From: Marnen Laibow-Koser <marnen@...>
Date: 2009-11-17T01:19:15+09:00
Subject: Re: Trajectories

Paul Smith wrote:
[...]
> No, I really mean your two points.
> 
> On the one hand, you say "If it gives you the wrong answer, it's a
> bug.  Period.   If your representation cannot give you the precision
> you need for the task at hand, then you need a different
> representation.  Period."
> 
> Then you say "No, becuase [representing irrational numbers is]
> impossible to do with a finite representation AFAIK.  If I'm wrong, I
> would love to know how this can be done."

Interesting question.  I don't think that's a contradiction so much as 
an acknowledgement of the fundamental limitations of digital computing. 
With data structures like BigDecimal and Rational, we can exactly 
represent any rational number we like in a finite amount of storage.

Irrational numbers are different. We could represent them exactly on an 
analog computer such as a slide rule, but there is no general method 
that I am aware of for doing so in a finite amount of digital storage. 
Certain numbers, such as square roots, can be represented with tricks 
like quadratic equations to which they are the root, but that won't work 
for transcendental numbers like e or π.  We can calculate those numbers 
to millions of decimal places if we need to -- but unlike rational 
numbers, we can never store them exactly.

So we do the best we can.  Since rational numbers can be represented 
exactly, it makes sense to do so.  Since (many) irrational numbers 
cannot be represented exactly, we get as close as we can.

> 
>>>>
>> Posted via http://www.ruby-forum.com/.
>>
>>
> 
> 
> 
> --
> Paul Smith
> http://www.nomadicfun.co.uk
> 
> paul@pollyandpaul.co.uk

Best,
--
Marnen Laibow-Koser
http://www.marnen.org
marnen@marnen.org
-- 
Posted via http://www.ruby-forum.com/.