> On 25 Jun 2018, at 16:05, John Clark <[email protected]> wrote: > > On Sun, Jun 24, 2018 at 5:35 AM, Russell Standish <[email protected] > <mailto:[email protected]>> wrote: > > >> If I define physics as the thing that can tell the difference between a > > correct computation and a incorrect computation and between a corrupted > >memory and a uncorrupted memory, and as long as we're at this philosophic > >meta level that's not a b ad definition, then I don't think anything is > >below physics. > > > If you define physics that way, then you are using the term differently > to Bruno, for whom physics is very definitely phenomenology - tables, chairs, > billiard balls, electrons and such. > > > Phenomenology is about direct experience and consciousness, if that is not > the result of the soul and be beyond the scientific method then it must be > produced by a calculation, and a very big one too. Big calculations are made > of lots of smaller calculations, but how can pure numbers have a working > memory that can remember what the answer to the small calculation is?
You can store a sequence of numbers in one number. For example you can store the sequence 7, 7, 7, 9, 8, 7, 9, 7, 6, 6 in the number x with (unique) prime decomposition: x = (2^7) * (3^7) * (5^7) *(7^9) * (11^8) * (13^7) * (17^9) * (19^7) * (23^6) * (29^6). Then you can define, following Gödel, n GL x (the nth term of the series x of numbers) by n Gl x = the least y such that y =< x & x divides (n Pr x)^y & not x divides (n Pr x)^(y +1) Where (n Pr x )is the nth (magnitude order) prime number dividing x. You can define divides, =<, prime, etc. easily using only the logical symbol and addition and multiplication. To be sure, you would still need to define the exponentiation, and that is a bit more tricky, but Gödel used a famous “Chinese lemma” to that effect. The fundamental theorem of arithmetic (uniqueness of prime decomposition if the prime powers are put in the magnitude order) assures that this can be used to store some result, and retrieve them, in the course of some (arithmetical) computation. An halting computation is coded similarly but a sequence of sequences, and the arithmetical truth assures that those are computations, which is also something provable in very weak theory. The answer of the computation can be obtained by such manipulations, which are themselves encodes (Gödel) or simply identified (Feferman, Franzen) with numbers. > Matter can remember things because an electron in an atom can be in different > orbitals and be in different states and that property can be used to record > information, but pure numbers are unchanging and unchangeable. Matter is also unchanging and unchangeable in the Block-Universe picture. A living amoeba looks like a dividing cylinder (a pant) in that structure. The space-time structure assures that such living object are indeed alive with some usual chemical definition of life (say). With arithmetic, we have a Block-Mindscape picture at the start, but we can recognise the equivalent of “living computation” is the relation that the numbers have with other numbers, like exemplified above. > How can the integer "7" be in a different state? By adding one to it, in some representation. Or by associating with some other number, like with the couple (7, t), that you would again represent by the sequence 7, t, using the method above. > You could claim the correct answer to the big calculation already exists in > Plato's etherial universe so it doesn't need to actually calculate it, but if > so incorrect answers exist in that world too and the are an infinite number > of incorrect answers and only one correct one. Arithmetic indeed implements also the buggy computations, but that is a relative notion. At the bare level of the sigma_1 truth, all computations are correct, like a physical computer getting an incorrect answer due to some bugs, does not violate the physical laws, nor the laws of arithmetic. > Physics simply won't let you do some things so you can use that fact to > arrange matter in such a way that it is incapable of making an incorrect > calculation You can do for a vast range of computations, but not all, and that is similar with what you can do in arithmetic. > and has no alternative but to crank out the correct one. Assuming no bugs, no electricity cut, no typo error, etc. But again, that can is isomorphic to what is possible in arithmetic. > But with pure numbers anything goes Of course not. You cannot decide that some x is a computation, no more than x is a prime number. The physical reality and the arithmetical reality can contain buggy computations, and correct one as well. > and that is not a good thing if you’re looking for one needle in a infinitely > large haystack. > > > The real point is that with computationalism (in particular the CT thesis), > > it doesn't matter what the computers are made of > A computer can be made of any thing but it must be made of some thing. > Yes, but those thing does not need to be physical. > And by "thing" I mean an object with the ability to exist in more than one > state and yet still be recognizable. > Yes, but such object does not need to be physical. > If an atom of silicon absorbs a photon we can tell that something has > happened to it because its electron has moved to a different orbital in a > excited state that is measurably different from its ground state. The atom > has in a sense remembered what has happened to it, and yet the atom has not > changed so much that it is unrecognizable, we can still tell its an atom of > silicon and know that’s where to look to find one bit of information. But > there is nothing comparable to that in the world of pure numbers, the integer > “8” can’t interrogate the integer “7” and measure what state its in and > deduce what happened to it yesterday because nothing can happen to the > integer “7”, it can only be in one state. > > Again, you could say that a physical event is just a point in block-space-time, and argue that it is unchangeable, …, but it is only because we look at it in that way. Similarly with the numbers. 7 can do nothing, but 7 + the laws of addition and multiplication can be part of a computations, which of course will usually involved bigger number, especially if we use Gödel’s coding, where even simple expression like “Ex(x + 2 = 4)” will be coded by a number far bigger than what we can write in the physical universe. But that inefficaciousness is not relevant to prove that the arithmetical (sigma_1) truth implements the universal dovetailer. Bruno > > John K Clark > > > > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected] > <mailto:[email protected]>. > To post to this group, send email to [email protected] > <mailto:[email protected]>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <https://groups.google.com/d/optout>. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
