# Re: The One

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On 12 Jan 2014, at 15:30, Richard Ruquist wrote:```
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Bruno: Those machines are enumerable. There is an enumeration of all of them: m_0, m_1, m_2, m_3, m_4, ...
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Richard: We are in close agreement if the digital machines are each a Calabi-Yau CY Compact Manifold that can be enumerated.
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Bruno: So, you can fix one universal language, like a base, and identify each machine with a number.
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Richard: Agreed presuming that the base is an m_i and the unique universal language to that machine involves all other machines.
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Bruno: Each programming language, or computers boolean net, correspond to some m_i, and are universal m_i, as they can imitate all others machines (accepting Church thesis).
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Richard: You seem to be identifying each machine with a programming language that has the property of imitating all other enumerated machine.
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Is it sheer coincidence that for more than one string theory consideration, each CY machine relects or perceives (or perhaps it can be said is conscious of) all other machines. So I conjecture that the CY machines satisfy the Church Thesis. Can that be proven or falsified?
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Wow! Pretty difficult question. To prove this you need not just to enumerate the objects, but to define how they compute: what they do when presenting data. What would be a data for a CY machines? Could a CY machines never stop? What would that mean? can you give me a CY which generates the Fibonacci numbers?
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Thanks to a work by Rogers, an enumeration of machine m_i is Turing universal, 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:
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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). 2) Automated Parametrization: all computable functions with n arguments (x, y, z, t, ...) can be transformed into a function of n-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 SMN is a metaprogram: it acts on the indices of the phi_i.
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If you prove "1)" and "2)" for the CY machines, you are done.

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Of course another way to prove that would be to directly construct one universal CY machines, emulating for example one universal Turing machine, or the SK combinators.
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Probably the paper by Schmidhuber on formal strings, that I refer to you some times ago, should help.
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Bruno

http://iridia.ulb.ac.be/~marchal/

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