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

I will answer Johnathan's question asap, but I have three busy days and I want to take some time to do that. The answer is, imo, contained in 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 Corgan

Hi Bruno,

I would like to add that the most important aspect of QM is the non-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 of knowledge, we can derive the logic 1 of the measure on computation, which, by UDA *is* physics. So if you give me a funding and reserachers to proceed, I would ask for a confirmation and precise proof that the measure one is non distributive, by using the arithmetical 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 Gödel number 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 & BD C) 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 implementation of G*, and of all hypostases, and the theorem prover found a counterexample, so we know that the measure one (the arithmetical observable) are not distributive. (But this, like the neutrino speed should 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 is to pursue the comparison of the existing quantum logics and the arithmetical quantum logics extracted form the comp hypothesis (and Theatetus type of knowledge).

And then, once we have enough information on the quantum logic, we can tackle 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 the notion 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 the arithmetical quantum logic be collapsing into classical logic, physics would have disappear, and our physical reality appearance would have been a purely geographical reality. The difference between physics and geography would have been conventional, and the physical reality would have contained all possible consistent laws (or comp is not correct).

Likewise, if the gravitational constant is not a theorem of the first order extension of the material hypostases, then it means there are other 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 rather quantum-like.





This translates to the nonexistence of a unique partition of observables into a unique set of mutually commuting quantities over (or on) the set of all possible observables. What I would like to know, other than the answer to Johnathan's question, is how do we bridge the gap between computations, which by UDA seems arbitrarily composable and thus distributive, to the non-distributive property of QM. If QM emerges from computations, exactly how does this happen?



Here I think that you are confusing the third person view on computations, and the first person views, which means that you don't really take the conclusion of the UDA into account. Physics does not emerge from the computations, it emerges from the computations *as seen from a universal numbers first person perspective*. By the first person indeterminacy (the global one which involves a continuum of histories) 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 distributive subsets on the set of observables as the set of Abelian (commutative) von Neumann algebras... But to see things this way points against the idea that we can derive QM from computations

It means that you have not (yet) really understand the UDA point. It does not leave any alternative: if comp is correct, then physics (whatever it is, QM or not) is given by a relative measure on all computational extensions, constrained by the laws of mind (with the comp laws of mind being the logics of self-reference and their intensional (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 other words, 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 derivable from comp. And AUDA explains why the task of doing the derivation is not trivial (already G and G* are not trivial, and even counter-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 derive all 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, and will prevent the distinction between qualia and quanta. We just cannot use that stuff. The goal is not to build a better physics, but a physics satisfying the 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 of substance (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 say that comp is plausibly false. But the hypostases just show already that matter exist and behave non trivially. The UDA is indeed an argument against substance-time-space, as being fundamental or primitive. It makes physics a branch of numbers' epistemology. It is a point against primary substance and, above all, against physicalism, not against the (non primary) existence of a physical and material reality.

    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

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