note
toma
Excellent post, I would like to see more of this
type of analysis here.<P>
I'll try to keep in a positive spirit and offer a few
suggestions.<P>
<I>There are seven basic kinds of information spaces</I><P>
Lest anyone get bored with having only seven information
spaces, there are plenty more to explore. For example,
there is [http://pup.princeton.edu/titles/6429.html|Quaternions and Rotation Sequences:
A Primer with Applications to Orbits, Aerospace and Virtual Reality]
which describes a four dimensional complex space.<P>
I enjoyed reading [isbn://073820675X|Flatterland] for an
entertaining tour of many geometric spaces.<P>
Or is there some sort of proof that all spaces can
be categorized into one of seven types of information
spaces?<P>
<I>Technically, computers can't handle irrational spaces at all.</I><P>
Languages like [http://www.ma.utexas.edu/users/wfs/maxima.html|Macsyma]
handle irrational numbers nicely. The MACSYMA program:<BR>
<CODE>
integrate(sin(x)*exp(x^2),x)
</CODE><BR>
returns
<CODE>
1/4 2 %I x + 1 2 %I x - 1
%E SQRT(%PI) (ERF(----------) - ERF(----------))
2 2
---------------------------------------------------
4
</CODE><BR>
which seems like a reasonable way to handle the irrationals.<P>
<B>Update:</B>
I forgot about numeric mode in MACSYMA, it does both
numeric and algebraic. As far as algebraic versus
numeric, it's all just LISP as far as I know, which
does both relatively efficiently.
<CODE>
integrate(sin(x)*exp(x^2),x,0,1)
</CODE><BR>
<CODE>
1/4 2 %I + 1 2 %I - 1 1/4 1
%E SQRT(%PI) (ERF(--------) - ERF(--------)) %E SQRT(%PI) ERF(-)
2 2 2
----------------------------------------------- - ----------------------
4 2
</CODE><BR>
<B>End of update</B><P>
It would be useful also to name a few modules that work in
these different spaces, especially the builtin modules
that fill the gaps where there are no appropriate
keywords. For example, date operations are available in [POSIX]
support the interval space, and complex space is
supported in [Math::Complex].<P>
Thanks for the post! It has inspired me to go try out
[cpan://Math::Calc::Units].<P>
<I>It should work perfectly the first time! - toma</I>
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