On Sun, Jan 12, 2014 at 11:32 AM, Bruno Marchal <[email protected]> wrote:
> > On 12 Jan 2014, at 15:30, Richard Ruquist wrote: > > Bruno: *Those machines are enumerable. There is an enumeration of all of > them: m_0, m_1, m_2, m_3, m_4, ...* > > Richard: We are in close agreement if the digital machines are each a > Calabi-Yau CY Compact Manifold that can be enumerated. > > Bruno: *So, you can fix one universal language, like a base, and identify > each machine with a number. * > > Richard: Agreed presuming that the base is an m_i and the unique universal > 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 imitate all others machines > (accepting Church thesis).* > > Richard: You seem to be identifying each machine with a programming > language that has the property of imitating all other enumerated machine. > > 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? > > > > > > > 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? > > 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: > > 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 has a unique perception.. > 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. > > 2) I do not understand. No wait. I am getting a glimmer. Lets suppose phi_i(x,y,z,t...) were the laws of physics. Ohh, nevermind (delete). Ref for Rogers, please? > If you prove "1)" and "2)" for the CY machines, you are done. > > 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. > > Probably the paper by Schmidhuber on formal strings, that I refer to you > some times ago, should help. > > 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 [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/groups/opt_out. > -- 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 http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
