my philosophy about expressivity
Nov. 21st, 2004 11:10 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
guslI wouldn't want to prove the Jordan Curve Theorem (a visually "obvious", but hard-to-prove theorem).
for the same reason that
a mathematician wouldn't want to *constructively* prove the Fundamental Theorem of Algebra.
(Freek interestingly likes the idea of the first project, but not the second one) (nice thoughts here... he expresses his vision of a natural medium for doing mathematics, analogous to a "Word Processor")
The reason is: for me, there is no reason to bend over backwards, just for the sake of minimality. If we have tools, why not use them?
While it's philosophically interesting to be able to derive everything from a minimal set of axioms, if you're trying to do practical things (whether they be science or phenomenology :-), so perhaps I shouldn't say "practical" ), and as long as you know your math is consistent (and truth-preserving?) it's irrelevant how many axioms you use.
This is analogous to finding the shortest possible way of coding a program, just to get a tight bound on the Kolmogorov Complexity of the problem: the tight bound may be a theoretically nice result, but you end up with an ugly hack: at least from the cognitive point of view, you've made things unintuitive / hard to understand and unwieldy.
This is my philosophy, and I think it's also the TUNES Philosophy.
for the same reason that
a mathematician wouldn't want to *constructively* prove the Fundamental Theorem of Algebra.
(Freek interestingly likes the idea of the first project, but not the second one) (nice thoughts here... he expresses his vision of a natural medium for doing mathematics, analogous to a "Word Processor")
The reason is: for me, there is no reason to bend over backwards, just for the sake of minimality. If we have tools, why not use them?
While it's philosophically interesting to be able to derive everything from a minimal set of axioms, if you're trying to do practical things (whether they be science or phenomenology :-), so perhaps I shouldn't say "practical" ), and as long as you know your math is consistent (and truth-preserving?) it's irrelevant how many axioms you use.
This is analogous to finding the shortest possible way of coding a program, just to get a tight bound on the Kolmogorov Complexity of the problem: the tight bound may be a theoretically nice result, but you end up with an ugly hack: at least from the cognitive point of view, you've made things unintuitive / hard to understand and unwieldy.
This is my philosophy, and I think it's also the TUNES Philosophy.