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From: Albert van der Horst <albert@spenarnc.xs4all.nl>
Subject: Re: are int, float, long, double, side-effects of computer engineering?
Date: 13 Mar 2012 10:40:29 GMT
Message-ID: <m0tkbh.7cb@spenarnc.xs4all.nl>
Lines: 30
Organization: Dutch Forth Workshop
References: <5aaded58-af09-41dc-9afd-56d7b7ced239@d7g2000pbl.googlegroups.com>
Xref: csiph.com comp.lang.lisp:8499 comp.lang.python:21559

In article <5aaded58-af09-41dc-9afd-56d7b7ced239@d7g2000pbl.googlegroups.com>,
Xah Lee  <xahlee@gmail.com> wrote:
<SNIP>
>
>what i meant to point out is that Mathematica deals with numbers at a
>high-level human way. That is, one doesn't think in terms of float,
>long, int, double. These words are never mentioned. Instead, you have
>concepts of machine precision, accuracy. The lang automatically handle
>the translation to hardware, and invoking exact value or infinite
>precision as required or requested.

With e.g. a vanderMonde matrix you can easily make Mathematica fail.
If you don't understand what a condition number is, you can't use
Mathematica. And yes condition numbers are fully in the realm
of concepts of machine precisions and accuracy.

Infinite precision takes infinite time. Approaching infinite precious
may take exponentional time.

>
> Xah

Groetjes Albert

--
-- 
Albert van der Horst, UTRECHT,THE NETHERLANDS
Economic growth -- being exponential -- ultimately falters.
albert@spe&ar&c.xs4all.nl &=n http://home.hccnet.nl/a.w.m.van.der.horst