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<node id="219826" title="Re: MOPT-01 - assumptions and spaces" created="2002-12-14 00:12:33" updated="2005-07-27 18:00:16">
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toma</author>
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Excellent post, I would like to see more of this
type of analysis here.&lt;P&gt;

I'll try to keep in a positive spirit and offer a few
suggestions.&lt;P&gt;

&lt;I&gt;There are seven basic kinds of information spaces&lt;/I&gt;&lt;P&gt;
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.&lt;P&gt;

I enjoyed reading [isbn://073820675X|Flatterland] for an
entertaining tour of many geometric spaces.&lt;P&gt;

Or is there some sort of proof that all spaces can
be categorized into one of seven types of information 
spaces?&lt;P&gt;

&lt;I&gt;Technically, computers can't handle irrational spaces at all.&lt;/I&gt;&lt;P&gt;

Languages like [http://www.ma.utexas.edu/users/wfs/maxima.html|Macsyma]
handle irrational numbers nicely.  The MACSYMA program:&lt;BR&gt;

&lt;CODE&gt;
integrate(sin(x)*exp(x^2),x)
&lt;/CODE&gt;&lt;BR&gt;

returns

&lt;CODE&gt;
 
                1/4                2 %I x + 1        2 %I x - 1
              %E    SQRT(%PI) (ERF(----------) - ERF(----------))
                                       2                 2
              ---------------------------------------------------
                                       4
&lt;/CODE&gt;&lt;BR&gt;

which seems like a reasonable way to handle the irrationals.&lt;P&gt;

&lt;B&gt;Update:&lt;/B&gt;
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.
&lt;CODE&gt;
integrate(sin(x)*exp(x^2),x,0,1)
&lt;/CODE&gt;&lt;BR&gt;

&lt;CODE&gt;
       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
&lt;/CODE&gt;&lt;BR&gt;
&lt;B&gt;End of update&lt;/B&gt;&lt;P&gt;


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].&lt;P&gt; 

Thanks for the post!  It has inspired me to go try out
[cpan://Math::Calc::Units].&lt;P&gt;

&lt;I&gt;It should work perfectly the first time! - toma&lt;/I&gt;</field>
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218729</field>
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218729</field>
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