On 18 May 2014, at 17:43, Craig Weinberg wrote:
Free Will Universe Model: Non-computability and its relationship to
the ‘hardware’ of our Universe
I saw his poster presentation at the TSC conference in Tucson and
thought it was pretty impressive. I'm not qualified to comment on
the math, but I don't see any obvious problems with his general
approach:
http://jamestagg.com/2014/04/26/free-will-universe-paper-text-pdf/
Some highlights:
Some Diophantine equations are easily solved
automatically, for example:
∃𝑥, ∃𝑦 𝑥² = 𝑦² , 𝑥 & 𝑦 ∈ ℤ
Any pair of integers will do, and a computer programmed
to step through all the possible solutions will find one
immediately at ‘1,1’. An analytical tool such as Mathematica,
Mathcad or Maple would also immediately give symbolic
solutions to this problem therefore these can be solved
mechanically. But, Hilbert did not ask if ‘some’ equations
could be solved, he asked if there was a general way to solve
any Diophantine equation.
...
Consequence
In 1995 Andrew Wiles – who had been secretly working on
Fermat’s ‘arbitrary equation’ since age eight – announced he
had found a proof. We now had the answers to both of our
questions: Fermat’s last theorem is provable (therefore
obviously decidable) and no algorithm could have found this
proof. This leads to a question; If no algorithm can have
found the proof what thought process did Wiles use to answer
the question: Put another way, Andrew Wiles can not be a
computer.
Also, he is the inventor of the LCD touchscreen, so that gives him
some credibility as well.
http://www.trustedreviews.com/news/i-never-expected-them-to-take-off-says-inventor-of-the-touchscreen-display
You will not convince Andrew Wiles or anyone with argument like that.
1) it is an open question if the use of non elementary means can be
eliminated from Wiles proof. Usually non elementary means are
eliminated after some time in Number theory, and there are conjectures
that this could be a case of general law.
2) machine can use non elementary means in searching proofs too. You
did not provide evidence that they cannot do that. And you could'nt as
a machine like ZF, or ZF + kappa, can prove things with quite non
elementary means.
Bruno
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