On 30 Jan 2011, at 07:41, Rex Allen wrote:

On Sat, Jan 29, 2011 at 6:48 AM, Bruno Marchal <marc...@ulb.ac.be> wrote:
Rex,

Well here I disagree (with Wikipedia, not with Turing, although he is
responsible for this widespread misconception).

Well, I'll buy that, I reckon.  Though the usage of the term "infinite
tape" is pretty widespread.  I see it lots of books, when I google
around.

Often they use infinite tape.  Less frequently, infinitely extensible
tape, or potentially infinite tape.

Infinite is usually in the mix somewhere.

Does their (and Turing's) use of the term "infinite tape" reflect an
actual difference of opinion?  Or just imprecise wording on their
part?  Or does it really make no difference, given that it's just an
abstract theoretical concept?


It is a difference of wording. The real theorem is that there is a universal turing machine, and the proof is that there is a 'number', or a finite instruction table, which when some number(s) is on its tape, can interpret it and compute a function, or relation. Likewise the universal dovetailer UD is a number, a finite thing which can be encoded digitally. The deployment itself UD* is an infinite mathematical object (even fractal).

Even just the tiny (Sigma_1 complete) set of arithmetical proposition emulates the universal dovetailer, and generates all the universal numbers and all their dynamical mirroring and self-mirroring qualities. Arithmetical reality does not just contains the description of all that. It contains the emulation of those computations, with computation defined in computer science (a branch of math). This define a consciousness flux which differentiates on all computations occurring below our substitution level, making matter emerging from consciousness, in a theoretical computer science specifiable manner, so that we can make the comparison with nature.

I am just saying to the physicists that physics (and the whole theology) does not depend on the choice of the phi, in the phi_i. The laws of physics are theory independent. The laws of physics don't change for the change of the basic ontological theory. If you don't take this into account, you will miss the qualia, eliminate consciousness, and confuse for sure appearance and reality (all that assuming DM).

Universal machine defines universal person, universal consciousness, etc. Through the arithmetical hypostases, this is made as clear as possible, and the material hypostases defines first person plural universal sharable realities. The math exists to compare this with physics. Up to now, it fits well thanks to the quantum.

In fact MEC + ~solipsism implies directly physical Many Worlds. QM saves MEC from solipsism, but this is not enough to solve the other mind problem, you have to extract ~solipsism from MEC. It is easy to justify the other, with MEC, but less easy how they can interact in a stable way. The comp first person measure problem (the white rabbit problem).

Bruno




The discovery of the universal machine by Turing is the discovery of a finite Turing machine capable of emulating all the other machine from a
number description (a program).

Turing machine are finite object. Their tape plays a role of always finite, but unbounded memory space. You personal computer is a universal (Turing) machine, and then this explains why, regularly, it asks for a supplement of
memory, and the user usually obliged by buying a bigger hard disk.

Universal numbers and universal machine are finite objects. All machine are finite objects. Human universality shows up when humans used walls and papers to process their calculation. Universal entity are typically growing
self-extending entities. They always want more 'memory-space-time'.


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



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