On 12 Jan 2014, at 17:50, Richard Ruquist wrote:

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On Sun, Jan 12, 2014 at 11:32 AM, Bruno Marchal <marc...@ulb.ac.be>wrote:On 12 Jan 2014, at 15:30, Richard Ruquist wrote:Bruno: Those machines are enumerable. There is an enumeration ofall of them: m_0, m_1, m_2, m_3, m_4, ...Richard: We are in close agreement if the digital machines are eacha Calabi-Yau CY Compact Manifold that can be enumerated.Bruno: So, you can fix one universal language, like a base, andidentify each machine with a number.Richard: Agreed presuming that the base is an m_i and the uniqueuniversal language to that machine involves all other machines.Bruno: Each programming language, or computers boolean net,correspond to some m_i, and are universal m_i, as they can imitateall others machines (accepting Church thesis).Richard: You seem to be identifying each machine with a programminglanguage that has the property of imitating all other enumeratedmachine.Is it sheer coincidence that for more than one string theoryconsideration, each CY machine relects or perceives (or perhaps itcan be said is conscious of) all other machines. So I conjecturethat the CY machines satisfy the Church Thesis. Can that be provenor falsified?Wow! Pretty difficult question. To prove this you need not just toenumerate the objects, but to define how they compute: what they dowhen presenting data. What would be a data for a CY machines? Coulda CY machines never stop? What would that mean? can you give me a CYwhich generates the Fibonacci numbers?Thanks to a work by Rogers, an enumeration of machine m_i is Turinguniversal, if each partial computable phi_i is computed by some m_i,and if the list of the corresponding phi_i obeys the two rules:1) Universal machine existence: there is a u such that phi_u(x, y) =phi_x(y) (U emulates x, for all x, on any y).1) seems almost obvious if each machine perceives all others yet hasa unique perception..

`Most m_i are not universal. Only the m_u are, which are those`

`computing the phi_u, capable of emulating all phi_i (as phi_u(i, x) =`

`phi_i(x)).`

`Having a unique perception will define your 1-person, but not your`

`universality. Universality is cheap, and the CY might be universal,`

`but I doubt that this is obvious.`

`In case you insist that it is obvious, just gives me the CY computing`

`the factorial function. Better: give me a program written in LISP`

`emulating the CY computing factorial(5).`

2) Automated Parametrization: all computable functions with narguments (x, y, z, t, ...) can be transformed into a function ofn-1 arguments by some function SMN fixing his argument to some value:phi_i(x, y, z, t, ...) = phi_SMN(x) (y, z, t, ...). Note that SMNis a metaprogram: it acts on the indices of the phi_i.2) I do not understand. No wait. I am getting a glimmer. Letssuppose phi_i(x,y,z,t...) were the laws of physics.

`No phi_i at all computes the physical laws, as the physical laws`

`emerges from all computations (or from our relative ignorance on which`

`computations supports us below our substitution level).`

`SMN just says that there is a program capable of doing the`

`parametrization. For example you give it a program computing the`

`addition x+y, and you give it x = 4, the parametrization program`

`(S21, here) will output the code of a program computing (4 + y).`

S21 (4, "x + y") = "4 + y".

`The SMN just do some substitution, and might eliminate some "read x"`

`in the program given as input.`

Ohh, nevermind (delete). Ref for Rogers, please?

`ROGERS H., 1958, GĂ¶del Numbering of the Partial Recursive Functions,`

`Journal of`

Symbolic Logic, 23, pp. 331-341.

`But it presupposes familiarity with theorems like the SMN theorem, so`

`you might buy the bible of recursion theory, written by the same Rogers:`

`ROGERS H.,1967, Theory of Recursive Functions and Effective`

`Computability, McGraw-`

Hill, 1967. (2ed, MIT Press, Cambridge, Massachusetts 1987). A good introductory book is the one by Cutland:

`CUTLAND N. J., 1980, Computability An introduction to recursive`

`function theory,`

Cambridge University Press.

`Someday I will prove Kleene's second recursion theorem (which is the`

`math of the Dx = "xx" method) by using only the SMN (and the`

`diagonalization).`

Bruno http://iridia.ulb.ac.be/~marchal/ -- 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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.