomes a way how nature chooses the the release of infinitesimal space dimensions based of previously released ( or not BASED on previous releases in totally chaotic case, origin case).
Interestingly, in space where only chaotic releases of space (
) are present, Newtons first law does not hold since nothing can move in straight line not even a single step as next release of infinitely small space dimension might happen where ever- there is no straight line in such space.
So gravitation in limit to produce 1/r^2 dependence has to be based on totally chaotic releases, having normal distribution ( As Steven A has notices earlier) while quantum uncertainty arises from bound , reduced distributions, having variance 1/sigma and leading to 1/r gravitation law in small scales .
Interestingly how this leads to philosophical notion of space as an extension of bodies. While it not be 100% as philosophers envisioned it, basically, it is true notion.
Foggy in formulation, but clear in direction.
Interestingly, in space where only chaotic releases of space (
) are present, Newtons first law does not hold since nothing can move in straight line not even a single step as next release of infinitely small space dimension might happen where ever- there is no straight line in such space. So gravitation in limit to produce 1/r^2 dependence has to be based on totally chaotic releases, having normal distribution ( As Steven A has notices earlier) while quantum uncertainty arises from bound , reduced distributions, having variance 1/sigma and leading to 1/r gravitation law in small scales .
Interestingly how this leads to philosophical notion of space as an extension of bodies. While it not be 100% as philosophers envisioned it, basically, it is true notion.
Foggy in formulation, but clear in direction.
Do any of you even know how to do calculations/methods involving variational principles, chaotic dynamical systems, multivariable calculus or quantum mechanics?
I bet all the maths in this thread will be on the remedial level of that so far posted by IAMoraes, which has nothing to do with vector calculus, Raphie posting Wiki links or Ivars clinging desperately to his numerology based h(z) idea. There'll be no actual variational principles, no quantum mechanics, no dynamical systems. All you'll do is wax lyrical about concepts you wish you understood but don't.
Must make you all feel great to BS to one another, each knowing the rest know nothing too but you all want that ego boost so you just keep spouting nonsense about concepts you're too scared to admit you don't understand, cannot do and don't want to even try to learn. You'd be a billion times more productive in your learning if you admitted that and started learning these ideas properly. Someone decent at mathematics (ie good enough to get onto a university physics course) can learn the required ground work to apply variational principles to say general relativity in under 3 years. But that's too much like hard work for you guys so you just BS instead.
Ivars, IAMoraes, you've both been here more than a year and I'm sure your 'interest' in physics is older than that. What attempts have you made to learn actual physics? Didn't one of you say he was learning vector calculus or fluid dynamics or complex analysis or something? How far did you get with that? By the looks of it, nowhere. In the many months since you claimed to be reading that you could be competent at it now. Not research level but enough to actually apply it to physical systems. But you squandered that time instead.
And for the record, I'm not claiming to be all knowing. I don't know anything about chaotic dynamical systems beyond the qualitative definition, but I do know the effort needed to learn such things as variational principles.
I bet all the maths in this thread will be on the remedial level of that so far posted by IAMoraes, which has nothing to do with vector calculus, Raphie posting Wiki links or Ivars clinging desperately to his numerology based h(z) idea. There'll be no actual variational principles, no quantum mechanics, no dynamical systems. All you'll do is wax lyrical about concepts you wish you understood but don't.
Must make you all feel great to BS to one another, each knowing the rest know nothing too but you all want that ego boost so you just keep spouting nonsense about concepts you're too scared to admit you don't understand, cannot do and don't want to even try to learn. You'd be a billion times more productive in your learning if you admitted that and started learning these ideas properly. Someone decent at mathematics (ie good enough to get onto a university physics course) can learn the required ground work to apply variational principles to say general relativity in under 3 years. But that's too much like hard work for you guys so you just BS instead.
Ivars, IAMoraes, you've both been here more than a year and I'm sure your 'interest' in physics is older than that. What attempts have you made to learn actual physics? Didn't one of you say he was learning vector calculus or fluid dynamics or complex analysis or something? How far did you get with that? By the looks of it, nowhere. In the many months since you claimed to be reading that you could be competent at it now. Not research level but enough to actually apply it to physical systems. But you squandered that time instead.
And for the record, I'm not claiming to be all knowing. I don't know anything about chaotic dynamical systems beyond the qualitative definition, but I do know the effort needed to learn such things as variational principles.
There is never anything wrong in my view with providing another information that may be of use to them, even from a probabilistic standpoint. If perhaps anyone takes issue, so be it.
As for the specifics of what I posted, Ivars, the scholar whose work I cited seems to be somewhat of an expert in epidemiology.... very related to Network Theory.
Albert Laszlo Barabasi devotes an entire chapter to the spread of viruses in his book "Linked."
Best,
Raphie
P.S. Ivars, Bravo on you for making the attempt to educate yourself.
As for the specifics of what I posted, Ivars, the scholar whose work I cited seems to be somewhat of an expert in epidemiology.... very related to Network Theory.
Albert Laszlo Barabasi devotes an entire chapter to the spread of viruses in his book "Linked."
Best,
Raphie
P.S. Ivars, Bravo on you for making the attempt to educate yourself.
Hi Alphanumeric
I am learning backwards. First check out where I want to be, then fill the details. Not yet in detail stage, as You have rightly noticed.
On other hand, year ago I even denied the need to look into set theory at all. So I think the rest will follow in due course.
I am learning backwards. First check out where I want to be, then fill the details. Not yet in detail stage, as You have rightly noticed.
On other hand, year ago I even denied the need to look into set theory at all. So I think the rest will follow in due course.
QUOTE (Raphie Frank+May 19 2008, 09:09 AM)
As for the specifics of what I posted, Ivars, the scholar whose work I cited seems to be somewhat of an expert in epidemiology.... very related to Network Theory.
Albert Laszlo Barabasi devotes an entire chapter to the spread of viruses in his book "Linked."
Hi Raphie
The space that is physical is not so different form space that gets filled by viruses as they spread- potential virus existance space.
Albert Laszlo Barabasi devotes an entire chapter to the spread of viruses in his book "Linked."
Hi Raphie
The space that is physical is not so different form space that gets filled by viruses as they spread- potential virus existance space.
QUOTE (Ivars+May 19 2008, 09:23 AM)
Hi Raphie
The space that is physical is not so different form space that gets filled by viruses as they spread- potential virus existance space.
Yes, in a general sense, this is what physicists are coming to undertsand, Ivars. From the outside perspective, there clearly seems to be a growing body of research supporting this. My view? In a few, or perhaps several, years only incompetent reactionary physicists, whom, alas, many will call rather unsavory names, will contend otherwise.
Best,
Raphie
The space that is physical is not so different form space that gets filled by viruses as they spread- potential virus existance space.
Yes, in a general sense, this is what physicists are coming to undertsand, Ivars. From the outside perspective, there clearly seems to be a growing body of research supporting this. My view? In a few, or perhaps several, years only incompetent reactionary physicists, whom, alas, many will call rather unsavory names, will contend otherwise.
Best,
Raphie
hi Raphie
See how simple it gets when pieces are engineered together. With everyhting in its proper place, even difficult theories are easy to understand on a high level.
See how simple it gets when pieces are engineered together. With everyhting in its proper place, even difficult theories are easy to understand on a high level.
QUOTE (Ivars+May 19 2008, 09:45 AM)
hi Raphie
See how simple it gets when pieces are engineered together. With everyhting in its proper place, even difficult theories are easy to understand on a high level.
I'm not sure we're quite there yet, Ivars... at the "simple" level. But I do believe we, as a society, tend to overcomplicate and then use overcomplexification as a justification to refute less complex explanations for "this or that." The Ptolomaic conception of the Cosmos comes to mind as just one such example of "overcomplexification". The insistence of mind / body duality, meanwhile, strikes me as the challenge of the contemporary Age.
It's no different to me that your average Johnny-Come-Lately buffoon who will try to tell you a styrofoam cup is not a part of nature...
Best,
Raphie
See how simple it gets when pieces are engineered together. With everyhting in its proper place, even difficult theories are easy to understand on a high level.
I'm not sure we're quite there yet, Ivars... at the "simple" level. But I do believe we, as a society, tend to overcomplicate and then use overcomplexification as a justification to refute less complex explanations for "this or that." The Ptolomaic conception of the Cosmos comes to mind as just one such example of "overcomplexification". The insistence of mind / body duality, meanwhile, strikes me as the challenge of the contemporary Age.
It's no different to me that your average Johnny-Come-Lately buffoon who will try to tell you a styrofoam cup is not a part of nature...
Best,
Raphie
TO continue:
Interestingly, in infinite dimensional potential space ( consisting of chaotic release of infinitesimal dimensions of space) there is :
-No lines, as space vanishes and appears, so Newtons first law does not hold
-No trajectories as such
-There are no circular motions as well, so there it is not possible to draw a ring in such space, so pi as a ratio is also not definable
- etc.
The one thing that is definable for such a space ( total chaos, pure motion, pure energy) is bukhs binary principle- either there is and infinitesimal spatial dimension, or there is not. This duality has to be represented in maths dealing with this state, as has the content, or, the number of states it can have + plus ways its subsets can be organized. So we get number 2.
According to set theory of Cantor, extrapolating a little to include imaginary time I as the source of the spatial infinitesimal chaotic dimensionalities, or , actually as another dimension of the same set ( dual , Yin-yang) set, we can write the basic equation for such "thing"= looking for "fixed point" :
I = 2^I where I is imaginary Unit.
Now, the evolution of Universe should be possible to calculate from this relation (yes I know this is a bit extremal to say, but - let us see)
.
Obviusly, pi is not a problem here since we are talking about space where lines and rings do not exist.
So, the solution to this requires:
pi/2=lnI/I = ln2
If pi/2 is a right angle, than in that chaotic space pi = 2ln2= ln4 and right angle is ln2, while "chaotic" ring is 2pi=2ln4= ln16 and spinor 4pi = 2ln16= ln 64.
That means that orthogonal systems in such space exist, but orthogonal means ln2.
also, I= e^Ipi/2 is valid, but now it reads I=e^Iln2.
As the space gets less chaotic, more connected pieces appear, most likely ln2-> pi/2 as we know it in case of Euclid space (normal Hilbert space).
I am not sure if e holds in this setting, but if it does, it has a deep meaning, as e is connected via its mathematical definition
e=lim n->inf (1+1/n)^n to harmonic series 1/n and natural numbers.
But existance of e in such space can only be related to probability distribution of chaotic releases of space since there is nothing else present. Obviosly, if these appearances are distributed so that e appears in distribution, e will be exactly defined in such space ( physically) as base of probability distribution and together with 2 and I form the 3 numbers that are needed to start things going.
I would opt for binomial distribution becuase of the same duality logic . From that we can get both Gaussian (1/r^2 gravity) and Poisson (1/r gravity) as enough (infinity) spatial infinitesimal dimensions get involved.
It was little difficult to give up pi, but obviously it has no obvious place in totally chaotic origins. We may find it however in the other end of Universe evolution, for which I do not have yet equations, but it seems Euler had them already.
So.
Interestingly, in infinite dimensional potential space ( consisting of chaotic release of infinitesimal dimensions of space) there is :
-No lines, as space vanishes and appears, so Newtons first law does not hold
-No trajectories as such
-There are no circular motions as well, so there it is not possible to draw a ring in such space, so pi as a ratio is also not definable
- etc.
The one thing that is definable for such a space ( total chaos, pure motion, pure energy) is bukhs binary principle- either there is and infinitesimal spatial dimension, or there is not. This duality has to be represented in maths dealing with this state, as has the content, or, the number of states it can have + plus ways its subsets can be organized. So we get number 2.
According to set theory of Cantor, extrapolating a little to include imaginary time I as the source of the spatial infinitesimal chaotic dimensionalities, or , actually as another dimension of the same set ( dual , Yin-yang) set, we can write the basic equation for such "thing"= looking for "fixed point" :
I = 2^I where I is imaginary Unit.
Now, the evolution of Universe should be possible to calculate from this relation (yes I know this is a bit extremal to say, but - let us see)
.
Obviusly, pi is not a problem here since we are talking about space where lines and rings do not exist.
So, the solution to this requires:
pi/2=lnI/I = ln2
If pi/2 is a right angle, than in that chaotic space pi = 2ln2= ln4 and right angle is ln2, while "chaotic" ring is 2pi=2ln4= ln16 and spinor 4pi = 2ln16= ln 64.
That means that orthogonal systems in such space exist, but orthogonal means ln2.
also, I= e^Ipi/2 is valid, but now it reads I=e^Iln2.
As the space gets less chaotic, more connected pieces appear, most likely ln2-> pi/2 as we know it in case of Euclid space (normal Hilbert space).
I am not sure if e holds in this setting, but if it does, it has a deep meaning, as e is connected via its mathematical definition
e=lim n->inf (1+1/n)^n to harmonic series 1/n and natural numbers.
But existance of e in such space can only be related to probability distribution of chaotic releases of space since there is nothing else present. Obviosly, if these appearances are distributed so that e appears in distribution, e will be exactly defined in such space ( physically) as base of probability distribution and together with 2 and I form the 3 numbers that are needed to start things going.
I would opt for binomial distribution becuase of the same duality logic . From that we can get both Gaussian (1/r^2 gravity) and Poisson (1/r gravity) as enough (infinity) spatial infinitesimal dimensions get involved.
It was little difficult to give up pi, but obviously it has no obvious place in totally chaotic origins. We may find it however in the other end of Universe evolution, for which I do not have yet equations, but it seems Euler had them already.
So.
QUOTE (Ivars+)
I started to read Cantors "Contributions to the founding of the theory of transfinite numbers" . It is rather heavy, I hope I have understood correctly that his "aggregates" are todays "sets".
Anyway, after first diagonal reading one idea is clear:
Cardinals (including transfinite) are numbers that can be applied to sets not taking into account any ordering that might be imposed on set in broadest sense;
Though no specific ordering might be necessary, I believe an implicit ordering must exist in a set in order that individual elements can be distinguished.
Basically, if we consider the problem of counting a set (this automatically implies temporal attributes to enumerating a set), then there must be a manner to distinguish between counted and uncounted elements or similarly a manner to traverse these elements, once and only once each.
So the existance of the size of set automatically implies a manner in which such a size can be determined and this implies a manner to count them and this implies a manner to traverse each element once and only once, which, even if a state counted/uncounted can be attached to each element, there must also be a manner to contain the elements uniquely and traverse/find all of them, which implies a unique serial ordering to a countable set (I don't know if it's possible to actually have an uncountable set in reality - such are denoted as existing mathematically, but in reality these appear to simply be non-specific sets that do not contain elements until constructed/determined etc. to be otherwise, much as something declared to be a number is not necessarily a number until determined, or made determinable, to be a number).
Anyway, after first diagonal reading one idea is clear:
Cardinals (including transfinite) are numbers that can be applied to sets not taking into account any ordering that might be imposed on set in broadest sense;
Though no specific ordering might be necessary, I believe an implicit ordering must exist in a set in order that individual elements can be distinguished.
Basically, if we consider the problem of counting a set (this automatically implies temporal attributes to enumerating a set), then there must be a manner to distinguish between counted and uncounted elements or similarly a manner to traverse these elements, once and only once each.
So the existance of the size of set automatically implies a manner in which such a size can be determined and this implies a manner to count them and this implies a manner to traverse each element once and only once, which, even if a state counted/uncounted can be attached to each element, there must also be a manner to contain the elements uniquely and traverse/find all of them, which implies a unique serial ordering to a countable set (I don't know if it's possible to actually have an uncountable set in reality - such are denoted as existing mathematically, but in reality these appear to simply be non-specific sets that do not contain elements until constructed/determined etc. to be otherwise, much as something declared to be a number is not necessarily a number until determined, or made determinable, to be a number).
QUOTE (Ivars+)
Ordinals (including transfinite) are numbers that are related to set taking into account simple ( but in principle any) ordering.
Yes, there would appear to be a necessary ordering to the elements of a set, even if we have a factorial growth in the number of possible permutations of an ordering (which would still appear likely to be derived from a single uniquely determined ordering, for which we can then traverse it and reorder elements to generate the permutations - in other words, though we can image a set to be rearranged, the fact that we can isolate the elements of the set in the first place, implies there is already a preexisting order that encapsulates the elements of the set, otherwise we could not find the elements of the set in order to construct permutations - which, the construction of these permutations, would appear to also require that we be able to append additional "next element" information to each preexisting element of a set, so the elements of a permutable set would actually be a pairing of {current element, next element} information, and there are factorially growing features embedded in such a permutable structure, which grows similar to tetration - n^n operations (though there's a logarithmic and fractally prime related feature in the ratio between n! and n^n as well ... just as an interesting sidenote - basically computing the product of n^n is similarly to computing the area of a square in a logarithmic space, whereas computing the product of n! in such a logarithmic space becomes one of summing a semi-fractal structure of logarithms from 1 to n - the area of this structure in a logarithmic space approaches the area of a square for large n, but it has fine scale differences)).
For example:
log(n^n)=n*log(n)=log(n)+log(n)+log(n)+...+log(n) (for n terms)
Whereas:
log(n!)=log(1)+log(2)+log(3)+...+log(n)
Notice that for large n, the last half of these terms, for example, log(n/2)+...+log(n) only differ, if we use a log base 2, by a single binary bit (a relatively small ratio compared the number of bits describing log(n)), and the same would be true for the recursive segment log(n/4)+...+log(n/2) or log(n/8)+...+log(n/4) etc.
Anyway, this is just one manner in which tetration and permutations or factorial operations can appear quite similar in magnitude (I think the factorial form is a more naturally arising one).
Yes, there would appear to be a necessary ordering to the elements of a set, even if we have a factorial growth in the number of possible permutations of an ordering (which would still appear likely to be derived from a single uniquely determined ordering, for which we can then traverse it and reorder elements to generate the permutations - in other words, though we can image a set to be rearranged, the fact that we can isolate the elements of the set in the first place, implies there is already a preexisting order that encapsulates the elements of the set, otherwise we could not find the elements of the set in order to construct permutations - which, the construction of these permutations, would appear to also require that we be able to append additional "next element" information to each preexisting element of a set, so the elements of a permutable set would actually be a pairing of {current element, next element} information, and there are factorially growing features embedded in such a permutable structure, which grows similar to tetration - n^n operations (though there's a logarithmic and fractally prime related feature in the ratio between n! and n^n as well ... just as an interesting sidenote - basically computing the product of n^n is similarly to computing the area of a square in a logarithmic space, whereas computing the product of n! in such a logarithmic space becomes one of summing a semi-fractal structure of logarithms from 1 to n - the area of this structure in a logarithmic space approaches the area of a square for large n, but it has fine scale differences)).
For example:
log(n^n)=n*log(n)=log(n)+log(n)+log(n)+...+log(n) (for n terms)
Whereas:
log(n!)=log(1)+log(2)+log(3)+...+log(n)
Notice that for large n, the last half of these terms, for example, log(n/2)+...+log(n) only differ, if we use a log base 2, by a single binary bit (a relatively small ratio compared the number of bits describing log(n)), and the same would be true for the recursive segment log(n/4)+...+log(n/2) or log(n/8)+...+log(n/4) etc.
Anyway, this is just one manner in which tetration and permutations or factorial operations can appear quite similar in magnitude (I think the factorial form is a more naturally arising one).
QUOTE (Ivars+)
Now what is interesting, is that in Ordinal arithmetic neither summation , nor multiplication is commutative, while for triples of Ordinals associative property in summation holds. etc.
What that means is that the result of operations performed with ordinals DEPENDS on the order ( or path ) how they are performed.
Without further explanations, it is quite obvious to me, that time, being ordered set
(see e.g Time Calculus) must have the same property ( as long as we consider domains where time is infinitely faster (e.g. speed is w in Cantor notation) than our discrete time- results depend on path.
Something similar to this line of thought that I've had is that if we considered a chaotic function, infinitesimal differences at one point in time become finite over time (and then potentially infinite after that, but if we assume that those finite features are first recognized and become predictable, then they wouldn't lead to an infinitely unpredictable result, but instead could be cancelled in influence by prediction - as a simple real life analogy - it could be seen to be entirely unpredictable that day and night exists, until observations of day and night are made and become predictable - at that point a new reference for this pervasive influence becomes established and features on finer scales are then analyzed - at any point of time, for an exponentially growing function, the relative ratio of quantities over a fixed unit of time remain the same, though the absolute quantities change, so if an observation was made from a memory of a moving point in time (the past) and compared to an exponentially growing future (of possibilities?) the ratio remains the same and the logarithm of this, which could be seen to represent an information content, is constant as well - so if you, for example, had a time line in which an exponential number of possibilities could unfold, this only appears, at any moment, as a single decision or a single unit of feedback as to the present state - though these are aggregated as a memory of the past - I'm just tossing out random ideas here to kick around, but this could be a good manner in which to analyze, from within a highly chaotic system, the potentially appearance of features portraying a subjectively rather constant and linear evolution).
What that means is that the result of operations performed with ordinals DEPENDS on the order ( or path ) how they are performed.
Without further explanations, it is quite obvious to me, that time, being ordered set
(see e.g Time Calculus) must have the same property ( as long as we consider domains where time is infinitely faster (e.g. speed is w in Cantor notation) than our discrete time- results depend on path.
Something similar to this line of thought that I've had is that if we considered a chaotic function, infinitesimal differences at one point in time become finite over time (and then potentially infinite after that, but if we assume that those finite features are first recognized and become predictable, then they wouldn't lead to an infinitely unpredictable result, but instead could be cancelled in influence by prediction - as a simple real life analogy - it could be seen to be entirely unpredictable that day and night exists, until observations of day and night are made and become predictable - at that point a new reference for this pervasive influence becomes established and features on finer scales are then analyzed - at any point of time, for an exponentially growing function, the relative ratio of quantities over a fixed unit of time remain the same, though the absolute quantities change, so if an observation was made from a memory of a moving point in time (the past) and compared to an exponentially growing future (of possibilities?) the ratio remains the same and the logarithm of this, which could be seen to represent an information content, is constant as well - so if you, for example, had a time line in which an exponential number of possibilities could unfold, this only appears, at any moment, as a single decision or a single unit of feedback as to the present state - though these are aggregated as a memory of the past - I'm just tossing out random ideas here to kick around, but this could be a good manner in which to analyze, from within a highly chaotic system, the potentially appearance of features portraying a subjectively rather constant and linear evolution).
QUOTE (Ivars+)
So , to summarize, in general principle of least action in physics must be derivable from the fact that Time is an ordered set.
Yes, rates and quantities are objective measures shared between observers, but actual individual timelines are specific orderings of these shared objective events that gives both the unique subjective permutations as well as the objectively identical (and lower information content) shared quantities.
So, for example, a group of 4 objects A, B, C and D, when counted yields an objective shared "reality" of 4 units, independent observational perspectives can be constructed in 4! or 1*2*3*4=24 possible ways, so there are 24 unique subjective perspectives in which 4 objects can be observed (though an additional manner in which to denote an isolate these 4 objects from a potentially larger set is still necessary - so some "fingerprint" or unique attribute must be paired with these elements/objects that indicate they're from the same set).
Yes, rates and quantities are objective measures shared between observers, but actual individual timelines are specific orderings of these shared objective events that gives both the unique subjective permutations as well as the objectively identical (and lower information content) shared quantities.
So, for example, a group of 4 objects A, B, C and D, when counted yields an objective shared "reality" of 4 units, independent observational perspectives can be constructed in 4! or 1*2*3*4=24 possible ways, so there are 24 unique subjective perspectives in which 4 objects can be observed (though an additional manner in which to denote an isolate these 4 objects from a potentially larger set is still necessary - so some "fingerprint" or unique attribute must be paired with these elements/objects that indicate they're from the same set).
QUOTE (Ivars+)
There has to exist certain order of operations in Time which is preferred by Nature to all others, and this order has to be possible to find from Cantors approach to numbers plus understanding that the physical finite time we measure is not the only time has to be accounted for.
Since all classical physics can be derived from not more than second derivative of time, for principle of least action, only 2 scales of time are important .
I'm not certain what you're referring to here, though it appears you could be saying something similar to my comment regarding ratios of events over time (if you split time into past, present and future, then you'd have implicit measurements of position, velocity and acceleration, if these 3 points were recursively differentially measured - for example, if we defined a'(t)=a(t)-a(t-1) and b'(t)=a'(t)-a'(t-1), then a string of events in a(t) would be seen as a(t)=position or quantity, a'(t) would be velocity or growth and b'(t) would be acceleration or also potentially interpretable as an exponential or compounded growth, depending upon how someone interpreted it, though a redudancy in information would be present if we constructed a'(t) and b'(t) for every a(t) - instead a triplet of a(t), a(t-1) and a(t-2), transformed into a(t), b'(t) and c'(t) would be informationally non-redundant - so if you constructed these measurements of position, velocity and acceleration, they should naturally occur every 3 samples, or alternately, this could be seen as transforming triplets of orthogonal information into a triplet descibing these spacial features).
Since all classical physics can be derived from not more than second derivative of time, for principle of least action, only 2 scales of time are important .
I'm not certain what you're referring to here, though it appears you could be saying something similar to my comment regarding ratios of events over time (if you split time into past, present and future, then you'd have implicit measurements of position, velocity and acceleration, if these 3 points were recursively differentially measured - for example, if we defined a'(t)=a(t)-a(t-1) and b'(t)=a'(t)-a'(t-1), then a string of events in a(t) would be seen as a(t)=position or quantity, a'(t) would be velocity or growth and b'(t) would be acceleration or also potentially interpretable as an exponential or compounded growth, depending upon how someone interpreted it, though a redudancy in information would be present if we constructed a'(t) and b'(t) for every a(t) - instead a triplet of a(t), a(t-1) and a(t-2), transformed into a(t), b'(t) and c'(t) would be informationally non-redundant - so if you constructed these measurements of position, velocity and acceleration, they should naturally occur every 3 samples, or alternately, this could be seen as transforming triplets of orthogonal information into a triplet descibing these spacial features).
I will run a little ahead of myself now, but may be this stirs some interest:
from I=2^I i obtained straight angle in space consisting of infinitesimal chaotic dimensions that pop in and out space- they create space as they appear, and decreate as disappear. In such space, there are no straight lines nor finite circles.
The resulting straight (or orthogonal ) angle was ln2.
If we compare this result to projective plane, the angle with reference to absolute points i ( 1,I,0) and j (1,-I,0) which are obtained as crossing of any circle with ideal line, the angle between 2 lines that intersect the ideal line in 2 other points p1 and p2 is given by Laguerre formula:
Phi(angle) = (1/(2*I)) * log Cr(p1,p2, i, j) where Cr is cross product. What is cross product in infinite dimensional disconnected space of chaotic infinitesimal space dimensions remains to be seen, but from previous we can see that in absolutely chaotic stage:
ln2 = (1/2*I) * ln (Cr ( p1,p2,i,j)) or
ln(Cr(p1,p2,i,j)) = I*2ln2 ; this may be as well taken as definition of cross product of 2 infinitesimal space dimensions in totally chaotic state.
Now in chaotic disconnected space pi=2ln2 ( as was shown earlier) . When we think how such space can develop, one of options is looping of imaginary time, or the moment when ln2-> pi/2. If we put this in the above, we can see:
ln(Cr(p1,p2,i,j)) = i*pi
by exponeating this equality, we get
( Cr(p1,p2,i,j)) = e^(I*pi) which is obviously Euler's equation, so
( Cr(p1,p2,i,j)) = -1 . (from e^(I*pi)+1=0)
This gives some insight what -1 is - it is a cross product of spatial dimensions when imaginary time loops and creates them; these are the first orthogonal space dimensions ( infinitesimal still) where orthogonality means 90 degrees, and pi is 3,1415.... By returning to previous equality,
ln(Cr(p1,p2,i,j)) = I*2ln2
and similarly exponentiating, we get;
(Cr(p1, p2, i, j) = e^(I*2ln2) = i^2 (when orthogonal angle =ln2) (however, i^2 may not be -1 there. I have doubts) which seems to be valid from chaotic infinitesimal to looping infinitesimal while "pi" changes from 2ln2 to 3,141592....
What is important, this formula still contains only I, 2 and e( in form of ln). Nothing more is present. The possible relsult of i^2 in such space would be:
i^2 = - 2ln2; or -2, or -4 , or -ln2, -1/2?, which leads to but this must be checked as complex math must hold, most likely.
The reason is, in space like that, there are no other numbers as I, 2 and e, so i^2 can not be - 1. -1 is created when time loops, but before that- no.
Interesting. Have to find out now what a cross product of infinitesimals of ultimate smallness may mean?
from I=2^I i obtained straight angle in space consisting of infinitesimal chaotic dimensions that pop in and out space- they create space as they appear, and decreate as disappear. In such space, there are no straight lines nor finite circles.
The resulting straight (or orthogonal ) angle was ln2.
If we compare this result to projective plane, the angle with reference to absolute points i ( 1,I,0) and j (1,-I,0) which are obtained as crossing of any circle with ideal line, the angle between 2 lines that intersect the ideal line in 2 other points p1 and p2 is given by Laguerre formula:
Phi(angle) = (1/(2*I)) * log Cr(p1,p2, i, j) where Cr is cross product. What is cross product in infinite dimensional disconnected space of chaotic infinitesimal space dimensions remains to be seen, but from previous we can see that in absolutely chaotic stage:
ln2 = (1/2*I) * ln (Cr ( p1,p2,i,j)) or
ln(Cr(p1,p2,i,j)) = I*2ln2 ; this may be as well taken as definition of cross product of 2 infinitesimal space dimensions in totally chaotic state.
Now in chaotic disconnected space pi=2ln2 ( as was shown earlier) . When we think how such space can develop, one of options is looping of imaginary time, or the moment when ln2-> pi/2. If we put this in the above, we can see:
ln(Cr(p1,p2,i,j)) = i*pi
by exponeating this equality, we get
( Cr(p1,p2,i,j)) = e^(I*pi) which is obviously Euler's equation, so
( Cr(p1,p2,i,j)) = -1 . (from e^(I*pi)+1=0)
This gives some insight what -1 is - it is a cross product of spatial dimensions when imaginary time loops and creates them; these are the first orthogonal space dimensions ( infinitesimal still) where orthogonality means 90 degrees, and pi is 3,1415.... By returning to previous equality,
ln(Cr(p1,p2,i,j)) = I*2ln2
and similarly exponentiating, we get;
(Cr(p1, p2, i, j) = e^(I*2ln2) = i^2 (when orthogonal angle =ln2) (however, i^2 may not be -1 there. I have doubts) which seems to be valid from chaotic infinitesimal to looping infinitesimal while "pi" changes from 2ln2 to 3,141592....
What is important, this formula still contains only I, 2 and e( in form of ln). Nothing more is present. The possible relsult of i^2 in such space would be:
i^2 = - 2ln2; or -2, or -4 , or -ln2, -1/2?, which leads to but this must be checked as complex math must hold, most likely.
The reason is, in space like that, there are no other numbers as I, 2 and e, so i^2 can not be - 1. -1 is created when time loops, but before that- no.
Interesting. Have to find out now what a cross product of infinitesimals of ultimate smallness may mean?
QUOTE (AlphaNumeric+May 19 2008, 04:45 AM)
bet all the maths in this thread will be on the remedial level of that so far posted by IAMoraes
(...)What attempts have you made to learn actual physics?
Thank you for such high regards!
(...)What attempts have you made to learn actual physics?
Thank you for such high regards!
Slowly adding reasoning behind I=2^I .
Speaking about "imagination" and what does imaginary powers and iterations mean, we can try the following analogy to get some idea what does I "count". We know that Cantor extended enumerability to infinite numbers, so why not try with imaginary?
So let us assume we have I of something. Let as say we have a set with I elements, or size I.
Now lets us ask ourselves a question: How many subsets does this set have? And let us answer ( or postulate) that as usual, the number of subsets is 2^I.
The solution for fixed points to such idea I=2^I would require that pi/2= ln2 which I do not have anything against, since pi/2 = 90 degrees only in spaces where such angles are possible. There could be spaces with chaotic character, disconnected, where straight lines and trajectories does not exist at all, so pi also does not have a meaning. But angle does.
This idea allows(?) to apply binomial coefficients to set with size I when looking for possible varieties of subsets. The question is, if the analoque of n is I, what is the analogue of k? Is it some fraction of I?
For example, if we take I/2 and ask how many subsets with size I/2 can happen within set with size I, we have
I!/((I/2)!(I-I/2)!) = I!/ (I/2)! *(I/2)!
Now of course i have never in my life seen factorials of Imaginary Unit. If we look at Gamma function, we see that Gamma(I) = -0,15495, Gamma(I/2) = -0,39928, so that -0,39928*-0,39928=0,159424
-0,15495/0,159424 = -0,97193 hmm I would have loved it better if the number of subsets would have turned out to be -1.
Perhaps gamma function is not the right one to generalize factorials to imaginary numbers. Or binomial coefficients are not, more likely.
Or the subsets in set with size I does not follow binomial distribution, because set size I is not discrete, obviosly.
Another try may be Poisson distribution as closest to binomial.
Somehow understanding about what "imagination" is has to be reached above pure formal placement of symbols.
Also, if we stick to integer values of n in I/n (for reasons unkonown) , we could require that all subset sizes together correspond to Cantors idea about size of transfinite cardinal sets:
Sum (I/n) = 2^I
That would be like Imaginary Harmonic series. I wonder if there has been any attempts to give value to them in some summation.
Speaking about "imagination" and what does imaginary powers and iterations mean, we can try the following analogy to get some idea what does I "count". We know that Cantor extended enumerability to infinite numbers, so why not try with imaginary?
So let us assume we have I of something. Let as say we have a set with I elements, or size I.
Now lets us ask ourselves a question: How many subsets does this set have? And let us answer ( or postulate) that as usual, the number of subsets is 2^I.
The solution for fixed points to such idea I=2^I would require that pi/2= ln2 which I do not have anything against, since pi/2 = 90 degrees only in spaces where such angles are possible. There could be spaces with chaotic character, disconnected, where straight lines and trajectories does not exist at all, so pi also does not have a meaning. But angle does.
This idea allows(?) to apply binomial coefficients to set with size I when looking for possible varieties of subsets. The question is, if the analoque of n is I, what is the analogue of k? Is it some fraction of I?
For example, if we take I/2 and ask how many subsets with size I/2 can happen within set with size I, we have
I!/((I/2)!(I-I/2)!) = I!/ (I/2)! *(I/2)!
Now of course i have never in my life seen factorials of Imaginary Unit. If we look at Gamma function, we see that Gamma(I) = -0,15495, Gamma(I/2) = -0,39928, so that -0,39928*-0,39928=0,159424
-0,15495/0,159424 = -0,97193 hmm I would have loved it better if the number of subsets would have turned out to be -1.
Perhaps gamma function is not the right one to generalize factorials to imaginary numbers. Or binomial coefficients are not, more likely.
Or the subsets in set with size I does not follow binomial distribution, because set size I is not discrete, obviosly.
Another try may be Poisson distribution as closest to binomial.
Somehow understanding about what "imagination" is has to be reached above pure formal placement of symbols.
Also, if we stick to integer values of n in I/n (for reasons unkonown) , we could require that all subset sizes together correspond to Cantors idea about size of transfinite cardinal sets:
Sum (I/n) = 2^I
That would be like Imaginary Harmonic series. I wonder if there has been any attempts to give value to them in some summation.
This stuff is worth its weight in gold! Keep it coming guys.
7/2 + 3 + 111929.9933 - pi + e^pi = X - 17
etc...
7/2 + 3 + 111929.9933 - pi + e^pi = X - 17
etc...
We surely will Euler. Glad to give you a smile and a wonderful opportunity to prove your worth by mocking others. It will 'stead you well with the other blokes at the pub next time around.
Best,
Raphie
Best,
Raphie
QUOTE (Raphie Frank+May 21 2008, 08:45 AM)
We surely will Euler. Glad to give you a smile and a wonderful opportunity to prove your worth by mocking others.
Hey - you're not just doing it for me, loads of people are laughing at you! It's all down to the multidimentional chaotic nature of the equation 19+d=e^i, but exponentially more so.
Hey - you're not just doing it for me, loads of people are laughing at you! It's all down to the multidimentional chaotic nature of the equation 19+d=e^i, but exponentially more so.
Wonderful to hear it, Euler. Laughter is an amazing addition to the human condition. Without it I believe many of us might well be lost.
Best,
Raphie
Best,
Raphie
QUOTE (Raphie Frank+May 21 2008, 08:58 AM)
Wonderful to hear it, Euler.
You like the fact that people are laughing at you? Ah, now I see - this was your intention all along! I knew you guys couldn't be serious: nobody's that stupid, right?
You like the fact that people are laughing at you? Ah, now I see - this was your intention all along! I knew you guys couldn't be serious: nobody's that stupid, right?
Tell you what Euler, I understand you believe hiding your identity an act of wisdom rather than cowardice, but help me out here. Give me a real life anecdote or two or even three detailing some of this laughter and I can include it as part of a little case study right along with some of your amazingly laughable statements in the past regarding honesty, intelligence and so on.
Because, you see, Euler, at least some of the people who will see this will get quite a chuckle from it and it will help me more than you can imagine. I would be quite grateful and, of course, I can only use material that is "opt-in."
Best,
Raphie
Because, you see, Euler, at least some of the people who will see this will get quite a chuckle from it and it will help me more than you can imagine. I would be quite grateful and, of course, I can only use material that is "opt-in."
Best,
Raphie
QUOTE (Raphie Frank+May 21 2008, 09:15 AM)
Give me a real life anecdote or two or even three detailing some of this laughter...
There are loads of instances: here's a good source. In a medium such as this one, I believe the common reaction would be described with a "lol".
There are loads of instances: here's a good source. In a medium such as this one, I believe the common reaction would be described with a "lol".
QUOTE (Raphie Frank+May 21 2008, 09:35 AM)
Okay, Euler, play time is over. Go ahead and have the last word, but, in case you have not figured it out, none of those you ridicule desires to be tested like a five year old, especially not by one who fails to grasp in any manner whatsoever the essential essence of the term "gestalt."
I bear you no ill will and am getting about as many smiles from this as I am sure you are.
PLEASE let those of good will, myself included, continue in their explorations unimpeded.
Best to you,
Raphie
I bear you no ill will and am getting about as many smiles from this as I am sure you are.
PLEASE let those of good will, myself included, continue in their explorations unimpeded.
Best to you,
Raphie
Don't be daft! If you insist on talking rubbish, throwing about scraps from wiki you don't understand and massaging one-anothers egos by pretending to do mathematics, then don't be surprised when people:
a) Laugh at you.
b) Call you up on it.
c) Ask you to substantiate your claims.
Now go-go-go internet mathematics!
a) Laugh at you.
b) Call you up on it.
c) Ask you to substantiate your claims.
Now go-go-go internet mathematics!
In space i mentioned earlier, first thing is to find its geometry.
Obviously, in such space of chaotic appearing/dissappearing infinitesimal space dimensions straight line is Brownian motion trajectory.
We choose point a on one infinitesimal, but we have no idea where the next neighbouring space infinitesimal dimension will appear . As it appears, we can continue drawing the line.
As Brownian motion, in this space it will be mathematical, ideal inertialess, so probably its Wiener process with Gausian distribution. But that has to decided later as there are many stohastic processes.
Now, as space infinitesimal dimensions aggregate from completely chaotic to continuos , in between there will be many infinitesimal aggregates of infinitesimal dimensions of space.
These aggregates will also have geometry similar to smallest level, but the distribution and mathematics of straight line definition must slightly differ with each scale . Simplest aggregate will have 2 infinitesimals together, etc.
Since these are still infinitesimals, there is a need to have a possibility to distinquish between them. Again, Cantors ordinal/cardinal numbers come in handy, as the whole idea originally was developed by Cantor based on his studies about point aggregates, not sets as is assumed usually.
The size of aggregates = infinitesimal space dimensions can be defined as I/w_n, where w_n are Cantor ordinals. As an example.
Probably all extensions of Cantor ordinals /cardinals to higher levels of infinity need to be included as well.
That settled, the missing things are functions/operations which can work on those numbers/infinitesimals and transform them from one scale into next. Such operations will be fast hyperoprations . So.
Obviously, in such space of chaotic appearing/dissappearing infinitesimal space dimensions straight line is Brownian motion trajectory.
We choose point a on one infinitesimal, but we have no idea where the next neighbouring space infinitesimal dimension will appear . As it appears, we can continue drawing the line.
As Brownian motion, in this space it will be mathematical, ideal inertialess, so probably its Wiener process with Gausian distribution. But that has to decided later as there are many stohastic processes.
Now, as space infinitesimal dimensions aggregate from completely chaotic to continuos , in between there will be many infinitesimal aggregates of infinitesimal dimensions of space.
These aggregates will also have geometry similar to smallest level, but the distribution and mathematics of straight line definition must slightly differ with each scale . Simplest aggregate will have 2 infinitesimals together, etc.
Since these are still infinitesimals, there is a need to have a possibility to distinquish between them. Again, Cantors ordinal/cardinal numbers come in handy, as the whole idea originally was developed by Cantor based on his studies about point aggregates, not sets as is assumed usually.
The size of aggregates = infinitesimal space dimensions can be defined as I/w_n, where w_n are Cantor ordinals. As an example.
Probably all extensions of Cantor ordinals /cardinals to higher levels of infinity need to be included as well.
That settled, the missing things are functions/operations which can work on those numbers/infinitesimals and transform them from one scale into next. Such operations will be fast hyperoprations . So.
Damn, and I thought that mott.carl was gibberish.
All hail the new reigning champ.
All hail the new reigning champ.
Dear Ivars,
I just now did a search for 1.80193774 , related to heptagonal triangles, as I posted earlier this evening on the "Contextual Mathematics" thread, and I came across the following (there were only 3 results...):
Inverse cascade in percolation model: hierarchical description of time-dependent scaling
Ilya Zaliapin, Henry Wong, Andrei Gabrielov
February 2, 2008
http://arxiv.org/pdf/cond-mat/0411398
Given your repeated mentions of "percolation" and recent mention of time as an "ordered set," I thought you might wish to take a gander. Cantor Sets are also mentioned in the paper as is the notion of "cluster fractals," interesting to me as I was recently reading about Arthur Koestler and his notions of "seriality," which is related to the clustering of events in the human domain.
Most of the above linked to paper will likely be above your head (as it is mine), certainly from a mathematical perspective, in any case, but I thought you might wish to at least take a look, as you may gain an insight or two from it...
Best,
Raphie
P.S. Regarding Koestler, a bit of trivia for you from Wikipedia that you may well appreciate...
In his younger days, the singer Sting was an avid reader of Koestler. His band of the time, The Police, were to name one of their albums Ghost in the Machine after one of Koestler's books. Their album Synchronicity was also inspired by Koestler's The Roots of Coincidence, which discusses Carl Jung's theory of the same name...
http://en.wikipedia.org/wiki/Arthur_Koestler
I just now did a search for 1.80193774 , related to heptagonal triangles, as I posted earlier this evening on the "Contextual Mathematics" thread, and I came across the following (there were only 3 results...):
Inverse cascade in percolation model: hierarchical description of time-dependent scaling
Ilya Zaliapin, Henry Wong, Andrei Gabrielov
February 2, 2008
http://arxiv.org/pdf/cond-mat/0411398
Given your repeated mentions of "percolation" and recent mention of time as an "ordered set," I thought you might wish to take a gander. Cantor Sets are also mentioned in the paper as is the notion of "cluster fractals," interesting to me as I was recently reading about Arthur Koestler and his notions of "seriality," which is related to the clustering of events in the human domain.
Most of the above linked to paper will likely be above your head (as it is mine), certainly from a mathematical perspective, in any case, but I thought you might wish to at least take a look, as you may gain an insight or two from it...
Best,
Raphie
P.S. Regarding Koestler, a bit of trivia for you from Wikipedia that you may well appreciate...
In his younger days, the singer Sting was an avid reader of Koestler. His band of the time, The Police, were to name one of their albums Ghost in the Machine after one of Koestler's books. Their album Synchronicity was also inspired by Koestler's The Roots of Coincidence, which discusses Carl Jung's theory of the same name...
http://en.wikipedia.org/wiki/Arthur_Koestler
QUOTE (Raphie Frank+May 24 2008, 04:14 AM)
=========================================
The Heptagon, the Golden Ratio & the Harmonic Mean
=========================================
Here is an interesting identity related to the Heptagon.
Let H-bar = Harmonic Mean
H-bar = (2 *(b*c))/(b+c))
Let b = 2*cos (pi/7) = 1.80193774 ...
Let c = 4*(cos (pi/7))^2 - 1 = 2.2469796 ...
These are two sides of a constructible scalene triangle one can create inside a Heptagon with unit sides = 1, if one connects vertices in position 1 and 2 with the fourth vertex. See:
The Heptagon, the Golden Ratio & the Harmonic Mean
=========================================
Here is an interesting identity related to the Heptagon.
Let H-bar = Harmonic Mean
H-bar = (2 *(b*c))/(b+c))
Let b = 2*cos (pi/7) = 1.80193774 ...
Let c = 4*(cos (pi/7))^2 - 1 = 2.2469796 ...
These are two sides of a constructible scalene triangle one can create inside a Heptagon with unit sides = 1, if one connects vertices in position 1 and 2 with the fourth vertex. See:
My prediction was correct. Nothing to do with the 'principle of least action'.
QUOTE (AlphaNumeric+May 25 2008, 09:33 PM)
My prediction was correct. Nothing to do with the 'principle of least action'.
Hi AlphaNumeric
You are right. The connection is not so obvious to work out after initial intuitive link.
But I have wandered into another territory: can You describe or prove non-existance of a set whose size/cardinality is I (imaginary unit) and powerset has size 2^I? I understand from Cantor that set/powerset relation holds for all sizes. Does it hold for I?
The question of what can be put in one to one relation with such a set with size I is another topic.
Hi AlphaNumeric
You are right. The connection is not so obvious to work out after initial intuitive link.
But I have wandered into another territory: can You describe or prove non-existance of a set whose size/cardinality is I (imaginary unit) and powerset has size 2^I? I understand from Cantor that set/powerset relation holds for all sizes. Does it hold for I?
The question of what can be put in one to one relation with such a set with size I is another topic.
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