Posted on 01/07/2002 8:19:37 AM PST by dead
I love this question!
I think math is an invention. I believe this because our math is very "imprecise". For example, the number (or value) psi is 3.14.........
It goes on forever. If our math system was accurate there should be a true, finite, value for the length of a circumference. After all, the circumference exists in merely 2 dimensions, but the best we can do is an approximation.
Likewise, the imaginary number i. This number contradicts fundmental real number characteristics, but is necessary to cover an embarrassing inconsistency, ie the square root of a negative number. It's duct tape applied to a leaky exhaust pipe.
And don't get me started on logrthyms, or natural "e". These numbers, although they work (roughly), bear no resemblance to the elegance manifest in every facet of the natural universe.
I believe this is the reason why no human manufacture will ever be perfect in the way a simple blade of grass is perfect. I also believe that language is another invention that likewise prevents us from approaching perfection.
Perfection will only ever be found in God.
They proved it by voting for clinton twice!Clinton raised my faith in the Word to make me a fundamentalst Christian extremist.
But, that's not the supernaturlist way.
There is no doubt that boy is a life-changing experience.
Though is it? The more deeply we look, the more uncertain things become. The electron orbital position of a constituent proton is precluded by information on its momentum.
So the universe is fundamentally uncertain, though we've yet derived a pretty accurate representational way of describing it.
A hand, or pneumatic hammer may not ultimitely be the best way to drive a nail. But they work.
Actually, I am an engineer, mathematician, and scientist (all three, depending on what hat I'm wearing). Don't confuse engineering and science, which merely USE mathematics with mathematics itself. A lot of the simplifications and empirical equations used in engineering and science are a way of dramatically reducing the computational complexity of a problem (which in many cases would otherwise be intractable) while still delivering adequate results. Mathematics is relatively clean and neat; the application of it in the real world is tempered by practical factors.
But mostly, it seems that your argument is with engineering and science. Math just describes relationships, and not liking the relationships it is used to describe isn't an example of inadequacy. It describes elegant relationships just as easily as it describes inelegant ones (a property which tends to indicate that it is quite adequate indeed).
A computer that crashes faster ?
;>
For those that would protest "science can't be left-wing" I refer y'all to Gross and Levitt's works for instance. Or Sokal's Transgressing the Boundaries.
The conspiracy of ignorance masquerades as common sense.
The vast conspiracy of ignorance masquerades as common sense.
A good test case for this statement (relating to the correspondence between mathematics and the universe) is the N-body problem. Current mathematics has no closed-form solution for it, despite which the N-bodies go blithely on their merry ways.
A basic philosophical question here is whether a true mathematical description of the system should be closed-form. One is tempted to say "yes," though the underlying requirements for the statement would require some very basic proofs which do not as yet exist.
Be that as it may, the present most-accurate mathematical approach is to integrate the equations of motion. Numerical integration is an explicit approximation of the problem to begin with. Beyond that, even an exact integration would be only as accurate as the force models (approximations), and also the truncation of forces being modeled.
Math just describes relationships, and not liking the relationships it is used to describe isn't an example of inadequacy.
This approach tends to treat math as something akin to a "force of nature," whose principles merely await discovery. In that vein, one can imagine a combination of perfect integrators, perfect models, and the inclusion of all perturbations, that would give exact results. However, these all presume perfect knowledge of the system -- not to mention assuming the availability of the mathematics necessary to implement the prediction. It seems quite unlikely that we can ever assemble such knowledge.
Bottom line: whether or not it's ultimately "perfect," mathematics is inadequate, because we are inadequate.
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