| The Constants of Nature (2008) | |||||||||||||
Abstract | |||||||||||||
| Consider the two constants G and G. The first G arises frequently when we manipulate special functions. We represent this G by dozens of series and integrals, we study its continued fraction expansion, and we calculate millions of its digits. Any mathematician who sees its definition knows that it is an interesting number. This first G, Catalan’s constant, is an exemplar of the mathematical constant: we are not surprised to see it appear in disparate problems in combinatorics and analysis, but we do not expect to ever learn that it has anything to do with the price of tea in China. How different it is from the second constant G. This second G is, for now, of little interest to the mathematician. We do not ask whether it is irrational. We do not, in fact, give it a second thought. This G, Newton’s gravitational constant, is an exemplar of the constant of nature, and it has everything to do with the price of tea in China. The contrast between the constants of mathematics and the constants of nature brings to Brian E. Blank is professor of mathematics at Washington | |||||||||||||
Publication details | |||||||||||||
| |||||||||||||