Re: LOGO-L> Infinity and like words

[mikedoyle@cix.compulink.co.uk (Mike Doyle)]

In-Reply-To: <m2204koc3d.fsf@chaos.fake>
Lex Wrote:

> > The purpose of representing this constant, which is related to the 
problem 
> > of squaring the circle, is to make use of it in calculations.

> Why is this purpose *the* purpose?

> And actually, you can still even use exact PI for "calculations".  I
> will assume, to be specific, that the "calculations" of interest are
> decimal (or binary) approximations.

All representations within a computer consist of strings of combinations 
of two characters. Because of the nature of the computer it is possible to 
represent binary arithmetic fairly straightforwardly. The word PI is a 
name for the numerical value relating the circumference to the radius of a 
circle. This number cannot be written down using any finite medium. When 
you say that you can represent PI exactly, what you mean is that you can 
place in a computer program a referent for the mental concept of PI. This 
referent can function as an unevaluated place holder in a calculation. 
When, however, evaluation eventually takes place this cannot be done by 
calculating the exact value of PI - the program would not terminate. The 
word PI must become a function that returns a suitable approximation. The 
limit of precision must, somehow, have been determined. 

Hence, the representation of PI within a computer is exactly the same as 
its representation using pencil and paper: a word the meaning of which is 
a mathematical convention and an associated range of approximate values. 
The difference being that the process of producing an appropriate 
approximation may be carried out within a computer without the 
intervention of the mental processes necessary for pencil and paper 
computation.

It follows, I contend, that PI may not be represented exactly in any 
medium other than the mind.

Micheal O Duill

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