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Author
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Topic: Cosmogony, Holography and Causality
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gedanken
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Member # 594
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posted 21. October 2003 16:36
Russell, From another thread: quote:
quote:
Gedankin:
Oh, another question: Where is the mathematically "straight line"?
According to the CTMU writings, the laws of mathematics distribute over the laws of physics but a mathematical ideal such as a perfectly straight line does not actually exist. Objects such as unicorns and mathematical ideals don't have a physical existence.
I'll presume Russell agrees with this (at least so far as my previous questions in this thread--please comment if I am in error).
If mathematically defined terms do not necessarily exist in reality (and 'mathematically' defined are among the most closely and carefully defined of human terms), why is it difficult to accept that less precisely defined terms as a "planatary rotation" might also not necessarily exist in reality?
I simply claim that statements like "this is my dog Spot" have a different level of abstraction from mathematical statements, but still can lack in clarity or certainty in terms of existing in the real world. Just we are much more certain (and less 'fuzzy') about our dog Spot, or even that the planet is rotating in a certain direction, or the pain in our smashed thumb.
Remember that communication itself is imperfect, so communication of a mathematical concept must also be imperfect. (And is memory perfect, either? So memory of the mathematical concept, possibly followed by refreshing from stored, e.g. transmitted, documentation is equivalent to communication.)
The rules of logic are mathematical in character. They may in fact be the most primitive of mathematical concepts, necessary for all other mathematical concepts.
BTW, I'll agree that to the extent one can properly measure them, that the mathematical relationship of conservation of enerty, momentum, hold closely. Of course the cases in which one can measure such relationships may be somewhat limited--but one can with great expectation of success make predictions based on those relationships.
[ 21. October 2003, 16:49: Message edited by: gedanken ]
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Rex Kerr
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posted 21. October 2003 22:52
In my opinion, the "real world" is an imprecisely defined concept that is of use when distinguishing between phenomena that can be agreed upon by independent observers and those that can't. The definition breaks down when you consider things like unicorns, as people can agree on what they are--so in some sense they are part of the real world--and also agree that no real unicorns exist.
One could also define the real world to be everything that affects anything real. If one is careful, one still has a halfway sensible measure of reality (e.g. thoughts of unicorns are real, unicorns are not real). This leads to potentially weird results, though, since not all of mathematics can be discovered by finite beings in finite time--so some mathematics is not real in any sense, while some mathematics is real by virtue of being thought about. This sense doesn't really capture what I mean when I say "real", but it is a more precise alternative.
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chimp
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posted 22. October 2003 02:20
quote:
Gedankin:
Does one's dog use "logic" in this association of action and pain?
???
http://evolution.massey.ac.nz/assign2/AC/page2.html
quote:
This led Pavlov to alter his experiment to study this phenomenon. Now, whenever the food was presented, Pavlov would ring a bell close to the dog. Shortly after this change in the feeding patterns, it was found that merely hearing the bell would also cause the dog to salivate, even though the bell had absolutely nothing to do with the food itself.
Conditioned response corresponds to an "if then" statement and salivatory expectation ![[Wink]](wink.gif)
If [Bell Rings] then [Food will Appear]
If A then B
A
therefore B
If Gedankin hits his thumb with a sledge hammer with 50 Newton's of force, Gedankin will damage his thumb?
Yes...?
quote:
Rex Kerr:
One could also define the real world to be everything that affects anything real. If one is careful, one still has a halfway sensible measure of reality.
If Langan is guilty of "circular definition" then physicist Lee Smolin is also guilty of it
http://www.pbs.org/wnet/hawking/mysteries/html/uns_smolin-1.html
quote:
A very important part of turning cosmology into a science is to understand all the implications of a seemingly trivial statement: There is nothing outside the universe. One aspect of this is that there can be no observer outside the universe. We must understand the universe in a way in which the scientific description of it is a description made and used by observers who are part of the system itself. This seems to go against the idea that the scientific view of nature is objective, and an objective description is always based on observations of a system from outside. If cosmology is to be a science, we must invent a new notion of objectivity that allows the observers of the system also to be part of it.
Has Professor Smolin been reading the CTMU writings?
quote:
As there can, by definition, be nothing outside the universe, a scientific cosmology must be based on a conception that the universe made itself.
The "universe" can be represented as a variable that is unknown.
At T = 0, X = X
Professor Smolin and Mr. Langan, say that there is "nothing outside the real universe". If there is nothing outside the real universe, then it is self contained:
[X] = [X]
We observe the universe "changing":
[X] changes by D[X] , where D is a "difference" operator.
[X] ---> [X + D[X]]
[X+D[X]] ---> [X + D[X + D[X]]]
[X+D[X+D[X]]]---> [X + D[X+D[X+D[X]]]]
etc.
etc.
etc.
X is self embedding.
So there should be a way to empirically verify this self embedding of the universe. Since all motion is relative, the universe cannot be expanding in an absolute sense.
It appears that the statement "the real universe contains all and only that which is real" can tell us something about reality after all.
quote:
C.M. Langan:
The real universe contains all and only that which is real...
quote:
Lee Smolin:
There is nothing outside the universe...
[ 22. October 2003, 03:06: Message edited by: Russell E. Rierson ]
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Rex Kerr
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posted 22. October 2003 03:13
It doesn't tell us anything about the universe. Rather, it defines the universe. (As everything, no less.)
Supposing we take that definition, though, what if we ask the following:
Are chairs real?
Are protons real?
Are gluons real?
Are unicorns real?
We can find chairs and observe them directly, so chairs are real. Protons can be observed fairly directly, so maybe they are real. Certainly the thought of them is real, but whether they are is less clear. Gluons are less clear still, as indirect evidence for them is sketchy. And unicorns are not real, but the concept of unicorn is real.
Here's where mathematical existence != physical existence (using the C "not equals" symbol !=). A straight line is conceptually real: ax+by+c=0. However, there are no real straight lines. Straight lines have the same status as unicorns.
This leaves us just as puzzled as before as to the unreasonable effectiveness of mathematics. Unicorns are not useful for explaining the real world. Why should straight lines be?
So I don't see that anything is gained by adopting this view of what is real / what the universe is. I suppose there are cases where it could be useful, but I'm more interested in why straight lines are more real than unicorns, and that doesn't seem to fit into this schema.
[ 22. October 2003, 03:14: Message edited by: Rex Kerr ]
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chimp
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posted 22. October 2003 04:34
quote:
Rex:
It doesn't tell us anything about the universe. Rather, it defines the universe. (As everything, no less.)
If there is nothing outside the universe, it cannot be expanding in any externally measured sense. The expansion can only be defined in terms of a local intrinsic perspective. So the theory of an expanding spacetime is equivalent to a theory of the rescaling of matter and energy at the quantum level, as the universe continually makes quantum jumps, i.e. matter is shrinking. Since you and Gedankin believe that there are no absolute truths that correspond to reality, spacetime expansion/matter contraction duality should make you happy. Sure the human ego will find it hard to accept that matter shrinks. All motion is relative, therefore, spacetime expansion is a relative perspective effect. The reality principle[tautology] tells us much, yes?
quote:
Supposing we take that definition, though, what if we ask the following:
Are chairs real?
Are protons real?
Are gluons real?
Are unicorns real?
We can find chairs and observe them directly, so chairs are real. Protons can be observed fairly directly, so maybe they are real. Certainly the thought of them is real, but whether they are is less clear. Gluons are less clear still, as indirect evidence for them is sketchy. And unicorns are not real, but the concept of unicorn is real.
Heisenberg says:
DxDp >= hbar/2
The chair is defined as being extremely close to classical realness.
Yes, real definitions tell us about reality?
Chair = [Classical configuration] + [RHO] , where, RHO is some uncertainty in measurement.
The same for the proton and other fundamental "particles". As the particles get smaller, their uncertainty increases.
The unicorn has no evolutionary history that corresponds to observed life forms on Earth. So unicorns do not, and never have, existed.
quote:
Here's where mathematical existence != physical existence (using the C "not equals" symbol !=). A straight line is conceptually real: ax+by+c=0. However, there are no real straight lines. Straight lines have the same status as unicorns.
This leaves us just as puzzled as before as to the unreasonable effectiveness of mathematics. Unicorns are not useful for explaining the real world. Why should straight lines be?
So I don't see that anything is gained by adopting this view of what is real / what the universe is. I suppose there are cases where it could be useful, but I'm more interested in why straight lines are more real than unicorns, and that doesn't seem to fit into this schema.
Exact straight line = ax+by+c + RHO = 0
Straight Line helps to construct buildings and various apparatuses in a space that is locally Euclidean...
Unicorn = Fairy Tale = Wishful Thinking = Entertainment...
Straight lines correspond to the physical world, but not exactly. Unicorns do not correspond to the physical world...
The correspondence of mathematics to the real world is extremely good, is it not?
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gedanken
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posted 22. October 2003 07:15
quote:
Straight lines correspond to the physical world, but not exactly. ... The correspondence of mathematics to the real world is extremely good, is it not?
Russell, physics predictions (made using mathematics) have born out quite well, "extremely good". I don't see how that is in any way in conflict with what either Rex nor I have said.
But mathematics is a means of producing models that operate with rules that we define and accept as part of the model. Even various logics themselves are among the most primitive rules in the mathematical art of modeling. But mathematics per se does not agree with the "real world", because some mathematical equations make useful predictions when applied in certain ways, and others don't. No more than "unicorn" concept is very predictive of a real world object.
You persist in presenting models, show that they often agree with considerable accuracy (or low fuziness) with the real world, and then propose that somehow conflicts with what Rex or I have said.
But I am glad that you recognize that the model we call a "straight line" does not exactly conform to any real world object. That is progress.
Now is the dog responding according to a model, or is the dog thinking through: "Ah, for all occurrences of 'bell rings' we have 'food appears'. This is a specific occurrence of 'bell rings', therefore deductively we must have 'food appears'. I think I'll salivate." I think not. Rather the logic model is (just as a control system might) a good model of the dog's action.
The dog surely does not use syntax in processing its response. Rather the syntax only exists in Russell's dog activation model.
Now tell me, if the dog hears a bell, while he is watching a large truck bear down directly toward him at high speed, and very close, will the dog salivate? (Or was the 'logic' model an imperfect model?)
The 50 newton sledge hammer force on the thumb is an interesting case. This is because it involves statements that depend upon models, depend upon measurement concepts based on logic, for its very specification. (Now I'm not sure that 50 newton, even distributed along my entire thumb in a just proper way would cause damage, but one could easily increase that to a statement of 500 newton.) The real question is how one knows that one has the situation in the first place. There are always issues of perception that will not be completely certain, and will be subject to matters of degree. Was the measurement made 500 'newton', or was it 500 milli-newton? Without a measurement, one does not have the conditions known. And if one has simply stated a logic model and then claimed that it obeys a logic model, that is hardly speaking about the real world.
[Note edits, I was still working on this when Russell made first response.]
[ 22. October 2003, 08:36: Message edited by: gedanken ]
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chimp
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posted 22. October 2003 07:59
quote:
Russell, physics predictions (made using mathematics) have born out quite well, "extremely good". I don't see how that is in any way in conflict with what either Rex nor I have said.
Thanks Rex and Gedankin.
The abstract is a syntactic generalization of the concrete.
I could make a statement such as "the universe exists" which is a truth but extremely trivial? Theories[mathematical descriptions] are corresponding with greater and greater accuracy. Our symbolic representations are compressing more and more information. For example, the series 1/n^2 1/1^2 + 1/2^2 + 1/3^2 + ... + 1/n^2
= [pi^2]/6
A distance interval [straight line] is given by the Pythagorean theorem in vertical and horizontal coordinates
x^2 + y^2 = z^2
Terms can be added to account for uncertainty and to obtain closer correspondence:
x^2 + y^2 = z^2 + RHO + ...+ RHO_n
There could be a version of "perfectly approximated line" as mathematical symbolism grows more sophisticated...
The tautology [X or ~X] is a general rule that corresponds to the physical world.
toss a quarter and it lands as either heads or tails, X or ~X. Now Gedankin and Rex will say that there is a extremely small but nonzero probability that the quarter will land on its edge Probability could not exist without a stable foundation of logical rules though
If [A or ~A] then X differs from Y , where X and Y are aspects of reality.
Certain rules must hold for certain conditions.
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gedanken
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posted 22. October 2003 08:03
quote:
The abstract is a syntactic generalization of the concrete.
But the "syntax" must be interpreted. Who does the interpretiing? Fuzziness occurs in interpretation, and in communication of "syntax". By itself, the "syntax" is meaningless, it must be accompanied by agent system capable of interpretation, and such communication and interpretation is inherently fuzzy.
Furthermore the "syntactic" model of logic of real-world activity is extremely brittle. Every little addition or condition that we realize modifies the description given so far requires syntactic changes to improve the model. (Given we have the agent of interpretation of the syntax, and with all the problems thereof, etc.) So here we wind up with the combinatorial explosion of syntactic elements to actually refine the "syntax" to a more nearly correct model. The more refined, the more the combinatorial explosion increases. We never asymtotically reach a full description or model in a finite syntactic space. And what we to achieve still fails somewhere. (Remember the hologram cannot immage itself!)
quote:
toss a quarter and it lands as either heads or tails, X or ~X. Now Gedankin and Rex will say that there is a extremely small but nonzero probability that the quarter will land on its edge ..
No, I would not speak of "probability". I agree that probability is a model concept, based on our human models that start with use as we see them of crisp logic. My point is not about probabiltiy (within crsip logic models), but of issues of measurement. What does it mean "heads"? That can in itself have degree, and that is separate from probablity.
(In other words, if one has fuzzy matter of degree, that fuzziness can be broken down into different kinds of aspects, with probability occurring as only one aspect of fuzzy knowledge.)
I can toss the quarter into a pile of rocks (of roughly quarter size) and guarantee an almost 100% probability that the quarter will be to some degree on edge.
Russell, you continue to use the model concept as justification for claims about the 'real world'.
[ 22. October 2003, 08:39: Message edited by: gedanken ]
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chimp
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posted 22. October 2003 09:23
The CTMU explains that the model of reality must agree with reality up to isomorphism.
Can you supply a mathematical proof that this is impossible?
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gedanken
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posted 22. October 2003 12:04
Thank you Russell, at least we have gotten out of the realm that these points were perhaps "intuitively obvious", and into pointing to a long argument for the point.
I will not attempt to answer that at present. But I am suspecting that the truly "isomorphic" component may be extremely 'thin' set of logically related statements, if any.
(And if we are allowing something akin to isomorphism with variations rather than exact mapping, then I see great difficulty with any analogy to computability--if I understand is intended. Aliet Jacob's other thread questioning computability aspects is of interest here.)
Within that, perhaps for a very 'thin' set of fully developed theories of physics (yet to come), there might be a mathematically exact (in certain terms) mapping. As far as modern physics has been able to determine, even that would have at least a probabilistic nature--and I am completely unconvinced that description might not be equally valid when presented in a "fuzzy logic" context or formulation. If this notion turns out to have a degree of correctness, then all the comments I have made (and Rex as well) could still apply to all other views of "reality", beyond that single mathematical theory of everything. And I personally have doubts that the TOE will encompas all, I mean that any theory will actually hold up as a TOE. I furthermore doubt that any such theory will be developed in my lifetime and tested as a scientific theory.
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Rex Kerr
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posted 23. October 2003 02:52
Here is (an outline of) a proof that a model of reality cannot agree with the universe up to (causal) isomorphism.
It's basically an embedding proof that shows that the above can hold only if the theory is the universe.
Let U be the universe and let T be a theory of the universe. T is our theory, and we are in U, so T is contained within U.
(Note that any two things that are causally related in U must either be in T, or must not be causally related to anything else in T or U, or else causal isomorphism is not preserved. Any aspect of the universe that is actually in T up to isomorphism must be causally related to T. We restrict ourselves to the casually connected subset of the universe containing T.)
Assume that T is a complete theory up to causal isomorphism. That is, there exists a mapping such that for each u,v in U there exists unique t,s in T such that u is caused by v iff t is caused by s.
T is in U, therefore something caused T. Therefore, there should exist T' in T that corresponds to T in U.
Let K(.) be the minimum information required to specify a theory, in the Kolmogorov-Chaitin sense. Since U contains T, which requires information K(T) to encode, T must contain T' by isomorphism, which requires information K(T') to encode. Since K(T) is minimal, K(T) is no greater than K(T'). But since K(T') is entirely contained within T, K(T) must be at least K(T'). Thus K(T) = K(T').
We now have two cases.
(1) K(T) is infinite. This does not conform to any real theory, since we cannot conceive of infinite theories (and they would have to be in an infinite universe).
(2) K(T) is finite. Let s and t be causally related. Now we ask: is this information encoded in T', or outside of T'? K(T') = K(T), so there is no room to encode more information, so s and t are encoded as part of T'. Therefore, our theory says that any causal relationship is part of the encoding of a theory of that causal relationship. But T is isomorphic to U, so that means that all causal relationships in U are part of the encoding of T. But this is no theory at all! This is just the universe.
Thus, it is not possible that
(1) A theory of the universe is finite, and
(2) that theory is causally isomorphic to the universe and
(3) that theory can explain in any way, shape, or form how it came about based upon any causation in the universe.
Since (1) is necessary, and (3) holds for any human-created theory, it follows that a model of reality cannot agree with reality up to isomorphism.
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chimp
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posted 23. October 2003 03:13
Thanks Rex. This is something to chew on for awhile
Perhaps also, Christopher Langan can answer your question - proof?
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Krandal
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posted 23. October 2003 11:57
Russell
I think you may be slightly misrepresenting the law of the excluded middle [X or ~X] and perhaps confusing it with bivalence [X or Y].
Using the coin flipping example to demonstrate the difference: while there is a possibility that a coin will land niether heads nor tails [~X and ~Y] effectivly making bivalance non applicable, the coin still must either land heads or NOT land heads [X or ~X], so the law of the excluded middle holds
no matter if the coin lands tails, lands on its side, turns into a butterfly etc.
Also perhaps you understand the CTMU better than I do, but do you really beleive that when Chris Langan is claiming that his model agrees with reality up to Isomorphism he means causal Isomorphism (of the type Rex Kerr provides)?
[ 23. October 2003, 11:59: Message edited by: Krandal ]
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chimp
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posted 23. October 2003 12:41
quote:
Russell
I think you may be slightly misrepresenting the law of the excluded middle [X or ~X] and perhaps confusing it with bivalence [X or Y].
Using the coin flipping example to demonstrate the difference: while there is a possibility that a coin will land niether heads nor tails [~X and ~Y] effectivly making bivalance non applicable, the coin still must either land heads or NOT land heads [X or ~X], so the law of the excluded middle holds
no matter if the coin lands tails, lands on its side, turns into a butterfly etc.
Good point Krandal. The quarter must land heads or not heads so the law of excluded middle is absolutely true. Of course, Gedankin and Rex will argue that if the quarter lands on its edge, or slanted, etc, it will fuzzily be in degrees of both heads and tails but if it is fuzzily in degrees of both heads and tails, it is not heads. An absolute truth. The law of excluded middle is exactly isomorphic to the universe in that regard.
Rex and Gedankin are refuted.
[ 23. October 2003, 12:46: Message edited by: Russell E. Rierson ]
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gedanken
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posted 23. October 2003 15:18
quote:
Of course, Gedankin and Rex will argue that if the quarter lands on its edge, or slanted, etc, it will fuzzily be in degrees of both heads and tails but if it is fuzzily in degrees of both heads and tails, it is not heads. An absolute truth. The law of excluded middle is exactly isomorphic to the universe in that regard.
I was just going to point out that our argument was virtually the same whether for A and B, or for A and ~A forms. Then I read that (LOL). By the way, Rex already went through this issue way back on page 3 or 4 or so.
Russell (again) you can define a property and claim that by definition it is an 'absolute' crisp distinction. But how can you actually determine if any real-world object obeys your definition? To do that, you have to deal in observing the real world.
If the coin is defined as "heads" only if it appears with head up, and is furthermore "not on a slope", then how little slope disqualifies the toss? Is 0.0000001 degree "on a slope"? Where do you make the distinction? Do you make it at 3 degrees, or 45 degrees, or 89.5 degrees? What is the angle refered to, Earth center of mass, or the table top. If the "mathematically perfect straight line" does not exist in the real world, how can the mathematically perfectly flat table top. Without that, how do you measure the angle with regard to the table top, in the real world, such that ther is no 'fuzziness', no question of degree of accuracy?
I'm really confused that you so readily jump to an "Aha!" These counter arguments seem so trivial to make, why do you make statements about what I might say and then knock them down, without even trying to make a better guess of what a realistic argument for the case might be?
[ 23. October 2003, 15:33: Message edited by: gedanken ]
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