[FOM] computing over the reals

William Tait wwtx at earthlink.net
Mon Feb 20 10:30:58 EST 2006

It is a nice paper.

I have difficulty locating the notion of computation behind the Blum  
et al model. Blum lectured on it at U of Chicago a few years ago and  
spoke as though there were two ideas of computation, one starting  
with the *assumption* of discreteness and the other with continuity.  
But Turing's analysis didn't *start* with the assumption of  
discreteness. As I understand him, he began simply with the aim of  
analyzing the notion of (human) mechanical computation, and  
discreteness was a result of his analysis. (As I recall, he derived  
it from the requirement that states be readable.)


Bill Tait

On Feb 20, 2006, at 8:58 AM, John Baldwin wrote:

> The lead article in the March 2006 AMS notices is entitled:  
> Computing over
> the reals: Foundations for Scientific Computing.
> Mark Braverman and Steve Cook begin with an illuminating discussion  
> of the
> difference between the algebraic model (e.g. Blum, Shub, and Smale)  
> and
> the bit model of computing over the reals. They continue with a more
> detailed exposition of the bit model.

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