On Jul 8, 5:53 pm, Bruno Marchal <marc...@ulb.ac.be> wrote:
> On 08 Jul 2011, at 02:35, meekerdb wrote:
> > On 7/7/2011 4:59 PM, Russell Standish wrote:
> >> On Wed, Jul 06, 2011 at 10:12:45PM -0700, meekerdb wrote:
> >>>> One that happens to be incompatible with
> >>>> theory that our minds are computer programs.
> >>> Can you explain that? It seems to be Bruno's central claim, but so
> >>> far as I can see he only tries to prove that a physical reality is
> >>> otiose.
> >>> Brent
> >> Here's my take on it. I guess you read the version I wrote 6 years
> >> ago
> >> in ToN.
> >> Once you allow the existence of a universal dovetailer, we are far
> >> more likely to be running on the dovetailer (which is a simple
> >> program) than on a much more complicated program (such as simulating
> >> the universe as we currently see it). Under COMP, the dovetailer is
> >> capable of generating all possible experiences (which is why it is
> >> universal). Therefore, everything we call physics (electrons, quarks,
> >> electromagnetic fields, etc) is phenomena caused by the running of
> >> the
> >> dovetailer. By Church-Turing thesis, the dovetailer could be running
> >> on anything capable of supporting universal computation. To use
> >> Kantian terminology, what the dovetailer runs on is the noumenon,
> >> unknowable reality, which need have no connection which the
> >> phenomenon
> >> we observe. In fact with the CT-thesis, we cannot even know which
> >> noumenon we're running on, in the case there may be more than one. We
> >> might just as well be running on some demigod's child's playstation,
> >> as running on Platonic arithmetic. It is in principle unknowable,
> >> even
> >> by any putative omniscient God - there is simply no matter of fact
> >> there to know.
> >> So ultimately, this is why Bruno eliminates the concrete dovetailer,
> >> in the manner of Laplace eliminating God "Sire, je n'ai besoin de cet
> >> hypothese".
> >> Anyway, Bruno will no doubt correct any mistaken conceptions here :).
> >> Cheers
> > That's what I thought he said. But I see no reason to suppose a UD
> > is running, much less running without physics. We don't know of any
> > computation that occurs immaterially.
> I'm afraid this is not true. Some people even argue that computation
> does not exist, the physical world only approximate them, according to
> I have not yet seen a physical definition of computation
How about "a series of causally connected states which process
>, except by
> natural phenomenon emulating a mathematical computation. Computer and
> computations have been discovered by mathematicians, and there many
> equivalent definition of the concept, but only if we accept Church
> Now if you accept the idea that the propositions like "if x divides 4
> then x divides 8", or "there is an infinity of twin primes" are true
> or false independently of you, then arithmetical truth makes *all* the
> propositions about all computations true or false independently of
> you. The root of why it is so is Gödel arithmetization of the syntax
> of arithmetic (or Principia). To be a piece of a computation is
> arithmetical, even if intensional (can depend on the *existence* of
> coding, but the coding is entirely arithmetical itself.
> In short, I can prove to you that there is computations in elementary
> arithmetical truth, but you have to speculate on many things to claim
> that there are physical computations. Locally, typing on this
> computer, makes me OK with the idea that the physical reality emulates
> computations, and that makes the white rabbit problems even more
> complex, but then we have not the choice, given the assumption.
> > So I assumed I didn't understand Bruno's argument correctly.
> You seem to have a difficulty to see that elementary arithmetic "run"
> the UD, not in time and space, but in the arithmetical truth.
He should. Truth is not existence.
> tiny Robinson arithmetic proves all the propositions of the form it
> exist i, j, s such that phi_i(j)^s is the s first step of the
> computation of phi_i(j). And RA gives already all the proves, and so
> already define a UD, which works is entirely made true by the
> arithmetical reality, which I hope you can imagine as being not
> dependent of us, the human, nor the alien, nor the Löbian machines
> themselves (RA+ the inductions).
> The arithmetization is not entirely obvious. It uses the Chinese
> theorem on remainders, you need Bezout theorem, and all in all it is
> like implementing a very high level programming languages in a very
> low level "machine language", with very few instructions.
> Matiyasevitch has deeply extended that result, by making it possible
> to construct a creative set (a universal machine) as the set of non
> negative integers of a degree four diophantine equation. This has the
> consequence that you can verify the presence (but not necessarily the
> absence) of *any* state in the UD (like the galactic state described
> above) in less that 100 additions and multiplications. That is weird!
> A degree 4 diophantine polynomial can emulate any arbitrary growing
> functions from N to N, and even from Q to Q. So if you agree that a
> natural numbers is solution or not, of a diophantine polynomial,
> independently of you, then all digital computations are realized, or
> not, independently of you, me, or the physical universe.
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