Re: Cantorian pseudomathematics

In article <MPG.1e2ee410e55128dc98a961@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow <aeo6@xxxxxxxxxxx> wrote:

> david petry said:
> >
> >



> > Mathematics is not only a tool we use to create models of the real
> > world, but is itself the study of a part of the real world - the
> > world of computation. As a conceptual aid, we can think of the
> > computer as being analogous to both a microscope and a test tube:
> > it helps us peer deeply into the world of computation, and it gives
> > us a way to perform experiments within that world of computation -
> > it gives us a way to interact with the world of computation - and
> > hence, this world of computation has the essential characteristics
> > of being "real". (We use the computer as a conceptual aid to drive
> > home the fact that the world of computation is not merely something
> > that lives in our imaginations) Then "real" mathematics is the
> > science which studies the phenomena observed in that world of
> > computation, and "real" mathematical statements are meaningful if
> > and only if they make testable predictions about the results of
> > computational experiments. All of the mathematics which is
> > scientifically applicable fits within this paradigm.

But one can find suddenly that the mathematics despised by those for
whom application is the only justification has suddenly become
applicable.

A fairly recent instance of this is the application of number theory to
the security of electronic transmission of information.

>
> To some extent, this is true. Computers are math machines. However,
> modern computers are all based on a similar underlying computational
> structure, strings of binary digits.

Finite strings of binary digits. and in all machines to date, the
strings have a fixed word size, usually of some fixed power of 2.

> Some areas of mathemtics seem to
> be less accessible than others in this context. For instance, I am
> trying to figure out the most efficient way to calculate any
> arbitrary binary fractional power of 2, in order to implement my
> H-riffic numbers, and there doesn't seem to be any good way, so far
> as I can tell.

Attempts to deal with the the unending with a finite machines is to
likely to produce much of any use.
.

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