On 11/21/2011 10:19 AM, Bruno Marchal wrote:

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I will answer Johnathan's question asap, but I have three busy daysand I want to take some time to do that. The answer is, imo, containedin the conclusion of UDA, and made clearer (technically) with AUDA,but I guess I shopuld explain this more clearly.Below I can answer to Stephen less demanding post. On 20 Nov 2011, at 21:52, Stephen P. King wrote:On 11/20/2011 2:56 PM, Johnathan Corgan wrote:Quoting Bruno Marchal: "UDA shows that physics is determined by a relative measure on computations. If this leads to predict that electron weight one ton then mechanism is disproved. UDA shows that physics is entirely reduce to computer science/number theory in a very specific and unique way (modulo a variation on the arithmetical definition of knowledge)." Bruno--could you please elaborate on this? It's a claim you've (credibly) made many times, and it would be useful to go the next step. I understand that the UDA argument and first-person indeterminacy demonstrates that there are an infinite number of paths through the execution of the UDA that may result in the present 1-pov experience. Since physics, when described from a 1-pov, is merely (!) the explanation of the regularities in those 1-povs, it should be possible to mathematically translate from "computational steps of the UDA" to "laws of physics." One of the best-confirmed formulations of physics has been quantum mechanics. And indeed, as far as I can tell, QM does not contradict your theory--but how would QM "emerge" from your more fundamental notions of computationalism and mechanism? Is this the forefront of your theory, or has work been done to reduce the explanatory gap between, say, modal logics and the Schrodinger equation? Let me ask this in a very different way. Suppose you had at your disposal the a fixed but large amount of funding and researchers to pursue a reformulation of QM based on the work you've done so far. How would you organize the effort? What would you prioritize first? What sub-portions of your theory would be amenable to be parceled out as individual problems to go off and solve? No pressure :-) Johnathan CorganHi Bruno,I would like to add that the most important aspect of QM is thenon-distributivity of the logic involved.And this answer a part of Johnathan question. Accepting the classical(S4, S4Grz, and the comp nuances: Z1*, S4Grz1, etc.) theory ofknowledge, we can derive the logic 1 of the measure on computation,which, by UDA *is* physics. So if you give me a funding andreserachers to proceed, I would ask for a confirmation and preciseproof that the measure one is non distributive, by using thearithmetical quantization. Basically, do we have that(A & B) V C <-> (A & C) V (B & C) which, translate in arithmetic becomes: BD((BD A & BD B) V BD C) <-> BD(BD A & BD C) V BD(BD B & BD C)

OK, i see the distributivity statement here.

With Bp = beweisbar ('p') & ~beweisbar ~('p') with 'p' being the Gödelnumber of the arithmetical proposition p.

`I did not see Bp in the sentence above or below. Are you taking the`

`Gödel number of the arithmetical sentence as part of G*? I think of 'p'`

`as the internal model of p in an algebra. Bisimulations are between`

`these (up to isomorphism).`

The question is really is "BD((BD A & BD B) V BD C) <-> BD(BD A & BDC) V BD(BD B & BD C)" true in the standard model of arithmetic?, or(thanks to Solovay) is the modal formula "BD((BD A & BD B) V BD C) <->BD(BD A & BD C) V BD(BD B & BD C)" a theorem of G*.Actually, this has been solved years ago, by using the implementationof G*, and of all hypostases, and the theorem prover found acounterexample, so we know that the measure one (the arithmeticalobservable) are not distributive. (But this, like the neutrino speedshould be verified again).

`Yes, that would be a very good idea as this is an extraordinary`

`claim requiring extraordinary evidence.`

We can do that for all quantum "tautologies", so a good work to do isto pursue the comparison of the existing quantum logics and thearithmetical quantum logics extracted form the comp hypothesis (andTheatetus type of knowledge).And then, once we have enough information on the quantum logic, we cantackle the complex problem of deriving an arithmetical tensor product.I did already found promising arithmetical Temperley Lieb algebra,years ago, (I explained this on the list, but it is very technical).The arithmetical Temperley-Lieb algebra might help to extract thenotion of space.

`I agree that the Temperley-Lieb algebra would generate the notion`

`of space, but one has to first have a way to express the notion of an`

`angle or a spinor. Could we discuss the specifics of how this is done?`

Physics is of course redefined (as UDA explains why). Would thearithmetical quantum logic be collapsing into classical logic, physicswould have disappear, and our physical reality appearance would havebeen a purely geographical reality. The difference between physics andgeography would have been conventional, and the physical reality wouldhave contained all possible consistent laws (or comp is not correct).Likewise, if the gravitational constant is not a theorem of the firstorder extension of the material hypostases, then it means there areother physical realities with different gravitational constant.

`Yes, local mutual consistency would induce the appearance of`

`semi-global constants for some mutually bisimulating collection of 1p.`

But the evidence from comp (and AUDA) is that there is a real physics,invariant for all universal numbers point of view, and already ratherquantum-like.This translates to the nonexistence of a unique partition ofobservables into a unique set of mutually commuting quantities over(or on) the set of all possible observables. What I would like toknow, other than the answer to Johnathan's question, is how do webridge the gap between computations, which by UDA seems arbitrarilycomposable and thus distributive, to the non-distributive property ofQM. If QM emerges from computations, exactly how does this happen?Here I think that you are confusing the third person view oncomputations, and the first person views, which means that you don'treally take the conclusion of the UDA into account. Physics does notemerge from the computations, it emerges from the computations *asseen from a universal numbers first person perspective*. By the firstperson indeterminacy (the global one which involves a continuum ofhistories) those are very different things.

`Yes, I did make that mistake, but my confusion arrises from a`

`problem with the use of classical teleportation in your papers that I`

`have, it seems to assume that there exists a 1p that can model an`

`unmeasurable set. I think that there is an alternative using`

`bisimulation between finite models where 3p is found in the limit of an`

`infinite number of 1p's. Similar to how a quantum (orthocomplete`

`lattice) logic can be approximated by an infinite number of boolean`

`logics. One has to show that analytic smoothness occurs. This is very`

`technical...`

It can easily be shown that there will always be distributivesubsets on the set of observables as the set of Abelian (commutative)von Neumann algebras... But to see things this way points againstthe idea that we can derive QM from computationsIt means that you have not (yet) really understand the UDA point. Itdoes not leave any alternative: if comp is correct, then physics(whatever it is, QM or not) is given by a relative measure on allcomputational extensions, constrained by the laws of mind (with thecomp laws of mind being the logics of self-reference and theirintensional (modal) variants).

`I agree, but my hypothesis is that this relative measure is not one`

`that can exist in an a priori way. It depends on the evolution of the`

`algebras relative to each other. This requires a notion of change as`

`primitive. The Platonic view does not seem to allow this.`

and toward the idea that we can derive computations from QM. In otherwords, while physics does not seem to be derivable from number theory,How do you know that? On the contrary, UDA shows that IF QM is(universally) correct, and if comp is correct, then QM is derivablefrom comp. And AUDA explains why the task of doing the derivation isnot trivial (already G and G* are not trivial, and evencounter-intuitive).

`My reasoning follows from the NP-Completeness of SAT, as discussed`

`here http://en.wikipedia.org/wiki/Boolean_satisfiability_problem . This`

`can be solved but requires the abandonment of a priori measures as I`

`hinted above.`

we need number theory to do physics. Why work so hard try to deriveall from computations when we obviously need both the numbers and the"stuff" to do physics.Any stuff coming from the usual way to do physics is treachery, andwill prevent the distinction between qualia and quanta. We just cannotuse that stuff.The goal is not to build a better physics, but a physics satisfyingthe mind-body problem 'solution' given by the comp hypothesis.

I agree.

As I see it, a duality of sorts between matter and mind is inevitable.Sure.

`OK, but can you see that change cannot be excluded from our models?`

`This is not to be confused with time as a primitive, because such a`

`notion of time requires a prior measure which cannot exist. A time is a`

`measure of change.`

The hard part is getting people to see the error of the assumption ofsubstance (http://plato.stanford.edu/entries/substance/).What I see in your result is an argument against the notion of"fundamental substance" not against the material world per se.If comp leads to the idea that matter does not exist, then I would saythat comp is plausibly false. But the hypostases just show alreadythat matter exist and behave non trivially. The UDA is indeed anargument against substance-time-space, as being fundamental orprimitive. It makes physics a branch of numbers' epistemology. It is apoint against primary substance and, above all, against physicalism,not against the (non primary) existence of a physical and materialreality.

In my thinking matter = profinite space.

Probably more explanations in my reply to Johnathan asap. Bruno http://iridia.ulb.ac.be/~marchal/

I look forward to reading your post to Johnathan. Onward! Stephen -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.