Cusa
QUOTE:
Negative infinity or infinity cancel is necessary for renormalization physics which is the trend of the future. All forces effect energy motion from point to point creating the necessity of renormalization.
Mitch Raemsch"
I like to think the same - but I am not including infinite - only until and no more than until the very last step - just before infinity is being reached so to speak. Infinity is not part of physical world and the "Origin of the Origin" is not to be created each time physical world renormalize.
QUOTE (bukh+Jan 4 2009, 12:28 PM)
Cusa
QUOTE:
Negative infinity or infinity cancel is necessary for renormalization physics which is the trend of the future. All forces effect energy motion from point to point creating the necessity of renormalization.
Mitch Raemsch"
I like to think the same - but I am not including infinite - only until and no more than until the very last step - just before infinity is being reached so to speak. Infinity is not part of physical world and the "Origin of the Origin" is not to be created each time physical world renormalize.
I want to make a point that forces and light need to be renrmalized because space is quantized by the infinitely small. You pass through every quantity mathematically in the continuum hypothesis.
Mitch Raemsch
QUOTE:
Negative infinity or infinity cancel is necessary for renormalization physics which is the trend of the future. All forces effect energy motion from point to point creating the necessity of renormalization.
Mitch Raemsch"
I like to think the same - but I am not including infinite - only until and no more than until the very last step - just before infinity is being reached so to speak. Infinity is not part of physical world and the "Origin of the Origin" is not to be created each time physical world renormalize.
I want to make a point that forces and light need to be renrmalized because space is quantized by the infinitely small. You pass through every quantity mathematically in the continuum hypothesis.
Mitch Raemsch
QUOTE (bukh+Jan 4 2009, 10:22 PM)
Hi Laidback - Iseason - et al -
Good to know -
And we are painfully aware that just as an atom is not into existence
Exactly!
The Theoretical Atom is only an inference to a definition that may be tied to a theoretical quanta or a dimensions value, gained via the use of an ELECTRON-ic device that results with a comparative figure or Test Result..
Good to know -
And we are painfully aware that just as an atom is not into existence
Exactly!
The Theoretical Atom is only an inference to a definition that may be tied to a theoretical quanta or a dimensions value, gained via the use of an ELECTRON-ic device that results with a comparative figure or Test Result..
QUOTE
- neither is a pixel into existence -but pixel is perhaps a better way of getting a mind-picture of the physical world -
Indeed QUOTE (->
| QUOTE |
| - neither is a pixel into existence -but pixel is perhaps a better way of getting a mind-picture of the physical world - |
Indeed But then what then is "the Origin of the Origin" - what IS into existence - and I like to think that the only to be into existence is: smallest "object of sameness" - and smallest object of sameness is defined as something having a shape and having a size - but neither shape nor size will ever be known and will never be definable because they constitutes Unit1 qualities - they are the yardsticks out from which everything is being defined and described.
I concur, its for this reason I constantly prefer to refer to references and or comparisons rather than to refer to the normal conventions used in everyday physics..
First non existence simply is impossible, it would be better to refer to the impossible best by referring to it as out of range...
This is because void or zero anywhere simply is not possible..
for example should we refer to HERE
.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
as being the closest to zero, but the problem is, whatever exists at such a near zero state may feel the above figure relative to its scale is best treated as, 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
so therefore its figure relative to its scale as per the above from HEREwould be closer to zero, but the only problem is, whatever exists at such a near zero state may feel the above figure relative to its scale is best treated as, 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
so therefore its figure as per the above from HEREwould be closer to zero..
Arghhhhhhhhhhhhhhhhhhhhh!
anyway this is the only reference where infinity is justified..
Cheers,
Peter J Schoen..
QUOTE
Smallest "object of sameness" can be anything from "size of universe" divided into two or more ratios - and to "size of universe" divided into as many ratios as physically possible, and that is just before "infinitely many" and therefore physically non-existing - so everything between 0 and infinite.
The above last statement I feel is flawed with human like reasoning - Err~that doesn't read as I intend - How can I put this better???First non existence simply is impossible, it would be better to refer to the impossible best by referring to it as out of range...
This is because void or zero anywhere simply is not possible..
for example should we refer to HERE
.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
as being the closest to zero, but the problem is, whatever exists at such a near zero state may feel the above figure relative to its scale is best treated as, 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
so therefore its figure relative to its scale as per the above from HEREwould be closer to zero, but the only problem is, whatever exists at such a near zero state may feel the above figure relative to its scale is best treated as, 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
so therefore its figure as per the above from HEREwould be closer to zero..
Arghhhhhhhhhhhhhhhhhhhhh!
anyway this is the only reference where infinity is justified..
Cheers,
Peter J Schoen..
The future is infinite. The aether is speeding up without end.
Mitch Raemsch
Mitch Raemsch
QUOTE (Cusa+Jan 5 2009, 07:34 AM)
The future is infinite.
Admissible
As that violates conservation laws..
Cheers,
Peter J Schoen..
Admissible
QUOTE
The aether is speeding up without end.
Mitch Raemsch
Rubbish!Mitch Raemsch
As that violates conservation laws..
Cheers,
Peter J Schoen..
QUOTE (Laidback+Jan 4 2009, 09:58 PM)
AdmissibleRubbish!
As that violates conservation laws..
Cheers,
Peter J Schoen..
Speed can transfer without acceleration in the phenomenon of momentum. Take two billiard balls one the cue the other black.
When you accelerate the cue ball with your stick it tranfers its motion instantaneously when it strikes the black and stops. Momentum can transfer motion from one thing to another. The black ball is now the one with motion and the cue ball is still as the black ball was.
This is motion exchange. But motion must be created first. So acceleration of the cue ball comes first. In momentum the motion transfering is conserved.
Mitch Raemsch
As that violates conservation laws..
Cheers,
Peter J Schoen..
Speed can transfer without acceleration in the phenomenon of momentum. Take two billiard balls one the cue the other black.
When you accelerate the cue ball with your stick it tranfers its motion instantaneously when it strikes the black and stops. Momentum can transfer motion from one thing to another. The black ball is now the one with motion and the cue ball is still as the black ball was.
This is motion exchange. But motion must be created first. So acceleration of the cue ball comes first. In momentum the motion transfering is conserved.
Mitch Raemsch
Laidback
QUOTE: "QUOTE
Smallest "object of sameness" can be anything from "size of universe" divided into two or more ratios - and to "size of universe" divided into as many ratios as physically possible, and that is just before "infinitely many" and therefore physically non-existing - so everything between 0 and infinite.
The above last statement I feel is flawed with human like reasoning - Err~that doesn't read as I intend - How can I put this better???"
Yeah - I know -
Actually - the one thing I tried to communicate with the above is that:
Everything is according to the accuracy we want or chose for our definition/explaining of physical world.
The more accurate we measure - the "smaller" ratios of universe is being used -
And Yes - I believe that "smallness" is being available or is being present at the site of measurement - because we are ourselves as human constituents of smallness to a high degree - we are complex - i.e. we are constituents of very small pixels - and as such we will never reach the border of smallness in our measurements -
Whereas other parts of universe may well be made/defined out out from bigger "building blocks" and such areas of the universe cannot be measured with the same accuracy - but who cares - as long as we are on earth and its near vicinity. But it may well have implications for how the projections work over the universe - and give rise to significant differences in projections and the "reality" we extract from our observations of space - what is distances - size - everything is a reflection of the projections we get from our pixel-grid.
And happy to know that you so well agreed with what I postulated - great !
QUOTE: "QUOTE
Smallest "object of sameness" can be anything from "size of universe" divided into two or more ratios - and to "size of universe" divided into as many ratios as physically possible, and that is just before "infinitely many" and therefore physically non-existing - so everything between 0 and infinite.
The above last statement I feel is flawed with human like reasoning - Err~that doesn't read as I intend - How can I put this better???"
Yeah - I know -
Actually - the one thing I tried to communicate with the above is that:
Everything is according to the accuracy we want or chose for our definition/explaining of physical world.
The more accurate we measure - the "smaller" ratios of universe is being used -
And Yes - I believe that "smallness" is being available or is being present at the site of measurement - because we are ourselves as human constituents of smallness to a high degree - we are complex - i.e. we are constituents of very small pixels - and as such we will never reach the border of smallness in our measurements -
Whereas other parts of universe may well be made/defined out out from bigger "building blocks" and such areas of the universe cannot be measured with the same accuracy - but who cares - as long as we are on earth and its near vicinity. But it may well have implications for how the projections work over the universe - and give rise to significant differences in projections and the "reality" we extract from our observations of space - what is distances - size - everything is a reflection of the projections we get from our pixel-grid.
And happy to know that you so well agreed with what I postulated - great !
Hi all
I agree with sameness / ratio, But consider how we interact. WE use multiple representations of our smallest perceivable energy..(photon/ electron).
How would this change if we were a much larger or smaller object?....Sure dimensions and size change , but the methodology remains the same. Multiples are still important in information....Without multiples no information can be imparted. Obviously patterns of sameness are a level of information transfer...But the multiples rule applies to all.
Gravity is a prime example...Personally , I favor the receiver (smaller) as the most active participant , merely because they are receiving more "information" than the larger object which MUST interfere with itself. Perhaps it is just that action that allows the smaller object to approach a larger object. The information leaving a larger object is "more easily Incorporated" by the smaller object than the larger.
This is not against previous posts , but looking at differing levels of the matrix patterns. Inevitable patterns make sense , certainly no less because we see them in the real world , yet we explain them by simply looking at the history of the pattern and expecting that the pattern is eternal. (in the sense that atoms formed everywhere "by chance") at the same levels. Even if this were true , constants could never be truly constant as the gravity effect for every pixel in space would be variable to the same degree. Meaning that a photon would change value as it moved through space according to it's distance from every other object in space.
Treating each position as a unique event makes more sense because they have to be unique in value based on the current gravity science.
Cheers
Iseason
I agree with sameness / ratio, But consider how we interact. WE use multiple representations of our smallest perceivable energy..(photon/ electron).
How would this change if we were a much larger or smaller object?....Sure dimensions and size change , but the methodology remains the same. Multiples are still important in information....Without multiples no information can be imparted. Obviously patterns of sameness are a level of information transfer...But the multiples rule applies to all.
Gravity is a prime example...Personally , I favor the receiver (smaller) as the most active participant , merely because they are receiving more "information" than the larger object which MUST interfere with itself. Perhaps it is just that action that allows the smaller object to approach a larger object. The information leaving a larger object is "more easily Incorporated" by the smaller object than the larger.
This is not against previous posts , but looking at differing levels of the matrix patterns. Inevitable patterns make sense , certainly no less because we see them in the real world , yet we explain them by simply looking at the history of the pattern and expecting that the pattern is eternal. (in the sense that atoms formed everywhere "by chance") at the same levels. Even if this were true , constants could never be truly constant as the gravity effect for every pixel in space would be variable to the same degree. Meaning that a photon would change value as it moved through space according to it's distance from every other object in space.
Treating each position as a unique event makes more sense because they have to be unique in value based on the current gravity science.
Cheers
Iseason
Hej Iseason
QUOTE: "Gravity is a prime example...Personally , I favor the receiver (smaller) as the most active participant , merely because they are receiving more "information" than the larger object which MUST interfere with itself. Perhaps it is just that action that allows the smaller object to approach a larger object. The information leaving a larger object is "more easily Incorporated" by the smaller object than the larger."
Yes it is the receiver - "The Observer" that is the interfering part (mainly) - it is the observer that create the constraints in spacetime fabric -
Of course one can say that spacetime fabric IS being composed of observers - all of them - to a certain extent and according to their said "size" or complexion. And this is why not two flashes are the same in the expression of universe - universe only exists once - even on smallest level there is a change to the next following flash - and changes on smallest level is being accomplished via constraints on smallest level - via observations on smallest level.
We humans like to think that such dynamic changes on lover levels - "like the fuzzing around of atoms" - that this is "natures way of expressing itself" and yes - of course - but WHY. Because of said above mentioned principle.
"Treating each position as a unique event makes more sense because they have to be unique in value based on the current gravity science."
YES - everything is unique - even on smallest level - but we are blind for this diversity because it is way beyond our measuring capabilities. A so called constant is just an approximation - but such approximations are more that good enough for the purposes where they are being applied. As I like to say - we decide the accuracy accordingly to what we want or need or can accomplish.
QUOTE: "Gravity is a prime example...Personally , I favor the receiver (smaller) as the most active participant , merely because they are receiving more "information" than the larger object which MUST interfere with itself. Perhaps it is just that action that allows the smaller object to approach a larger object. The information leaving a larger object is "more easily Incorporated" by the smaller object than the larger."
Yes it is the receiver - "The Observer" that is the interfering part (mainly) - it is the observer that create the constraints in spacetime fabric -
Of course one can say that spacetime fabric IS being composed of observers - all of them - to a certain extent and according to their said "size" or complexion. And this is why not two flashes are the same in the expression of universe - universe only exists once - even on smallest level there is a change to the next following flash - and changes on smallest level is being accomplished via constraints on smallest level - via observations on smallest level.
We humans like to think that such dynamic changes on lover levels - "like the fuzzing around of atoms" - that this is "natures way of expressing itself" and yes - of course - but WHY. Because of said above mentioned principle.
"Treating each position as a unique event makes more sense because they have to be unique in value based on the current gravity science."
YES - everything is unique - even on smallest level - but we are blind for this diversity because it is way beyond our measuring capabilities. A so called constant is just an approximation - but such approximations are more that good enough for the purposes where they are being applied. As I like to say - we decide the accuracy accordingly to what we want or need or can accomplish.
QUOTE (Cusa+Jan 5 2009, 08:49 AM)
Speed can transfer without acceleration in the phenomenon of momentum. Take two billiard balls one the cue the other black.
When you accelerate the cue ball with your stick it transfers its motion instantaneously when it strikes the black and stops. Momentum can transfer motion from one thing to another. The black ball is now the one with motion and the cue ball is still as the black ball was.
This is motion exchange. But motion must be created first. So acceleration of the cue ball comes first. In momentum the motion transferring is conserved.
Mitch Raemsch
Let me point our direction to your very own words in BOLD RED where it points out a violation with respects to your earlier statement as per quoted..
Lets say your WHOLE aether is with maximum velocity "c" "The speed of Light", and it was to speed up, How prey tell - would this be possible? specially if the whole Aether is already at maximum velocity?
what I am getting at, is that - for your referred Aether to speed up any faster, there would have to be something else even faster to push or accelerate the Aether to speed up, but this would mean the Aether is not at maximum velocity and therefore a medium must exist that is even less dense and more kinetic than the NEAR-Vacuum {SPACE} and or as you prefer to refer to it as the Aether..
I Hope I have pointed out a depth of reasoning far beyond previous reasoning by your good self, so you may sort out your contradictory statements..
Cheers,
Peter J Schoen..
When you accelerate the cue ball with your stick it transfers its motion instantaneously when it strikes the black and stops. Momentum can transfer motion from one thing to another. The black ball is now the one with motion and the cue ball is still as the black ball was.
This is motion exchange. But motion must be created first. So acceleration of the cue ball comes first. In momentum the motion transferring is conserved.
Mitch Raemsch
Let me point our direction to your very own words in BOLD RED where it points out a violation with respects to your earlier statement as per quoted..
QUOTE
The Aether is speeding up without end.
Mitch Raemsch
Mitch Raemsch
Lets say your WHOLE aether is with maximum velocity "c" "The speed of Light", and it was to speed up, How prey tell - would this be possible? specially if the whole Aether is already at maximum velocity?
what I am getting at, is that - for your referred Aether to speed up any faster, there would have to be something else even faster to push or accelerate the Aether to speed up, but this would mean the Aether is not at maximum velocity and therefore a medium must exist that is even less dense and more kinetic than the NEAR-Vacuum {SPACE} and or as you prefer to refer to it as the Aether..
I Hope I have pointed out a depth of reasoning far beyond previous reasoning by your good self, so you may sort out your contradictory statements..
Cheers,
Peter J Schoen..
QUOTE (bukh+Jan 5 2009, 09:01 AM)
Laidback
QUOTE: "QUOTE
Smallest "object of sameness" can be anything from "size of universe" divided into two or more ratios - and to "size of universe" divided into as many ratios as physically possible, and that is just before "infinitely many" and therefore physically non-existing - so everything between 0 and infinite.
The above last statement I feel is flawed with human like reasoning - Err~that doesn't read as I intend - How can I put this better???"
Yeah - I know -
Actually - the one thing I tried to communicate with the above is that:
Everything is according to the accuracy we want or chose for our definition/explaining of physical world.
The more accurate we measure - the "smaller" ratios of universe is being used -
And Yes - I believe that "smallness" is being available or is being present at the site of measurement - because we are ourselves as human constituents of smallness to a high degree - we are complex - i.e. we are constituents of very small pixels - and as such we will never reach the border of smallness in our measurements -
Whereas other parts of universe may well be made/defined out out from bigger "building blocks" and such areas of the universe cannot be measured with the same accuracy - but who cares - as long as we are on earth and its near vicinity. But it may well have implications for how the projections work over the universe - and give rise to significant differences in projections and the "reality" we extract from our observations of space - what is distances - size - everything is a reflection of the projections we get from our pixel-grid.
And happy to know that you so well agreed with what I postulated - great !
No problems,
Cheers,
Peter J Schoen..
QUOTE: "QUOTE
Smallest "object of sameness" can be anything from "size of universe" divided into two or more ratios - and to "size of universe" divided into as many ratios as physically possible, and that is just before "infinitely many" and therefore physically non-existing - so everything between 0 and infinite.
The above last statement I feel is flawed with human like reasoning - Err~that doesn't read as I intend - How can I put this better???"
Yeah - I know -
Actually - the one thing I tried to communicate with the above is that:
Everything is according to the accuracy we want or chose for our definition/explaining of physical world.
The more accurate we measure - the "smaller" ratios of universe is being used -
And Yes - I believe that "smallness" is being available or is being present at the site of measurement - because we are ourselves as human constituents of smallness to a high degree - we are complex - i.e. we are constituents of very small pixels - and as such we will never reach the border of smallness in our measurements -
Whereas other parts of universe may well be made/defined out out from bigger "building blocks" and such areas of the universe cannot be measured with the same accuracy - but who cares - as long as we are on earth and its near vicinity. But it may well have implications for how the projections work over the universe - and give rise to significant differences in projections and the "reality" we extract from our observations of space - what is distances - size - everything is a reflection of the projections we get from our pixel-grid.
And happy to know that you so well agreed with what I postulated - great !
No problems,
Cheers,
Peter J Schoen..
QUOTE (iseason+Jan 7 2009, 04:23 PM)
Hi all
I agree with sameness / ratio, But consider how we interact. WE use multiple representations of our smallest perceivable energy..(photon/ electron).
How would this change if we were a much larger or smaller object?....Sure dimensions and size change , but the methodology remains the same. Multiples are still important in information....Without multiples no information can be imparted. Obviously patterns of sameness are a level of information transfer...But the multiples rule applies to all.
Gravity is a prime example...Personally , I favor the receiver (smaller) as the most active participant , merely because they are receiving more "information" than the larger object which MUST interfere with itself. Perhaps it is just that action that allows the smaller object to approach a larger object. The information leaving a larger object is "more easily Incorporated" by the smaller object than the larger.
This is not against previous posts , but looking at differing levels of the matrix patterns. Inevitable patterns make sense , certainly no less because we see them in the real world , yet we explain them by simply looking at the history of the pattern and expecting that the pattern is eternal. (in the sense that atoms formed everywhere "by chance") at the same levels. Even if this were true , constants could never be truly constant as the gravity effect for every pixel in space would be variable to the same degree. Meaning that a photon would change value as it moved through space according to it's distance from every other object in space.
Treating each position as a unique event makes more sense because they have to be unique in value based on the current gravity science.
Cheers
Iseason
I see much is unravelling, and we are all converging on one of the last frontiers that is met with much difficulties under the current guise and or inference being gravity..
We have a new participant Cusa who I feel may provide some new insight, but obviously is in need of much grooming and or catchup, hope you guys can help him or her out and or put me straight if I am in error when I converse with him or her..
Cheers,
Peter J Schoen..
I agree with sameness / ratio, But consider how we interact. WE use multiple representations of our smallest perceivable energy..(photon/ electron).
How would this change if we were a much larger or smaller object?....Sure dimensions and size change , but the methodology remains the same. Multiples are still important in information....Without multiples no information can be imparted. Obviously patterns of sameness are a level of information transfer...But the multiples rule applies to all.
Gravity is a prime example...Personally , I favor the receiver (smaller) as the most active participant , merely because they are receiving more "information" than the larger object which MUST interfere with itself. Perhaps it is just that action that allows the smaller object to approach a larger object. The information leaving a larger object is "more easily Incorporated" by the smaller object than the larger.
This is not against previous posts , but looking at differing levels of the matrix patterns. Inevitable patterns make sense , certainly no less because we see them in the real world , yet we explain them by simply looking at the history of the pattern and expecting that the pattern is eternal. (in the sense that atoms formed everywhere "by chance") at the same levels. Even if this were true , constants could never be truly constant as the gravity effect for every pixel in space would be variable to the same degree. Meaning that a photon would change value as it moved through space according to it's distance from every other object in space.
Treating each position as a unique event makes more sense because they have to be unique in value based on the current gravity science.
Cheers
Iseason
I see much is unravelling, and we are all converging on one of the last frontiers that is met with much difficulties under the current guise and or inference being gravity..
We have a new participant Cusa who I feel may provide some new insight, but obviously is in need of much grooming and or catchup, hope you guys can help him or her out and or put me straight if I am in error when I converse with him or her..
Cheers,
Peter J Schoen..
Hi Guys
Gravity is an interesting one. Although we can almost universally agree with "what it does", there is certainly an open agenda as to what it IS.
I wrote a post on oxygen being the instigator of Fire, but as a preventer of greater loss of energy. Gravity theory seeks to give the larger object an almost unlimited resource to attract a smaller object , which is against a conservative universe. This is my reasoning for seeing the smaller object as the instigator.
1. it has a greater opportunity to gain "rest state"
2. on it's own a particle moves according to being "hit" by even smaller energy.(waves).
3. Therefore, A larger object (just being a grouping of smaller particles), Can only send out a "combined" wave into space, which is unique to that object alone.
That means that at some level, the signal "means something" to other objects. But that is dependent on the object and not the larger mass. They smaller object may find greatest rest v work in the zone where the information from the larger object "makes sense" and seek to aline itself to that position according to it's own make up as a "receiver".....Remembering that it is itself made up of many smaller objects and gives a unique wave signal as well.
So upon a surface like terrestial earth, there are "best fit" levels of interaction right down to the lowest level, but not dictated by the biggest "drawing the smallest", but by the smaller finding the "best fit".
To what can the earth add to an object which is moving. Would it be sensible to say that the earth is preventing it from doing so?....to what benefit to the earth?...and at what cost?....The earth would be required to continually "hold" the object in place, even reaching outwards to "draw" the object back as it left.
But the earth is just a grouping of base elements, with no central "brain function", so how does it decide ? Isn't it more logical that the parts "choose" to group because this is mutually beneficial. This would then be individual groupings deciding on Best fit.
Here is an example.....I am a Gold atom.....Currently I am in a perfectly conservative arrangement, but by information I receive from around me I can do better by moving further into the mass....So I won't roll uphill.
Since people are made up of groupings like the gold example, we are moving it into less conservative positions than it would otherwise choose for itself, so we must force the particles within us to act against their best choices.
Cheers
Iseason
Gravity is an interesting one. Although we can almost universally agree with "what it does", there is certainly an open agenda as to what it IS.
I wrote a post on oxygen being the instigator of Fire, but as a preventer of greater loss of energy. Gravity theory seeks to give the larger object an almost unlimited resource to attract a smaller object , which is against a conservative universe. This is my reasoning for seeing the smaller object as the instigator.
1. it has a greater opportunity to gain "rest state"
2. on it's own a particle moves according to being "hit" by even smaller energy.(waves).
3. Therefore, A larger object (just being a grouping of smaller particles), Can only send out a "combined" wave into space, which is unique to that object alone.
That means that at some level, the signal "means something" to other objects. But that is dependent on the object and not the larger mass. They smaller object may find greatest rest v work in the zone where the information from the larger object "makes sense" and seek to aline itself to that position according to it's own make up as a "receiver".....Remembering that it is itself made up of many smaller objects and gives a unique wave signal as well.
So upon a surface like terrestial earth, there are "best fit" levels of interaction right down to the lowest level, but not dictated by the biggest "drawing the smallest", but by the smaller finding the "best fit".
To what can the earth add to an object which is moving. Would it be sensible to say that the earth is preventing it from doing so?....to what benefit to the earth?...and at what cost?....The earth would be required to continually "hold" the object in place, even reaching outwards to "draw" the object back as it left.
But the earth is just a grouping of base elements, with no central "brain function", so how does it decide ? Isn't it more logical that the parts "choose" to group because this is mutually beneficial. This would then be individual groupings deciding on Best fit.
Here is an example.....I am a Gold atom.....Currently I am in a perfectly conservative arrangement, but by information I receive from around me I can do better by moving further into the mass....So I won't roll uphill.
Since people are made up of groupings like the gold example, we are moving it into less conservative positions than it would otherwise choose for itself, so we must force the particles within us to act against their best choices.
Cheers
Iseason
When it comes to Gravity, I feel I am very alone, as my model is based Strictly on Force and Motion Laws, but it is critical that one gives much deep thought on how force is enacted based strictly on what is laid out by Force and Motion Laws, thus far no one else I know - I don't think have come to the same conclusion as I where I insist,
Force can only ever be Repulsive..
Seriously - I feel attraction is not a force on its own accord, but rather attraction is a PERCEPTION resulting from repulsion and or a POTENTIAL presenting its stored energy via its opposing velocities (REPULSION)..
Needless to say I have held this model, which rejects the inference "That force can also be attractive" for quite a few decades now, and since the Internet connected up world wide, I was quietly confident most would catch up to my reasoning, but alas this has not happened as yet, and I don't think this will happen for quite some time, in fact I feel it may be centuries before my reasoning is commonly accepted..
But on the off chance someone else is willing to put the same effort into a difficult construct,
LET ME POINT OUT WHY FORCE CAN ONLY EVER BE TREATED AS BEING REPULSIVE..
Lets refer to the following symbols..
LET ">" equal a Velocity to the right, ergo a push by it will be experienced on our left by it, which results with our density or mass to be also with a velocity to the left if we were out in Space (NEAR-Vacuum).
LET "<" equal a Velocity to the left, ergo a push by it will be experienced on our right by it, which results with our density or mass to be also with a velocity to the right if we were out in Space (NEAR-Vacuum).
Now lets consider each of the following symbols in the following models as astronauts in a NEAR-Vacuum with the intent to move towards the suggested directions and lets conclude whether a change is possible..
> > Here each astronaut jumps to the right but even so, they still do not make contact with each other and they remain where they are.
< < Here each astronaut jumps to the left but even so they still do not make contact and they remain where they are.
<> Here each astronaut jumps with the other astronaut jumping in the opposite direction, importantly they begin by standing on each other, so each astronaut will end up with a velocity, (a repulsive action) using their combined Potential energy.
> < But as each Astronaut departs they fear the departure so they turn them selves around and action out a jump in order they meet up again ( An attractive action), the result is their velocity remains without change to it so they continue to part, ergo eventually their mass may stike another mass of much the same density and with their respective motion, it is percieved as force upon each other, noting each density was motioned by a previous Repulsion..
Hmm not an easy subject to describe, but what is important to consider here is that force and motion rely on each other to be possible and the only way motion is possible is via repulsion..
Put simply for force to be experienced we need a density to be with momentum to it, and for a density to be moved we need a force to be presented to it.
Another model at this point to consider is, where we have two balloons, each are the same size but one has twice the density stored within it..
So that when we prod them one presents as harder, as one has more mass or stored energy within {More cancelled out opposing velocities}
Now if we consider Energy laws and how Kinetic energy is converted to Potential energy, we should be able to reason how one balloon is able to present more rigid and or solid simply by the following rule..
Two opposing velocities that converge, cancels out velocities and becuase velocity is an inference to kinetic energy, while a solid density is an inference to stored kinetic energy, but how does one store motion?..
Here is a mathematical model where a positive number is treated as a left trajectory (velocity) and a negative number as a right trajectory (velocity).
Ke(-C) + Ke(+C) = Ke^2(C=Zero)
Here is a two framed depiction of the above maths, where each mass is with (Width=Ke) * (Height=Pe) and each are depicted as the following form in the quotes "-"
"--" Here, each density is with maximum converging velocity one at -c velocity the other at +c velocity
"=" Here, they are merged (zero c velocity) representing a single density with twice the Potential, importantly each as far as they are concerned are still with a velocity @c, but to all else they are going nowhere!.. REFERENCES: Relativity
Note how in our first moment we have maximum width (kinetics or implied momentum) with very little height (potential or stored motion), and in our final frame we have minimum width (kinetic energy) with maxium height (Potential energy), note how kinetic value is converted to Potential value, where we initially had a near vacuum density with very little force and or potential to it, ending up with a relative solid that is with very little momentum to it but with a prominant presence of something rigid, put simply consider how a ratio of potential to kinetic energy is important in presenting a density as either a near vacuum, gas, liquid, and or a solid and note the more compressed (cancelled out Kinetics or velocities) the more solid the density, and another consideration is how the speed of light is propagated slower in a solid density than via a Near vacuum density, to which in the above model hopefully clearly shows us why this is so..
I am restricted with time today, as I have to produce some BlueRay Disks with the videos I have taken over the festivities using my New HD camcorder, so I will catch ya all later..
Cheers,
Peter J Schoen..
Force can only ever be Repulsive..
Seriously - I feel attraction is not a force on its own accord, but rather attraction is a PERCEPTION resulting from repulsion and or a POTENTIAL presenting its stored energy via its opposing velocities (REPULSION)..
Needless to say I have held this model, which rejects the inference "That force can also be attractive" for quite a few decades now, and since the Internet connected up world wide, I was quietly confident most would catch up to my reasoning, but alas this has not happened as yet, and I don't think this will happen for quite some time, in fact I feel it may be centuries before my reasoning is commonly accepted..
But on the off chance someone else is willing to put the same effort into a difficult construct,
LET ME POINT OUT WHY FORCE CAN ONLY EVER BE TREATED AS BEING REPULSIVE..
Lets refer to the following symbols..
LET ">" equal a Velocity to the right, ergo a push by it will be experienced on our left by it, which results with our density or mass to be also with a velocity to the left if we were out in Space (NEAR-Vacuum).
LET "<" equal a Velocity to the left, ergo a push by it will be experienced on our right by it, which results with our density or mass to be also with a velocity to the right if we were out in Space (NEAR-Vacuum).
Now lets consider each of the following symbols in the following models as astronauts in a NEAR-Vacuum with the intent to move towards the suggested directions and lets conclude whether a change is possible..
> > Here each astronaut jumps to the right but even so, they still do not make contact with each other and they remain where they are.
< < Here each astronaut jumps to the left but even so they still do not make contact and they remain where they are.
<> Here each astronaut jumps with the other astronaut jumping in the opposite direction, importantly they begin by standing on each other, so each astronaut will end up with a velocity, (a repulsive action) using their combined Potential energy.
> < But as each Astronaut departs they fear the departure so they turn them selves around and action out a jump in order they meet up again ( An attractive action), the result is their velocity remains without change to it so they continue to part, ergo eventually their mass may stike another mass of much the same density and with their respective motion, it is percieved as force upon each other, noting each density was motioned by a previous Repulsion..
Hmm not an easy subject to describe, but what is important to consider here is that force and motion rely on each other to be possible and the only way motion is possible is via repulsion..
Put simply for force to be experienced we need a density to be with momentum to it, and for a density to be moved we need a force to be presented to it.
Another model at this point to consider is, where we have two balloons, each are the same size but one has twice the density stored within it..
So that when we prod them one presents as harder, as one has more mass or stored energy within {More cancelled out opposing velocities}
Now if we consider Energy laws and how Kinetic energy is converted to Potential energy, we should be able to reason how one balloon is able to present more rigid and or solid simply by the following rule..
Two opposing velocities that converge, cancels out velocities and becuase velocity is an inference to kinetic energy, while a solid density is an inference to stored kinetic energy, but how does one store motion?..
Here is a mathematical model where a positive number is treated as a left trajectory (velocity) and a negative number as a right trajectory (velocity).
Ke(-C) + Ke(+C) = Ke^2(C=Zero)
Here is a two framed depiction of the above maths, where each mass is with (Width=Ke) * (Height=Pe) and each are depicted as the following form in the quotes "-"
"--" Here, each density is with maximum converging velocity one at -c velocity the other at +c velocity
"=" Here, they are merged (zero c velocity) representing a single density with twice the Potential, importantly each as far as they are concerned are still with a velocity @c, but to all else they are going nowhere!.. REFERENCES: Relativity
Note how in our first moment we have maximum width (kinetics or implied momentum) with very little height (potential or stored motion), and in our final frame we have minimum width (kinetic energy) with maxium height (Potential energy), note how kinetic value is converted to Potential value, where we initially had a near vacuum density with very little force and or potential to it, ending up with a relative solid that is with very little momentum to it but with a prominant presence of something rigid, put simply consider how a ratio of potential to kinetic energy is important in presenting a density as either a near vacuum, gas, liquid, and or a solid and note the more compressed (cancelled out Kinetics or velocities) the more solid the density, and another consideration is how the speed of light is propagated slower in a solid density than via a Near vacuum density, to which in the above model hopefully clearly shows us why this is so..
I am restricted with time today, as I have to produce some BlueRay Disks with the videos I have taken over the festivities using my New HD camcorder, so I will catch ya all later..
Cheers,
Peter J Schoen..
Hi Laidback
First. I understand what you are trying to say. (despite probably using conflicting terminology)
There is also a way I see gravity forces/actions which seems hard for current thinking to grasp. That is that the relationship cannot simply change because a smaller mass becomes part of a larger mass. Therefore small objects always act like small objects.
To elaborate, every mass needs to know where it is in relation to every other mass. This is not a secondary action to singular particle function , but what we observe using multiples.
When we observe a mass, the initial conclusion is that it is sending waves OUTWARDS. But as you have rightly pointed out, they cannot do so unless they first have something to "bounce off". I call this action inventory. In it's smallest state, mass is formed by standing waves, so why change the theme just because there are two or more. When multiples appear together, it is logical that a sampling of the mass creates a local center, regardless of the shape or change in density....There may even be numerous centers in close proximity (as in atomic)
Let's say our mass is a ball. The ball could not possibly send out waves unless it were depleting it's own resources considerably, making it unconservative. This is precisely what science says is occurring, that the sun is "holding" us via a force which must first know we are there , then decide to take an action.
But let's say the ball sends waves inwardly as a first action. This is in line with it as a standing wave. The center has a given local mass that is part of the "informational" wave that travels outwardly. In every direction, the frequency of the wave tells whatever it encounters exactly what it is. Likewise the waves that are received from other masses gives it important information of what is around it.
Importantly, each individual "mass " has a contribution to the outward wave made possible only if it has first put the information into a local collection point. From there gravity theory can work as stated in mainstream, but the initiation of the gravity wave is "what am I "
This is why gravity is so weak. Each mass(atomic) only has to contribute to be measured. the outward moving wave needs only to have the information, not a "force"
Then the receiving mass can act on information it has received, not be drawn into anything. "I go to earth because my mass can perceive a more conservative position exists than the one I occupy".
Cheers
Iseason
First. I understand what you are trying to say. (despite probably using conflicting terminology)
There is also a way I see gravity forces/actions which seems hard for current thinking to grasp. That is that the relationship cannot simply change because a smaller mass becomes part of a larger mass. Therefore small objects always act like small objects.
To elaborate, every mass needs to know where it is in relation to every other mass. This is not a secondary action to singular particle function , but what we observe using multiples.
When we observe a mass, the initial conclusion is that it is sending waves OUTWARDS. But as you have rightly pointed out, they cannot do so unless they first have something to "bounce off". I call this action inventory. In it's smallest state, mass is formed by standing waves, so why change the theme just because there are two or more. When multiples appear together, it is logical that a sampling of the mass creates a local center, regardless of the shape or change in density....There may even be numerous centers in close proximity (as in atomic)
Let's say our mass is a ball. The ball could not possibly send out waves unless it were depleting it's own resources considerably, making it unconservative. This is precisely what science says is occurring, that the sun is "holding" us via a force which must first know we are there , then decide to take an action.
But let's say the ball sends waves inwardly as a first action. This is in line with it as a standing wave. The center has a given local mass that is part of the "informational" wave that travels outwardly. In every direction, the frequency of the wave tells whatever it encounters exactly what it is. Likewise the waves that are received from other masses gives it important information of what is around it.
Importantly, each individual "mass " has a contribution to the outward wave made possible only if it has first put the information into a local collection point. From there gravity theory can work as stated in mainstream, but the initiation of the gravity wave is "what am I "
This is why gravity is so weak. Each mass(atomic) only has to contribute to be measured. the outward moving wave needs only to have the information, not a "force"
Then the receiving mass can act on information it has received, not be drawn into anything. "I go to earth because my mass can perceive a more conservative position exists than the one I occupy".
Cheers
Iseason
Hej
Forces are repulsive - yes - but I think it is perhaps even important to ponder what a force IS.
Force is showing change and I like to see change as the forerunner of force - first something change and then we see it as a force.
The underlying mechanism of change is how dimensionalities constantly change their belonging - at one moment a certain dimensionality is defining - is being part of - one object and in the next following moment the said dimension is part of another object. So it as about where and when a dimensionality is part of an object - and this is being decided by the ever ongoing re-arrangements in space of smallest dimensionality's -
Any change - any force is being initiated by such a re-arrangement - and any such re-arrangement is domino-like involving all the surroundings - of course with inertia - and with smaller and smaller effects as it spreads and is being counteracted. But all changes are being initialized at a place and then spread out and counteracted - so in Principal all forces are repulsive.
Season: "That is that the relationship cannot simply change because a smaller mass becomes part of a larger mass. Therefore small objects always act like small objects."
Hmm - I would say that relationships ALWAYS change - sooner or later - hierarchically of course. Particle-structures are stable - an atom is an atom in the sense that it is made as a stable repeating configuration - but being configured of ever changing smaller objects as the atom change position.
Iseason: "To elaborate, every mass needs to know where it is in relation to every other mass. This is not a secondary action to singular particle function , but what we observe using multiples."
Yes - exactly - every mass knows its exact position relative to its surroundings - and definition of mass is relative as to the re-arrangement pattern - it is the pattern as seen by the observer that defines where the mass is, relativity is absolute and relevant into the smallest - of course. It is not possible to define a "mass" or a "particle" without defining the observer frame.
Forces are repulsive - yes - but I think it is perhaps even important to ponder what a force IS.
Force is showing change and I like to see change as the forerunner of force - first something change and then we see it as a force.
The underlying mechanism of change is how dimensionalities constantly change their belonging - at one moment a certain dimensionality is defining - is being part of - one object and in the next following moment the said dimension is part of another object. So it as about where and when a dimensionality is part of an object - and this is being decided by the ever ongoing re-arrangements in space of smallest dimensionality's -
Any change - any force is being initiated by such a re-arrangement - and any such re-arrangement is domino-like involving all the surroundings - of course with inertia - and with smaller and smaller effects as it spreads and is being counteracted. But all changes are being initialized at a place and then spread out and counteracted - so in Principal all forces are repulsive.
Season: "That is that the relationship cannot simply change because a smaller mass becomes part of a larger mass. Therefore small objects always act like small objects."
Hmm - I would say that relationships ALWAYS change - sooner or later - hierarchically of course. Particle-structures are stable - an atom is an atom in the sense that it is made as a stable repeating configuration - but being configured of ever changing smaller objects as the atom change position.
Iseason: "To elaborate, every mass needs to know where it is in relation to every other mass. This is not a secondary action to singular particle function , but what we observe using multiples."
Yes - exactly - every mass knows its exact position relative to its surroundings - and definition of mass is relative as to the re-arrangement pattern - it is the pattern as seen by the observer that defines where the mass is, relativity is absolute and relevant into the smallest - of course. It is not possible to define a "mass" or a "particle" without defining the observer frame.
The speed of light acts like an infinity to the speed of matter.
Mitch Raemsch
Mitch Raemsch
Hi Guys
The depth of reasoning here is fantastic!
Both of you Buhk and Iseason,
I have to say are both on much the same page, and between you there sits a critical key point that answers much about how change or information is negotiated, what I am trying to convey is a concept or a simple inference that links your models to each others in an astoundingly clear way to me..
There is one small hick-up I feel is a slight hindrance, {Hope I am wrong?} anyway I feel the following may help..
My problem is if I do mention an inference to it or if I were to refer to models it may still not become clear to either of you, but the risk I am about to take - I feel justifies the following..
First, lets consider the whole Universe as a single body of energy.
Second step is to consider if said body is to present itself, it would need an audience.
But as a single unchanging mass this is simply not possible.
Unless change ergo an exchange is possible..
But for change to be possible, an exchange must also be possible, and this requires more than one (Self) and whats more acknowledgement and agreement by said two.
So if we consider what I just stated, I have in fact referred to some pre-existing Rules and conformity to said rules..
In fact thus far I have only implied to two Rules, which are really Rules with further in-depth complexity which are dependent on agreed exchanged allowances and or possibilities between said two.. Oy! already the complexity has increased more than I could care for..
Anyway,
1/. To exist is to present to an audience that importantly acknowledges.
2/. Therefore to exist is to also acknowledge all presentations..
At this point to keep it as simple as possible, let me simply state "Reciprocal" and to consider the following models,
but first there is one small point I would like to point out in that we consider that all mass or densities are never at rest simply because to cease exchange is to cease to exist, also It wont hurt to mention conservation of energy laws, in particular what energy exists right now has always existed, so our Universe should be treated as a closed system with a given value of energy and further more implied values are implied individuals that may devour ergo increase in value, spawn and or create individuals (divisions) to present or express an increase of value to else by them devouring or acknowledging presented value..
Anyway here's that model I promised - one could say its a two pixel model,
There are two frames of time, referring to a start and end cycle and the other moment is an out of phase start and end cycle, and mind you the model is only to imply how change must be acknowledged and adhered to - if ones own existence is to be possible..
".." Here is the End and Start of a cycle or existence and or Death and Birth or if one wishes - The presenter on the left has completed an expression, as the one on the right has listened or devoured presentation and is now about to present itself..
".." And Here is the Middle of our cycle or one could also consider it as an out of phase start and end cycle and or Birth and Death.
The above modeling should be treated as a closed system where if modelled to the Universe or as any given Particle as we know it, each must cycle in much the same fashion, but I concede in a much more complex manner and perhaps at levels that may be beyond human reasoning, to which I feel I must with-hold at this point what modelling I have thus far considered - so I don't confuse or inject to much as to how change is initiated, bar of course the suggestion of the above model in this case models a Universe with a single galaxy which in this case is on the right in our first instance or moment if it were relative to our galaxy..
I hope I have been clear, and importantly cryptic enough so other unrelated critical considerations have come to mind, for example : Like when you were reading my above statements and a thought sprang to your mind, Its that very thought that needs to be aired here, as my statements were written to eek exactly those thoughts out, Err~I Hope you don't mind this unusual method of my probing BTW?
Cheers,
Peter J Schoen
The depth of reasoning here is fantastic!
Both of you Buhk and Iseason,
I have to say are both on much the same page, and between you there sits a critical key point that answers much about how change or information is negotiated, what I am trying to convey is a concept or a simple inference that links your models to each others in an astoundingly clear way to me..
There is one small hick-up I feel is a slight hindrance, {Hope I am wrong?} anyway I feel the following may help..
My problem is if I do mention an inference to it or if I were to refer to models it may still not become clear to either of you, but the risk I am about to take - I feel justifies the following..
First, lets consider the whole Universe as a single body of energy.
Second step is to consider if said body is to present itself, it would need an audience.
But as a single unchanging mass this is simply not possible.
Unless change ergo an exchange is possible..
But for change to be possible, an exchange must also be possible, and this requires more than one (Self) and whats more acknowledgement and agreement by said two.
So if we consider what I just stated, I have in fact referred to some pre-existing Rules and conformity to said rules..
In fact thus far I have only implied to two Rules, which are really Rules with further in-depth complexity which are dependent on agreed exchanged allowances and or possibilities between said two.. Oy! already the complexity has increased more than I could care for..
Anyway,
1/. To exist is to present to an audience that importantly acknowledges.
2/. Therefore to exist is to also acknowledge all presentations..
At this point to keep it as simple as possible, let me simply state "Reciprocal" and to consider the following models,
but first there is one small point I would like to point out in that we consider that all mass or densities are never at rest simply because to cease exchange is to cease to exist, also It wont hurt to mention conservation of energy laws, in particular what energy exists right now has always existed, so our Universe should be treated as a closed system with a given value of energy and further more implied values are implied individuals that may devour ergo increase in value, spawn and or create individuals (divisions) to present or express an increase of value to else by them devouring or acknowledging presented value..
Anyway here's that model I promised - one could say its a two pixel model,
There are two frames of time, referring to a start and end cycle and the other moment is an out of phase start and end cycle, and mind you the model is only to imply how change must be acknowledged and adhered to - if ones own existence is to be possible..
".." Here is the End and Start of a cycle or existence and or Death and Birth or if one wishes - The presenter on the left has completed an expression, as the one on the right has listened or devoured presentation and is now about to present itself..
".." And Here is the Middle of our cycle or one could also consider it as an out of phase start and end cycle and or Birth and Death.
The above modeling should be treated as a closed system where if modelled to the Universe or as any given Particle as we know it, each must cycle in much the same fashion, but I concede in a much more complex manner and perhaps at levels that may be beyond human reasoning, to which I feel I must with-hold at this point what modelling I have thus far considered - so I don't confuse or inject to much as to how change is initiated, bar of course the suggestion of the above model in this case models a Universe with a single galaxy which in this case is on the right in our first instance or moment if it were relative to our galaxy..
I hope I have been clear, and importantly cryptic enough so other unrelated critical considerations have come to mind, for example : Like when you were reading my above statements and a thought sprang to your mind, Its that very thought that needs to be aired here, as my statements were written to eek exactly those thoughts out, Err~I Hope you don't mind this unusual method of my probing BTW?
Cheers,
Peter J Schoen
QUOTE (Cusa+Jan 15 2009, 06:35 AM)
The speed of light acts like an infinity to the speed of matter.
Mitch Raemsch
Yeah OK Mitch~And?..
Cheers,
Peter J Schoen..
Mitch Raemsch
Yeah OK Mitch~And?..
Cheers,
Peter J Schoen..
QUOTE (Laidback+Jan 14 2009, 11:08 PM)
Yeah OK Mitch~And?..
Cheers,
Peter J Schoen..
Also there are sizes of infinity of the infinitely small.
Mitch Raemsch
Cheers,
Peter J Schoen..
Also there are sizes of infinity of the infinitely small.
Mitch Raemsch
QUOTE (Cusa+Jan 15 2009, 09:35 AM)
The speed of light acts like an infinity to the speed of matter.
Mitch Raemsch
This is correct. Only, That Matter stands still in order to give light a speed of "one".
Light doesn't have infinate speeds ....Sorry.
Cheers
Iseason
Mitch Raemsch
This is correct. Only, That Matter stands still in order to give light a speed of "one".
Light doesn't have infinate speeds ....Sorry.
Cheers
Iseason
QUOTE (iseason+Jan 15 2009, 04:40 PM)
This is correct. Only, That Matter stands still in order to give light a speed of "one".
Light doesn't have infinate speeds ....Sorry.
Cheers
Iseason
Sorry. This is not clear.
This is correct.
But you are assuming that light speed requiring infinite energy for mass to achieve is
1.possible
2.out of relativity.
If Light (electron/photon level) were to be seen relatively then it would see ANY mass moving at "mass speed" which is in fact light speed reversed. So If anything were to change, it affects both by an equal degree.
Cheers
Iseason
Light doesn't have infinate speeds ....Sorry.
Cheers
Iseason
Sorry. This is not clear.
This is correct.
But you are assuming that light speed requiring infinite energy for mass to achieve is
1.possible
2.out of relativity.
If Light (electron/photon level) were to be seen relatively then it would see ANY mass moving at "mass speed" which is in fact light speed reversed. So If anything were to change, it affects both by an equal degree.
Cheers
Iseason
Hi all
With respect to all answers.
We need to be able to show these parameters. I don't know what the symbols are for universal or "whole" so I will use the word. I also need to use beginning and end and so I will use A and O (alpha and omega) to denote time. So from either the smallest or largest position we get .
Whole = A=O
When considering a singular position within the above equation , it would be
Whole = A (-) O = Whole
Multiples can be seen in various guises depending on where you look , but must always retain the distinction of their effect. These are denoted via their brackets.
So the above equation could be written Whole = A (-) O=Whole
If we are showing multiples then the change is shown as
Whole = A((=))O= Whole Or Whole = A((((= =))))O= Whole.
In that way the system is closed but shows the relationship between the beginning and end. As mass increases, it increases the gravity and resistant nature but retains the need to add weight for each additional mass .
Because as we recall, The graviton is expected to be in every particle. The brackets build the gravity along with the mass.
Two clusters are
Whole= A((((==)))) + ((((==))))O = Whole
Cheers
Iseason
With respect to all answers.
We need to be able to show these parameters. I don't know what the symbols are for universal or "whole" so I will use the word. I also need to use beginning and end and so I will use A and O (alpha and omega) to denote time. So from either the smallest or largest position we get .
Whole = A=O
When considering a singular position within the above equation , it would be
Whole = A (-) O = Whole
Multiples can be seen in various guises depending on where you look , but must always retain the distinction of their effect. These are denoted via their brackets.
So the above equation could be written Whole = A (-) O=Whole
If we are showing multiples then the change is shown as
Whole = A((=))O= Whole Or Whole = A((((= =))))O= Whole.
In that way the system is closed but shows the relationship between the beginning and end. As mass increases, it increases the gravity and resistant nature but retains the need to add weight for each additional mass .
Because as we recall, The graviton is expected to be in every particle. The brackets build the gravity along with the mass.
Two clusters are
Whole= A((((==)))) + ((((==))))O = Whole
Cheers
Iseason
hi
QUOTE (Lisa11+Jan 15 2009, 09:47 PM)
hi
Hi Lisa11
Welcome to the forum.
Iseason
Hi Lisa11
Welcome to the forum.
Iseason
QUOTE (iseason+Jan 15 2009, 03:25 AM)
Hi all
With respect to all answers.
We need to be able to show these parameters. I don't know what the symbols are for universal or "whole" so I will use the word. I also need to use beginning and end and so I will use A and O (alpha and omega) to denote time. So from either the smallest or largest position we get .
Whole = A=O
When considering a singular position within the above equation , it would be
Whole = A (-) O = Whole
Multiples can be seen in various guises depending on where you look , but must always retain the distinction of their effect. These are denoted via their brackets.
So the above equation could be written Whole = A (-) O=Whole
If we are showing multiples then the change is shown as
Whole = A((=))O= Whole Or Whole = A((((= =))))O= Whole.
In that way the system is closed but shows the relationship between the beginning and end. As mass increases, it increases the gravity and resistant nature but retains the need to add weight for each additional mass .
Because as we recall, The graviton is expected to be in every particle. The brackets build the gravity along with the mass.
Two clusters are
Whole= A((((==)))) + ((((==))))O = Whole
Cheers
Iseason
Total gibberish.
With respect to all answers.
We need to be able to show these parameters. I don't know what the symbols are for universal or "whole" so I will use the word. I also need to use beginning and end and so I will use A and O (alpha and omega) to denote time. So from either the smallest or largest position we get .
Whole = A=O
When considering a singular position within the above equation , it would be
Whole = A (-) O = Whole
Multiples can be seen in various guises depending on where you look , but must always retain the distinction of their effect. These are denoted via their brackets.
So the above equation could be written Whole = A (-) O=Whole
If we are showing multiples then the change is shown as
Whole = A((=))O= Whole Or Whole = A((((= =))))O= Whole.
In that way the system is closed but shows the relationship between the beginning and end. As mass increases, it increases the gravity and resistant nature but retains the need to add weight for each additional mass .
Because as we recall, The graviton is expected to be in every particle. The brackets build the gravity along with the mass.
Two clusters are
Whole= A((((==)))) + ((((==))))O = Whole
Cheers
Iseason
Total gibberish.
QUOTE (iseason+Jan 15 2009, 03:40 AM)
This is correct. Only, That Matter stands still in order to give light a speed of "one".
Light doesn't have infinate speeds ....Sorry.
Cheers
Iseason
You can move behind light.
Light doesn't have infinate speeds ....Sorry.
Cheers
Iseason
You can move behind light.
Axiom of infinity is that there is a set that contains zero and the next element of each of its elements. If so, it should, that there is a set that contains zero and the previous element of each of its elements. Does such a set? :-)
In our world there are two global powers. Of attraction and repulsion. If the force of gravity is the attraction, the strength of repulsion is entropy. If there is only one force, the universe will be unstable. Without any existing form.
hmmmmmm
----------------------------
www.logica-bg.com
In our world there are two global powers. Of attraction and repulsion. If the force of gravity is the attraction, the strength of repulsion is entropy. If there is only one force, the universe will be unstable. Without any existing form.
hmmmmmm
----------------------------
www.logica-bg.com
QUOTE (Cusa+Jan 15 2009, 09:13 AM)
Also there are sizes of infinity of the infinitely small.
Mitch Raemsch
OK lets stop here and lets get back to your first statement, and please state a statement with some proper logic to it, rather than some meaningless religious like gibber..
Whats your point or Intent?
2~Duh-Loo!
Peter J Schoen..
Mitch Raemsch
OK lets stop here and lets get back to your first statement, and please state a statement with some proper logic to it, rather than some meaningless religious like gibber..
Whats your point or Intent?
2~Duh-Loo!
Peter J Schoen..
QUOTE (Laidback+Jan 16 2009, 10:59 PM)
OK lets stop here and lets get back to your first statement, and please state a statement with some proper logic to it, rather than some meaningless religious like gibber..
Whats your point or Intent?
2~Duh-Loo!
Peter J Schoen..
There are two "math" points. One zero dimensional and the other infinitely small nonzero.
Mitch Raemsch
Whats your point or Intent?
2~Duh-Loo!
Peter J Schoen..
There are two "math" points. One zero dimensional and the other infinitely small nonzero.
Mitch Raemsch
hej Cusa et al -
QUOTE: "Also there are sizes of infinity of the infinitely small. --There are two "math" points. One zero dimensional and the other infinitely small nonzero."
My take on the above is related to the idea that physical world best can be seen as how information is being created and eventually de-coded by humans.
Physical Universe IS information, information has taken the disguise of dimensionality - or "object of sameness" with a SHAPE. Everything in physical world can be defined as a shape in space, and each shape is being defined out from how smallest dimensionalities are configuring and re-configuring such shapes - flashlike, so "Universe Exists Only Once" - in each such flash configuration - and in the next following moment is has taken a new configuration.
Smallest or Discreteness - to me it would seem that the question about quantization is merely a question about scaling - meaning that it is always possible in theory to downscale as long as one wish - and continuity is just another word for -"I am not in the mood to scale further down", because irrespective the scale we decide to look at, it will always be possible to define a smaller - and so-called smallest can always be further divided. True zero is not into existence. True zero is a mathematical concept - is a virtual existence - is a true mind invention - and has no bearing to physical world.
And the Holographic principle to me is something that must be - it is inevitable - because there exist no such thing as "an instructor" - there is no underlying principle that can govern universe - universe is a full system with the principles included in the system - the system is self explanatory - self developing, so to speak.
So even in the smallest there must be the full and needed information for the next following step - next following scale - or whatever one wish to call it.
So even the smallest MUST harbor all the needed information - there cannot be such a thing as "null-dimensional" - because that is the same as accepting "null-informational" - it is meaningless to operate with principles like null-dimensions - OK they can be "null" - when seen in a certain scale relative to another - and so on - but this has to do with scales - it has not to do with true zero.
QUOTE: "Also there are sizes of infinity of the infinitely small. --There are two "math" points. One zero dimensional and the other infinitely small nonzero."
My take on the above is related to the idea that physical world best can be seen as how information is being created and eventually de-coded by humans.
Physical Universe IS information, information has taken the disguise of dimensionality - or "object of sameness" with a SHAPE. Everything in physical world can be defined as a shape in space, and each shape is being defined out from how smallest dimensionalities are configuring and re-configuring such shapes - flashlike, so "Universe Exists Only Once" - in each such flash configuration - and in the next following moment is has taken a new configuration.
Smallest or Discreteness - to me it would seem that the question about quantization is merely a question about scaling - meaning that it is always possible in theory to downscale as long as one wish - and continuity is just another word for -"I am not in the mood to scale further down", because irrespective the scale we decide to look at, it will always be possible to define a smaller - and so-called smallest can always be further divided. True zero is not into existence. True zero is a mathematical concept - is a virtual existence - is a true mind invention - and has no bearing to physical world.
And the Holographic principle to me is something that must be - it is inevitable - because there exist no such thing as "an instructor" - there is no underlying principle that can govern universe - universe is a full system with the principles included in the system - the system is self explanatory - self developing, so to speak.
So even in the smallest there must be the full and needed information for the next following step - next following scale - or whatever one wish to call it.
So even the smallest MUST harbor all the needed information - there cannot be such a thing as "null-dimensional" - because that is the same as accepting "null-informational" - it is meaningless to operate with principles like null-dimensions - OK they can be "null" - when seen in a certain scale relative to another - and so on - but this has to do with scales - it has not to do with true zero.
Perhaps information is recycled via sub event horizon convergence, spared as a direct consequence of an energy based Lorentz transformational affect, thus allowing constant universal evolution.
The Crank.
The Crank.
Geoff
QUOTE: "Perhaps information is recycled via sub event horizon convergence, spared as a direct consequence of an energy based Lorentz transformational affect, thus allowing constant universal evolution.
The Crank."
Fundamentally I like the idea that physical world IS information -
There is no need to make artificial distinctions between so called physical expressions and informational expressions - they are fundamentally the same - and we humans are tempted not to see the similarities.
You say "energy based Lorentz transformation" - and already here you are indicating that energy is something physical, but fundamentally I see energy as information.
Whenever we refer to energy it is related to changes. When a "particle" is moved from A to B in our physical world, we call it energy - and fundamentally it is information, information how to define the said particle in one place and then how the particle is re-placed cinematographically -like a movie strip - to the next place - and it is fundamentally about how smallest dimensionality's are configuring and re-configuring the "particle" in space, and all what is being involved is fundamentally the information that exactly tells the belongingness at each moment of relevant smallest dimensionality's -like a pixel-screen configuring pictures.
Now "Pixel" is a fairly --- well let me call it sensitive word!
Perhaps "pixel" signal a kind of solidness which easily can be misunderstood. Nothing is solid and nothing is into lasting existence - everything is a flux, but thanks to scale wise arrangements of dimensionalitiy's - we get the illusion of lastingness and the illusion of solidness, not being sharp in our focus to realize that everything is explained and understood via wave-particle duality. Any wave is being composed of particles as their medium and any particle is being expressed via standing wave-patterns.
Everything is about how dimensionality's arrange and re-arrange in space so as to give rise to domino-like quakes or waves in a particle-fabric, and such waves enter into standing patterns that express particles in the next following scale. So it is an ever ongoing transformation from a particle-defined medium and into a wave-defined world and vice versa.
When the informational stream is running from smaller to bigger scales the physical world is going to be expressed via the particle-structures that express the scale that is being observed, and physical scale is the equivalent of the human scale, the equivalent of human physical senses, equivalent to the scale of photon / electron. Any scale is defined via the informational qubit, that is being used, when information observe information. Physical world is the equivalent of how humans (photon qubit scale) observes the surroundings. Matter formation is via photon-wave patterns (mainly or exclusively - still a question to me).
When information is running from physical expressed world and inwards - deeper and deeper (holographically) it is equivalent to the reverse process of one oscillation - and it can be seen as the period in the universal beat where anti-matter is being expressed. Matter and anti-matter cannot co-exist, matter is being expressed in the outwards informational stream and anti-matter in the inwards informational stream. And a full beat is the sum of these two informational streams, so each new expression is a fully new calculated configuration.
CPT violations are the result of how information observes (and thus interferes with) observation, in all scales. Each observation (interference) implicates a kind of constraint in the ideal entanglement flow.
Information is being kind of recycled (from our scale to SQscale) via BH's which are locations in spacetime where information in the photon-scale is being reverted into the next following smaller scale, where "particle" structures are smaller and wave-frequencies are higher, and thus cannot be interfered with - cannot be observed by human.
QUOTE: "Perhaps information is recycled via sub event horizon convergence, spared as a direct consequence of an energy based Lorentz transformational affect, thus allowing constant universal evolution.
The Crank."
Fundamentally I like the idea that physical world IS information -
There is no need to make artificial distinctions between so called physical expressions and informational expressions - they are fundamentally the same - and we humans are tempted not to see the similarities.
You say "energy based Lorentz transformation" - and already here you are indicating that energy is something physical, but fundamentally I see energy as information.
Whenever we refer to energy it is related to changes. When a "particle" is moved from A to B in our physical world, we call it energy - and fundamentally it is information, information how to define the said particle in one place and then how the particle is re-placed cinematographically -like a movie strip - to the next place - and it is fundamentally about how smallest dimensionality's are configuring and re-configuring the "particle" in space, and all what is being involved is fundamentally the information that exactly tells the belongingness at each moment of relevant smallest dimensionality's -like a pixel-screen configuring pictures.
Now "Pixel" is a fairly --- well let me call it sensitive word!
Perhaps "pixel" signal a kind of solidness which easily can be misunderstood. Nothing is solid and nothing is into lasting existence - everything is a flux, but thanks to scale wise arrangements of dimensionalitiy's - we get the illusion of lastingness and the illusion of solidness, not being sharp in our focus to realize that everything is explained and understood via wave-particle duality. Any wave is being composed of particles as their medium and any particle is being expressed via standing wave-patterns.
Everything is about how dimensionality's arrange and re-arrange in space so as to give rise to domino-like quakes or waves in a particle-fabric, and such waves enter into standing patterns that express particles in the next following scale. So it is an ever ongoing transformation from a particle-defined medium and into a wave-defined world and vice versa.
When the informational stream is running from smaller to bigger scales the physical world is going to be expressed via the particle-structures that express the scale that is being observed, and physical scale is the equivalent of the human scale, the equivalent of human physical senses, equivalent to the scale of photon / electron. Any scale is defined via the informational qubit, that is being used, when information observe information. Physical world is the equivalent of how humans (photon qubit scale) observes the surroundings. Matter formation is via photon-wave patterns (mainly or exclusively - still a question to me).
When information is running from physical expressed world and inwards - deeper and deeper (holographically) it is equivalent to the reverse process of one oscillation - and it can be seen as the period in the universal beat where anti-matter is being expressed. Matter and anti-matter cannot co-exist, matter is being expressed in the outwards informational stream and anti-matter in the inwards informational stream. And a full beat is the sum of these two informational streams, so each new expression is a fully new calculated configuration.
CPT violations are the result of how information observes (and thus interferes with) observation, in all scales. Each observation (interference) implicates a kind of constraint in the ideal entanglement flow.
Information is being kind of recycled (from our scale to SQscale) via BH's which are locations in spacetime where information in the photon-scale is being reverted into the next following smaller scale, where "particle" structures are smaller and wave-frequencies are higher, and thus cannot be interfered with - cannot be observed by human.
Hi All
Bukh . I liked the last couple of answers that you gave.
I would argue that " as soon as you begin to define anything lesser or greater than 'everything' , you are defining a relative position , whether you are referring to your own or any other position".
If the pixel model can be correct , then it must be seen as changeable only via multiple representations of itself within the whole, but while referring to the complete whole in order to get that definition. Therefore , each pixel must know both where it is as an individual AND where every other position was or ever will be..
Cheers
Iseason
Bukh . I liked the last couple of answers that you gave.
I would argue that " as soon as you begin to define anything lesser or greater than 'everything' , you are defining a relative position , whether you are referring to your own or any other position".
If the pixel model can be correct , then it must be seen as changeable only via multiple representations of itself within the whole, but while referring to the complete whole in order to get that definition. Therefore , each pixel must know both where it is as an individual AND where every other position was or ever will be..
Cheers
Iseason
Hej Geoff
Thanks for pointing at the above -
Thanks for pointing at the above -
Iseason
QUOTE: "If the pixel model can be correct , then it must be seen as changeable only via multiple representations of itself within the whole, but while referring to the complete whole in order to get that definition. Therefore , each pixel must know both where it is as an individual AND where every other position was or ever will be."
Relativity and frame is an absolute absolute - and perhaps even more more absolute than most people like to think.
Nothing can be observed or recorded without being relative to something else,
Physical world is therefore fully dependent on change - existence is founded on change.
You say that each pixel must know where it is as an individual - and I like to think that that a pixel must know its neighbors - and the more neighbors it knows the more the pixel know about the world.
However - one single pixel can have no knowledge by its position except that it has a few pixels around itself - and that is that. An extremely narrow horizon. And virtually no information.
So pixels have to collaborate in order to "produce" information. They must create "stable complexions" involving a lot of pixels, o they collectively get an insight not only into its own complexion - but also the ability to "sampling" - "de-coding" surrounding pixel structures.
The important note is that EVERYTHING is about de-coding the ever ongoing flux of re-arrangements of the pixels, at each flash-expression each and any pixel has a well defined relationship to surrounding pixels, have a well defined belonging /affiliation to surrounding pixels, which specific pixels are configuring what -
The higher the complexion - the more pixels being involved in such an "observing qubit" - the more the said qubit knows about itself and the surrounding world. And obviously there is very little information in one flash expression - it is the repeated sampling of the ever changing configurations that put together the observation, the more pictures - the "longer the movie strip" the more accurate and complete is the observation. And in order to observe a complex structure - logically it is necessary to make a lot of repeated observations before there is a clear picture about what is around. It takes time to be conscious and aware of surroundings.
So when you say: "AND where every other position was or ever will be.." - you are right in the sense that an observation is 100% dependent on the repetitive aspect. In order for something to be observed it must be repeated to the observer, a repetition is the foundation for an interference to be measured, and it is made obvious to us by the fact that in order for something to be observed it must take form of a "particle-like" expression. A photon cannot be observed per se - it has to translate into a repetitive "electron-like" expression.
And that is why I define particle as something that is expressing itself as a repetition in the frame of observation. Everything is being de-coded via cinematographically samplings of ever changing wave-expressions. A wave can be decoded via its frequency - which is Time - and via its angle - which is spatiality (pixel - corpus - object) - it is not possible to think physical world without a kind of spatiality - a kind of inertial wave-like change.
So yes - a full observation include the dynamic changing picture in a repeated form, to tell pixel-configuration in past and future - to include a time-period.
As a side note - only God knows everything because God is the everything, the qubit of God is the universe.
QUOTE: "If the pixel model can be correct , then it must be seen as changeable only via multiple representations of itself within the whole, but while referring to the complete whole in order to get that definition. Therefore , each pixel must know both where it is as an individual AND where every other position was or ever will be."
Relativity and frame is an absolute absolute - and perhaps even more more absolute than most people like to think.
Nothing can be observed or recorded without being relative to something else,
Physical world is therefore fully dependent on change - existence is founded on change.
You say that each pixel must know where it is as an individual - and I like to think that that a pixel must know its neighbors - and the more neighbors it knows the more the pixel know about the world.
However - one single pixel can have no knowledge by its position except that it has a few pixels around itself - and that is that. An extremely narrow horizon. And virtually no information.
So pixels have to collaborate in order to "produce" information. They must create "stable complexions" involving a lot of pixels, o they collectively get an insight not only into its own complexion - but also the ability to "sampling" - "de-coding" surrounding pixel structures.
The important note is that EVERYTHING is about de-coding the ever ongoing flux of re-arrangements of the pixels, at each flash-expression each and any pixel has a well defined relationship to surrounding pixels, have a well defined belonging /affiliation to surrounding pixels, which specific pixels are configuring what -
The higher the complexion - the more pixels being involved in such an "observing qubit" - the more the said qubit knows about itself and the surrounding world. And obviously there is very little information in one flash expression - it is the repeated sampling of the ever changing configurations that put together the observation, the more pictures - the "longer the movie strip" the more accurate and complete is the observation. And in order to observe a complex structure - logically it is necessary to make a lot of repeated observations before there is a clear picture about what is around. It takes time to be conscious and aware of surroundings.
So when you say: "AND where every other position was or ever will be.." - you are right in the sense that an observation is 100% dependent on the repetitive aspect. In order for something to be observed it must be repeated to the observer, a repetition is the foundation for an interference to be measured, and it is made obvious to us by the fact that in order for something to be observed it must take form of a "particle-like" expression. A photon cannot be observed per se - it has to translate into a repetitive "electron-like" expression.
And that is why I define particle as something that is expressing itself as a repetition in the frame of observation. Everything is being de-coded via cinematographically samplings of ever changing wave-expressions. A wave can be decoded via its frequency - which is Time - and via its angle - which is spatiality (pixel - corpus - object) - it is not possible to think physical world without a kind of spatiality - a kind of inertial wave-like change.
So yes - a full observation include the dynamic changing picture in a repeated form, to tell pixel-configuration in past and future - to include a time-period.
As a side note - only God knows everything because God is the everything, the qubit of God is the universe.
QUOTE (bukh+Jan 22 2009, 03:14 PM)
God knows everything because God is the everything, the qubit of God is the universe.
Oh dear, the mindfuck's gone and blown a gasket!.
Oh dear, the mindfuck's gone and blown a gasket!.
Geoff
"Oh dear, the mindfuck's gone and blown a gasket!."
Easy easy my friend - Don't worry - I am still on earth
"Oh dear, the mindfuck's gone and blown a gasket!."
Easy easy my friend - Don't worry - I am still on earth
QUOTE (Cusa+Jan 17 2009, 12:12 PM)
There are two "math" points. One zero dimensional and the other infinitely small nonzero.
Mitch Raemsch
Hi Mitch,
What I am about to state may seem to be malicious, but this is not my intent, my motive by this post is to instill a new clarity that you may never have ever experienced before, its based on pure truth and a trust that if statements are made they are not with bad intent or some put down..
Now..
With your implied values, In what reference are they compared too?
Examples of proper conventions:
Zero or void simply is nothing at all, and in fact is PRACTICALLY impossible.
Two is Twice as much as One, Four is twice as much as Two, One plus Two in fact is Three - so on and so forth..
And let me now kindly point out a flaw in your statement and how it refers to only one inference and importantly it is not a reference to a logical value in a normal and agreed upon convention..
Examples:
A reference in the following models shall be defined via the following symbol within said quotes ""<-- Start and ending quotes..
"" zero or nothing if we disregard containing quotes.
"." one if we disregard containing quotes.
".." two if we disregard containing quotes.
so on and so forth where the more symbols {Pixels} the greater the implied modelled universe in reference to the implied dots {pixels}..
Now Following is what I think you attempted to express with your statement
"" <- on the left we have your zero dimensional and on the right infinitely small non zero ->"."
but when we refer to your two inferences we are in fact implying deceit and or a contradiction. for example here is your nonzero "." and here is your two inference together where a zero and nonzero are referred too "." put simply your statement needs to be reconfigured if you wish to be completely truthful..
You do want to be truthful I hope?
So that's where I feel you have a problem, because you have referred to a quanta with out another reference with regards to a Valid or properly defined Scale.
Therefore if you then referred to a dot it may be as small as the following dot "." to which with my introduction of even a smaller dot means the following may be depicted by me "." of course what I have just implied is in the opposite of the normal convention until the definition "smaller" is exchanged with the definition "larger" and the definition "larger" is exchanged to "smaller"..
Q/. So why did I just mention all that?
A/. Its to point out we need to use proper definitions AND CONVENTIONS in line with each other if we are all to be on the same page, so if you refer to a definition please ensure readers hold much the same definition and or convention as you do..
what I am saying is I hope you decide to loose the confusing and or illogical conventions usually instilled {Brainwashed} via most backward religious cultures, which I feel have most followers {victims} left with difficulties in learning the real and proper truth about the Universe..
2~Duh~Loo!
Peter J Schoen..
Mitch Raemsch
Hi Mitch,
What I am about to state may seem to be malicious, but this is not my intent, my motive by this post is to instill a new clarity that you may never have ever experienced before, its based on pure truth and a trust that if statements are made they are not with bad intent or some put down..
Now..
With your implied values, In what reference are they compared too?
Examples of proper conventions:
Zero or void simply is nothing at all, and in fact is PRACTICALLY impossible.
Two is Twice as much as One, Four is twice as much as Two, One plus Two in fact is Three - so on and so forth..
And let me now kindly point out a flaw in your statement and how it refers to only one inference and importantly it is not a reference to a logical value in a normal and agreed upon convention..
Examples:
A reference in the following models shall be defined via the following symbol within said quotes ""<-- Start and ending quotes..
"" zero or nothing if we disregard containing quotes.
"." one if we disregard containing quotes.
".." two if we disregard containing quotes.
so on and so forth where the more symbols {Pixels} the greater the implied modelled universe in reference to the implied dots {pixels}..
Now Following is what I think you attempted to express with your statement
QUOTE
There are two "math" points. One zero dimensional and the other infinitely small nonzero.
"" <- on the left we have your zero dimensional and on the right infinitely small non zero ->"."
but when we refer to your two inferences we are in fact implying deceit and or a contradiction. for example here is your nonzero "." and here is your two inference together where a zero and nonzero are referred too "." put simply your statement needs to be reconfigured if you wish to be completely truthful..
You do want to be truthful I hope?
So that's where I feel you have a problem, because you have referred to a quanta with out another reference with regards to a Valid or properly defined Scale.
Therefore if you then referred to a dot it may be as small as the following dot "." to which with my introduction of even a smaller dot means the following may be depicted by me "." of course what I have just implied is in the opposite of the normal convention until the definition "smaller" is exchanged with the definition "larger" and the definition "larger" is exchanged to "smaller"..
Q/. So why did I just mention all that?
A/. Its to point out we need to use proper definitions AND CONVENTIONS in line with each other if we are all to be on the same page, so if you refer to a definition please ensure readers hold much the same definition and or convention as you do..
what I am saying is I hope you decide to loose the confusing and or illogical conventions usually instilled {Brainwashed} via most backward religious cultures, which I feel have most followers {victims} left with difficulties in learning the real and proper truth about the Universe..
2~Duh~Loo!
Peter J Schoen..
bump to counter crank spammer.
Hi All
Bukh
" Relativity and frame is an absolute absolute - and perhaps even more more absolute than most people like to think."
This is something that I can totally agree with. my apologies if we are always clarifying "where" we are talking about. This is an inevitable consequence of descriptive explanations.(which all explanations must be). Unless we are giving the result, we can only be EVER referring to a part of the cause.
EG: I move this energy to there........this MUST have an effect on every other position, time , gravity, and relative past and future.
This is ONLY if I am referring to Einsteins laws of relativity. If EVERY position IS relative, then every change in position changes the relativity of EVERY other position REGARDLESS of time or space.
Cheers
Iseason
Bukh
" Relativity and frame is an absolute absolute - and perhaps even more more absolute than most people like to think."
This is something that I can totally agree with. my apologies if we are always clarifying "where" we are talking about. This is an inevitable consequence of descriptive explanations.(which all explanations must be). Unless we are giving the result, we can only be EVER referring to a part of the cause.
EG: I move this energy to there........this MUST have an effect on every other position, time , gravity, and relative past and future.
This is ONLY if I am referring to Einsteins laws of relativity. If EVERY position IS relative, then every change in position changes the relativity of EVERY other position REGARDLESS of time or space.
Cheers
Iseason
Here's a related quote from a different thread:
http://www.physicsforums.com/archive/index.php/t-55579.html
http://www.physicsforums.com/archive/index.php/t-55579.html
QUOTE (NeutronStar+)
This might be a stupid question, but how can you construct something that has an irrational length? For example if you make a right triangle with the 2 sides=1 the hypotenuse is sqrt(2). How can sqrt(2) be a length if that number goes on for ever and never repeats?
Don't worry too much about it. Irrational numbers are just an inconsistent fabrication of abstract mathematics. Irrational lengths can't exist in the real world. There is no way that you are going to construct a perfect circle or perfect triangle in the real universe. Planck's constant and the Heisenberg uncertainty principle will prevent it. There simply aren't any "physical" irrational lengths in the universe. They don't exist. Even the universe rounds off irrational quantities. :biggrin:
The universe behaves more like a physicist than a mathematician. :approve:
I've found that the best way to think of irrational numbers are in terms of the self-referenced situations that give rise to them. Thinking of them in this way we can clearly see that these quantities are merely reflections of a self-referenced situation (like putting two mirrors back-to-back). The images go on forever (or at least they appear to). We know that in the real universe even those images in "perfect" mirrors would have to end at the resolution of a photon. So again, the universe even rounds off this situation.
The universe is great at rounding things off. :wink:
By the way, abstract mathematics is inconsistent in that they treat irrational numbers as being both, infinite decimal expansions, and precise calculus limits.
In other words, Cantor's famous diagonal proof that the set of real numbers has a larger cardinality than the set of natural numbers depends on the infinite expansion of decimal numbers. Yet, by formal definition these real numbers are said to be equal to their calculus limits. That's an inconsistency in logic. After all, if we take the real numbers to be equal to the calculus limits of their decimal expansions then each real number is a finite quantity.
In other words, we could simply represent each real number by a symbol such as pi, or e, or the square root of 2, or whatever symbol we wish to use.
Well, if we do this look what happens!!!
Let Sn be a symbol for a limit of a real decimal expansion. Then the real numbers can be listed as S1, S2, S3, .... and so on.
In other words, I've just put the real numbers into a direct bijection with the natural numbers proving that they have the same cardinality!!! And I did this by using the formal definition of mathematics that the real numbers are equal to the limit of their decimal expansions!!!
Mathematicians want to have their cake and eat it too. They want to claim that the decimal expansion of real numbers are equal to their limits, yet at the same time they want to claim that the cardinality of the set of real numbers is somehow larger than the cardinality of the natural numbers.
Either 0.999... does not equal 1 and Cantor's conclusions about cardinality is correct.
Or
0.999... does equal 1 and Cantor was wrong! The set of natural numbers and the set of real numbers have precisely the same cardinality.
Both of the above can't be true simultaneously! Mathematical formalism is inconsistent. The mathematical community needs to decide which way they are going to do things and stick to their guns. In the meantime they're making me dizzy!
In short, don't take abstract mathematics too literally! :yuck:
Don't worry too much about it. Irrational numbers are just an inconsistent fabrication of abstract mathematics. Irrational lengths can't exist in the real world. There is no way that you are going to construct a perfect circle or perfect triangle in the real universe. Planck's constant and the Heisenberg uncertainty principle will prevent it. There simply aren't any "physical" irrational lengths in the universe. They don't exist. Even the universe rounds off irrational quantities. :biggrin:
The universe behaves more like a physicist than a mathematician. :approve:
I've found that the best way to think of irrational numbers are in terms of the self-referenced situations that give rise to them. Thinking of them in this way we can clearly see that these quantities are merely reflections of a self-referenced situation (like putting two mirrors back-to-back). The images go on forever (or at least they appear to). We know that in the real universe even those images in "perfect" mirrors would have to end at the resolution of a photon. So again, the universe even rounds off this situation.
The universe is great at rounding things off. :wink:
By the way, abstract mathematics is inconsistent in that they treat irrational numbers as being both, infinite decimal expansions, and precise calculus limits.
In other words, Cantor's famous diagonal proof that the set of real numbers has a larger cardinality than the set of natural numbers depends on the infinite expansion of decimal numbers. Yet, by formal definition these real numbers are said to be equal to their calculus limits. That's an inconsistency in logic. After all, if we take the real numbers to be equal to the calculus limits of their decimal expansions then each real number is a finite quantity.
In other words, we could simply represent each real number by a symbol such as pi, or e, or the square root of 2, or whatever symbol we wish to use.
Well, if we do this look what happens!!!
Let Sn be a symbol for a limit of a real decimal expansion. Then the real numbers can be listed as S1, S2, S3, .... and so on.
In other words, I've just put the real numbers into a direct bijection with the natural numbers proving that they have the same cardinality!!! And I did this by using the formal definition of mathematics that the real numbers are equal to the limit of their decimal expansions!!!
Mathematicians want to have their cake and eat it too. They want to claim that the decimal expansion of real numbers are equal to their limits, yet at the same time they want to claim that the cardinality of the set of real numbers is somehow larger than the cardinality of the natural numbers.
Either 0.999... does not equal 1 and Cantor's conclusions about cardinality is correct.
Or
0.999... does equal 1 and Cantor was wrong! The set of natural numbers and the set of real numbers have precisely the same cardinality.
Both of the above can't be true simultaneously! Mathematical formalism is inconsistent. The mathematical community needs to decide which way they are going to do things and stick to their guns. In the meantime they're making me dizzy!
In short, don't take abstract mathematics too literally! :yuck:
None of that post you quote is anywhere close to correct Steve. You're just parroting someone as ignorant as you and I'm certain will have done as little actual maths as you, ie none past high school.
Do any of you cranks notice how you all pat each other on the back in threads like this, posting BS you just come up with or your unsupported assumptions after spending 6 seconds reading Wikipedia, yet despite you ALL thinking you've got some great understanding people like myself, ie 'the establishment', have missed or don't understand, you're all still stuck wallowing on these forums? Despite years of thinking you've got some amazing views/insight/results, none of you get anywhere.
It's just funny to see you all involved in a crank 'circle jerk' about how great you think each other's insight is but none of you can even do childrens homeworks.
Do any of you cranks notice how you all pat each other on the back in threads like this, posting BS you just come up with or your unsupported assumptions after spending 6 seconds reading Wikipedia, yet despite you ALL thinking you've got some great understanding people like myself, ie 'the establishment', have missed or don't understand, you're all still stuck wallowing on these forums? Despite years of thinking you've got some amazing views/insight/results, none of you get anywhere.
It's just funny to see you all involved in a crank 'circle jerk' about how great you think each other's insight is but none of you can even do childrens homeworks.
QUOTE (AlphaNumeric+Jan 28 2009, 10:37 PM)
None of that post you quote is anywhere close to correct Steve. You're just parroting someone as ignorant as you and I'm certain will have done as little actual maths as you, ie none past high school.
Do any of you cranks notice how you all pat each other on the back in threads like this, posting BS you just come up with or your unsupported assumptions after spending 6 seconds reading Wikipedia, yet despite you ALL thinking you've got some great understanding people like myself, ie 'the establishment', have missed or don't understand, you're all still stuck wallowing on these forums? Despite years of thinking you've got some amazing views/insight/results, none of you get anywhere.
It's just funny to see you all involved in a crank 'circle jerk' about how great you think each other's insight is but none of you can even do childrens homeworks.
"AlphaNumeric"
Supporting freedom of expression here since June 2006.
Do any of you cranks notice how you all pat each other on the back in threads like this, posting BS you just come up with or your unsupported assumptions after spending 6 seconds reading Wikipedia, yet despite you ALL thinking you've got some great understanding people like myself, ie 'the establishment', have missed or don't understand, you're all still stuck wallowing on these forums? Despite years of thinking you've got some amazing views/insight/results, none of you get anywhere.
It's just funny to see you all involved in a crank 'circle jerk' about how great you think each other's insight is but none of you can even do childrens homeworks.
"AlphaNumeric"
Supporting freedom of expression here since June 2006.
Obviously you have a little difficulty understanding logic.
Suppose I have two postulates
1. Fossil fuels burn to produce carbon dioxide
2. Methane is a fossil fuel
Now the corrollary of those postulates is that 'Burning methane makes carbon dioxide'. No ifs, no buts, given the postulates the implication is undeniably correct. To say otherwise is to not agree with the concept of logic.
Saying "0.9r doesn't equal 1" is the same, because you are taking the postulates of mathematics to be true and the outcome 0.9r=1 is unavoidably, undeniably correct. Similarly with Cantor's work in cardinality. So the lartge quote of Steven's where the person says those two mathematical results are incompatible is flat out wrong. That isn't me surpressing 'free expression' or being a maths Nazi or whatever you wish to label me with. It's just the outcome of logic, though that logic is obviously beyond the grasp of the majority of people in this thread.
People like Steve go even a step further, they don't even agree with the definition of certain words! The word 'linear' to a mathematician means a particular thing, but whenever Steven reads it he translates it, automatically, into his own version and then proceeds to try to take apart the work of mathematicians on the grounds that when he redefines the word to mean something else, mathematicians are wrong. It's like me translating the French words 'Bon jour' to mean 'Table window' and then complaining that French is an incoherent language.
It is perfectly possibly to discuss the validity of mathematics and any other logic system, but you do that by considering what postulates/assumptions you take as you axioms and how changing them alters the resultant series of logical conclusions. Some people even debate the validity of logic. This thread does neither of those. It's a 'circle jerk' between people who never studied maths, don't want to study maths and it would seem make enormous effort to avoid picking up anything simply from conversations. I don't study medicine but I've managed to learn the names of various body parts and diseases by watching TV, reading books and talking with medics. You guys spend a lot of time on these forums but you seem to pick up nothing.
There's plenty of things to discuss in maths and physics, but all you guys every do is whine about how your versions of concepts mean that mainstream work doesn't seem coherent to you (not surprisingly) and how your uninformed, biased, ignorant assumptions about phenomena you never examined or mathematical concepts you never learnt or read about are obviously superior to all those academics, whose work you don't read, even when I give you specific links.
For instance, Steven claims that 0x+0y is not a linear combination of x's and y's. Given Wikipedia, the definition of a 'linear combination' and even the lecture notes of a Cambridge professor of mathematics say otherwise, he claims his definition of a word mathematicians defined is correct.
Of course the fact he's never done any linear algebra beyond high school level is not something which bothers him. Or any of you, since you all keep feeding one anothers egos.
And if you think I'm surpressing people (or trying to), don't forget that I offered to be £500 with Steven that if he typed up his work I'd format it into a form acceptable for a reputable mathematics journal, he could then submit it and we'd see their response. I actively tried to get him to spread his work. He refused. As did Ubanatova (or whatever it is), Farsight, Precursor and plenty of others. You guys keep your 'work' confined to forums because you know you'd all spectacularly fail peer review.
Suppose I have two postulates
1. Fossil fuels burn to produce carbon dioxide
2. Methane is a fossil fuel
Now the corrollary of those postulates is that 'Burning methane makes carbon dioxide'. No ifs, no buts, given the postulates the implication is undeniably correct. To say otherwise is to not agree with the concept of logic.
Saying "0.9r doesn't equal 1" is the same, because you are taking the postulates of mathematics to be true and the outcome 0.9r=1 is unavoidably, undeniably correct. Similarly with Cantor's work in cardinality. So the lartge quote of Steven's where the person says those two mathematical results are incompatible is flat out wrong. That isn't me surpressing 'free expression' or being a maths Nazi or whatever you wish to label me with. It's just the outcome of logic, though that logic is obviously beyond the grasp of the majority of people in this thread.
People like Steve go even a step further, they don't even agree with the definition of certain words! The word 'linear' to a mathematician means a particular thing, but whenever Steven reads it he translates it, automatically, into his own version and then proceeds to try to take apart the work of mathematicians on the grounds that when he redefines the word to mean something else, mathematicians are wrong. It's like me translating the French words 'Bon jour' to mean 'Table window' and then complaining that French is an incoherent language.
It is perfectly possibly to discuss the validity of mathematics and any other logic system, but you do that by considering what postulates/assumptions you take as you axioms and how changing them alters the resultant series of logical conclusions. Some people even debate the validity of logic. This thread does neither of those. It's a 'circle jerk' between people who never studied maths, don't want to study maths and it would seem make enormous effort to avoid picking up anything simply from conversations. I don't study medicine but I've managed to learn the names of various body parts and diseases by watching TV, reading books and talking with medics. You guys spend a lot of time on these forums but you seem to pick up nothing.
There's plenty of things to discuss in maths and physics, but all you guys every do is whine about how your versions of concepts mean that mainstream work doesn't seem coherent to you (not surprisingly) and how your uninformed, biased, ignorant assumptions about phenomena you never examined or mathematical concepts you never learnt or read about are obviously superior to all those academics, whose work you don't read, even when I give you specific links.
For instance, Steven claims that 0x+0y is not a linear combination of x's and y's. Given Wikipedia, the definition of a 'linear combination' and even the lecture notes of a Cambridge professor of mathematics say otherwise, he claims his definition of a word mathematicians defined is correct.
Of course the fact he's never done any linear algebra beyond high school level is not something which bothers him. Or any of you, since you all keep feeding one anothers egos.
And if you think I'm surpressing people (or trying to), don't forget that I offered to be £500 with Steven that if he typed up his work I'd format it into a form acceptable for a reputable mathematics journal, he could then submit it and we'd see their response. I actively tried to get him to spread his work. He refused. As did Ubanatova (or whatever it is), Farsight, Precursor and plenty of others. You guys keep your 'work' confined to forums because you know you'd all spectacularly fail peer review.
QUOTE (AlphaNumeric+Jan 28 2009, 09:37 AM)
None of that post you quote is anywhere close to correct Steve. You're just parroting someone as ignorant as you and I'm certain will have done as little actual maths as you, ie none past high school.
So you claim Cantor's ideas can be shot down by high schoolers? (What happened to the elementary school comments ... are we progressing? LOL!)
So you claim Cantor's ideas can be shot down by high schoolers? (What happened to the elementary school comments ... are we progressing? LOL!)
QUOTE (AlphaNumeric+)
Do any of you cranks notice how you all pat each other on the back in threads like this, posting BS you just come up with or your unsupported assumptions after spending 6 seconds reading Wikipedia, yet despite you ALL thinking you've got some great understanding people like myself, ie 'the establishment', have missed or don't understand, you're all still stuck wallowing on these forums? Despite years of thinking you've got some amazing views/insight/results, none of you get anywhere.
Why don't you spend 6 seconds considering that Cantor was already shown the paradox regarding the diagonal expansions of .0999... and .1000... both differing in decimal digits, yet also being claimed to be equal, hence his diagonal argument should at be immediately questioned.
Then once someone recognizes that in order to construct a diagonal, the matrix must be a square matrix, but that's not the case for a (decimal) digital representation because the quantity of numbers representably by n digits grows as b^n, where b is the base of the digital representation, hence for 2 decimal digits, we have 10^2 numbers constructable and so we have a 2 x 100 array of digits:
.00
...
.09
.10
...
.99
A 2 by 100 array of decimal digits for which no digit can be changed without creating a number already in the list.
We can of course expand this to 3 or more digits:
.000
...
.999
.000...
...
.999...
And no digit can be altered without recreating another number in the list (if we were to allow the construction of infinite numbers such as Cantor desired).
Why don't you spend 6 seconds considering that Cantor was already shown the paradox regarding the diagonal expansions of .0999... and .1000... both differing in decimal digits, yet also being claimed to be equal, hence his diagonal argument should at be immediately questioned.
Then once someone recognizes that in order to construct a diagonal, the matrix must be a square matrix, but that's not the case for a (decimal) digital representation because the quantity of numbers representably by n digits grows as b^n, where b is the base of the digital representation, hence for 2 decimal digits, we have 10^2 numbers constructable and so we have a 2 x 100 array of digits:
.00
...
.09
.10
...
.99
A 2 by 100 array of decimal digits for which no digit can be changed without creating a number already in the list.
We can of course expand this to 3 or more digits:
.000
...
.999
.000...
...
.999...
And no digit can be altered without recreating another number in the list (if we were to allow the construction of infinite numbers such as Cantor desired).
QUOTE (AlphaNumeric+)
It's just funny to see you all involved in a crank 'circle jerk' about how great you think each other's insight is but none of you can even do childrens homeworks.
You started it. We're simply learning from the best
You started it. We're simply learning from the best
QUOTE (AlphaNumeric+)
Obviously you have a little difficulty understanding logic.
Suppose I have two postulates
1. Fossil fuels burn to produce carbon dioxide
2. Methane is a fossil fuel
Now the corrollary of those postulates is that 'Burning methane makes carbon dioxide'. No ifs, no buts, given the postulates the implication is undeniably correct. To say otherwise is to not agree with the concept of logic.
Saying "0.9r doesn't equal 1" is the same, because you are taking the postulates of mathematics to be true and the outcome 0.9r=1 is unavoidably, undeniably correct. Similarly with Cantor's work in cardinality. So the lartge quote of Steven's where the person says those two mathematical results are incompatible is flat out wrong. That isn't me surpressing 'free expression' or being a maths Nazi or whatever you wish to label me with. It's just the outcome of logic, though that logic is obviously beyond the grasp of the majority of people in this thread.
People like Steve go even a step further, they don't even agree with the definition of certain words! The word 'linear' to a mathematician means a particular thing, but whenever Steven reads it he translates it, automatically, into his own version and then proceeds to try to take apart the work of mathematicians on the grounds that when he redefines the word to mean something else, mathematicians are wrong. It's like me translating the French words 'Bon jour' to mean 'Table window' and then complaining that French is an incoherent language.
Ah, so now you want to discuss who's responsible for warping the meanings of words around.
The question is whether or not the word linear was originally created to denote things that possessed the properties of lines (and their specific useful traits) or whether the word linear was intended to have a randomly reinterpretable meaning.
I use the word LINEar as it's generally intended and as most dictionaries define it and as most mathematicians intend to use it (even if they're misled by poor mathematical definitions):
http://dictionary.reference.com/browse/linear
I do have a complaint about 7b though and that's when someone considers [i]no effect to represent a linear effect.
For example, if we have:
x=2y
A linear relationship between x and y exists, but per my extremely rational perspective, the above equation is only implicitly specified in 2 dimensions and every unique value of x has an associated unique value of y and a 1 to 1 correspondence between points can be made and x and y are informationally identical, other than for a 2:1 ratio (constant of proportionality) being associated between the y and x dimensions.
Your view, on the other hand, leaves this equation in potentially an infinite number of underspecified and indeterminant dimensions (it's similarly a linear equation in z if we "add" +0z to either side).
So we can create, by your view, an unlimited number of linear equations by simply multiplying things by zero:
x=2y+0z+0(price of tea in China)
Now, first of all, when we plot the possible solutions of this we find that the solution space no longer contains a line but a 3 dimensional volume within a 4 dimensional space.
Notice that if we plot any two of these variables, it's only the xy plane that describes a line and the other planes could be anything and this causes problems in mathematics when, for example, someone assumes a value for z can be computed from the equation.
Notice that we can 3 equations with 3 unknowns, like this:
x+y+0z=2
x-y+0z=0
x+2y+0z=4
And no solution is possible despite the fact that the equations are written in the form of assumed linear equations.
Notice that if we wrote these equations in a different form:
x/a+y/b+z/c=d
Then a, b and c are implicitly not 0 and for any selection of the 4 constants solutions exist and the dimensionality of the space or the solutions doesn't change (it always describes a 2 dimensional plane within a 3 dimensional space), though we still have issues of orthogonality with respect to other constructed planes if we were to look at the dimensionality of intersections of these.
But you'll notice that a linear equation in this form:
ax+by+cz+...=d
Has a paragraph of footnotes as to the conditions under which it's actually a linear equation, ignoring the fact that it can actually describe objects that are n dimensional objects, including n>1 versus the form:
(x+a)/b=(y+c)/d=(z+e)/f=...
Which is a form of relationship that always gives you line in any space with at least 2 dimensions and there are no special footnotes attached because b, d and f etc. cannot be 0 or infinite.
I do have a complaint about 7b though and that's when someone considers [i]no effect to represent a linear effect.
For example, if we have:
x=2y
A linear relationship between x and y exists, but per my extremely rational perspective, the above equation is only implicitly specified in 2 dimensions and every unique value of x has an associated unique value of y and a 1 to 1 correspondence between points can be made and x and y are informationally identical, other than for a 2:1 ratio (constant of proportionality) being associated between the y and x dimensions.
Your view, on the other hand, leaves this equation in potentially an infinite number of underspecified and indeterminant dimensions (it's similarly a linear equation in z if we "add" +0z to either side).
So we can create, by your view, an unlimited number of linear equations by simply multiplying things by zero:
x=2y+0z+0(price of tea in China)
Now, first of all, when we plot the possible solutions of this we find that the solution space no longer contains a line but a 3 dimensional volume within a 4 dimensional space.
Notice that if we plot any two of these variables, it's only the xy plane that describes a line and the other planes could be anything and this causes problems in mathematics when, for example, someone assumes a value for z can be computed from the equation.
Notice that we can 3 equations with 3 unknowns, like this:
x+y+0z=2
x-y+0z=0
x+2y+0z=4
And no solution is possible despite the fact that the equations are written in the form of assumed linear equations.
Notice that if we wrote these equations in a different form:
x/a+y/b+z/c=d
Then a, b and c are implicitly not 0 and for any selection of the 4 constants solutions exist and the dimensionality of the space or the solutions doesn't change (it always describes a 2 dimensional plane within a 3 dimensional space), though we still have issues of orthogonality with respect to other constructed planes if we were to look at the dimensionality of intersections of these.
But you'll notice that a linear equation in this form:
ax+by+cz+...=d
Has a paragraph of footnotes as to the conditions under which it's actually a linear equation, ignoring the fact that it can actually describe objects that are n dimensional objects, including n>1 versus the form:
(x+a)/b=(y+c)/d=(z+e)/f=...
Which is a form of relationship that always gives you line in any space with at least 2 dimensions and there are no special footnotes attached because b, d and f etc. cannot be 0 or infinite.
It is perfectly possibly to discuss the validity of mathematics and any other logic system, but you do that by considering what postulates/assumptions you take as you axioms and how changing them alters the resultant series of logical conclusions.
Correct and the fact that some people have assumed f(x)+f(y)=f(x+y) and af(x)=f(ax) is sufficient to describe linear operations has led to a logical conflict with other technical and non-technical fields in that these are no longer required to describe lines or proportional changes between dimensions etc.
Suppose I have two postulates
1. Fossil fuels burn to produce carbon dioxide
2. Methane is a fossil fuel
Now the corrollary of those postulates is that 'Burning methane makes carbon dioxide'. No ifs, no buts, given the postulates the implication is undeniably correct. To say otherwise is to not agree with the concept of logic.
Saying "0.9r doesn't equal 1" is the same, because you are taking the postulates of mathematics to be true and the outcome 0.9r=1 is unavoidably, undeniably correct. Similarly with Cantor's work in cardinality. So the lartge quote of Steven's where the person says those two mathematical results are incompatible is flat out wrong. That isn't me surpressing 'free expression' or being a maths Nazi or whatever you wish to label me with. It's just the outcome of logic, though that logic is obviously beyond the grasp of the majority of people in this thread.
People like Steve go even a step further, they don't even agree with the definition of certain words! The word 'linear' to a mathematician means a particular thing, but whenever Steven reads it he translates it, automatically, into his own version and then proceeds to try to take apart the work of mathematicians on the grounds that when he redefines the word to mean something else, mathematicians are wrong. It's like me translating the French words 'Bon jour' to mean 'Table window' and then complaining that French is an incoherent language.
Ah, so now you want to discuss who's responsible for warping the meanings of words around.
The question is whether or not the word linear was originally created to denote things that possessed the properties of lines (and their specific useful traits) or whether the word linear was intended to have a randomly reinterpretable meaning.
I use the word LINEar as it's generally intended and as most dictionaries define it and as most mathematicians intend to use it (even if they're misled by poor mathematical definitions):
http://dictionary.reference.com/browse/linear
QUOTE
lin⋅e⋅ar
/ˈlɪniər/ Show Spelled Pronunciation [lin-ee-er] Show IPA Pronunciation
–adjective
1. of, consisting of, or using lines: linear design.
2. pertaining to or represented by lines: linear dimensions.
3. extended or arranged in a line: a linear series.
4. involving measurement in one dimension only; pertaining to length: linear measure.
5. of or pertaining to the characteristics of a work of art in which forms and rhythms are defined chiefly in terms of line.
6. having the form of or resembling a line: linear nebulae.
7. Mathematics.
a. consisting of, involving, or describable by terms of the first degree.
b. having the same effect on a sum as on each of the summands: a linear operation./i]
8. Electronics. delivering an output that is directly proportional to the input: a linear circuit; a linear amplifier.
9. threadlike; narrow and elongated: a linear leaf.
/ˈlɪniər/ Show Spelled Pronunciation [lin-ee-er] Show IPA Pronunciation
–adjective
1. of, consisting of, or using lines: linear design.
2. pertaining to or represented by lines: linear dimensions.
3. extended or arranged in a line: a linear series.
4. involving measurement in one dimension only; pertaining to length: linear measure.
5. of or pertaining to the characteristics of a work of art in which forms and rhythms are defined chiefly in terms of line.
6. having the form of or resembling a line: linear nebulae.
7. Mathematics.
a. consisting of, involving, or describable by terms of the first degree.
b. having the same effect on a sum as on each of the summands: a linear operation./i]
8. Electronics. delivering an output that is directly proportional to the input: a linear circuit; a linear amplifier.
9. threadlike; narrow and elongated: a linear leaf.
I do have a complaint about 7b though and that's when someone considers [i]no effect to represent a linear effect.
For example, if we have:
x=2y
A linear relationship between x and y exists, but per my extremely rational perspective
, the above equation is only implicitly specified in 2 dimensions and every unique value of x has an associated unique value of y and a 1 to 1 correspondence between points can be made and x and y are informationally identical, other than for a 2:1 ratio (constant of proportionality) being associated between the y and x dimensions.Your view, on the other hand, leaves this equation in potentially an infinite number of underspecified and indeterminant dimensions (it's similarly a linear equation in z if we "add" +0z to either side).
So we can create, by your view, an unlimited number of linear equations by simply multiplying things by zero:
x=2y+0z+0(price of tea in China)
Now, first of all, when we plot the possible solutions of this we find that the solution space no longer contains a line but a 3 dimensional volume within a 4 dimensional space.
Notice that if we plot any two of these variables, it's only the xy plane that describes a line and the other planes could be anything and this causes problems in mathematics when, for example, someone assumes a value for z can be computed from the equation.
Notice that we can 3 equations with 3 unknowns, like this:
x+y+0z=2
x-y+0z=0
x+2y+0z=4
And no solution is possible despite the fact that the equations are written in the form of assumed linear equations.
Notice that if we wrote these equations in a different form:
x/a+y/b+z/c=d
Then a, b and c are implicitly not 0 and for any selection of the 4 constants solutions exist and the dimensionality of the space or the solutions doesn't change (it always describes a 2 dimensional plane within a 3 dimensional space), though we still have issues of orthogonality with respect to other constructed planes if we were to look at the dimensionality of intersections of these.
But you'll notice that a linear equation in this form:
ax+by+cz+...=d
Has a paragraph of footnotes as to the conditions under which it's actually a linear equation, ignoring the fact that it can actually describe objects that are n dimensional objects, including n>1 versus the form:
(x+a)/b=(y+c)/d=(z+e)/f=...
Which is a form of relationship that always gives you line in any space with at least 2 dimensions and there are no special footnotes attached because b, d and f etc. cannot be 0 or infinite.
QUOTE (->
| QUOTE |
| lin⋅e⋅ar /ˈlɪniər/ Show Spelled Pronunciation [lin-ee-er] Show IPA Pronunciation –adjective 1. of, consisting of, or using lines: linear design. 2. pertaining to or represented by lines: linear dimensions. 3. extended or arranged in a line: a linear series. 4. involving measurement in one dimension only; pertaining to length: linear measure. 5. of or pertaining to the characteristics of a work of art in which forms and rhythms are defined chiefly in terms of line. 6. having the form of or resembling a line: linear nebulae. 7. Mathematics. a. consisting of, involving, or describable by terms of the first degree. b. having the same effect on a sum as on each of the summands: a linear operation./i] 8. Electronics. delivering an output that is directly proportional to the input: a linear circuit; a linear amplifier. 9. threadlike; narrow and elongated: a linear leaf. |
I do have a complaint about 7b though and that's when someone considers [i]no effect to represent a linear effect.
For example, if we have:
x=2y
A linear relationship between x and y exists, but per my extremely rational perspective
, the above equation is only implicitly specified in 2 dimensions and every unique value of x has an associated unique value of y and a 1 to 1 correspondence between points can be made and x and y are informationally identical, other than for a 2:1 ratio (constant of proportionality) being associated between the y and x dimensions.Your view, on the other hand, leaves this equation in potentially an infinite number of underspecified and indeterminant dimensions (it's similarly a linear equation in z if we "add" +0z to either side).
So we can create, by your view, an unlimited number of linear equations by simply multiplying things by zero:
x=2y+0z+0(price of tea in China)
Now, first of all, when we plot the possible solutions of this we find that the solution space no longer contains a line but a 3 dimensional volume within a 4 dimensional space.
Notice that if we plot any two of these variables, it's only the xy plane that describes a line and the other planes could be anything and this causes problems in mathematics when, for example, someone assumes a value for z can be computed from the equation.
Notice that we can 3 equations with 3 unknowns, like this:
x+y+0z=2
x-y+0z=0
x+2y+0z=4
And no solution is possible despite the fact that the equations are written in the form of assumed linear equations.
Notice that if we wrote these equations in a different form:
x/a+y/b+z/c=d
Then a, b and c are implicitly not 0 and for any selection of the 4 constants solutions exist and the dimensionality of the space or the solutions doesn't change (it always describes a 2 dimensional plane within a 3 dimensional space), though we still have issues of orthogonality with respect to other constructed planes if we were to look at the dimensionality of intersections of these.
But you'll notice that a linear equation in this form:
ax+by+cz+...=d
Has a paragraph of footnotes as to the conditions under which it's actually a linear equation, ignoring the fact that it can actually describe objects that are n dimensional objects, including n>1 versus the form:
(x+a)/b=(y+c)/d=(z+e)/f=...
Which is a form of relationship that always gives you line in any space with at least 2 dimensions and there are no special footnotes attached because b, d and f etc. cannot be 0 or infinite.
It is perfectly possibly to discuss the validity of mathematics and any other logic system, but you do that by considering what postulates/assumptions you take as you axioms and how changing them alters the resultant series of logical conclusions.
Correct and the fact that some people have assumed f(x)+f(y)=f(x+y) and af(x)=f(ax) is sufficient to describe linear operations has led to a logical conflict with other technical and non-technical fields in that these are no longer required to describe lines or proportional changes between dimensions etc.
QUOTE (AlphaNumeric+)
Some people even debate the validity of logic.
What's the logic behind the arbitrary "(or to zero)" around the 6th line of this page:
http://mathworld.wolfram.com/LinearTransformation.html
Now what's the logic behind that? Lines are always mapped to lines ..... or maybe points or even lower dimensional objects that have no solution. What geometric object is "zero"? Is zero a point, a plane, a circle, a scatterplot or an apple?
What definition of linear implies that lines can also be points or even empty spaces!? Only the misdefined mathematical form that results in unsolvable equations and paragraphs of footnotes as to when "wrinkles" occur in linear equations:
http://aleph0.clarku.edu/~djoyce/ma105/simultaneous.html
I know perfectly well what a line is and what useful mathematical properties is has (multiple dimensions can be treated as a single dimension).
You sir, memorized an equation without understanding the importance of the relationships it was intended to define.
Now what's the logic behind that? Lines are always mapped to lines ..... or maybe points or even lower dimensional objects that have no solution. What geometric object is "zero"? Is zero a point, a plane, a circle, a scatterplot or an apple?
What definition of linear implies that lines can also be points or even empty spaces!? Only the misdefined mathematical form that results in unsolvable equations and paragraphs of footnotes as to when "wrinkles" occur in linear equations:
http://aleph0.clarku.edu/~djoyce/ma105/simultaneous.html
I know perfectly well what a line is and what useful mathematical properties is has (multiple dimensions can be treated as a single dimension).
You sir, memorized an equation without understanding the importance of the relationships it was intended to define.
This thread does neither of those.
No, your posts do not do these.
What's the logic behind the arbitrary "(or to zero)" around the 6th line of this page:
http://mathworld.wolfram.com/LinearTransformation.html
QUOTE
Also, a linear transformation always maps lines to lines (or to zero).
Now what's the logic behind that? Lines are always mapped to lines ..... or maybe points or even lower dimensional objects that have no solution. What geometric object is "zero"? Is zero a point, a plane, a circle, a scatterplot or an apple?
What definition of linear implies that lines can also be points or even empty spaces!? Only the misdefined mathematical form that results in unsolvable equations and paragraphs of footnotes as to when "wrinkles" occur in linear equations:
http://aleph0.clarku.edu/~djoyce/ma105/simultaneous.html
I know perfectly well what a line is and what useful mathematical properties is has (multiple dimensions can be treated as a single dimension).
You sir, memorized an equation without understanding the importance of the relationships it was intended to define.
QUOTE (->
| QUOTE |
| Also, a linear transformation always maps lines to lines (or to zero). |
Now what's the logic behind that? Lines are always mapped to lines ..... or maybe points or even lower dimensional objects that have no solution. What geometric object is "zero"? Is zero a point, a plane, a circle, a scatterplot or an apple?
What definition of linear implies that lines can also be points or even empty spaces!? Only the misdefined mathematical form that results in unsolvable equations and paragraphs of footnotes as to when "wrinkles" occur in linear equations:
http://aleph0.clarku.edu/~djoyce/ma105/simultaneous.html
I know perfectly well what a line is and what useful mathematical properties is has (multiple dimensions can be treated as a single dimension).
You sir, memorized an equation without understanding the importance of the relationships it was intended to define.
This thread does neither of those.
No, your posts do not do these.
QUOTE (AlphaNumeric+)
It's a 'circle jerk' between people who never studied maths,
Oh, and you don't have a stream of compliments from Trout in his various incarnations (who barely try to discuss mathematics)?
I've seen 'circle jerks' around here and the forum mafia is the elephant that fills the room in that respect.
Oh, and you don't have a stream of compliments from Trout in his various incarnations (who barely try to discuss mathematics)?
I've seen 'circle jerks' around here and the forum mafia is the elephant that fills the room in that respect.
QUOTE (AlphaNumeric+)
For instance, Steven claims that 0x+0y is not a linear combination of x's and y's. Given Wikipedia, the definition of a 'linear combination' and even the lecture notes of a Cambridge professor of mathematics say otherwise, he claims his definition of a word mathematicians defined is correct.
See, this is the problem, you believe that 'nothing' is a linear combination of no apples and no pears. Well, if that were true then it's also a linear combination of nothing of any random other thing or set of things.
Why not whip out calculus at this point and show that if we combine an unlimited quantity of nothings we can actually arrive at something that's no longer nothing.
OMG, your 'logic' is of the same type and caliber as Cantor's! LOL! You inherited it via. your education.
See, this is the problem, you believe that 'nothing' is a linear combination of no apples and no pears. Well, if that were true then it's also a linear combination of nothing of any random other thing or set of things.
Why not whip out calculus at this point and show that if we combine an unlimited quantity of nothings we can actually arrive at something that's no longer nothing.
OMG, your 'logic' is of the same type and caliber as Cantor's! LOL!
You inherited it via. your education.QUOTE (AlphaNumeric+)
Of course the fact he's never done any linear algebra beyond high school level is not something which bothers him. Or any of you, since you all keep feeding one anothers egos.
There was little point to have gone further in formal institutions. Yes, I could have picked up some alternate knowledge along the way, but I did anyway though in real world applications where "zero" isn't an answer sufficient for customers.
I tried going to college twice but it was obviously a waste of time for me as I was generally teaching the teachers.
So you claim Cantor's ideas can be shot down by high schoolers? (What happened to the elementary school comments ... are we progressing? LOL!)
No I just havn't been bothering with you guys as much lately.
I can just picture you using an ufortuneate flying type bat playing baseball.
Mathematicians use the mathemetical definition of linear. The fact that it has other meanings is irrelevent.
Just as physics and the physical world are irrelevent to pure math.
So you claim Cantor's ideas can be shot down by high schoolers?
No he is saying you havn't shot down Cantor.
You keep going back to "constructing".
There have been buildings that have collapsed during construction. Had the building been completed it would have been totally stable. It was simply that half built it couldn't stand.
0.999... is the same way. It is equal to 1.
But if you try and construct it, you will find it is not equal to 1 because you can not finish it.
There was little point to have gone further in formal institutions. Yes, I could have picked up some alternate knowledge along the way, but I did anyway though in real world applications where "zero" isn't an answer sufficient for customers.
I tried going to college twice but it was obviously a waste of time for me as I was generally teaching the teachers.
QUOTE (AlphaNumeric+)
And if you think I'm surpressing people (or trying to), don't forget that I offered to be £500 with Steven that if he typed up his work I'd format it into a form acceptable for a reputable mathematics journal, he could then submit it and we'd see their response. I actively tried to get him to spread his work. He refused. As did Ubanatova (or whatever it is), Farsight, Precursor and plenty of others. You guys keep your 'work' confined to forums because you know you'd all spectacularly fail peer review.
I admit that I should organize things better and refine them into simpler kernels that can be much more easily presented and a coherent "whole" seen, but it's a lot of work and it grows as more things are uncovered or when some areas need to be further detailed and defined etc.
I also admit I haven't uncovered any obvious new laws of physics, though I don't particularly consider that a failure as the reward has been a greater ability to see the details of "run of the mill" physical phenomenon as well as a realization that things do extend beyond what physical sciences can address.
I also admit I hate doing paperwork (though I can type volumes in a chat or speak with someone for hours on end, but that's in good company) and any personel department, QA, tax agencies, or teacher in most any class I've attended could likely vouch for that.
You do your thing and I'll do mine and time will tell what path was most rewarding.
I admit that I should organize things better and refine them into simpler kernels that can be much more easily presented and a coherent "whole" seen, but it's a lot of work and it grows as more things are uncovered or when some areas need to be further detailed and defined etc.
I also admit I haven't uncovered any obvious new laws of physics, though I don't particularly consider that a failure as the reward has been a greater ability to see the details of "run of the mill" physical phenomenon as well as a realization that things do extend beyond what physical sciences can address.
I also admit I hate doing paperwork (though I can type volumes in a chat or speak with someone for hours on end, but that's in good company) and any personel department, QA, tax agencies, or teacher in most any class I've attended could likely vouch for that.
You do your thing and I'll do mine and time will tell what path was most rewarding.
[/scroll]
QUOTE (SteveA2+Jan 28 2009, 01:40 PM)
So you claim Cantor's ideas can be shot down by high schoolers? (What happened to the elementary school comments ... are we progressing? LOL!)
No I just havn't been bothering with you guys as much lately.
I can just picture you using an ufortuneate flying type bat playing baseball.
Mathematicians use the mathemetical definition of linear. The fact that it has other meanings is irrelevent.
Just as physics and the physical world are irrelevent to pure math.
QUOTE (SteveA2+Jan 28 2009, 01:40 PM)
So you claim Cantor's ideas can be shot down by high schoolers?
No he is saying you havn't shot down Cantor.
You keep going back to "constructing".
There have been buildings that have collapsed during construction. Had the building been completed it would have been totally stable. It was simply that half built it couldn't stand.
0.999... is the same way. It is equal to 1.
But if you try and construct it, you will find it is not equal to 1 because you can not finish it.
Buttershug
"But if you try and construct it, you will find it is not equal to 1 because you can not finish it."
To me this is the same as saying that zero and 1 is not part of physical world - everything is being expressed by ratios of 1 - and it is not possible to reach true zero -
the same applies for math world - because math world is using "physical mind concepts" - math world is using numbers - and you cannot think of a number without "materializing" said number.
"But if you try and construct it, you will find it is not equal to 1 because you can not finish it."
To me this is the same as saying that zero and 1 is not part of physical world - everything is being expressed by ratios of 1 - and it is not possible to reach true zero -
the same applies for math world - because math world is using "physical mind concepts" - math world is using numbers - and you cannot think of a number without "materializing" said number.
QUOTE (buttershug+Jan 28 2009, 06:06 PM)
No I just havn't been bothering with you guys as much lately.
I can just picture you using an ufortuneate flying type bat playing baseball.
Mathematicians use the mathemetical definition of linear. The fact that it has other meanings is irrelevent.
Then the mathematical definition of linear is irrelevant and it doesn't define what mathematicians intended it to define.
I can just picture you using an ufortuneate flying type bat playing baseball.
Mathematicians use the mathemetical definition of linear. The fact that it has other meanings is irrelevent.
Then the mathematical definition of linear is irrelevant and it doesn't define what mathematicians intended it to define.
QUOTE (buttershug+)
Just as physics and the physical world are irrelevent to pure math.
I used to believe this was true also, but I've found that physics is not irrelevant to mathematical institutions because they're limited to using physical means to prove things and that even applies to things that are considered purely logical.
By the way, pick a random number. Now try to prove that the number you picked is random. (Ok, I admit that's a "random" comment and not directly related)
I used to believe this was true also, but I've found that physics is not irrelevant to mathematical institutions because they're limited to using physical means to prove things and that even applies to things that are considered purely logical.
By the way, pick a random number. Now try to prove that the number you picked is random. (Ok, I admit that's a "random" comment and not directly related)
QUOTE (buttershug+)
No he is saying you havn't shot down Cantor.
You keep going back to "constructing".
There have been buildings that have collapsed during construction. Had the building been completed it would have been totally stable. It was simply that half built it couldn't stand.
Well you still need to know what the house is. If you can't at least give an address of where to find it then noone's going to know which house you're referring to.
In other words, if I said that I've proved that some object exists, then for this to be of use to anyone else, I've got to at least be able to describe what the object is in order that someone else can find it out of all the other possible objects that could exist. If you can't describe it, or at least present what properties it has, so that someone else can find it if it's not physically presentable, then it may as well not exist in terms of a scientific institution.
http://en.wikipedia.org/wiki/Dedekind_completion
Here's an interesting comment:
It appears Dedekind recognized that numbers are mathematically constructed (or at least selected).
Notice though that at the end he makes a mistake when he says that a cut can correspond with an irrational number.
An irrational number is not constructed by such a cut as such a cut would result in a rational number.
For example, there is no point at which we could terminate a digital representation of pi and have it be an irrational number as any such termination would be a rational number.
Notice that, we could define pi to be a rational number lying midway between two decimal expansions:
3.14
3.15
For this pair of cuts (notice that pi can't be defined by a single point but instead a range over which it must lie, which is actually a 2 dimensional value as it could be defined as 3.14 +/- e, where e>0), pi would be equal to 3.145 or 629/200.
If the cut is made finer, we could proceed to 3.141 and 3.142 with pi being the "cut" at 3.1415, but pi is still rational and remains rational no matter how many such refinements in precision are made.
It appears Dedekind recognized that numbers are mathematically constructed (or at least selected).
Notice though that at the end he makes a mistake when he says that a cut can correspond with an irrational number.
An irrational number is not constructed by such a cut as such a cut would result in a rational number.
For example, there is no point at which we could terminate a digital representation of pi and have it be an irrational number as any such termination would be a rational number.
Notice that, we could define pi to be a rational number lying midway between two decimal expansions:
3.14
3.15
For this pair of cuts (notice that pi can't be defined by a single point but instead a range over which it must lie, which is actually a 2 dimensional value as it could be defined as 3.14 +/- e, where e>0), pi would be equal to 3.145 or 629/200.
If the cut is made finer, we could proceed to 3.141 and 3.142 with pi being the "cut" at 3.1415, but pi is still rational and remains rational no matter how many such refinements in precision are made.
0.999... is the same way. It is equal to 1.
But if you try and construct it, you will find it is not equal to 1 because you can not finish it.
Cantor already "proved" this to be incorrect with his diagonal argument as we have at least one decimal digit differ between the values and so they must each be unique numbers.
http://www.mathpages.com/home/kmath371.htm
I love how two wrongs can make a right in mathematics!
Hi all
I agree with this statement. 0.9999r could not define anything or be said to equal 1 any more than 0.1111r could be said to. Both are in fact an equal distance from one via "infinity". Even mathematics needs dimensions to be relevant. 0.999r is an assumption that the intervening value does not matter or is relatively increasing alongside what you are measuring.
It is borrowing from an unknown quantity.
Cheers
Iseason
0.999r can not be anything other than 1.
There is no difference between it and 1.
If it is not 1 then what is the difference?
If you find a difference then it is NOT 0.999r.
It is, and therefore does not need to be constructed or materialized or anything else.
IT JUST BLOODY WELL IS WHAT IT IS.
complete and full and nontangible.
There is no intervening value.
It is not growing.
It is defined complete.
It is not borrowing.
It is not doing anything other than existing in a nonphysical nontangible way.
It is not a process.
It is not a method.
a, b and c are FOR ANY VALUES OF mij linear combinations of x, y and z.
This is all explained in the first 10 pages or so of the lecture notes I've linked to. We both know you don't understand them, but you will not read them, deluding yourself into believing you have some great understanding but not once have you managed to do a question put to you expected of even 17 year olds.
What were you teaching the teachers if you know nothing? Clearly you were stroking your own ego from a very early age. I do worry about the kind of warping effect you'll have had on your children. Hopefully you didn't home school them? After all, why send them to school where you know they'll be taught incorrect things?
I agree that numbers arise from finite properties, but consider how did you recognize that a quarter was larger than a penny.
Absolutely totally irrelevent.
The quarter is larger without us recognizing it.
And all the rest of post rests on the opposite being true.
Which means all the rest of your post is bunkum.
@Bukh have you considered you havn't been getting numbers from anywhere?
And AN is not a media statisitian. Your question does make sense if you were talking to someone who wrote a report.
That 0.999... already "exists" and doen't need us?
You keep going back to "constructing".
There have been buildings that have collapsed during construction. Had the building been completed it would have been totally stable. It was simply that half built it couldn't stand.
Well you still need to know what the house is. If you can't at least give an address of where to find it then noone's going to know which house you're referring to.
In other words, if I said that I've proved that some object exists, then for this to be of use to anyone else, I've got to at least be able to describe what the object is in order that someone else can find it out of all the other possible objects that could exist. If you can't describe it, or at least present what properties it has, so that someone else can find it if it's not physically presentable, then it may as well not exist in terms of a scientific institution.
http://en.wikipedia.org/wiki/Dedekind_completion
Here's an interesting comment:
QUOTE
Wherever a cut occurs and it is not on a real rational number, an irrational number (which is also a real number) is created by the mathematician. Through the use of this device, there is considered to be a real number, either rational or irrational, at every point on the number line continuum, with no discontinuity.
Whenever, then, we have to do with a cut produced by no rational number, we create a new, an irrational number, which we regard as completely defined by this cut ... . From now on, therefore, to every definite cut there corresponds a definite rational or irrational number ....
Whenever, then, we have to do with a cut produced by no rational number, we create a new, an irrational number, which we regard as completely defined by this cut ... . From now on, therefore, to every definite cut there corresponds a definite rational or irrational number ....
It appears Dedekind recognized that numbers are mathematically constructed (or at least selected).
Notice though that at the end he makes a mistake when he says that a cut can correspond with an irrational number.
An irrational number is not constructed by such a cut as such a cut would result in a rational number.
For example, there is no point at which we could terminate a digital representation of pi and have it be an irrational number as any such termination would be a rational number.
Notice that, we could define pi to be a rational number lying midway between two decimal expansions:
3.14
3.15
For this pair of cuts (notice that pi can't be defined by a single point but instead a range over which it must lie, which is actually a 2 dimensional value as it could be defined as 3.14 +/- e, where e>0), pi would be equal to 3.145 or 629/200.
If the cut is made finer, we could proceed to 3.141 and 3.142 with pi being the "cut" at 3.1415, but pi is still rational and remains rational no matter how many such refinements in precision are made.
QUOTE (->
| QUOTE |
| Wherever a cut occurs and it is not on a real rational number, an irrational number (which is also a real number) is created by the mathematician. Through the use of this device, there is considered to be a real number, either rational or irrational, at every point on the number line continuum, with no discontinuity. Whenever, then, we have to do with a cut produced by no rational number, we create a new, an irrational number, which we regard as completely defined by this cut ... . From now on, therefore, to every definite cut there corresponds a definite rational or irrational number .... |
It appears Dedekind recognized that numbers are mathematically constructed (or at least selected).
Notice though that at the end he makes a mistake when he says that a cut can correspond with an irrational number.
An irrational number is not constructed by such a cut as such a cut would result in a rational number.
For example, there is no point at which we could terminate a digital representation of pi and have it be an irrational number as any such termination would be a rational number.
Notice that, we could define pi to be a rational number lying midway between two decimal expansions:
3.14
3.15
For this pair of cuts (notice that pi can't be defined by a single point but instead a range over which it must lie, which is actually a 2 dimensional value as it could be defined as 3.14 +/- e, where e>0), pi would be equal to 3.145 or 629/200.
If the cut is made finer, we could proceed to 3.141 and 3.142 with pi being the "cut" at 3.1415, but pi is still rational and remains rational no matter how many such refinements in precision are made.
0.999... is the same way. It is equal to 1.
But if you try and construct it, you will find it is not equal to 1 because you can not finish it.
Cantor already "proved" this to be incorrect with his diagonal argument as we have at least one decimal digit differ between the values and so they must each be unique numbers.
http://www.mathpages.com/home/kmath371.htm
I love how two wrongs can make a right in mathematics!
QUOTE (bukh+Jan 28 2009, 07:09 PM)
Buttershug
"But if you try and construct it, you will find it is not equal to 1 because you can not finish it."
To me this is the same as saying that zero and 1 is not part of physical world - everything is being expressed by ratios of 1 - and it is not possible to reach true zero -
the same applies for math world - because math world is using "physical mind concepts" - math world is using numbers - and you cannot think of a number without "materializing" said number.
Speak for yourself.
I can think of numbers without materializing said number.
"But if you try and construct it, you will find it is not equal to 1 because you can not finish it."
To me this is the same as saying that zero and 1 is not part of physical world - everything is being expressed by ratios of 1 - and it is not possible to reach true zero -
the same applies for math world - because math world is using "physical mind concepts" - math world is using numbers - and you cannot think of a number without "materializing" said number.
Speak for yourself.
I can think of numbers without materializing said number.
QUOTE (SteveA2+Jan 28 2009, 07:22 PM)
Then the mathematical definition of linear is irrelevant and it doesn't define what mathematicians intended it to define.
In other words, if I said that I've proved that some object exists, then for this to be of use to anyone else,
It's usefull to mathematicians and is only usefull to mathematicians if it is restricted to the mathematical definition. If you allow it to mean whatever else it can mean then it is not usefull to mathematicians.
And still you talk about objects.
And constructing numbers.
Stop thinking physciallly.
And it doesn't matter is mathematicians use physical analogies. That does not make what they are talking about physical.
Not once ever have you talked about 0.999...
You always talk about something very close to it but it itself.
In other words, if I said that I've proved that some object exists, then for this to be of use to anyone else,
It's usefull to mathematicians and is only usefull to mathematicians if it is restricted to the mathematical definition. If you allow it to mean whatever else it can mean then it is not usefull to mathematicians.
And still you talk about objects.
And constructing numbers.
Stop thinking physciallly.
And it doesn't matter is mathematicians use physical analogies. That does not make what they are talking about physical.
Not once ever have you talked about 0.999...
You always talk about something very close to it but it itself.
QUOTE (bukh+Jan 29 2009, 08:09 AM)
Buttershug
"But if you try and construct it, you will find it is not equal to 1 because you can not finish it."
Hi all
I agree with this statement. 0.9999r could not define anything or be said to equal 1 any more than 0.1111r could be said to. Both are in fact an equal distance from one via "infinity". Even mathematics needs dimensions to be relevant. 0.999r is an assumption that the intervening value does not matter or is relatively increasing alongside what you are measuring.
It is borrowing from an unknown quantity.
Cheers
Iseason
"But if you try and construct it, you will find it is not equal to 1 because you can not finish it."
Hi all
I agree with this statement. 0.9999r could not define anything or be said to equal 1 any more than 0.1111r could be said to. Both are in fact an equal distance from one via "infinity". Even mathematics needs dimensions to be relevant. 0.999r is an assumption that the intervening value does not matter or is relatively increasing alongside what you are measuring.
It is borrowing from an unknown quantity.
Cheers
Iseason
buttershug
"I can think of numbers without materializing said number."
Wow !
"I can think of numbers without materializing said number."
Wow !
QUOTE (buttershug+Jan 29 2009, 03:14 AM)
Speak for yourself.
I can think of numbers without materializing said number.
But you at least know what number it is for yourself. Otherwise you're not thinking of a specific number but about possible numbers or sets.
I bet none of them have been a randomly selected natural number from the "set of all natural numbers", otherwise we should be amazed at the probability of it not being over a googleplex (10^(10^100)).
Now if you happened to pick a random number over a googleplex, we should then be amazed at the probability that it was so easily compressible into a small finite representation such as (10^(11^(12^13))), for which "nearby" integers would typically not be so easily factored and require a massive number of digits to represent.
Yet no matter how large or complex a description for a number, we're effectively not even moving relative to infinity ... or are we?
Well, what's infinity in terms of natural numbers? It's larger than any natural number.
So if we counted to 3: 1,2,3 then infinity could be 4 ... except that once we created 4, then infinity, being larger would have to be 5 ... oops, I just created 5, so infinity would have to be 6, yikes, this appears to be circular.
Ok, let's try defining (infinity-1) to be the largest natural number and that makes sense because once we've gone past natural numbers (I'm just working on a natural number line), we're at infinity.
So if we try counting to 3 again, 1,2,3 then the next number should be infinity, so it would be 1,2,3,infinity or 1,2,3,... and we don't have a problem here because infinity isn't a natural number and infinity+1 isn't defined, so we can finally stop counting as we've reached infinity
Notice that we also no longer have a problem with trying to define infinity+1=infinity, which implies infinity=infinity-1 and leads to the vicious recursion infinity=infinity-1-1-1-1...=infinity-infinity.
If we begin with 1,2,3,infinity and if we created 2*3=6, would 6 now be larger than infinity? By definition, it couldn't be and if 6 was the largest natural number then infinity would be ~7.
The point of this is to show that infinity needs not preexist as some incredibly massive quantity that we can't even begin to approach but instead is dynamically created by processes and infinity effectively exists in the present.
In some mathematical texts there are various forms of infinities that may or may not be arranged into various magnitudes or relative rates of growth, and consider how such structures are created:
If we began to create a row of numbers by progressing with this sequence:
1
1 1
2 1
2 1 1
2 2 1
3 2 1
3 2 1 1
3 2 2 1
3 3 2 1
4 3 2 1
...
We could "grow" this over time into this sequence
1
2 1
3 2 1
4 3 2 1
5 4 3 2 1
...
Now notice that every number at each position along this row never decreases and is periodically incremented. If we continued incrementing individual numbers according to the top sequence an "infinite number" of times, then we'd end up with a row of numbers and each number growing "infinitely large".
So we've converted a single infinite quantity into an infinite quantity of infinite numbers. (It's magic, right?)
Well, at moment, this structure is nothing more than a finite number of finite values and all that "infinity" means is that it's intended to be continually increased, but obviously we couldn't have it increased without being synchronized with us in time, otherwise we'd have no ability to measure specific values. For example, if even one of these numbers was truly infinite, in the context that if we were to somehow be able to measure it, we could never measure it as a specific number, then is there any usefulness to infinity in that respect. If there is, it's not very obvious to me.
Now image that we jumped forward to some unknown time in this sequence (we took a vacation for 20 years and someone else kept repeating this pattern into larger and larger representations (in space ... he has to have room to record the results, otherwise it's some other sequence)), what properties could we assume to still hold true?
If we knew approximately how many updates per second were occurring over that period (we're assuming there's a synchronization in time between us and the generation of this structure) we could divide this down in various ways to determine approximately what values should be at each location.
Also by knowing a single value at some location in this sequence (and these values must maintain a specific linear ordering in space (a spacial dimension) in order that "next" elements in the row can be determined), we could determine within a single unit what all the other values were in the row as we know they differ by 1, except for a possible single duplicate element.
Anyway, we could quickly "synchronize" ourselves with the state of this count by knowing just a few properties.
Now if we jump back to the vague description of having an infinite quantity of infinite numbers, we could try to create a table showing which of these are larger than other values and this should lead us to the question of which is the largest.
If we simply look at the numbers, no number in the row will be larger than the first number and in that case we might define infinity to be anything larger than the first number in the row, but there's still a quantity involved, though not immediately "tangible" that's larger than this ... I'll give you a second to think it over ... ok, 2 more seconds ... any guesses as to what's the largest quantity in this structure? It's the number of steps or increment operations that were performed.
So if we added up all the numbers, we could determine how many (vague) "units" of time this process had undergone, though it also takes a certain amount of time to locate elements in the row and add new spaces for additional digits or terms and these aren't ignorable in real life, but notice that if we added all the numbers together we get a simple count over time, 1,2,3,4,... or 1,2,3, infinity and "infinity" is always what's happening in the present.
Though there could, from one perspective, be an infinite number of infinite quantities, these infinities refer to the fact that there are no predetermined bounds on the time the process could execute for (though a random asteroid strike, boredom or a power outage could terminate infinity early) and there is truly only a single "infinite" value involved which is subdivided into ever increasing subsets that are smaller than it, just as we could create two infinite values by alternating operations between two numbers, but if we performed these operations on a single value, it would be (at least approximately) updated twice as fast. So there's always a largest infinity and it's always dependent upon what operations are available to be performed over time.
Imagining things beyond this leads to confusion over what properties infinity possesses.
In calculus we have functions that are reliant upon the statistical properties of convergence for an unbounded sequence such as 1/2+1/4+1/8+1/16+... or .999...
The properties of these sequences are based upon physical concepts of proximity or nearness or smallness etc.
For example, the "proof" that 1=1/2+1/4+1/8+1/16+... is based upon the idea of recursively cutting an object into halves, but there's a paradox in that if an object can always be cut in half, then something must always remain after than cut and the remainder cannot be 0 and we can prove that 1 is not equal to 1/2+1/4+1/8+1/16+... using similar logic because we begin with 1/2 and constantly multiply this value by 1/2, which generates the sequence, 1/2, 1/4, 1/8 and at each iteration the value is a positive, non-zero number by definition, if a>0 and b>0 then a*b>0 and so is (a*
*b>0 etc. and we can also verify this by recognizing that only a multiplication by 0 results in 0 and we never began with a zero available to generate a zero result from multiplication, so the value simply converges toward, but never reaches this boundary or limit.
Now the question could become one of, whether or not this difference can always be made smaller than any other number.
Notice that this requires, similar to concept of multiple infinities, that we never expect any other number to also be the smallest number.
So if we had the two series .5, .75, .875, ... and .9, .99, .999 we can see the differences between these and 1 as decreasing 1-.5=1/2, 1-.75=1/4, 1-.875=1/8, ... and similarly 1-.9=1/10, 1-.99=1/100, 1-.999=1/1000, ...
So we have two decreasing series 2^-n and 10^-m that converge toward 0, but can we select an element from each set that's smaller than the other? No, and for n.m>0 they can't be equal to each other either.
If we never used more than a single such limit in an equation, there would generally be no such problem and we could simply compute what a convergence appeared to tend toward - notice that the reason why this is possible is because there's only a single infinite quantity (time) and we would have no issues about how to multiplex it between various processes to determine a desired result because we'd only have a single choice - continue with the next value in a single series, but if it comes to generating multiple "infinite" sets, then the question over what the desired ordering of these computations is, comes into play.
If we have an equation like this:
y=lim(sqrt(pi*x)/x) as x->+0
Then we have irrational values embedded within a limit, but the irrational values themselves are (ill) defined as limits themselves.
So we can rewrite this abstractly to emphasize the multiple nested infinite structures like this:
y=lim(lim(sqrt(lim(pi)*x)/x)) as x->+0
In this case (if we ignore some potential problems with irrational numbers being defined in terms of inequalities only) we can still determine the convergence of the limit without major problems because the influence of irrational values is decreasing and we can, by increasing the number of iterations or precision of each inner approximation, find that y converges toward 0.
But we do not have the same ability to determine a specific convergence for a fourier transform:
fourier(y)=integral(f(x)*e^(-2*pi*i*y))dx (-infinity<x<infinity)
Here we once again have multiple infinite sequences involved, but they operate in parallel in determining the value of a non-monotonic function and are nested within an infinite structure that provides unlimited sensitivity to variations of these irrational numbers.
Notice that the typical response is to quickly rewrite this using Euler's Identity in terms of geometric operations on a circle (and I've shown the paradoxes that arise from this as well), but is this truly an identity? No.
Also consider that for physics, this process is rather backwards - circles are created from "e" processes being integrated into observations over time and so the description should of pi in terms of an integration of a frequency component of the "e" process.
Notice that if we create a complex unit of rotation:
e=lim((1+i/n)^n) as n->infinity
Consider that if this were to describe a circle (or similar object in some high dimensional space), then the radius should remain 1, but we find this is not the case:
|1+i/n|=1^2+(i^2)/n^2=1-1/(n^2)
And we can see that this spirals inward (though we could similarly have it spiral outward) instead of remaining on the perimeter of a circle. We can approximate for the magnitude of this change over iterations of the exponentiation by n by a simple rescaling to 1-1/n (n>>1).
Now as n->infinity, we have this magnitude approach 1 and less of a divergence occurs, but in the case of a fourier transform we have the influence of this integrated over an infinite number of cycles and sensitive to the irrational variances of pi as well as potentially unbounded values of y (frequency).
What we can step back and recognize that there is only one infinite value available - time and other infinite values must be created as smaller, but growing, structures of this.
So what's the correct ordering of these infinite values with respect to a physical process performing a fourier transform?
We can build these up from observations.
We first need at least 2 quantities changing over time.
I'll write it like this:
x(0)=1
y(0)=0
x(t)=x(t-1)+y(t-1)/n
y(t)=y(t-1)-x(t-1)/n
To give a quick example of this for small n, we have with n=1:
{1,0},{1,-1},{0,-2},{2,-2},{-4,0},{-4,4},{0,8},{8,8},{16,0},...
So we have a process that cycles every 8 phases and has a gain of 16:1 per cycle, or a mean increase in amplitude each cycle of 16^(1/8)=2^(4*1/8)=sqrt(2)~=1.4142
There are ways to make this better and generate some correlations with a fibonacci expansion instead of a binary splitting (the above algorithm is performing two divisions by n per unit of t and we could split this into a single division by n process which more closely resembles a single infinite process multiplexed between different operations).
But anyway, as we increase the value of n, which should be performed by increasing the values of x or increasing the times over which the process occurs, the growth of the magnitude of these spirals slows (in terms of ratios of changes of magnitude each cycle) and the time period over which a repetition occurs approaches 2*pi*n.
So for large n we can approximate the growth of these simple operations as:
x(t)~=cos(t/(2*pi*n))*(e^(a*t))
y(t)~=sin(t/(2*pi*n))*(e^(a*t))
Where a approaches 0 as n increases and I believe the quantity a*n should approach a non-zero constant, though I might have that wrong.
Anyway, the point is that the fourier transform is written in terms of a nested sequence of infinite operations that is likely not natural, though the approximate geometric identity of a rotation around a circle does not reveal the dynamic properties of the space and atoms in which this circle is dynamically constructed. So to begin with the constraint of a circle and then attempt to derive discrete units from this (as most continuous field theories attempt to do) is backwards. The circles arise from discrete operations over time and irrational numbers are not fundamental units as other processes would first be required to generate those before iterating those values in another infinite process, but the irrational process would never terminate and have time to allow its results to be interleaved with anything else.
So notice again, that a single simple discrete process of converting between two quantities generates a process that simultaineously creates irrational ratios for e, pi and trigonometric identities, and it we recognize that the irrational components are simply imagined to exist but intangible, then every present moment, t, can be associated with a precise value of pi, e and it's associated rotational vector all in a pair of numbers (which we could probably even find a way to encode as a single number or a growing string).
There's just one infinity and it's always finite when you look at it. Alephs are nothing more than studying the manner in which quantities are subdivided within that single process (or similarly the recurring elements and how the figurative DNA strand appears folded in space by these recurring properties).
If you still insist, you can have your non-materialized numbers, but if you can't even maintain a record of one of them in your thoughts, then you're still (irrationally) waiting for pi to end despite the fact that you've already imagined a circle intended to define it - what came first - a circle or pi? Don't tell me 3.1415... came first. Now, what came before the infinitely continuous circle or did we begin with circles? No, the center came first - and how did we determine a center - we had a collection - and what came first in the collection - an element and what came before an element? You can jump to conscious qualities and say you can't precisely describe it to me and I'm fine with that, though you can still maybe take it back further in an immaterial form, but you're on your own there, except if you tell me you were already finding numbers before that, we're just going to have to agree to disagree on that. You need a memory to construct numbers.
I can think of numbers without materializing said number.
But you at least know what number it is for yourself. Otherwise you're not thinking of a specific number but about possible numbers or sets.
I bet none of them have been a randomly selected natural number from the "set of all natural numbers", otherwise we should be amazed at the probability of it not being over a googleplex (10^(10^100)).
Now if you happened to pick a random number over a googleplex, we should then be amazed at the probability that it was so easily compressible into a small finite representation such as (10^(11^(12^13))), for which "nearby" integers would typically not be so easily factored and require a massive number of digits to represent.
Yet no matter how large or complex a description for a number, we're effectively not even moving relative to infinity ... or are we?
Well, what's infinity in terms of natural numbers? It's larger than any natural number.
So if we counted to 3: 1,2,3 then infinity could be 4 ... except that once we created 4, then infinity, being larger would have to be 5 ... oops, I just created 5, so infinity would have to be 6, yikes, this appears to be circular.
Ok, let's try defining (infinity-1) to be the largest natural number and that makes sense because once we've gone past natural numbers (I'm just working on a natural number line), we're at infinity.
So if we try counting to 3 again, 1,2,3 then the next number should be infinity, so it would be 1,2,3,infinity or 1,2,3,... and we don't have a problem here because infinity isn't a natural number and infinity+1 isn't defined, so we can finally stop counting as we've reached infinity
Notice that we also no longer have a problem with trying to define infinity+1=infinity, which implies infinity=infinity-1 and leads to the vicious recursion infinity=infinity-1-1-1-1...=infinity-infinity.
If we begin with 1,2,3,infinity and if we created 2*3=6, would 6 now be larger than infinity? By definition, it couldn't be and if 6 was the largest natural number then infinity would be ~7.
The point of this is to show that infinity needs not preexist as some incredibly massive quantity that we can't even begin to approach but instead is dynamically created by processes and infinity effectively exists in the present.
In some mathematical texts there are various forms of infinities that may or may not be arranged into various magnitudes or relative rates of growth, and consider how such structures are created:
If we began to create a row of numbers by progressing with this sequence:
1
1 1
2 1
2 1 1
2 2 1
3 2 1
3 2 1 1
3 2 2 1
3 3 2 1
4 3 2 1
...
We could "grow" this over time into this sequence
1
2 1
3 2 1
4 3 2 1
5 4 3 2 1
...
Now notice that every number at each position along this row never decreases and is periodically incremented. If we continued incrementing individual numbers according to the top sequence an "infinite number" of times, then we'd end up with a row of numbers and each number growing "infinitely large".
So we've converted a single infinite quantity into an infinite quantity of infinite numbers. (It's magic, right?)
Well, at moment, this structure is nothing more than a finite number of finite values and all that "infinity" means is that it's intended to be continually increased, but obviously we couldn't have it increased without being synchronized with us in time, otherwise we'd have no ability to measure specific values. For example, if even one of these numbers was truly infinite, in the context that if we were to somehow be able to measure it, we could never measure it as a specific number, then is there any usefulness to infinity in that respect. If there is, it's not very obvious to me.
Now image that we jumped forward to some unknown time in this sequence (we took a vacation for 20 years and someone else kept repeating this pattern into larger and larger representations (in space ... he has to have room to record the results, otherwise it's some other sequence)), what properties could we assume to still hold true?
If we knew approximately how many updates per second were occurring over that period (we're assuming there's a synchronization in time between us and the generation of this structure) we could divide this down in various ways to determine approximately what values should be at each location.
Also by knowing a single value at some location in this sequence (and these values must maintain a specific linear ordering in space (a spacial dimension) in order that "next" elements in the row can be determined), we could determine within a single unit what all the other values were in the row as we know they differ by 1, except for a possible single duplicate element.
Anyway, we could quickly "synchronize" ourselves with the state of this count by knowing just a few properties.
Now if we jump back to the vague description of having an infinite quantity of infinite numbers, we could try to create a table showing which of these are larger than other values and this should lead us to the question of which is the largest.
If we simply look at the numbers, no number in the row will be larger than the first number and in that case we might define infinity to be anything larger than the first number in the row, but there's still a quantity involved, though not immediately "tangible" that's larger than this ... I'll give you a second to think it over ... ok, 2 more seconds ... any guesses as to what's the largest quantity in this structure? It's the number of steps or increment operations that were performed.
So if we added up all the numbers, we could determine how many (vague) "units" of time this process had undergone, though it also takes a certain amount of time to locate elements in the row and add new spaces for additional digits or terms and these aren't ignorable in real life, but notice that if we added all the numbers together we get a simple count over time, 1,2,3,4,... or 1,2,3, infinity and "infinity" is always what's happening in the present.
Though there could, from one perspective, be an infinite number of infinite quantities, these infinities refer to the fact that there are no predetermined bounds on the time the process could execute for (though a random asteroid strike, boredom or a power outage could terminate infinity early) and there is truly only a single "infinite" value involved which is subdivided into ever increasing subsets that are smaller than it, just as we could create two infinite values by alternating operations between two numbers, but if we performed these operations on a single value, it would be (at least approximately) updated twice as fast. So there's always a largest infinity and it's always dependent upon what operations are available to be performed over time.
Imagining things beyond this leads to confusion over what properties infinity possesses.
In calculus we have functions that are reliant upon the statistical properties of convergence for an unbounded sequence such as 1/2+1/4+1/8+1/16+... or .999...
The properties of these sequences are based upon physical concepts of proximity or nearness or smallness etc.
For example, the "proof" that 1=1/2+1/4+1/8+1/16+... is based upon the idea of recursively cutting an object into halves, but there's a paradox in that if an object can always be cut in half, then something must always remain after than cut and the remainder cannot be 0 and we can prove that 1 is not equal to 1/2+1/4+1/8+1/16+... using similar logic because we begin with 1/2 and constantly multiply this value by 1/2, which generates the sequence, 1/2, 1/4, 1/8 and at each iteration the value is a positive, non-zero number by definition, if a>0 and b>0 then a*b>0 and so is (a*
*b>0 etc. and we can also verify this by recognizing that only a multiplication by 0 results in 0 and we never began with a zero available to generate a zero result from multiplication, so the value simply converges toward, but never reaches this boundary or limit.Now the question could become one of, whether or not this difference can always be made smaller than any other number.
Notice that this requires, similar to concept of multiple infinities, that we never expect any other number to also be the smallest number.
So if we had the two series .5, .75, .875, ... and .9, .99, .999 we can see the differences between these and 1 as decreasing 1-.5=1/2, 1-.75=1/4, 1-.875=1/8, ... and similarly 1-.9=1/10, 1-.99=1/100, 1-.999=1/1000, ...
So we have two decreasing series 2^-n and 10^-m that converge toward 0, but can we select an element from each set that's smaller than the other? No, and for n.m>0 they can't be equal to each other either.
If we never used more than a single such limit in an equation, there would generally be no such problem and we could simply compute what a convergence appeared to tend toward - notice that the reason why this is possible is because there's only a single infinite quantity (time) and we would have no issues about how to multiplex it between various processes to determine a desired result because we'd only have a single choice - continue with the next value in a single series, but if it comes to generating multiple "infinite" sets, then the question over what the desired ordering of these computations is, comes into play.
If we have an equation like this:
y=lim(sqrt(pi*x)/x) as x->+0
Then we have irrational values embedded within a limit, but the irrational values themselves are (ill) defined as limits themselves.
So we can rewrite this abstractly to emphasize the multiple nested infinite structures like this:
y=lim(lim(sqrt(lim(pi)*x)/x)) as x->+0
In this case (if we ignore some potential problems with irrational numbers being defined in terms of inequalities only) we can still determine the convergence of the limit without major problems because the influence of irrational values is decreasing and we can, by increasing the number of iterations or precision of each inner approximation, find that y converges toward 0.
But we do not have the same ability to determine a specific convergence for a fourier transform:
fourier(y)=integral(f(x)*e^(-2*pi*i*y))dx (-infinity<x<infinity)
Here we once again have multiple infinite sequences involved, but they operate in parallel in determining the value of a non-monotonic function and are nested within an infinite structure that provides unlimited sensitivity to variations of these irrational numbers.
Notice that the typical response is to quickly rewrite this using Euler's Identity in terms of geometric operations on a circle (and I've shown the paradoxes that arise from this as well), but is this truly an identity? No.
Also consider that for physics, this process is rather backwards - circles are created from "e" processes being integrated into observations over time and so the description should of pi in terms of an integration of a frequency component of the "e" process.
Notice that if we create a complex unit of rotation:
e=lim((1+i/n)^n) as n->infinity
Consider that if this were to describe a circle (or similar object in some high dimensional space), then the radius should remain 1, but we find this is not the case:
|1+i/n|=1^2+(i^2)/n^2=1-1/(n^2)
And we can see that this spirals inward (though we could similarly have it spiral outward) instead of remaining on the perimeter of a circle. We can approximate for the magnitude of this change over iterations of the exponentiation by n by a simple rescaling to 1-1/n (n>>1).
Now as n->infinity, we have this magnitude approach 1 and less of a divergence occurs, but in the case of a fourier transform we have the influence of this integrated over an infinite number of cycles and sensitive to the irrational variances of pi as well as potentially unbounded values of y (frequency).
What we can step back and recognize that there is only one infinite value available - time and other infinite values must be created as smaller, but growing, structures of this.
So what's the correct ordering of these infinite values with respect to a physical process performing a fourier transform?
We can build these up from observations.
We first need at least 2 quantities changing over time.
I'll write it like this:
x(0)=1
y(0)=0
x(t)=x(t-1)+y(t-1)/n
y(t)=y(t-1)-x(t-1)/n
To give a quick example of this for small n, we have with n=1:
{1,0},{1,-1},{0,-2},{2,-2},{-4,0},{-4,4},{0,8},{8,8},{16,0},...
So we have a process that cycles every 8 phases and has a gain of 16:1 per cycle, or a mean increase in amplitude each cycle of 16^(1/8)=2^(4*1/8)=sqrt(2)~=1.4142
There are ways to make this better and generate some correlations with a fibonacci expansion instead of a binary splitting (the above algorithm is performing two divisions by n per unit of t and we could split this into a single division by n process which more closely resembles a single infinite process multiplexed between different operations).
But anyway, as we increase the value of n, which should be performed by increasing the values of x or increasing the times over which the process occurs, the growth of the magnitude of these spirals slows (in terms of ratios of changes of magnitude each cycle) and the time period over which a repetition occurs approaches 2*pi*n.
So for large n we can approximate the growth of these simple operations as:
x(t)~=cos(t/(2*pi*n))*(e^(a*t))
y(t)~=sin(t/(2*pi*n))*(e^(a*t))
Where a approaches 0 as n increases and I believe the quantity a*n should approach a non-zero constant, though I might have that wrong.
Anyway, the point is that the fourier transform is written in terms of a nested sequence of infinite operations that is likely not natural, though the approximate geometric identity of a rotation around a circle does not reveal the dynamic properties of the space and atoms in which this circle is dynamically constructed. So to begin with the constraint of a circle and then attempt to derive discrete units from this (as most continuous field theories attempt to do) is backwards. The circles arise from discrete operations over time and irrational numbers are not fundamental units as other processes would first be required to generate those before iterating those values in another infinite process, but the irrational process would never terminate and have time to allow its results to be interleaved with anything else.
So notice again, that a single simple discrete process of converting between two quantities generates a process that simultaineously creates irrational ratios for e, pi and trigonometric identities, and it we recognize that the irrational components are simply imagined to exist but intangible, then every present moment, t, can be associated with a precise value of pi, e and it's associated rotational vector all in a pair of numbers (which we could probably even find a way to encode as a single number or a growing string).
There's just one infinity and it's always finite when you look at it. Alephs are nothing more than studying the manner in which quantities are subdivided within that single process (or similarly the recurring elements and how the figurative DNA strand appears folded in space by these recurring properties).
If you still insist, you can have your non-materialized numbers, but if you can't even maintain a record of one of them in your thoughts, then you're still (irrationally) waiting for pi to end despite the fact that you've already imagined a circle intended to define it - what came first - a circle or pi? Don't tell me 3.1415... came first. Now, what came before the infinitely continuous circle or did we begin with circles? No, the center came first - and how did we determine a center - we had a collection - and what came first in the collection - an element and what came before an element? You can jump to conscious qualities and say you can't precisely describe it to me and I'm fine with that, though you can still maybe take it back further in an immaterial form, but you're on your own there, except if you tell me you were already finding numbers before that, we're just going to have to agree to disagree on that. You need a memory to construct numbers.
SteveA2
"You need a memory to construct numbers."
Exactly - and it is a little funny to think that it (perhaps) takes a point with content to create a memory, so it takes an "object" to create a "non-object"
"You need a memory to construct numbers."
Exactly - and it is a little funny to think that it (perhaps) takes a point with content to create a memory, so it takes an "object" to create a "non-object"
QUOTE (bukh+Jan 29 2009, 07:21 PM)
SteveA2
"You need a memory to construct numbers."
Exactly - and it is a little funny to think that it (perhaps) takes a point with content to create a memory, so it takes an "object" to create a "non-object"
That could be a way of looking at it. A collection of objects reaches a point at which they become described by a smaller set of rules of interaction and then the objects are reinterpreted as a point in a new collection that contains those rules of interaction, but at a different scale of abstraction. So you can see it as recursively embedded sets over time. A possible reason why this may be the case is from data compression. If observations increase faster than an ability to record and interpret them (and record those interpretations as well), then some form of data compression is required to store the results (all of human knowledge can't be fit into a single textbook - in fact it appears human senses compress information by a huge ratio before conscious recognition occurs)) and so objects or observations are grouped until common features can be extracted and the common features are retained, while the individual events are (generally) discarded, though we can also invert this relationship and say that observations are fractally unfolded into perceptions via. prior learned/grown structures.
Something to consider is that an observation in a moment of time exists in different times or spaces than the properties that evolve over time. One's figuratively a dot and the other a line, or similarly ones an observation and the other are rules of interactions derived from a collection of observations (though we could even draw this a little finer in that we have objects over time, collected into common features and the those recognized features can present recognized rules of interaction ... and if we go further and over how those rules of interaction might change over time, then we're "seeing" or deriving properties that describe the evolution of laws of interaction and I guess we could go beyond that, but it's a single chain of events that accumulates along an axis and then folds into a new dimension that describes how the sequences along that axis have evolved. None of these axises are infinitely wide though, they just need to be large enough to contain enough samples that someone considers the patterns to be predictable within some measure of reliability).
So if we try to think about or observe something that doesn't change over time, then there's nothing to learn or extract from this and effectively draw a line (or curve or other simpler approximation or compressed representation to the data) from a collection of points in order that it's rules or form over time is known.
Now someone might try to deny this occurs in science or physics, but unless science exists as something outside comprehension, then physics would appear to be inevitably confined to those things which are comprehensible (and that's not necessarily something static but an evolving process).
"You need a memory to construct numbers."
Exactly - and it is a little funny to think that it (perhaps) takes a point with content to create a memory, so it takes an "object" to create a "non-object"
That could be a way of looking at it. A collection of objects reaches a point at which they become described by a smaller set of rules of interaction and then the objects are reinterpreted as a point in a new collection that contains those rules of interaction, but at a different scale of abstraction. So you can see it as recursively embedded sets over time. A possible reason why this may be the case is from data compression. If observations increase faster than an ability to record and interpret them (and record those interpretations as well), then some form of data compression is required to store the results (all of human knowledge can't be fit into a single textbook
- in fact it appears human senses compress information by a huge ratio before conscious recognition occurs)) and so objects or observations are grouped until common features can be extracted and the common features are retained, while the individual events are (generally) discarded, though we can also invert this relationship and say that observations are fractally unfolded into perceptions via. prior learned/grown structures.Something to consider is that an observation in a moment of time exists in different times or spaces than the properties that evolve over time. One's figuratively a dot and the other a line, or similarly ones an observation and the other are rules of interactions derived from a collection of observations (though we could even draw this a little finer in that we have objects over time, collected into common features and the those recognized features can present recognized rules of interaction ... and if we go further and over how those rules of interaction might change over time, then we're "seeing" or deriving properties that describe the evolution of laws of interaction and I guess we could go beyond that, but it's a single chain of events that accumulates along an axis and then folds into a new dimension that describes how the sequences along that axis have evolved. None of these axises are infinitely wide though, they just need to be large enough to contain enough samples that someone considers the patterns to be predictable within some measure of reliability).
So if we try to think about or observe something that doesn't change over time, then there's nothing to learn or extract from this and effectively draw a line (or curve or other simpler approximation or compressed representation to the data) from a collection of points in order that it's rules or form over time is known.
Now someone might try to deny this occurs in science or physics, but unless science exists as something outside comprehension, then physics would appear to be inevitably confined to those things which are comprehensible (and that's not necessarily something static but an evolving process).
SteveA2
"A collection of objects reaches a point at which they become described by a smaller set of rules of interaction and then the objects are reinterpreted as a point in a new collection that contains those rules of interaction, but at a different scale of abstraction."
Such a pleasure to read someone with an open an imaginative mind and being so easy to follow in logic and serious wit so to speak. Your above description is much in line with the 3D Pixel Universe - not that I intent to force this concept through - but the more the physical world can be seen with "information optics" the better.
I like to think that Physical Universe was born the very moment that space - defined as an object of sameness unfolded into two and further segregated into more and more ratios of this "One" - creating smaller objects of sameness - or points in space - each with an exact knowledge about its relative position in space - knowing its neighbors. And following one other superior principle - namely the strive for achieving most optimal - most even fit in space of all such objects configuring bigger stable repetitive patterns.
Imagine that at a certain state of development - with the creation of a certain number of such smallest objects, they will enter into stable repetitive patterns and create a new Unit1, comprising a number (very very large number) of such smallest points in a totally stable repetitive pattern, with a certain amount of information build into. And the next scale has been established.
And at this point we have to be very cautious about direction - because there cannot be established a "bigger" space - the ongoing division of objects create inward complexion, smaller and smaller russian dolls, but the physical expression is the outward dolls - and the inwards complexion is the ongoing creation of information.
Exactly how the system now is being de-coded - understood - communicated - well that is solely up to the informational complexion that de-code - and in the case of physical universe it is being defined and de-coded by the informational qubit that is THE human.
"A collection of objects reaches a point at which they become described by a smaller set of rules of interaction and then the objects are reinterpreted as a point in a new collection that contains those rules of interaction, but at a different scale of abstraction."
Such a pleasure to read someone with an open an imaginative mind and being so easy to follow in logic and serious wit so to speak. Your above description is much in line with the 3D Pixel Universe - not that I intent to force this concept through - but the more the physical world can be seen with "information optics" the better.
I like to think that Physical Universe was born the very moment that space - defined as an object of sameness unfolded into two and further segregated into more and more ratios of this "One" - creating smaller objects of sameness - or points in space - each with an exact knowledge about its relative position in space - knowing its neighbors. And following one other superior principle - namely the strive for achieving most optimal - most even fit in space of all such objects configuring bigger stable repetitive patterns.
Imagine that at a certain state of development - with the creation of a certain number of such smallest objects, they will enter into stable repetitive patterns and create a new Unit1, comprising a number (very very large number) of such smallest points in a totally stable repetitive pattern, with a certain amount of information build into. And the next scale has been established.
And at this point we have to be very cautious about direction - because there cannot be established a "bigger" space - the ongoing division of objects create inward complexion, smaller and smaller russian dolls, but the physical expression is the outward dolls - and the inwards complexion is the ongoing creation of information.
Exactly how the system now is being de-coded - understood - communicated - well that is solely up to the informational complexion that de-code - and in the case of physical universe it is being defined and de-coded by the informational qubit that is THE human.
QUOTE (bukh+Jan 29 2009, 07:21 PM)
SteveA2
"You need a memory to construct numbers."
Exactly - and it is a little funny to think that it (perhaps) takes a point with content to create a memory, so it takes an "object" to create a "non-object"
BUT you don't need to construct numbers!!!!!!!!!!!!!!!!!!!
That is what you guys have your minds closed to.
Please try and be a bit more open minded.
"You need a memory to construct numbers."
Exactly - and it is a little funny to think that it (perhaps) takes a point with content to create a memory, so it takes an "object" to create a "non-object"
BUT you don't need to construct numbers!!!!!!!!!!!!!!!!!!!
That is what you guys have your minds closed to.
Please try and be a bit more open minded.
Getting back to physics and or physical inferences and or references, it is important to be mindful that if one compares for example a density, particle or mass and it is implied or measured to be one electron-volt, REF: http://en.wikipedia.org/wiki/Electronvolt
then that's what it is - One electron-volt.. Likewise if one refers to one Particle then that's what it is - ONE PARTICLE, until someone insists it is .9~9 or 1.0~1 of a Partcile to which that's their problem..
I concede that all mass is constantly changing and if we measure enough times the measurements may be more or less than one electron-volt or what other comparison, such as .9~9 electron-volt and then 1.0~1 electron-volt, so that on average a finite figure can be referred to, So if we were able to measure or compare everything possible and all in the same instance, all of it together, will indeed equate to ONE UNIVERSE, no less and no more, so therefore all statements in reference to .99, 1.0~1 or similar are at this point really mute..
No ifs and no buts!
And before comments are made that I am not in line with what is being posted of late, I am quite aware of this, but should anyone care to go back far enough, most of the discussion of late is a complete waste of time anyway, that is if one is referring to physical concepts and or constructs by way of references and or comparisons using given definitions with a defined scale with a given value..
The point I am trying to stress is that the values used today are themeselves a comparitive figure..
Cheers,
Peter J Schoen..
then that's what it is - One electron-volt.. Likewise if one refers to one Particle then that's what it is - ONE PARTICLE, until someone insists it is .9~9 or 1.0~1 of a Partcile to which that's their problem..
I concede that all mass is constantly changing and if we measure enough times the measurements may be more or less than one electron-volt or what other comparison, such as .9~9 electron-volt and then 1.0~1 electron-volt, so that on average a finite figure can be referred to, So if we were able to measure or compare everything possible and all in the same instance, all of it together, will indeed equate to ONE UNIVERSE, no less and no more, so therefore all statements in reference to .99, 1.0~1 or similar are at this point really mute..
No ifs and no buts!
And before comments are made that I am not in line with what is being posted of late, I am quite aware of this, but should anyone care to go back far enough, most of the discussion of late is a complete waste of time anyway, that is if one is referring to physical concepts and or constructs by way of references and or comparisons using given definitions with a defined scale with a given value..
The point I am trying to stress is that the values used today are themeselves a comparitive figure..
Cheers,
Peter J Schoen..
Buttershug
"BUT you don't need to construct numbers!!!!!!!!!!!!!!!!!!!"
OK - from where do you get Your numbers ?
"BUT you don't need to construct numbers!!!!!!!!!!!!!!!!!!!"
OK - from where do you get Your numbers ?
QUOTE (iseason+Jan 29 2009, 05:22 AM)
Hi all
I agree with this statement. 0.9999r could not define anything or be said to equal 1 any more than 0.1111r could be said to. Both are in fact an equal distance from one via "infinity". Even mathematics needs dimensions to be relevant. 0.999r is an assumption that the intervening value does not matter or is relatively increasing alongside what you are measuring.
It is borrowing from an unknown quantity.
Cheers
Iseason
0.999r can not be anything other than 1.
There is no difference between it and 1.
If it is not 1 then what is the difference?
If you find a difference then it is NOT 0.999r.
It is, and therefore does not need to be constructed or materialized or anything else.
IT JUST BLOODY WELL IS WHAT IT IS.
complete and full and nontangible.
There is no intervening value.
It is not growing.
It is defined complete.
It is not borrowing.
It is not doing anything other than existing in a nonphysical nontangible way.
It is not a process.
It is not a method.
QUOTE (bukh+Jan 29 2009, 10:28 PM)
Buttershug
"BUT you don't need to construct numbers!!!!!!!!!!!!!!!!!!!"
OK - from where do you get Your numbers ?
From the number store down the street, I have an open P.O. with them.
You don't need to get numbers from anywhere.
They are intangible nonphysical concepts.
You merely have to define them.
They are pre-existing to the extent that they need to be.
Get a penny and a quarter.
Put them on your desk.
Did you have to make one bigger than the other or did they already have that property?
Or did that property simply exist?
I say one was bigger than other by virtue of them being different sizes.
And that the Sun was bigger than the Earth before anybody could notice it.
And that numbers are the same way.
Edit I forgot to ask what makes you think you need to get numbers from anywhere? They are not physical or tangible.
"BUT you don't need to construct numbers!!!!!!!!!!!!!!!!!!!"
OK - from where do you get Your numbers ?
From the number store down the street, I have an open P.O. with them.
You don't need to get numbers from anywhere.
They are intangible nonphysical concepts.
You merely have to define them.
They are pre-existing to the extent that they need to be.
Get a penny and a quarter.
Put them on your desk.
Did you have to make one bigger than the other or did they already have that property?
Or did that property simply exist?
I say one was bigger than other by virtue of them being different sizes.
And that the Sun was bigger than the Earth before anybody could notice it.
And that numbers are the same way.
Edit I forgot to ask what makes you think you need to get numbers from anywhere? They are not physical or tangible.
QUOTE (buttershug+Jan 29 2009, 10:46 PM)
From the number store down the street, I have an open P.O. with them.
You don't need to get numbers from anywhere.
They are intangible nonphysical concepts.
You merely have to define them.
They are pre-existing to the extent that they need to be.
Get a penny and a quarter.
Put them on your desk.
Did you have to make one bigger than the other or did they already have that property?
Or did that property simply exist?
I say one was bigger than other by virtue of them being different sizes.
And that the Sun was bigger than the Earth before anybody could notice it.
And that numbers are the same way.
Edit I forgot to ask what makes you think you need to get numbers from anywhere? They are not physical or tangible.
I agree that numbers arise from finite properties, but consider how did you recognize that a quarter was larger than a penny. In order to recognize that one is larger than the other you have to be able to measure those quantities and perform operations on collections of them.
Your body does a lot of things for your already, but let's say we wanted to build a machine that could determine that a quarter was larger than a penny. What inputs and outputs would it need and what forms of computation would it require. If you want to dig deeper, how can these computations be connected to other computations that form a space in which the machine, with its inputs and outputs can communicate with space, pennies and quarters to determine the sizes of these things.
If the machine can only perform logical operations, but not possess a memory then it would need to see everything simultaineously and instantly make a decision. This seems an unrealistic model and not particularly convenient or easily malleable one.
So, though you claim that numbers can preexist cognition of them, this isn't particularly useful and not something we can verify either (so it may be somehow that numbers actually do NOT exist outside cognition of them - though I'm skeptical of that).
Anyway, what properties, in detail, would a machine need in order to be able to verify your claim that pennies and quarters actually do differ in size?
You don't need to get numbers from anywhere.
They are intangible nonphysical concepts.
You merely have to define them.
They are pre-existing to the extent that they need to be.
Get a penny and a quarter.
Put them on your desk.
Did you have to make one bigger than the other or did they already have that property?
Or did that property simply exist?
I say one was bigger than other by virtue of them being different sizes.
And that the Sun was bigger than the Earth before anybody could notice it.
And that numbers are the same way.
Edit I forgot to ask what makes you think you need to get numbers from anywhere? They are not physical or tangible.
I agree that numbers arise from finite properties, but consider how did you recognize that a quarter was larger than a penny. In order to recognize that one is larger than the other you have to be able to measure those quantities and perform operations on collections of them.
Your body does a lot of things for your already, but let's say we wanted to build a machine that could determine that a quarter was larger than a penny. What inputs and outputs would it need and what forms of computation would it require. If you want to dig deeper, how can these computations be connected to other computations that form a space in which the machine, with its inputs and outputs can communicate with space, pennies and quarters to determine the sizes of these things.
If the machine can only perform logical operations, but not possess a memory then it would need to see everything simultaineously and instantly make a decision. This seems an unrealistic model and not particularly convenient or easily malleable one.
So, though you claim that numbers can preexist cognition of them, this isn't particularly useful and not something we can verify either (so it may be somehow that numbers actually do NOT exist outside cognition of them - though I'm skeptical of that).
Anyway, what properties, in detail, would a machine need in order to be able to verify your claim that pennies and quarters actually do differ in size?
Steven, you (along with people like Precursor) seem obsessed with reaching for a dictionary when someone asks you if you know the meaning of a mathematical concept. Further more, when you do that, you ignore some of the definitions and tend to preferencely use particular ones, which match your preconceptions. And you don't allow for the fact a wordy dictionary aimed at non-mathematicians isn't going to define mathematical terms very well. Particularly if they only allow one or two lines for what might be a very complicated topic.
Mathematical meanings of 'linear' can be one of the following things:
y = mx+c is a linear graph, the relationship between x and y is linear. However, f(x) = mx+c is NOT a linear map on x.
f(x) = kx IS a linear map, since f(ax) = af(x) and f(x+y) = f(x)+f(y). k=0 satisfies this condition, so f(x) = 0 is a linear map. And before jumping into an ignorant tirade, I suggest you look up what 'kernel' means to people using transformations and morphisms.
The expression Ax+By+Cz is a linear combination of x, y, z for any A, B, C because it only involves variables x, y, z at linear order and there's no constant. This is NOT about drawing lines or graphs, it's about just summations of things. 0x+0y+0z is a linear combination of x, y and z. Things like 'the price of tea in China' doesn't come into it because a linear transformation, which generates such linear combinations, has a defined domain and range. When you're doing 3d modelling, there's no direction called 'price of tea in China', just x, y and z, because you've defined a domain spanned by (x,y,z). You, Steven, are ignorant of this so assume anythnig you can pull out of your backside is valid.
Of course you won't take my word for it. What about a Cambridge professor (top of page 9)?
You say things like how you were teaching the teachers, but why can't you even do homeworks expected of 17 year olds? Why are you unfamiliar with basic terminology that you have to go to dictionary websites? That set of lecture notes I just linked you to covers linear combinations, linear transformations, linear operators in detail. I'm sure you don't even know what a dual vector space is (something essential in the realm of linear transforms), but you don't stop to think "I've never heard of that, maybe I don't understand it!".
y=mx+c is how 12 year olds are taught about one concept which involves the word 'linear'. When you get to doing a bit of vector calculus (something you never did) you discover there's more meanings and a linear map doesn't plot a line through a 2d plane, it takes an n dimensional space to an m dimensional space and the graph of that is generally impossible to draw.
For instance, all rotations can be expressed as linear transformations. A rotation of a 3d space results in another 3d space. To graph the action of the transformation you'd need a 6 dimensional graph. For instance, let (x,y,z) be in R^3 and M be a matrix on it. Then you have
( m11 m12 m13 )( x ) ( a )
( m21 m22 m23 )( y ) = ( b )
( m31 m32 m33 )( z ) ( c )
Mathematical meanings of 'linear' can be one of the following things:
y = mx+c is a linear graph, the relationship between x and y is linear. However, f(x) = mx+c is NOT a linear map on x.
f(x) = kx IS a linear map, since f(ax) = af(x) and f(x+y) = f(x)+f(y). k=0 satisfies this condition, so f(x) = 0 is a linear map. And before jumping into an ignorant tirade, I suggest you look up what 'kernel' means to people using transformations and morphisms.
The expression Ax+By+Cz is a linear combination of x, y, z for any A, B, C because it only involves variables x, y, z at linear order and there's no constant. This is NOT about drawing lines or graphs, it's about just summations of things. 0x+0y+0z is a linear combination of x, y and z. Things like 'the price of tea in China' doesn't come into it because a linear transformation, which generates such linear combinations, has a defined domain and range. When you're doing 3d modelling, there's no direction called 'price of tea in China', just x, y and z, because you've defined a domain spanned by (x,y,z). You, Steven, are ignorant of this so assume anythnig you can pull out of your backside is valid.
Of course you won't take my word for it. What about a Cambridge professor (top of page 9)?
You say things like how you were teaching the teachers, but why can't you even do homeworks expected of 17 year olds? Why are you unfamiliar with basic terminology that you have to go to dictionary websites?
That set of lecture notes I just linked you to covers linear combinations, linear transformations, linear operators in detail. I'm sure you don't even know what a dual vector space is (something essential in the realm of linear transforms), but you don't stop to think "I've never heard of that, maybe I don't understand it!". y=mx+c is how 12 year olds are taught about one concept which involves the word 'linear'. When you get to doing a bit of vector calculus (something you never did) you discover there's more meanings and a linear map doesn't plot a line through a 2d plane, it takes an n dimensional space to an m dimensional space and the graph of that is generally impossible to draw.
For instance, all rotations can be expressed as linear transformations. A rotation of a 3d space results in another 3d space. To graph the action of the transformation you'd need a 6 dimensional graph. For instance, let (x,y,z) be in R^3 and M be a matrix on it. Then you have
CODE
( m11 m12 m13 )( x ) ( a )
( m21 m22 m23 )( y ) = ( b )
( m31 m32 m33 )( z ) ( c )
a, b and c are FOR ANY VALUES OF mij linear combinations of x, y and z.
This is all explained in the first 10 pages or so of the lecture notes I've linked to. We both know you don't understand them, but you will not read them, deluding yourself into believing you have some great understanding but not once have you managed to do a question put to you expected of even 17 year olds.
What were you teaching the teachers if you know nothing? Clearly you were stroking your own ego from a very early age. I do worry about the kind of warping effect you'll have had on your children. Hopefully you didn't home school them? After all, why send them to school where you know they'll be taught incorrect things?
SteveA2
"Something to consider is that an observation in a moment of time exists in different times or spaces than the properties that evolve over time. One's figuratively a dot and the other a line, or similarly ones an observation and the other are rules of interactions derived from a collection of observations (though we could even draw this a little finer in that we have objects over time, collected into common features and the those recognized features can present recognized rules of interaction ... and if we go further and over how those rules of interaction might change over time, then we're "seeing" or deriving properties that describe the evolution of laws of interaction and I guess we could go beyond that, but it's a single chain of events that accumulates along an axis and then folds into a new dimension that describes how the sequences along that axis have evolved. None of these axises are infinitely wide though, they just need to be large enough to contain enough samples that someone considers the patterns to be predictable within some measure of reliability)."
To me the above are very essential considerations.
I would like to think that "Universe Exists Only Once"
Universe is an oscillating out-folding and in-folding - in the sense that information is being "Recalculated" and "Re-expressed" and further created, at each beat of universe.
To me this is the logic consequence of dynamic - it is not possible to change something without changing everything at each beat. The "trick" is that universal change is being arranged scale-wise - and we have chosen to be concerned - from a practical point of view - only by the outermost expressions - those expressions that we can sense physically - and then we are ignoring all deeper changes - and refer to them as non-physical -
And everything IS the effect of everything including all kind of mind-concepts and mind-related expressions and experiences (including the feeling that numbers are at hand), but it is close to being non-comprehendable that the information in universe can exhibit such an amount of calculus in each flash - but we ignore the fact that calculus is self-organizing - calculus takes no instruction - calculus simple happens because of the principles laid down in "Shape and Least Void. (this principle is being explained in a bit more detail in the 3D Pixel Universe)
Well - I do not think that we are in dis-agreement (apart from perhaps the more concrete ideas of the 3D pixel universe)
My sole point is that re-calculation is necessary right from the smallest of the smallest, at each and every flash expression.
When I say flash expression - at the same time I indicate that human physical world and all what relates to mind, fundamentally is being discrete events - that it is not possible to deal with a system which harbor continuity and infinity as part of the system.
The truth in the sense that one can say that "This is HOW it is" - is naturally not into existence as such - everything is being understood and described and communicated out from premises - out from axioms - and I have chosen the axiom that everything best can be understood - described and communicated out from "object of sameness" as the Tool.
"Something to consider is that an observation in a moment of time exists in different times or spaces than the properties that evolve over time. One's figuratively a dot and the other a line, or similarly ones an observation and the other are rules of interactions derived from a collection of observations (though we could even draw this a little finer in that we have objects over time, collected into common features and the those recognized features can present recognized rules of interaction ... and if we go further and over how those rules of interaction might change over time, then we're "seeing" or deriving properties that describe the evolution of laws of interaction and I guess we could go beyond that, but it's a single chain of events that accumulates along an axis and then folds into a new dimension that describes how the sequences along that axis have evolved. None of these axises are infinitely wide though, they just need to be large enough to contain enough samples that someone considers the patterns to be predictable within some measure of reliability)."
To me the above are very essential considerations.
I would like to think that "Universe Exists Only Once"
Universe is an oscillating out-folding and in-folding - in the sense that information is being "Recalculated" and "Re-expressed" and further created, at each beat of universe.
To me this is the logic consequence of dynamic - it is not possible to change something without changing everything at each beat. The "trick" is that universal change is being arranged scale-wise - and we have chosen to be concerned - from a practical point of view - only by the outermost expressions - those expressions that we can sense physically - and then we are ignoring all deeper changes - and refer to them as non-physical -
And everything IS the effect of everything including all kind of mind-concepts and mind-related expressions and experiences (including the feeling that numbers are at hand), but it is close to being non-comprehendable that the information in universe can exhibit such an amount of calculus in each flash - but we ignore the fact that calculus is self-organizing - calculus takes no instruction - calculus simple happens because of the principles laid down in "Shape and Least Void. (this principle is being explained in a bit more detail in the 3D Pixel Universe)
Well - I do not think that we are in dis-agreement (apart from perhaps the more concrete ideas of the 3D pixel universe)
My sole point is that re-calculation is necessary right from the smallest of the smallest, at each and every flash expression.
When I say flash expression - at the same time I indicate that human physical world and all what relates to mind, fundamentally is being discrete events - that it is not possible to deal with a system which harbor continuity and infinity as part of the system.
The truth in the sense that one can say that "This is HOW it is" - is naturally not into existence as such - everything is being understood and described and communicated out from premises - out from axioms - and I have chosen the axiom that everything best can be understood - described and communicated out from "object of sameness" as the Tool.
AN
Just curious - but have You been considering from where You get Your numbers ?
Just curious - but have You been considering from where You get Your numbers ?
QUOTE (SteveA2+Jan 30 2009, 01:38 AM)
I agree that numbers arise from finite properties, but consider how did you recognize that a quarter was larger than a penny.
Absolutely totally irrelevent.
The quarter is larger without us recognizing it.
And all the rest of post rests on the opposite being true.
Which means all the rest of your post is bunkum.
@Bukh have you considered you havn't been getting numbers from anywhere?
And AN is not a media statisitian. Your question does make sense if you were talking to someone who wrote a report.
That 0.999... already "exists" and doen't need us?
butetrshug
"@Bukh have you considered you havn't been getting numbers from anywhere?
And AN is not a media statisitian. Your question does make sense if you were talking to someone who wrote a report."
Thanks for answering on behalf of AN -
well - you say that one cannot get numbers from anywhere ? - or do you say that one get numbers from anywhere ?. Anyhow - the question is of the same relevance - namely from where do You get Your numbers.
I have a feeling that You are not considering the deeper philosophical aspects of the question - and that is OK - except that it easily become meaningless to have this kind of discussions with You. On the contrary - I understand every single word of SteveA2 - and I feel great inspiration to have him around - so perhaps on the bottom line is it more about taste and mind - because as I trust that we can agree on - "Truth" can best be seen as a majority phenomenon.
"@Bukh have you considered you havn't been getting numbers from anywhere?
And AN is not a media statisitian. Your question does make sense if you were talking to someone who wrote a report."
Thanks for answering on behalf of AN -
well - you say that one cannot get numbers from anywhere ? - or do you say that one get numbers from anywhere ?. Anyhow - the question is of the same relevance - namely from where do You get Your numbers.
I have a feeling that You are not considering the deeper philosophical aspects of the question - and that is OK - except that it easily become meaningless to have this kind of discussions with You. On the contrary - I understand every single word of SteveA2 - and I feel great inspiration to have him around - so perhaps on the bottom line is it more about taste and mind - because as I trust that we can agree on - "Truth" can best be seen as a majority phenomenon.
QUOTE (bukh+Jan 30 2009, 01:00 PM)
butetrshug
"@Bukh have you considered you havn't been getting numbers from anywhere?
And AN is not a media statisitian. Your question does make sense if you were talking to someone who wrote a report."
Thanks for answering on behalf of AN -
well - you say that one cannot get numbers from anywhere ? - or do you say that one get numbers from anywhere ?. Anyhow - the question is of the same relevance - namely from where do You get Your numbers.
I have a feeling that You are not considering the deeper philosophical aspects of the question - and that is OK - except that it easily become meaningless to have this kind of discussions with You. On the contrary - I understand every single word of SteveA2 - and I feel great inspiration to have him around - so perhaps on the bottom line is it more about taste and mind - because as I trust that we can agree on - "Truth" can best be seen as a majority phenomenon.
I don't "get" numbers from anywhere.
Please explain that concept.
Why do you need to "get" numbers from anywhere?
How about trying to think this way;
You need to "get" an understanding of numbers.
StevenA will not consider the possibility that math is intangible.
Keep that in mind when you listen to him.
And please don't think he is the open minded one.
And he sounds like I thought before High School.
edit basically been there done that and moved on.
I would love to know how the person that won't consider the intangible to be the one with the deeper philisphical meaning?
"@Bukh have you considered you havn't been getting numbers from anywhere?
And AN is not a media statisitian. Your question does make sense if you were talking to someone who wrote a report."
Thanks for answering on behalf of AN -
well - you say that one cannot get numbers from anywhere ? - or do you say that one get numbers from anywhere ?. Anyhow - the question is of the same relevance - namely from where do You get Your numbers.
I have a feeling that You are not considering the deeper philosophical aspects of the question - and that is OK - except that it easily become meaningless to have this kind of discussions with You. On the contrary - I understand every single word of SteveA2 - and I feel great inspiration to have him around - so perhaps on the bottom line is it more about taste and mind - because as I trust that we can agree on - "Truth" can best be seen as a majority phenomenon.
I don't "get" numbers from anywhere.
Please explain that concept.
Why do you need to "get" numbers from anywhere?
How about trying to think this way;
You need to "get" an understanding of numbers.
StevenA will not consider the possibility that math is intangible.
Keep that in mind when you listen to him.
And please don't think he is the open minded one.
And he sounds like I thought before High School.
edit basically been there done that and moved on.
I would love to know how the person that won't consider the intangible to be the one with the deeper philisphical meaning?
buttershug
"You need to "get" an understanding of numbers."
OK - then we refer to an "understanding" - but the question has the same validity - from where do You get Your understanding.
You cannot escape the philosophical aspect -
If I recall rightly - we have earlier crossed this concept of intangible - and the deeper meaning of this word - well it is still quite philosophical to me - very difficult to get the deeper feeling for that concept - and very difficult to grasp. I would be grateful to hear your take on intangible - no Wiki.
"And he sounds like I thought before High School." - Oh - then I would have skipped the High School.
"You need to "get" an understanding of numbers."
OK - then we refer to an "understanding" - but the question has the same validity - from where do You get Your understanding.
You cannot escape the philosophical aspect -
If I recall rightly - we have earlier crossed this concept of intangible - and the deeper meaning of this word - well it is still quite philosophical to me - very difficult to get the deeper feeling for that concept - and very difficult to grasp. I would be grateful to hear your take on intangible - no Wiki.
"And he sounds like I thought before High School." - Oh - then I would have skipped the High School.
Laidback
"Likewise if one refers to one Particle then that's what it is - ONE PARTICLE, until someone insists it is .9~9 or 1.0~1 of a Partcile to which that's their problem.."
Yeah - a particle is a particle if it according to the set definitions of such a particle . But that is not the same as saying that a particular particle is exactly the same as another like particle - we may simply not be in a position to measure with sufficient accuracy to distinguish one particle from another.
There will always be one reality that mirrors the practical physical universe - and then we have the more subtle - the more philosophical way of seeing everything - where we can afford to be flying above ground and think airy.
"Likewise if one refers to one Particle then that's what it is - ONE PARTICLE, until someone insists it is .9~9 or 1.0~1 of a Partcile to which that's their problem.."
Yeah - a particle is a particle if it according to the set definitions of such a particle . But that is not the same as saying that a particular particle is exactly the same as another like particle - we may simply not be in a position to measure with sufficient accuracy to distinguish one particle from another.
There will always be one reality that mirrors the practical physical universe - and then we have the more subtle - the more philosophical way of seeing everything - where we can afford to be flying above ground and think airy.
QUOTE (buttershug+Jan 29 2009, 10:32 PM)
0.999r can not be anything other than 1.
There is no difference between it and 1.
If it is not 1 then what is the difference?
If you find a difference then it is NOT 0.999r.
It is, and therefore does not need to be constructed or materialized or anything else.
IT JUST BLOODY WELL IS WHAT IT IS.
complete and full and nontangible.
There are many differences between .999... and 1.
The first being that one can never equal the other because there is always a non-zero remainder.
The second is that 1 is used to derive the concept of .999... and not visa versa.
The third is that one is "constructed" (and I used that term loosely) from a non-terminating set of elements. How elements is that exactly?
The fourth is that, if some expansion of .999... could equal 1, well we'd still have to add more 9s and the first one would result in a value >1, so you could never stop and .999... could never equal 1.
The fifth through eleveth reasons arise from going back to all the attempted proofs that .999...=1 and correcting the mistakes in their logic and proving that .999...!=1 using all these techniques.
Notice that 1-1=0 and so does (1-1)*10=0*10 and we could also go on like this "forever" in the same sense that .999... is suppose to have an infinite number of digits, but for (1-.999...)*10*10*10*... to be equal to 0, we have to multiply yb 10 an "infinitely" fewer times than there are digits of .999... because every multiplication by 10 effectively removes a digit of .999..., and if .999... ever began at .9 then at some point this multiplication by 10 needs to return the value to equally .9, otherwise it was never .999...
Here's another interesting example:
If .999... going on for an infinite number of digits actually equalled 1, then we should compute:
1=lim((1-.1^n)^(10^n)) as n->infinity
But what do we actually get?
(1-.1)^10=.9^10~=.3487
(1-.01)^100=.99^100~=.3660
(1-.001)^1000=.999^1000~=.3677
...
.999...^1000...~=1/e~=.36788<1
This precise value is only true of there are an equal number of 0s in 1000... as there are 9s in .999... but the result is always <1 even when these differ. Notice also that if we had instead used the integer 1, then no amount of exponentiation alters the value and it would remain at 1:
1^1000....=1
So where did mainstream mathematics go wrong? Well it almost certainly occured when someone decided that when they tried to divide 1 by 3 and saw the repeating .333... that this meant they were equal, but notice that the remainder at each stage of this division is a constant value of 1 and not 0, hence .333... is always less than 1/3 and the limit of 1/3 in this case is a value .333... cannot reach.
Of course if we're talking about rough physical approximations then they can appear indistinguishable, but logically and mathematically they're not the same.
There is no difference between it and 1.
If it is not 1 then what is the difference?
If you find a difference then it is NOT 0.999r.
It is, and therefore does not need to be constructed or materialized or anything else.
IT JUST BLOODY WELL IS WHAT IT IS.
complete and full and nontangible.
There are many differences between .999... and 1.
The first being that one can never equal the other because there is always a non-zero remainder.
The second is that 1 is used to derive the concept of .999... and not visa versa.
The third is that one is "constructed" (and I used that term loosely) from a non-terminating set of elements. How elements is that exactly?
The fourth is that, if some expansion of .999... could equal 1, well we'd still have to add more 9s and the first one would result in a value >1, so you could never stop and .999... could never equal 1.
The fifth through eleveth reasons arise from going back to all the attempted proofs that .999...=1 and correcting the mistakes in their logic and proving that .999...!=1 using all these techniques.
Notice that 1-1=0 and so does (1-1)*10=0*10 and we could also go on like this "forever" in the same sense that .999... is suppose to have an infinite number of digits, but for (1-.999...)*10*10*10*... to be equal to 0, we have to multiply yb 10 an "infinitely" fewer times than there are digits of .999... because every multiplication by 10 effectively removes a digit of .999..., and if .999... ever began at .9 then at some point this multiplication by 10 needs to return the value to equally .9, otherwise it was never .999...
Here's another interesting example:
If .999... going on for an infinite number of digits actually equalled 1, then we should compute:
1=lim((1-.1^n)^(10^n)) as n->infinity
But what do we actually get?
(1-.1)^10=.9^10~=.3487
(1-.01)^100=.99^100~=.3660
(1-.001)^1000=.999^1000~=.3677
...
.999...^1000...~=1/e~=.36788<1
This precise value is only true of there are an equal number of 0s in 1000... as there are 9s in .999... but the result is always <1 even when these differ. Notice also that if we had instead used the integer 1, then no amount of exponentiation alters the value and it would remain at 1:
1^1000....=1
So where did mainstream mathematics go wrong? Well it almost certainly occured when someone decided that when they tried to divide 1 by 3 and saw the repeating .333... that this meant they were equal, but notice that the remainder at each stage of this division is a constant value of 1 and not 0, hence .333... is always less than 1/3 and the limit of 1/3 in this case is a value .333... cannot reach.
Of course if we're talking about rough physical approximations then they can appear indistinguishable, but logically and mathematically they're not the same.
QUOTE (buttershug+)
There is no intervening value.
It is not growing.
It is defined complete.
It is not borrowing.
It is not doing anything other than existing in a nonphysical nontangible way.
It is not a process.
It is not a method.
Thank you for pointing out the difference here also. This rules out the construction of .999... as an infinite process but it still allows us to use the integer 1.
If .999... and 1 were identical, you could not specify a manner to exclude .999... and keep 1, so you've also shown that there is a difference between an infinite process and a number.
It is not growing.
It is defined complete.
It is not borrowing.
It is not doing anything other than existing in a nonphysical nontangible way.
It is not a process.
It is not a method.
Thank you for pointing out the difference here also. This rules out the construction of .999... as an infinite process but it still allows us to use the integer 1.
If .999... and 1 were identical, you could not specify a manner to exclude .999... and keep 1, so you've also shown that there is a difference between an infinite process and a number.
QUOTE (buttershug+)
"And he sounds like I thought before High School."
Yes, there's the High School version of mathematics and then things get a bit more complex later. For example, in Middle School pi is often 22/7 or maybe 3.14 and then later this is refined some and learning progresses (hopefully) into a ability to deal with a wider variety of more complex structures.
Ironically though, most people who've not yet been overly educated can still easily see the difference between an exponential process and constant values and I personally think that's great.
You may not have much familiarity with ideas in calculus, but if so, then consider that a function is not required to, and in some cases it can be specifically defined from reach a value equal to its limit.
For example if we have:
f(x)={x : x<0 ; -1 : x>=0}
and we compute the limit of this function as x approaches 0, then the limit is 0 but the function is explicitly denied from being equal to 0 and this is similar to saying that if x<1, then the upper limit of x is 1, but x can only equal value less than 1 and that's true for .999...
Yes, there's the High School version of mathematics and then things get a bit more complex later. For example, in Middle School pi is often 22/7 or maybe 3.14 and then later this is refined some and learning progresses (hopefully) into a ability to deal with a wider variety of more complex structures.
Ironically though, most people who've not yet been overly educated can still easily see the difference between an exponential process and constant values and I personally think that's great.
You may not have much familiarity with ideas in calculus, but if so, then consider that a function is not required to, and in some cases it can be specifically defined from reach a value equal to its limit.
For example if we have:
f(x)={x : x<0 ; -1 : x>=0}
and we compute the limit of this function as x approaches 0, then the limit is 0 but the function is explicitly denied from being equal to 0 and this is similar to saying that if x<1, then the upper limit of x is 1, but x can only equal value less than 1 and that's true for .999...
QUOTE (SteveA2+Jan 30 2009, 04:21 PM)
There are many differences between .999... and 1.
The first being that one can never equal the other because there is always a non-zero remainder.
I meant the mathematical term "difference"
ex. the difference between 5 and 3 is 2.
And if there is a non-zero remainder then it is NOT 0.999...
what is 1-0.999...?
And I mean the complete 0.999...
not some partial construction or other.
Edit
If .999... and 1 were identical, you could not specify a manner to exclude .999... and keep 1, so you've also shown that there is a difference between an infinite process and a number.
What process?
There is no process in 0.999...
Yes, there's the High School version of mathematics and then things get a bit more complex later. For example, in Middle School pi is often 22/7 or maybe 3.14 and then later this is refined some and learning progresses (hopefully) into a ability to deal with a wider variety of more complex structures.
pi is never 22/7 that is just an approximation we use.
We can't write pi down as numbers.
But for those of us who learn past your understanding we can still use pi.
The first being that one can never equal the other because there is always a non-zero remainder.
I meant the mathematical term "difference"
ex. the difference between 5 and 3 is 2.
And if there is a non-zero remainder then it is NOT 0.999...
what is 1-0.999...?
And I mean the complete 0.999...
not some partial construction or other.
Edit
QUOTE (SteveA2+Jan 30 2009, 04:21 PM)
If .999... and 1 were identical, you could not specify a manner to exclude .999... and keep 1, so you've also shown that there is a difference between an infinite process and a number.
What process?
There is no process in 0.999...
QUOTE (SteveA2+Jan 30 2009, 04:21 PM)
Yes, there's the High School version of mathematics and then things get a bit more complex later. For example, in Middle School pi is often 22/7 or maybe 3.14 and then later this is refined some and learning progresses (hopefully) into a ability to deal with a wider variety of more complex structures.
pi is never 22/7 that is just an approximation we use.
We can't write pi down as numbers.
But for those of us who learn past your understanding we can still use pi.
QUOTE (bukh+Jan 31 2009, 02:07 AM)
Laidback
QUOTE (Laidback+)
Likewise if one refers to one Particle then that's what it is - ONE PARTICLE, until someone insists it is .9~9 or 1.0~1 of a Particle to which that's their problem.."
Yeah - a particle is a particle if it according to the set definitions of such a particle . But that is not the same as saying that a particular particle is exactly the same as another like particle - we may simply not be in a position to measure with sufficient accuracy to distinguish one particle from another.
There will always be one reality that mirrors the practical physical universe - and then we have the more subtle - the more philosophical way of seeing everything - where we can afford to be flying above ground and think airy.
Agreed, and whats more if a particle were measured or compared at a given point in time, it may never EVER measure and or compare as it once did, simply because both the implied particle and our comparison are with constant change, via mass is never at rest.
Cheers,
Peter J Schoen..
Well then you're stuck, because pi is always used as an approximation, so either noone has ever computed with pi or pi is a set of finite approximations (yes, and this is even true for a definition using a limit of a convergence unless you can show that all convergences are equal to each other and you should recognize this is impossible from the .9r != 1 discussions. Notice that in the case of alternate descriptions for pi this can be impossible if the terms give relatively prime denominators)
So anyway, which is it?
Either
1) Noone has computed using pi
or
2) Pi is a (a potentially unlimited) set of accepted (finite) approximations
Not true there are equations where is it used.
And neither.
You are operating under a false dichotomy.
Pi is infinite. We will never know all the digits but we don't have to.
It simply is and does not need to be made.
BTW Bukh that the sun the moon and earth were not 3 objects before man?
StevenA doesn't think they were three objects before someone counted them.
Yeah - a particle is a particle if it according to the set definitions of such a particle . But that is not the same as saying that a particular particle is exactly the same as another like particle - we may simply not be in a position to measure with sufficient accuracy to distinguish one particle from another.
There will always be one reality that mirrors the practical physical universe - and then we have the more subtle - the more philosophical way of seeing everything - where we can afford to be flying above ground and think airy.[/QUOTE]
Agreed, and whats more if a particle were measured or compared at a given point in time, it may never EVER measure and or compare as it once did, simply because both the implied particle and our comparison are with constant change, via mass is never at rest.
Cheers,
Peter J Schoen..
There is an ancient Chinese question;
Can a man step in the same stream twice?
The answer of course is no.
Oh and I saw a Phillip K. *** quote.
Reality is what remains when you don't.
Yeah - a particle is a particle if it according to the set definitions of such a particle . But that is not the same as saying that a particular particle is exactly the same as another like particle - we may simply not be in a position to measure with sufficient accuracy to distinguish one particle from another.
There will always be one reality that mirrors the practical physical universe - and then we have the more subtle - the more philosophical way of seeing everything - where we can afford to be flying above ground and think airy.
Agreed, and whats more if a particle were measured or compared at a given point in time, it may never EVER measure and or compare as it once did, simply because both the implied particle and our comparison are with constant change, via mass is never at rest.
Cheers,
Peter J Schoen..
QUOTE (buttershug+Jan 30 2009, 05:55 PM)
pi is never 22/7 that is just an approximation we use.
Well then you're stuck, because pi is always used as an approximation, so either noone has ever computed with pi or pi is a set of finite approximations (yes, and this is even true for a definition using a limit of a convergence unless you can show that all convergences are equal to each other and you should recognize this is impossible from the .9r != 1 discussions. Notice that in the case of alternate descriptions for pi this can be impossible if the terms give relatively prime denominators)
So anyway, which is it?
Either
1) Noone has computed using pi
or
2) Pi is a (a potentially unlimited) set of accepted (finite) approximations
Well then you're stuck, because pi is always used as an approximation, so either noone has ever computed with pi or pi is a set of finite approximations (yes, and this is even true for a definition using a limit of a convergence unless you can show that all convergences are equal to each other and you should recognize this is impossible from the .9r != 1 discussions. Notice that in the case of alternate descriptions for pi this can be impossible if the terms give relatively prime denominators)
So anyway, which is it?
Either
1) Noone has computed using pi
or
2) Pi is a (a potentially unlimited) set of accepted (finite) approximations
QUOTE (SteveA2+Jan 31 2009, 01:02 AM)
Well then you're stuck, because pi is always used as an approximation, so either noone has ever computed with pi or pi is a set of finite approximations (yes, and this is even true for a definition using a limit of a convergence unless you can show that all convergences are equal to each other and you should recognize this is impossible from the .9r != 1 discussions. Notice that in the case of alternate descriptions for pi this can be impossible if the terms give relatively prime denominators)
So anyway, which is it?
Either
1) Noone has computed using pi
or
2) Pi is a (a potentially unlimited) set of accepted (finite) approximations
Not true there are equations where is it used.
And neither.
You are operating under a false dichotomy.
Pi is infinite. We will never know all the digits but we don't have to.
It simply is and does not need to be made.
BTW Bukh that the sun the moon and earth were not 3 objects before man?
StevenA doesn't think they were three objects before someone counted them.
QUOTE (Laidback+Jan 31 2009, 12:52 AM)
Yeah - a particle is a particle if it according to the set definitions of such a particle . But that is not the same as saying that a particular particle is exactly the same as another like particle - we may simply not be in a position to measure with sufficient accuracy to distinguish one particle from another.
There will always be one reality that mirrors the practical physical universe - and then we have the more subtle - the more philosophical way of seeing everything - where we can afford to be flying above ground and think airy.[/QUOTE]
Agreed, and whats more if a particle were measured or compared at a given point in time, it may never EVER measure and or compare as it once did, simply because both the implied particle and our comparison are with constant change, via mass is never at rest.
Cheers,
Peter J Schoen..
There is an ancient Chinese question;
Can a man step in the same stream twice?
The answer of course is no.
Oh and I saw a Phillip K. *** quote.
Reality is what remains when you don't.
QUOTE (buttershug+Jan 31 2009, 01:43 AM)
And neither.
You are operating under a false dichotomy.
Pi is infinite. We will never know all the digits but we don't have to.
It simply is and does not need to be made.
Well then it apparently wasn't a dichotomy as you selected the first option:
1) Noone has computed using pi
You are operating under a false dichotomy.
Pi is infinite. We will never know all the digits but we don't have to.
It simply is and does not need to be made.
Well then it apparently wasn't a dichotomy as you selected the first option:
1) Noone has computed using pi
QUOTE (SteveA2+Jan 31 2009, 02:35 AM)
Well then it apparently wasn't a dichotomy as you selected the first option:
1) Noone has computed using pi
But that makes no difference to it's usefullness.
It also makes no difference to it's existense.
It makes no difference to it's completeness.
So what if no one has computed it fully?
There is no consequense to that.
And I'm not stuck.
Just as you don't need to compute 0.99...
1) Noone has computed using pi
But that makes no difference to it's usefullness.
It also makes no difference to it's existense.
It makes no difference to it's completeness.
So what if no one has computed it fully?
There is no consequense to that.
And I'm not stuck.
Just as you don't need to compute 0.99...
QUOTE (buttershug+)
But that makes no difference to it's usefullness.
No fair changing your mind now, you already selected:
1) Noone has computed using pi
and not
2) Pi is a (a potentially unlimited) set of accepted (finite) approximations
It's only useful when it's used in an approximate form, and you've been sticking to the uncomputable infinite definition.
No fair changing your mind now, you already selected:
1) Noone has computed using pi
and not
2) Pi is a (a potentially unlimited) set of accepted (finite) approximations
It's only useful when it's used in an approximate form, and you've been sticking to the uncomputable infinite definition.
QUOTE (buttershug+)
It also makes no difference to it's existense.
It makes no difference to it's completeness.
See what I mean. You want to claim it's infinite and intangible on one hand, yet "complete" on the other.
It makes no difference to it's completeness.
See what I mean. You want to claim it's infinite and intangible on one hand, yet "complete" on the other.
QUOTE (buttershug+)
So what if no one has computed it fully?
There is no consequense to that.
And now you're claiming the (potentially unlimited) set of rational approximations people use are just fine.
...
Ok, if you really want to change your view, fine. We can go with pi as a set of approximations instead.
There is no consequense to that.
And now you're claiming the (potentially unlimited) set of rational approximations people use are just fine.
...
Ok, if you really want to change your view, fine. We can go with pi as a set of approximations instead.
QUOTE (buttershug+)
And I'm not stuck.
Great, then we're in agreement that pi is actually a set of acceptable approximations and not a number (in fact we can call it a variable as variables can define a set of possible solutions).
Great, then we're in agreement that pi is actually a set of acceptable approximations and not a number (in fact we can call it a variable as variables can define a set of possible solutions).
QUOTE (buttershug+)
Just as you don't need to compute 0.99...
Right, because it's not a number.
Now, after all that, I'll have to state that truly there is a use for irrational "numbers", but they aren't accurately described as single values but as sets (at a minimum you need to know a tolerance in order that you can refine an approximation when necessary), but it's much more fun to argue with people who want to be stubborn
Right, because it's not a number.
Now, after all that, I'll have to state that truly there is a use for irrational "numbers", but they aren't accurately described as single values but as sets (at a minimum you need to know a tolerance in order that you can refine an approximation when necessary), but it's much more fun to argue with people who want to be stubborn
buttershug
"BTW Bukh that the sun the moon and earth were not 3 objects before man?"
Yes and No
One could also ask the question: How best to describe and define what is in the "internet" before it is been de-coded in your computer. Likewise with Universe - it is not necessarily looking like You imagine - and like You are used to think it "objectively" shall look. Your idea about the physical world is a result of Your decoding of the Universe. And then You say that all other people have more or less exactly the same imagination and definition - so it must be true - but try to ask a "stone" how it looks - and you will probably get quite another picture.
Essentially physical universe perhaps best can be seen as a flux of "changes" - (and do not ask how changes comes up - or what energies are or anything like that arise from - because this will be the origin of the origin.) - and such changes can arrange themselves i patterns and such patterns become self-sensing - self-observing - self-decoding. Everything is about how information observe information.
Human is such a self-sensing pattern - and our "reality" is based upon our very specific skills in the de-coding process - is being based upon our configuration. How are we being configures so as to de-code Universe, because each configuration makes its own "reality".
So it is a good question whether earth sun and moon "existed" as "three" before man.
And You are very welcome to reconsider from where you get Your understanding and Your numbers.
"BTW Bukh that the sun the moon and earth were not 3 objects before man?"
Yes and No
One could also ask the question: How best to describe and define what is in the "internet" before it is been de-coded in your computer. Likewise with Universe - it is not necessarily looking like You imagine - and like You are used to think it "objectively" shall look. Your idea about the physical world is a result of Your decoding of the Universe. And then You say that all other people have more or less exactly the same imagination and definition - so it must be true - but try to ask a "stone" how it looks - and you will probably get quite another picture.
Essentially physical universe perhaps best can be seen as a flux of "changes" - (and do not ask how changes comes up - or what energies are or anything like that arise from - because this will be the origin of the origin.) - and such changes can arrange themselves i patterns and such patterns become self-sensing - self-observing - self-decoding. Everything is about how information observe information.
Human is such a self-sensing pattern - and our "reality" is based upon our very specific skills in the de-coding process - is being based upon our configuration. How are we being configures so as to de-code Universe, because each configuration makes its own "reality".
So it is a good question whether earth sun and moon "existed" as "three" before man.
And You are very welcome to reconsider from where you get Your understanding and Your numbers.
Laidback
"Agreed, and whats more if a particle were measured or compared at a given point in time, it may never EVER measure and or compare as it once did, simply because both the implied particle and our comparison are with constant change, via mass is never at rest."
Universe exist only once - it is an oscillating expression of ever changing configurations (information) - and change is down to smallest at each flash - Universe is being recalculated from the deepest in each flash - so YES - I totally agree. It is thanks to scale wise arrangements that we can operate with concepts like particle and mass and physical energy.
"Agreed, and whats more if a particle were measured or compared at a given point in time, it may never EVER measure and or compare as it once did, simply because both the implied particle and our comparison are with constant change, via mass is never at rest."
Universe exist only once - it is an oscillating expression of ever changing configurations (information) - and change is down to smallest at each flash - Universe is being recalculated from the deepest in each flash - so YES - I totally agree. It is thanks to scale wise arrangements that we can operate with concepts like particle and mass and physical energy.
QUOTE (bukh+Jan 31 2009, 09:35 AM)
buttershug
"BTW Bukh that the sun the moon and earth were not 3 objects before man?"
Yes and No
One could also ask the question: How best to describe and define what is in the "internet" before it is been de-coded in your computer.
Finally we are making progress.
So there must be "something" about the Sun the Moon and the Earth being 3 without humans to say so?
That "something" is what I"m talking about.
If you wanted to take up horseback riding, would you ask about riding chickens?
Why do you go onto other subjects?
I am only talking about that aspect of "threeness" that the aforementioned bodies have. All the other stuff does not take away from that.
edit I just clued into your and my problem communicating.
You think I am denying what you are saying. That is not the case.
I accept your "yes and no" answer.
StevenA does not. He claims that there was no "threeness" to the Sun, The Moon and the Earth.
I recognize that without humans those three objects can't be associated with the Trinity (no not the chick from the Matrix). But that does not take away from their being "three".
And you can apply that to the circumferance of a circle divided by it's diameter. There is a property that is not dependant on humans. There being other properties dependant on humans does not remove that property. StevenA does not believe in the human independant property, only the human dependant ones.
"BTW Bukh that the sun the moon and earth were not 3 objects before man?"
Yes and No
One could also ask the question: How best to describe and define what is in the "internet" before it is been de-coded in your computer.
Finally we are making progress.
So there must be "something" about the Sun the Moon and the Earth being 3 without humans to say so?
That "something" is what I"m talking about.
If you wanted to take up horseback riding, would you ask about riding chickens?
Why do you go onto other subjects?
I am only talking about that aspect of "threeness" that the aforementioned bodies have. All the other stuff does not take away from that.
edit I just clued into your and my problem communicating.
You think I am denying what you are saying. That is not the case.
I accept your "yes and no" answer.
StevenA does not. He claims that there was no "threeness" to the Sun, The Moon and the Earth.
I recognize that without humans those three objects can't be associated with the Trinity (no not the chick from the Matrix). But that does not take away from their being "three".
And you can apply that to the circumferance of a circle divided by it's diameter. There is a property that is not dependant on humans. There being other properties dependant on humans does not remove that property. StevenA does not believe in the human independant property, only the human dependant ones.
QUOTE (SteveA2+Jan 31 2009, 02:58 AM)
No fair changing your mind now, you already selected:
1) Noone has computed using pi
and not
2) Pi is a (a potentially unlimited) set of accepted (finite) approximations
It's only useful when it's used in an approximate form, and you've been sticking to the uncomputable infinite definition.
See what I mean. You want to claim it's infinite and intangible on one hand, yet "complete" on the other.
Great, then we're in agreement that pi is actually a set of acceptable approximations and not a number (in fact we can call it a variable as variables can define a set of possible solutions).
1) Noone has computed using pi
and not
2) Pi is a (a potentially unlimited) set of accepted (finite) approximations
It's only useful when it's used in an approximate form, and you've been sticking to the uncomputable infinite definition.
See what I mean. You want to claim it's infinite and intangible on one hand, yet "complete" on the other.
Great, then we're in agreement that pi is actually a set of acceptable approximations and not a number (in fact we can call it a variable as variables can define a set of possible solutions).
QUOTE (buttershug+)
Just as you don't need to compute 0.99...
Right, because it's not a number.
Now, after all that, I'll have to state that truly there is a use for irrational "numbers", but they aren't accurately described as single values but as sets (at a minimum you need to know a tolerance in order that you can refine an approximation when necessary), but it's much more fun to argue with people who want to be stubborn
It is only usefull in an approximate form for people doing physical things.
Mathematicians use it as a number.
I"m too lazy at the moment to look up some example(I have to go have a blood test taken)
Maybe AN can give an example.
No it is not "on the other hand"
It's completeness is what makes it infinite and intangible.
It is all "on the same hand".
What we(you and I but not including mathematicians) use for pi is an acceptable approximation.
It is not a variable. It is a number.
0.999.. is not an irrational number, it is a rational number.
Add new position in dimensions (so we're really doing 2*infinity)
And place apples until full (1^2=1 step in this case):
Now we go back and do 2 units of extending dimensions:
And we're finished multiplexing our linear process so we continue with the parabolic m=n^2 one:
etc.
That's infinity. The difficult part is in breaking things into the smallest units to construct the various smaller infinities within it and of course doing that also requires some of those infinite units (of time, computation or action).
Notice also "infinitesimal" things are still discrete things and they never change size and there remains at least one of them but that from a growing perspective they can appear insignificant (but you still need a memory or space to integrate and retain records of all these infinitesimals otherwise the infinity wouldn't exist)
Right, because it's not a number.
Now, after all that, I'll have to state that truly there is a use for irrational "numbers", but they aren't accurately described as single values but as sets (at a minimum you need to know a tolerance in order that you can refine an approximation when necessary), but it's much more fun to argue with people who want to be stubborn
It is only usefull in an approximate form for people doing physical things.
Mathematicians use it as a number.
I"m too lazy at the moment to look up some example(I have to go have a blood test taken)
Maybe AN can give an example.
No it is not "on the other hand"
It's completeness is what makes it infinite and intangible.
It is all "on the same hand".
What we(you and I but not including mathematicians) use for pi is an acceptable approximation.
It is not a variable. It is a number.
0.999.. is not an irrational number, it is a rational number.
buttershug
"Finally we are making progress.
So there must be "something" about the Sun the Moon and the Earth being 3 without humans to say so?"
Ah - not exactly - what I tried to say is that physical Universe - or Our Physical Universe is a mind concept - in the sense that it is a result of how our brain de-code the surroundings - so the form that the surroundings take is solely up to how we interpret - how we translate this flux into a picture. So moon earth and sun is not into existence as 3 objects - not as such - but to us humans they translate into 3 such objects. Likewise a picture on your computer is not into existence as such - it is into existence as a flux of signals that is being translated into a pixel pattern that you as a human see on your screen. The computer and its screen is your interface between the signals and what you see.
"Finally we are making progress.
So there must be "something" about the Sun the Moon and the Earth being 3 without humans to say so?"
Ah - not exactly - what I tried to say is that physical Universe - or Our Physical Universe is a mind concept - in the sense that it is a result of how our brain de-code the surroundings - so the form that the surroundings take is solely up to how we interpret - how we translate this flux into a picture. So moon earth and sun is not into existence as 3 objects - not as such - but to us humans they translate into 3 such objects. Likewise a picture on your computer is not into existence as such - it is into existence as a flux of signals that is being translated into a pixel pattern that you as a human see on your screen. The computer and its screen is your interface between the signals and what you see.
QUOTE (bukh+Feb 1 2009, 04:17 PM)
buttershug
"Finally we are making progress.
So there must be "something" about the Sun the Moon and the Earth being 3 without humans to say so?"
Ah - not exactly - what I tried to say is that physical Universe - or Our Physical Universe is a mind concept - in the sense that it is a result of how our brain de-code the surroundings - so the form that the surroundings take is solely up to how we interpret - how we translate this flux into a picture. So moon earth and sun is not into existence as 3 objects - not as such - but to us humans they translate into 3 such objects. Likewise a picture on your computer is not into existence as such - it is into existence as a flux of signals that is being translated into a pixel pattern that you as a human see on your screen. The computer and its screen is your interface between the signals and what you see.
So you are limiting yourself to that?
Why take the limits of something and apply them to other things.
You take the threeness of the Sun the Earth and the Moon and then move onto other things then backtrack and put the restrictions on the other things upon the threeness of the Sun the Earth and the Moon.
why go backwards why not go forwards?
then what did you mean when you said "yes and no"?
"Finally we are making progress.
So there must be "something" about the Sun the Moon and the Earth being 3 without humans to say so?"
Ah - not exactly - what I tried to say is that physical Universe - or Our Physical Universe is a mind concept - in the sense that it is a result of how our brain de-code the surroundings - so the form that the surroundings take is solely up to how we interpret - how we translate this flux into a picture. So moon earth and sun is not into existence as 3 objects - not as such - but to us humans they translate into 3 such objects. Likewise a picture on your computer is not into existence as such - it is into existence as a flux of signals that is being translated into a pixel pattern that you as a human see on your screen. The computer and its screen is your interface between the signals and what you see.
So you are limiting yourself to that?
Why take the limits of something and apply them to other things.
You take the threeness of the Sun the Earth and the Moon and then move onto other things then backtrack and put the restrictions on the other things upon the threeness of the Sun the Earth and the Moon.
why go backwards why not go forwards?
then what did you mean when you said "yes and no"?
QUOTE (bukh+Feb 1 2009, 04:17 PM)
buttershug
"Finally we are making progress.
So there must be "something" about the Sun the Moon and the Earth being 3 without humans to say so?"
Ah - not exactly - what I tried to say is that physical Universe - or Our Physical Universe is a mind concept - in the sense that it is a result of how our brain de-code the surroundings - so the form that the surroundings take is solely up to how we interpret - how we translate this flux into a picture. So moon earth and sun is not into existence as 3 objects - not as such - but to us humans they translate into 3 such objects. Likewise a picture on your computer is not into existence as such - it is into existence as a flux of signals that is being translated into a pixel pattern that you as a human see on your screen. The computer and its screen is your interface between the signals and what you see.
Yes, atoms don't have labels saying they are Moon atoms or Sun atoms or Earth atoms, those are labels we place upon them from how we measure statistical properties of matter.
"Finally we are making progress.
So there must be "something" about the Sun the Moon and the Earth being 3 without humans to say so?"
Ah - not exactly - what I tried to say is that physical Universe - or Our Physical Universe is a mind concept - in the sense that it is a result of how our brain de-code the surroundings - so the form that the surroundings take is solely up to how we interpret - how we translate this flux into a picture. So moon earth and sun is not into existence as 3 objects - not as such - but to us humans they translate into 3 such objects. Likewise a picture on your computer is not into existence as such - it is into existence as a flux of signals that is being translated into a pixel pattern that you as a human see on your screen. The computer and its screen is your interface between the signals and what you see.
Yes, atoms don't have labels saying they are Moon atoms or Sun atoms or Earth atoms, those are labels we place upon them from how we measure statistical properties of matter.
QUOTE (SteveA2+Feb 2 2009, 01:58 AM)
Yes, atoms don't have labels saying they are Moon atoms or Sun atoms or Earth atoms, those are labels we place upon them from how we measure statistical properties of matter.
So it's a good thing for them that they don't need them.
Or us.
OR need to be labeled as Sun Earth and Moon to be three bodies in the solar system.
Yes there is more to it than that but the extra does not take away, it adds.
So it's a good thing for them that they don't need them.
Or us.
OR need to be labeled as Sun Earth and Moon to be three bodies in the solar system.
Yes there is more to it than that but the extra does not take away, it adds.
buttershug
Yes of course we need to limit ourselves to the reality that belongs to us - as humans. We do not have access to all other kinds of observations of the Universe - it should be quite obvious that we cannot get it all. We can only get what we "work" for.
When I said yes and no, it was a bit of a philosophical founded answer - because on one hand numbers - like everything else - are not defined without the intervention by the human mind - and then it is a kind of philosophical question - whether the "potential" to be there counts as "being" there - if you can follow me.
Yes of course we need to limit ourselves to the reality that belongs to us - as humans. We do not have access to all other kinds of observations of the Universe - it should be quite obvious that we cannot get it all. We can only get what we "work" for.
When I said yes and no, it was a bit of a philosophical founded answer - because on one hand numbers - like everything else - are not defined without the intervention by the human mind - and then it is a kind of philosophical question - whether the "potential" to be there counts as "being" there - if you can follow me.
QUOTE (bukh+Feb 2 2009, 08:54 AM)
buttershug
Yes of course we need to limit ourselves to the reality that belongs to us - as humans. We do not have access to all other kinds of observations of the Universe - it should be quite obvious that we cannot get it all. We can only get what we "work" for.
When I said yes and no, it was a bit of a philosophical founded answer - because on one hand numbers - like everything else - are not defined without the intervention by the human mind - and then it is a kind of philosophical question - whether the "potential" to be there counts as "being" there - if you can follow me.
We have some access but because we don't have it all you deny a lot of what we do have access to.
Numbers don't need to be defined by the human mind, it's the human mind that needs them defined.
And I hope some day you won't be so limited (close minded).
If you really work at it I"m sure you will see that dividing a mathematical circle by it's circumferance gives a number. I don't think StevenA will ever progress to that point though.
For pi only the potential needs to be there unless you are not a mathematician.
Carpenters and engineers can only use an approximation but that works for them.
0.99... is useless for carpentery or engineering so the limits of those areas are not relevent to 0.99... .
But if you only need the potential then you can work with it. And if it doesn't equal 1 then it is not 0.99... .
Can we make 0.99...? No
Do we need to? No
Yes of course we need to limit ourselves to the reality that belongs to us - as humans. We do not have access to all other kinds of observations of the Universe - it should be quite obvious that we cannot get it all. We can only get what we "work" for.
When I said yes and no, it was a bit of a philosophical founded answer - because on one hand numbers - like everything else - are not defined without the intervention by the human mind - and then it is a kind of philosophical question - whether the "potential" to be there counts as "being" there - if you can follow me.
We have some access but because we don't have it all you deny a lot of what we do have access to.
Numbers don't need to be defined by the human mind, it's the human mind that needs them defined.
And I hope some day you won't be so limited (close minded).
If you really work at it I"m sure you will see that dividing a mathematical circle by it's circumferance gives a number. I don't think StevenA will ever progress to that point though.
For pi only the potential needs to be there unless you are not a mathematician.
Carpenters and engineers can only use an approximation but that works for them.
0.99... is useless for carpentery or engineering so the limits of those areas are not relevent to 0.99... .
But if you only need the potential then you can work with it. And if it doesn't equal 1 then it is not 0.99... .
Can we make 0.99...? No
Do we need to? No
buttershug
"Numbers don't need to be defined by the human mind, it's the human mind that needs them defined.
And I hope some day you won't be so limited (close minded)."
I think I understand your take - and I think that we are discussing somewhat in parallel -
When I answered yes and no, my intention was to indicate that I made a distinction between "the potential" and the "physical being" a number.
I do not think that I am narrow minded - but more a question that we define slightly differently.
"Numbers don't need to be defined by the human mind, it's the human mind that needs them defined.
And I hope some day you won't be so limited (close minded)."
I think I understand your take - and I think that we are discussing somewhat in parallel -
When I answered yes and no, my intention was to indicate that I made a distinction between "the potential" and the "physical being" a number.
I do not think that I am narrow minded - but more a question that we define slightly differently.
QUOTE (bukh+Feb 2 2009, 05:53 PM)
"Numbers don't need to be defined by the human mind, it's the human mind that needs them defined."
There we go. That'll have to go in my famous quotes file. Thanks
There we go. That'll have to go in my famous quotes file. Thanks
INFINITY
Just because you cannot measure or see it doesn't mean it does not exist.
For some reason you can imagine it yet still cannot fathom it.
Infinity exists as a concept.
In reality if you could measure it it would not be infinite just really big or small.
1 billion computers counting at 100 Thz would not be able to count to infinity even if they were able to keep counting infinitely.
So infinity is both a concept and a reality that you will never be truly able to perceive even though you may have a complete understanding of the concept.
Infinity^2= Infinity
Infinity^infinity = infinity
infinity*anything except 0 =infinity
Infinity*0 =0
One question I would ask is is infinitely small actually zero or just infinitely close?
Infinity is the point at which one says screw it gives up on the measurement and decides call it infinite.
Infinity is the distance between you and the goal you will not reach before you die.
Infinity is both irrational and true.
I could go on for an infinite amount of time but I have decided to say screw it.
Have a nice day.
Ed Wood
Just because you cannot measure or see it doesn't mean it does not exist.
For some reason you can imagine it yet still cannot fathom it.
Infinity exists as a concept.
In reality if you could measure it it would not be infinite just really big or small.
1 billion computers counting at 100 Thz would not be able to count to infinity even if they were able to keep counting infinitely.
So infinity is both a concept and a reality that you will never be truly able to perceive even though you may have a complete understanding of the concept.
Infinity^2= Infinity
Infinity^infinity = infinity
infinity*anything except 0 =infinity
Infinity*0 =0
One question I would ask is is infinitely small actually zero or just infinitely close?
Infinity is the point at which one says screw it gives up on the measurement and decides call it infinite.
Infinity is the distance between you and the goal you will not reach before you die.
Infinity is both irrational and true.
I could go on for an infinite amount of time but I have decided to say screw it.
Have a nice day.
Ed Wood
Infinity need not be a vague concept. There is only one infinity and it arises from an ongoing process - time. There are only so many hours in a day and you won't get more (it's already plenty).
Infinitely small arises from the reciprocal view (1/infinity) and refers to the vanishing "smallness" of a fixed quantity of time relative to a growing memory over time.
Instead of computing infinity^2, which would be something larger than infinite and we can't finish the first one to even begin to get to an infinite number of other ones, you can instead determine how much time or fundamental units of computation or whatever are available to construct this idealized infinity^2, then recognize that infinity^2 is already that infinite quantity and construct or multiplex and interleave an array of square root of infinity "threads" running in parallel.
For example if we have some value n, that is suppose to go to infinity, then if we define m as n^2, m will become larger than n, which is already infinite and un"doable".
So if you need these:
n=infinity
m=infinity^2
Then you construct the total sum of these:
infinity=n+m=n+n^2
And then divide time as it occurs into units of these, which we can do, for example, in this manner.
For each unit of time:
if m<n^2 do another m "thing" otherwise do another n "thing".
So if m is, for example, laying out a row of apples in an array that's n by n and n is the length of the array, then these two infinite processes represent:
1) Begin by adding a unit dimension on each axis
2) Fill the new space with apples and repeat #1
So it grows like this over time:
Infinitely small arises from the reciprocal view (1/infinity) and refers to the vanishing "smallness" of a fixed quantity of time relative to a growing memory over time.
Instead of computing infinity^2, which would be something larger than infinite and we can't finish the first one to even begin to get to an infinite number of other ones, you can instead determine how much time or fundamental units of computation or whatever are available to construct this idealized infinity^2, then recognize that infinity^2 is already that infinite quantity and construct or multiplex and interleave an array of square root of infinity "threads" running in parallel.
For example if we have some value n, that is suppose to go to infinity, then if we define m as n^2, m will become larger than n, which is already infinite and un"doable".
So if you need these:
n=infinity
m=infinity^2
Then you construct the total sum of these:
infinity=n+m=n+n^2
And then divide time as it occurs into units of these, which we can do, for example, in this manner.
For each unit of time:
if m<n^2 do another m "thing" otherwise do another n "thing".
So if m is, for example, laying out a row of apples in an array that's n by n and n is the length of the array, then these two infinite processes represent:
1) Begin by adding a unit dimension on each axis
2) Fill the new space with apples and repeat #1
So it grows like this over time:
CODE
+
Add new position in dimensions (so we're really doing 2*infinity)
CODE
+D
D.
D.
And place apples until full (1^2=1 step in this case):
CODE
+D
DA
DA
Now we go back and do 2 units of extending dimensions:
CODE
+DD
D..
D..
D..
D..
And we're finished multiplexing our linear process so we continue with the parabolic m=n^2 one:
CODE
+DD
DAA
DAA
DAA
DAA
etc.
That's infinity. The difficult part is in breaking things into the smallest units to construct the various smaller infinities within it and of course doing that also requires some of those infinite units (of time, computation or action).
Notice also "infinitesimal" things are still discrete things and they never change size and there remains at least one of them but that from a growing perspective they can appear insignificant (but you still need a memory or space to integrate and retain records of all these infinitesimals otherwise the infinity wouldn't exist)
LOL
Ed Wood
My take on this is easy for me...Seems to be difficult for others.
Because I can measure/perceive ANYTHING, then infinity in terms of time space and energy is simply impossible.
Both ends of an infinite string are continually moving away(even that picture is flawed). So the middle can not achieve a measurable difference.
Cheers
Iseason
Ed Wood
My take on this is easy for me...Seems to be difficult for others.
Because I can measure/perceive ANYTHING, then infinity in terms of time space and energy is simply impossible.
Both ends of an infinite string are continually moving away(even that picture is flawed). So the middle can not achieve a measurable difference.
Cheers
Iseason
There's a flip side of this coin though.
Yes, the things you measure, or at least what you know and communicate about them precisely have specific boundaries and are constrained to only being finite (at least that's ideal of there is no uncertainty - you could translate everything into specific words of some language).
But the time these all occur in time is different.
Consider the simple ability to count to 5 ... 1, 2, 3, 4, and then 5.
Now the object #1 is not equal to 2 and not equal to 3 or anything else. It is unique and the same is true of 2 and 3 etc.
If we put 1 in a box, 1 can't count past itself. It just stays 1. There is no time inside the box, there is never another 1. It's still and remains 1 and can't know anything about itself etc.
The same is true for 2 and 3 etc.
Now if we put 1 and 2 in a box, can they change into each other? No. They're still just 1 and 2 and in order for change to occur something else needs to happen - if you reached in and pulled one of them out, without looking or selecting which, you'd figuratively, ahead of time, from a mental perspective be pulling out a "superposition" or randomly selected element from the set, though that's just virtual. In reality you'd just get one of the other. If you reached in and pulled out the next, you'd have this value appended to your last value, though we could say that the "current" state or number changed.
Now the numbers themselves were timeless and always existed. They didn't create change. The symbols or letters 1 and 2 are arbitrary and they could be a color or a thought, we only need to be able to arrange them in order to have time.
So let's say we put all 5 numbers in their own little universe separated from everything else and we aren't their to watch them. How can the numbers count themselves?
Can we describe a manner in which some current count be selected?
For example we say the universe is in some specific state, then one of these numbers needs to be selected and this state itself is a number that could be 1 to 5. Well adding this creates a new non-specific number, or variable to the universe, which would mean the universe could not be closed.
But we have a problem because 1 ust stay 1 and not become 2 etc. otherwise they are not specific numbers and 1 could count itself to any other number or no specific number at all.
Ok, let's cheat and say we can add a counter to this universe (so we quick pop open the universe and throw in a counter and tell him to count things - now we should be fine right?).
Ok, let's say the counters rules are to start at 1 and then find another number and refer to that one by its unique symbol (2 in this case) and then continue doing this until no new symbols are found (he could count in any order, but lets ignore that).
So he could construct this set of transitions:
(nothing)->1
1->2
2->3
3->4
4->5
5->? (I guess he has to stop unless he counts himself as 6)
We can either have 5 loop to itself (and remain static) or loop to some other number and form an infinite cycle.
Now because he's in his own universe we can't watch him count. We don't know what number he's on at any moment - "moments" don't exist in common between his space and ours. Obviously we'd have to look in and see what the current count is. In order to do that we have to become synchronized in time to see a specific number - he can't be rapidly flipping through numbers unless we see a blur.
So he would have to stop counting when we looked in on his universe if we ever had a hope of "seeing", via. his count, one of the five numbers.
But notice that he has no such rule in his counting about stopping when something else is looking. He can't even stop at 1 but must count to 2 and can't do anything, even including contemplating any numeric properties about it, he's driven to 3, which is actually similarly not a number because it's a transition to 4 which is a transition to 5 ... and finally if he's to continually remain at 5, then when we look in (assuming time has passed for him) we'll see a solid 5.
But we can't see him remaining at 4, if it was 4 he was still counting a number, nor could we see the number as all "paths" lead to 5 in this example. The only thing that's a number is the stopping point and not intermediate symbols leading to it.
If he instead looped back to 1 then he'd never arrive at a number and we could never see a specific number via. his counting.
If we try to have him stop at whatever random number he might be on, then he needs to have his rules of counting go outside his universe and include an additional rule to stop at a current number when something else is looking - so his universe cannot count when it's closed (he can't see a number until he stops counting and then he just sees a number and cannot decide to start counting after some random time later to select any other number).
Now this problem extends beyond him land applies to us as well. If the universe was entirely closed informationally with deterministic laws of nature that always were precise, the universe would ultimately have to repeat, but such a repetition would require that an ability within the universe exists to count such repetitions, but the universe itsellf could not contain this because it already did everything and it was the first and in order to repeat it would have to do everything in a different context as the second time, but there would be no room within the universe to store this count, hence the universe would have to expand to add a counter in order that it could repeat, but now it's not truly repeating and the counter would have to grow ... etc. etc. etc. If the universe was ever closed and finite, time would have already stopped and never started.
Also, everything in space that follows patterns over time is synchronized to the same process creating time, so there is a common fabric that ties everything that changes in time to everything else that changes and the things that do not change form the rules, logic and natural laws describing the growth of the universe. It would also appear that some components of growth are likely unpredictable and effectively random and creative (it's very difficult to distinguish between extreme complexity and randomness, though absolute randomness should have no specific physical form and could be seen likely as changes in the laws of physics themselves).
Yes, the things you measure, or at least what you know and communicate about them precisely have specific boundaries and are constrained to only being finite (at least that's ideal of there is no uncertainty - you could translate everything into specific words of some language).
But the time these all occur in time is different.
Consider the simple ability to count to 5 ... 1, 2, 3, 4, and then 5.
Now the object #1 is not equal to 2 and not equal to 3 or anything else. It is unique and the same is true of 2 and 3 etc.
If we put 1 in a box, 1 can't count past itself. It just stays 1. There is no time inside the box, there is never another 1. It's still and remains 1 and can't know anything about itself etc.
The same is true for 2 and 3 etc.
Now if we put 1 and 2 in a box, can they change into each other? No. They're still just 1 and 2 and in order for change to occur something else needs to happen - if you reached in and pulled one of them out, without looking or selecting which, you'd figuratively, ahead of time, from a mental perspective be pulling out a "superposition" or randomly selected element from the set, though that's just virtual. In reality you'd just get one of the other. If you reached in and pulled out the next, you'd have this value appended to your last value, though we could say that the "current" state or number changed.
Now the numbers themselves were timeless and always existed. They didn't create change. The symbols or letters 1 and 2 are arbitrary and they could be a color or a thought, we only need to be able to arrange them in order to have time.
So let's say we put all 5 numbers in their own little universe separated from everything else and we aren't their to watch them. How can the numbers count themselves?
Can we describe a manner in which some current count be selected?
For example we say the universe is in some specific state, then one of these numbers needs to be selected and this state itself is a number that could be 1 to 5. Well adding this creates a new non-specific number, or variable to the universe, which would mean the universe could not be closed.
But we have a problem because 1 ust stay 1 and not become 2 etc. otherwise they are not specific numbers and 1 could count itself to any other number or no specific number at all.
Ok, let's cheat and say we can add a counter to this universe (so we quick pop open the universe and throw in a counter and tell him to count things - now we should be fine right?).
Ok, let's say the counters rules are to start at 1 and then find another number and refer to that one by its unique symbol (2 in this case) and then continue doing this until no new symbols are found (he could count in any order, but lets ignore that).
So he could construct this set of transitions:
(nothing)->1
1->2
2->3
3->4
4->5
5->? (I guess he has to stop unless he counts himself as 6)
We can either have 5 loop to itself (and remain static) or loop to some other number and form an infinite cycle.
Now because he's in his own universe we can't watch him count. We don't know what number he's on at any moment - "moments" don't exist in common between his space and ours. Obviously we'd have to look in and see what the current count is. In order to do that we have to become synchronized in time to see a specific number - he can't be rapidly flipping through numbers unless we see a blur.
So he would have to stop counting when we looked in on his universe if we ever had a hope of "seeing", via. his count, one of the five numbers.
But notice that he has no such rule in his counting about stopping when something else is looking. He can't even stop at 1 but must count to 2 and can't do anything, even including contemplating any numeric properties about it, he's driven to 3, which is actually similarly not a number because it's a transition to 4 which is a transition to 5 ... and finally if he's to continually remain at 5, then when we look in (assuming time has passed for him) we'll see a solid 5.
But we can't see him remaining at 4, if it was 4 he was still counting a number, nor could we see the number as all "paths" lead to 5 in this example. The only thing that's a number is the stopping point and not intermediate symbols leading to it.
If he instead looped back to 1 then he'd never arrive at a number and we could never see a specific number via. his counting.
If we try to have him stop at whatever random number he might be on, then he needs to have his rules of counting go outside his universe and include an additional rule to stop at a current number when something else is looking - so his universe cannot count when it's closed (he can't see a number until he stops counting and then he just sees a number and cannot decide to start counting after some random time later to select any other number).
Now this problem extends beyond him land applies to us as well. If the universe was entirely closed informationally with deterministic laws of nature that always were precise, the universe would ultimately have to repeat, but such a repetition would require that an ability within the universe exists to count such repetitions, but the universe itsellf could not contain this because it already did everything and it was the first and in order to repeat it would have to do everything in a different context as the second time, but there would be no room within the universe to store this count, hence the universe would have to expand to add a counter in order that it could repeat, but now it's not truly repeating and the counter would have to grow ... etc. etc. etc. If the universe was ever closed and finite, time would have already stopped and never started.
Also, everything in space that follows patterns over time is synchronized to the same process creating time, so there is a common fabric that ties everything that changes in time to everything else that changes and the things that do not change form the rules, logic and natural laws describing the growth of the universe. It would also appear that some components of growth are likely unpredictable and effectively random and creative (it's very difficult to distinguish between extreme complexity and randomness, though absolute randomness should have no specific physical form and could be seen likely as changes in the laws of physics themselves).
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