[FOM] Kieu's work

Piyush P Kurur ppk at imsc.res.in
Thu Mar 11 00:59:14 EST 2004

Dear FOMer's

On Wed, Mar 10, 2004 at 06:31:15PM -0600, Laura Elena Morales Gro. wrote:
> Motivated mainly by the interest of Martin in the 
> subject I decided to go and have a look at it and 
> here is my opinion on Kieu's work.

	I believe that Turing's insistence on the alphabet of Turing
machine being finite is that if alphabet set were infinite and each
element were to be written in a finite region (cell)  then it becomes
impossible (with human eye or a with any instrument with bounded
resolution) to make out the difference between two alphabets of very
similar shape.  Of course the maximum size of the alphabet set depends 
on how good and "eye" one has. Nonetheless it is finite
	Proceeding on this line of argument if one had some instrument
with say some way of "read outs" and if the computation of the 
hyper-computer is to depend on some parameters that are controlled
"looking" at the values shown in such an instrument, one should make the
assumption that the instrument has a "least-count" (one cannot measure
arbitrary small values). Even without appealing to Heisenberg's
uncertainty principle I see this as a big limitation. At least as strong
as the finite alphabet restriction of Turing machines. 


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