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)
With Bp = beweisbar ('p') & ~beweisbar ~('p') with 'p' being the Gödel
number of the arithmetical proposition p.
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).
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.
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.
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.
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).
and toward the idea that we can derive computations from QM. In
other words, while physics does nto 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).
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.
As I see it, a duality of sorts between matter and mind is inevitable.
Sure.
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.
Probably more explanations in my reply to Johnathan asap.
Bruno
http://iridia.ulb.ac.be/~marchal/
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