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Excellent post, I would like to see more of this type of analysis here.
I'll try to keep in a positive spirit and offer a few suggestions.
There are seven basic kinds of information spaces
Lest anyone get bored with having only seven information spaces, there are plenty more to explore. For example, there is Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace and Virtual Reality which describes a four dimensional complex space.
I enjoyed reading Flatterland for an entertaining tour of many geometric spaces.
Or is there some sort of proof that all spaces can be categorized into one of seven types of information spaces?
Technically, computers can't handle irrational spaces at all.
Languages like Macsyma
handle irrational numbers nicely. The MACSYMA program:
which seems like a reasonable way to handle the irrationals.
Update: 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.
End of update
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.
Thanks for the post! It has inspired me to go try out Math::Calc::Units.
It should work perfectly the first time! - toma