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

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?

> 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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