Re: An Equivalence Principle
On Wed, Apr 23, 2008 at 06:04:25AM -0700, Youness Ayaita wrote: The equivalence principle states that we don't contradict ourselves by taking the two apparently different roads at the same time. But the reconciliation of QM and GR might be as difficult as explaining the concept of observer moments starting from a description of worlds and vice versa. Since the last step includes (explaining observer moments out of the ensemble of worlds) a neurological theory, we can speculate whether the moment is near when our revolutionary view of the interdependence of physics and neurology/psychology is needed to find new physics. Very interesting point Youness. I'm still compiling a response to your critique of my appendix D - it may be ready by the end of next week. I have a conference paper due in less than two days, which is absorbing most of my time at present. -- A/Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 [EMAIL PROTECTED] Australiahttp://www.hpcoders.com.au --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Which mathematical structure -is- the universe in Physics?
On Apr 22, 11:28 pm, Brian Tenneson [EMAIL PROTECTED] wrote: Perhaps Hilbert was right and Physics ought to have been axiomatized when he suggested it. ;) Then again, there might not have been a motivation to until recently with Tegmark's MUH paper and related material (like by David Wolpert of NASA). The logical positivists were motivated to axiomatize in the predicate calculus the laws of scientific theories in the early 20th century, first because they believed that it would guarantee the cognitive significance of theoretical terms in the theory (such as the unphysical ether of maxwell's electromagnetism), and then later because it had evolved into an attempt to specify the proper form of a scientific theory. In practice this had too many problems and was eventually abandoned. One of the consequences of this program was that axiomatizing the laws of a theory in first order predicate calculus with equality was that such a formulation of a theory always implied various unintended interpretations. The amount of effort needed to block these unintended interpretations was out of proportion with the benefit received by axiomatization. I was trying to answer Bruno's objections regarding set theory being too rich to be the 'ultimate math' the MUH needs to propose what the universe is and I quipped that that was because math is invented or discovered to further its own end by logicians, for the most part, and that metamathematicians such as Cantor had no apparent interest in physical things or furthering the pursuit of Physics. Another question of Bruno's was my motivation. I started this quest hoping that three truth values were sufficient to develop a set theory with a universal set that was in a classical logic sense consistent to ZFC set theory. Or, if not true, prove that and figure out why. Perhaps more truth values would solve that. My main motivation has definitely not been to rescue a major apparent shortcoming in the MUH as I started this on-and-off quest in 2003 with no internet connection or resources such as a deluge of journals (ie, a good library). How it started was that someone online in a place such as this used Russell-like arguments to -prove- that the Physic's universe -does not exist- for essentially the same reasons a universal set can't seem to be non-antimonious. Suppose Everything is well defined along with its partner, containment (such as the earth is contained in the solar system by the definitions of both). Then Everything does not exist. Proof: Consider the thing, call it this something, that is the qualia of all things that do not contain themselves. Then this something contains itself if and only if this something does not contain itself. I am suspect of the claim that a logical argument such as the above, which relies on a paradox of self-reference, could be used to demonstrate the non-existence of the so-called Everything. Also, I personally remain unconvinced that there is anything problematic about the exitence of the universe of universes, or the ensemble of all possible mathematical structures, thought it may not be well defined at present. I don't believe that this is simply the union of all axiomatic systems. If trying to define the Everything as a set implies a contradiction, then fine -- it isn't a set, it's an ensemble, which doesn't carry any of the connotations that are implied by the use of set in the mathematical sense. Therefore each entity in the ensemble is a unique collection of n axioms that has no necessary relationship to any other axiom collection. What happens in an axiom system stays in that axiom system, and can't bleed over to the next one on the list. Some of these may be equivalent to each other. A = The collection of all finite axiom systems B = The collection of all consistent finite axiom systems The cardinality of B is not greater than the cardinality of A. (Scare qutoes since cardinality is a property of sets and these may not be sets if that would imply contradiction.) It is B that is interesting from the point of this discussion since it is believed (I don't know of any proof of this) that only systems in B could produce the type of rational and orderly physical existence capable of containing observers who can think about their existence as we do (SASs, or Self-Aware Substructures). The collection of all those systems capable of containing SASs is the most interesting from the point of view of the present discussion, and must have a cardinality not greater than that of B, since many axiom systems are too simple to contain SAS, and the ones with them are expected to predominate. The idea of this ensemble so propounded does not seem to entail an ad absurdum paradox such as you gave above. Further, didn't I see you say somewhere that you don't even believe in sets? I apologize if I am mistaken, but if that is true, I can't see how that statement would reconcile with sincere belief in the validity of
Re: Which mathematical structure -is- the universe in Physics?
I was attempting to -invalidate- that argument against the existence of the universe, actually, by saying that in three truth values, which the Physicists can't rule out as being the more accurate logic of their universe, the argument reductio ad absurdum is not a tautology and, therefore, can't necessarily be applied. However, in binary logic, the Physicist's universe (or whatever Everything means) can't exist. I doubt self-reference is inherently the problem in light of things like Tarski's fixed point theorems which provide concrete examples of wffs that are self-referencing, in terms of Godel numbers, if I recall. That proof I was exposed to was not an existence proof of self-referencing wffs merely by logical flamboyancy but by the providing an example of an actual -class- of self-referencing wffs. Obviously, the above argument does not explicitly involve wffs (it does, however, implicitly), and I am -only- making a case for plausibility at this particular moment. I see no problems with the argument given that in binary logic, their universe can't exist; this, to me, convinces me that the Physicist's universe can't operate on binary logic by Occam's Razor as -none- of the data in any experiment would fit the result that confirms their speculation that their universe exists. Ergo, the Physicist's universe must operate on at least three truth values. (Consequently, it exists.) This to me is a more elegant solution to the argument than citing self-referencing issues as automatically damning. If natural language can be used to prove the Heine-Borel theorem, without the need for wffs, then why must a statement about Everything be formalized in machine-level code with wffs? If there is further objection to my line of thinking, -please- point it out to Everyone (which I hope is well-defined or else no one would know what I mean, right?) ;) Thank you for your remarks; I find all input extremely productive!! On Apr 24, 9:26 am, nichomachus [EMAIL PROTECTED] wrote: On Apr 22, 11:28 pm, Brian Tenneson [EMAIL PROTECTED] wrote: Perhaps Hilbert was right and Physics ought to have been axiomatized when he suggested it. ;) Then again, there might not have been a motivation to until recently with Tegmark's MUH paper and related material (like by David Wolpert of NASA). The logical positivists were motivated to axiomatize in the predicate calculus the laws of scientific theories in the early 20th century, first because they believed that it would guarantee the cognitive significance of theoretical terms in the theory (such as the unphysical ether of maxwell's electromagnetism), and then later because it had evolved into an attempt to specify the proper form of a scientific theory. In practice this had too many problems and was eventually abandoned. One of the consequences of this program was that axiomatizing the laws of a theory in first order predicate calculus with equality was that such a formulation of a theory always implied various unintended interpretations. The amount of effort needed to block these unintended interpretations was out of proportion with the benefit received by axiomatization. I was trying to answer Bruno's objections regarding set theory being too rich to be the 'ultimate math' the MUH needs to propose what the universe is and I quipped that that was because math is invented or discovered to further its own end by logicians, for the most part, and that metamathematicians such as Cantor had no apparent interest in physical things or furthering the pursuit of Physics. Another question of Bruno's was my motivation. I started this quest hoping that three truth values were sufficient to develop a set theory with a universal set that was in a classical logic sense consistent to ZFC set theory. Or, if not true, prove that and figure out why. Perhaps more truth values would solve that. My main motivation has definitely not been to rescue a major apparent shortcoming in the MUH as I started this on-and-off quest in 2003 with no internet connection or resources such as a deluge of journals (ie, a good library). How it started was that someone online in a place such as this used Russell-like arguments to -prove- that the Physic's universe -does not exist- for essentially the same reasons a universal set can't seem to be non-antimonious. Suppose Everything is well defined along with its partner, containment (such as the earth is contained in the solar system by the definitions of both). Then Everything does not exist. Proof: Consider the thing, call it this something, that is the qualia of all things that do not contain themselves. Then this something contains itself if and only if this something does not contain itself. I am suspect of the claim that a logical argument such as the above, which relies on a paradox of self-reference, could be used to demonstrate the non-existence of the so-called
Re: Which mathematical structure -is- the universe in Physics?
On Thu, Apr 24, 2008 at 10:08:16AM -0700, Brian Tenneson wrote: I was attempting to -invalidate- that argument against the existence of the universe, actually, by saying that in three truth values, which the Physicists can't rule out as being the more accurate logic of their universe, the argument reductio ad absurdum is not a tautology and, therefore, can't necessarily be applied. However, in binary logic, the Physicist's universe (or whatever Everything means) can't exist. ... If there is further objection to my line of thinking, -please- point it out to Everyone (which I hope is well-defined or else no one would know what I mean, right?) ;) Thank you for your remarks; I find all input extremely productive!! Isn't the sort of everything you have in mind a bit like omnipotence (which has problems such as creating the immovable object, then moving it). Perhaps such an everything really is logically impossible. The sorts of everything we've discussed here on the list are much more modest beasts - even Tegmark's all mathmatics tends to be viewed in terms of recursive enumerable structures (or finite axiomatic systems). Cheers -- A/Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 [EMAIL PROTECTED] Australiahttp://www.hpcoders.com.au --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
