Posted on 06/26/2007 5:59:25 AM PDT by BGHater
If there was that much dust, it would restrict our view of distant stars, and we’d see the dust’s absorption lines in all the stellar spectra we took.
Well, perhaps. It wouldn't be hard to come up with a more fundamental example to cite for you, say the static relationship between the diameter of a circle and its circumference. This of course is the number we call pi, and it amounts to 3.14 and an infinite number of digits to the right of the decimal. The number is a flaky one indeed, being irrational...yet it's a fundamental trait of a circle, and it's used every day to solve real-world engineering problems like "How much paint will I need to paint this oil tank?"
Indeed, your litany of mathematical disciplines..."numbers, counting, adding, multiplication, functions, calculus, topology, geometry, and so forth"...possibly indeed could have been deduced in a vacuum, but in fact were not. Every single one of them was developed as a means to solve one or more physical-world problems. The first time a neolithic villager sat down to figure out how many buffalo he'd have to kill to get his extended family through the winter, he was using numbers and counting. His answer may have been "A buffalo for all the fingers on this hand plus this and this finger on the other hand," but he was using math to reach a real-world answer...a real-world answer on which his life and the life of his family depended.
Basic math operations were necessary for trade. Advanced math operations (such as the calculus used in analytical geometry) were necessary for serious engineering, allowing the student to find surface areas and volumes for irregular shapes for example, or to invent the parabolic reflector, or to model Boyle's Law in a steam engine as the crank turns. The point being, all of this math is at least partly tied to physical things, the behavior of real objects...and I wouldn't know how to solve the problems they represent without the capability of mathematical analysis.
The numbers can be a discipline unto themselves, it's true. It's also true that they don't have to be. They originally came about as a useful way to talk about real-world stuff. That is the first purpose of numbers.
Amnesty for gravity; it’s been the hardest-working contributer to the world for lo, these many years, now is not the time to mess with tradition.
Dark matter?
Well, mostly. I'm not sure the dichotomy is as clear as you say. For example, Newton had to do a lot of skullwork to come up with a good working description of the motion of planets, and in doing so he happened to invent calculus.
Physical observations presented the conundrum, but the solution was all formulated in Sir Isaac's head. No, the math wasn't done in a vacuum...but neither can the physics be divorced from the math.
Look, I know that there are mathematicians (perhaps even most mathematicians any more) who do their daily work with paper, pencil, theory, and nothing else. My point is that while that is part of the story, it's not all the story. The roots of mathematics are in application.
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