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 > them. > I have not yet seen a physical definition of computation
How about "a series of causally connected states which process information" >, 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 > thesis. > > 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. >Even the > 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. > > Bruno > > http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
