[ExI] [Extropolis] Gödel and physical reality

[Jason Resch]

On Wed, Nov 3, 2021 at 9:41 AM Giulio Prisco via extropy-chat <
extropy-chat at lists.extropy.org> wrote:

> On Wed, Nov 3, 2021 at 2:05 PM John Clark <johnkclark at gmail.com> wrote:
> >
> > On Wed, Nov 3, 2021 at 6:08 AM Giulio Prisco <giulio at gmail.com> wrote:
> >
> >> > Gödel and physical reality. What are the implications of Gödel's
> >> theorem for fundamental science and metaphysics?
> >
> >
> > For one thing it means that something like Asimov's 3 laws of robotics
> can never be made foolproof; and of course we  don't need Gödel to tell us
> that such laws that attempt to turn something smarter than humans into
> their slaves are ethically compromised.
> >
> >> > What does Gödel’s theorem say about physical reality?
> >
> >
> > Gödel’s theorem may or may not say something about fundamental physics,
> nobody knows, but there's more to physics than just fundamental physics
> just as there's more to chess than just learning what the rules are,
> andGödel’s theorem certainly has something to say about physical reality at
> a higher level. For example, it would be easy to set up a physical system
> such as a Turing Machine in such a way that it will find the first even
> number greater than 2 that is not the sum of 2 prime numbers and then stop,
> but there is no way to predict if that physical system will actually stop
> or not, all you can do is watch it and wait for it to stop, and you might
> be waiting forever.
>

You could, with the appropriate mathematics, find a proof that it will
either stop at some point, or you could find a proof that it will continue
forever. Either proof will allow you to predict its behavior without having
to wait forever. This is an example that makes clear that our physical
theories are a subset of our mathematical theories. Since our mathematical
theories will always be incomplete, so too will our physical theories
remain incomplete. There will always be physical problems that are
insoluble for the given set of mathematical theories (by this I mean
axiomatic systems) we are using.


> >
> >> > Does the nondeterminism found in quantum and chaos physics -
> >> it’s impossible to predict (prove) the future from the present and the
> >> laws of physics - have something to do with Gödel’s incompleteness?
> >
> >
> > According to the book "Conversations With A Mathematician by Gregory
> Chaitin" John Wheeler, Richard Feynman's PhD thesis advisor and the guy who
> invented the term "Black Hole" once asked Kurt Gödel that same question:
> >
> > "One day I was at the Institute For Advanced Study at Princeton and went
> into Gödel’s office and said 'Professor Gödel, what connection do you see
> between your incompleteness theorem in Heisenberg's uncertainty principle?'
> and Gödel got angry and threw me out of his office".
>
> Wheeler tells the story in his own book, and says "Gödel confessed to
> me why he had been unwilling to talk with Kip Thorne, Charlie Misner,
> and me about any possible connection between the undecidability he had
> discovered in the world of logic and the indeterminism that is a
> central feature of modern quantum mechanics. Because, he revealed, he
> did not believe in quantum mechanics. Gödel was a friend of Einstein
> and apparently the two had walked and talked so much that Einstein had
> convinced him to abandon the teachings of Bohr and Heisenberg."
>
>
In retrospect, Einstein's disbelief in God playing dice with the universe
was vindicated by Everett's (objectively) deterministic interpretation,
which showed uncertainty and the unpredictability of wave function collapse
can be seen as a subjective phenomenon is related to an observer's
inherently limited ability to self-locate within the
wavefunction/multiverse.

Jason
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