- R. W. Hamming, The unreasonable effectiveness of mathematics
- (e.g.) D.Abbott, The Reasonable Ineffectiveness of Mathematics
However, there is one thing that is really interesting: That the gravitational law is a simple square law. Why is it so that one of the easier observable patterns in this world--namely, how the moon and the planets move; it is at least so easy to observe that to our knowledge, "all people at every time and everywhere have noticed it"--can be described by mathematics which is easy to learn and seems to have been part of the earliest mathematics we know about--there are quadratic equations in very old Egyptian and Babylonian texts--, and which we can teach to all children?
There are other parts of physics that require wildly more complicated mathematics: Maxwell's laws (vector analysis), relativity (matrices), quantum physics (complex operators)--but the areas they apply to ("controlled" electricity, in contrast to things like lightning; speeds near the speed of light; effects on the atomic level) are also very hard to observe.
So, the question is: Why happen easily observable things (falling bodies, circling planets) to have easily describable formulas?
One answer: This is so by extreme cherry-picking. Almost all other easily observable things around us do not at all have simple formulas, or mathematical formulas at all that describe them. It is no wonder it took 2000 years from e.g. Aristoteles's attempts to understand the world conceptually ("scientifically") to Galileo and Kepler, who found the first tiny segments of reality that gave simple answers to the question "how?".
Still: It might have been that there is no such segment at all. Or does there have to be some "required simple and observable part" of the world?
No comments:
Post a Comment