Hi Noson,
On 12 Jul 2017, at 01:26, Noson Yanofsky wrote:
Hi,
I agree that without axioms, there would be no theorems. But I am
not sure that means there would be no physics.
There would still be a physical universe (just to be clear), but the
science physics use many assumptions/axioms/theories. In particular
all theories in physics uses the natral numbers, and this means that
they are using (most of the time implicitly) axioms defining or
characterizing natural number (or Church-Turing equivalent).
Keep in mind that we cannot prove in pure logic that x+0 = x. That
kind of thing is so obvious that many before Dedekind and Gödel, have
thought that we can prove that in logic alone. Note also that logic
itself relies on assumptions, that we can make explicit or not.
The universe works perfectly whether we look at it or not.
In which theory? (and that concerns the theory of "we" as much as the
theory of the "universe").
Here, what I can justify is only that IF the brain/body works like a
digital machine (or, more weakly, is emulable by a digital machine)
THEN The physical universe "does not exist" when we don't look at,
with "we" meaning us, the universal digital machine (which exists only
in the arithmetical reality).
I refer you the fact that Digital Mechanism is not epistemologically
compatible with the existence of a logically primary physical
universe. If we are digital machine, the physical reality must be
recovered from a statistics on all computation "seen from inside".
"Seen from inside" has to be made precise through the mathematical
logic of machine self-reference (and this works up to now, but I would
be please when we get a physical theorem refuted by Nature).
In fact, with mechanism, the universe does not exist even when we look
at it, a bit like a rainbow which is not an object there, but an
optical illusion, yet sharable by many observers.
There could be chaos or order without mathematics.
Let us not confuse a mathematical theory and a mathematical reality.
If we are digital machine, which is a mathematical, even an
arithmetical, notion, it can be shown that the fundamental reality is
"pure" arithmetic. Pure arithmetic contains all execution of all
computers, and the physical realm emerges from a first person plural
view.
Chaos and order are mathematical notion, so I am not sure there could
be chaos and order without a mathematical reality (although I agree
that there could be chaos and order without a mathematical theory of
chaos and order).
Ants do not have mathematics, but the physical world around them
works nicely.
That is why if we assume digital mechanism, we must explain the
appearances of ants (and humans) and physical reality from the
mathematical properties of relative computational states. That gives
also an advantage to distinguish qualia and quanta.
Now, even without going that far, I am not sure Ants do not have some
implicit mathematical theories. The case is probably even clearer with
cicada whose life span are prime numbers, so as to minimize some
conflict of interest. (Google on "cicada prime number"). This does not
mean that the Cicada have some knowledge of prime numbers, but it
means that "evolution" has used the prime number reality (not theory)
to help the cicada on its path, and so, without prime number they
might disappeared, or be less developed.
I have to look into your mechanism.
OK. Ask any question. What is sometimes not obvious for the
physicists is that the arithmetical reality emulates in a static way
the whole set of all possible dreams/experiences. It does it in the
manner a block-universe (of general relativity, for example)
instantiates all observer-lines in a static way, and time is treated
like an indexical.
You can consult my paper here:
http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html
(A better version, corrected by Kim, is also available, but I have not
yet put it on my webpage). If you or your institution is on research
gate, or academia, you can read:
Marchal B. The computationalist reformulation of the mind-body
problem. Prog Biophys Mol Biol; 2013 Sep;113(1):127-40
Marchal B. The Universal Numbers. From Biology to Physics, Progress in
Biophysics and Molecular Biology, 2015, Vol. 119, Issue 3, 368-381.
Best regards,
Bruno
Noson
From: Bruno Marchal [mailto:[email protected]]
Sent: Tuesday, July 11, 2017 4:39 AM
To: [email protected]
Cc: Noson Yanofsky <[email protected]>
Subject: Re: Lawrence Krauss Should Have Paid Attention to Vic
On 11 Jul 2017, at 05:22, Brent Meeker wrote:
Interesting essay. When I was helping edit Vic's books I made a
similar argument too him - that the reason his Point-of-View-
Invariance seemed so powerful in rederiving physics is that
physicist were only interested in things that obeyed POVI.
You wrote:
Let us say we were interested in describing all phenomena in our
universe. What type of mathematics would we need? How many axioms
would be needed for mathematical structure to describe all the
phenomena? Of course, it is hard to predict, but it is even harder
not to speculate. One possible conclusion would be that if we look
at the universe in totality and not bracket any subset of phenomena,
the mathematics we would need would have no axioms at all.
With no axiom at all, we get all models of reality, but no theorem,
so we can no more even use 1+1=2, even in everyday life. That leads
to total "occasionalism". There is some coffee in my cup by pure
chance!
It is a good insight though, but some axioms are needed, like x+0 =
x, ... or the combinators laws Kxy = x, Sxyz = xz(yz).
And if we assume Mechanism (in cognitive science, not in physics)
then we can prove that the whole physics is entirely determined by
any (first order) logical specification of any universal (in the
Church or Turing sense) machine.
That is, the universe in totality is devoid of structure and needs
no axioms to describe it. Total lawlessness!
That would have been the case if the self-reference logic collapsed.
In that case physics would have been boolean logic (still needing
some axiom), but the physical would have become purely contingent
(no laws indeed). But with mechanism, we know (or should know) that
quantum mechanics, or a quantum mechanics is part of the physical
laws.
The mechanist hypothesis in the mind science saves physics!
The problem: physicists do not study (mathematical) logic (and
rarely philosophy of mind or cognitive science).
The mathematics are just plain sets without structure. This would
finally eliminate all metaphysics when dealing with the laws of
nature and mathematical structure. It is only the way we look at the
universe that gives us the illusion of structure.
I"m sure you're aware of Max Tegmark's "Mathematical Universe
Hypothesis" in which all possible mathematical structures obtain in
some universe; and his later restriction of this idea to the
"Computable Universe Hypothesis" in which only Turing computable
universes exist. But you are probably not aware of the ideas of
Bruno Marchal, a mathematical logician in Brussels. He has a much
more worked out idea of reality based on the Universal Dovetailing
computer which he combines with the assumption that consciousness is
certain kind of information processing to conclude that the UD
computation produces all experience and implies physics. It seems
like a crankish idea at first, but Bruno is a very nice and serious
guy, not at all a crank (though I don't agree with all of his
theories). Here's his basic paper:http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html
I know him from his posting on the Everything list; [email protected]
Thanks Brent,
Bruno
Brent
On 7/10/2017 3:56 PM, Noson Yanofsky wrote:
Thank you!
Vic Stenger’s books are always very interesting!!!
Attached is a paper on finding lawlessness.
And here is a link to another paper that was just published:
http://nautil.us/issue/49/the-absurd/chaos-makes-the-multiverse-unnecessary
Please pass them on to whoever would be interested in them.
All the best,
Noson
From: Brent Meeker [mailto:[email protected]]
Sent: Monday, July 10, 2017 4:48 PM
To: spinozalens via Free Thinkers Physics Discussion Group <[email protected]
>; [email protected]; Atvoid-2 <[email protected]>
Subject: Re: Lawrence Krauss Should Have Paid Attention to Vic
It's gratifying to see Vic's contribution to the philosophy of
science recognized. I think it's important to recognize though that
mathematics is not "effective" in weeding out false physics
theories. Intelligence has evolutionary advantage insofar as it is
good at prediction; which is implicitly projection of regularities
into the future. So humans have a built-in tendency to see patterns
- even where they are specious. They can build mathematical
theories which don't have any reference reality, just as they can
invent superstitions about physical events.
Anyway, thanks to Prof Yanofsky.
Brent
On 7/10/2017 8:14 AM, spinozalens via Free Thinkers Physics
Discussion Group wrote:
In Marcus Chown's delightful book " The Never Ending Days of Being
Dead" a whole chapter ( Patterns in the Void) is devoted to Vic's
ideas " Where The Laws Of Physics Comes From" Chown used good
judgement including this chapter in his book. I think that had
Lawrence Krauss been more familiar with Vic's work , he possibly
wouldn't have walked in the minefield he did with his book. "A
Universe From Nothing" In my opinion Vic had a very good answer to
this question. This answer has not received enough attention in the
physics and philosophy communities. Here mathematician Noson S
Yanofky fleshes out these ideas in more detail.
Bob Zannelli
Why Mathematics Works So Well
Noson S. Yanofsky
(Submitted on 28 Jun 2015)
A major question in philosophy of science involves the unreasonable
effectiveness of mathematics in physics. Why should mathematics,
created or discovered, with nothing empirical in mind be so
perfectly suited to describe the laws of the physical universe? We
review the well-known fact that the symmetries of the laws of
physics are their defining properties. We show that there are
similar symmetries of mathematical facts and that these symmetries
are the defining properties of mathematics. By examining the
symmetries of physics and mathematics, we show that the
effectiveness is actually quite reasonable. In essence, we show that
the regularities of physics are a subset of the regularities of
mathematics.
https://arxiv.org/abs/1506.08426
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