Apr 27, 2015 0

## Glorious tables of numbers

At some point, in one of the many universities where I have spent time, I ran across a pile of old books that were being given away to anyone who wanted them. I was attracted (who wouldn’t be?) by the *Table of Circular and Hyperbolic Tangents and Cotangents for Radian Arguments*, which was published in 1943 by the Columbia University Press; mine is the second (1947) printing. It consists of page upon page of digits, row upon row and column upon column of tan(x), cot(x), tanh(x), and coth(x), enumerated to roughly eight significant digits.

This was before the time of calculators and computers, and I really was attracted by the sprawling, rippling, hypnotic lists of numbers. It sits proudly on my bookshelf next to the copy of Gradshteyn and Ryzhik’s *Table of Integrals, Series, and Products* that I bought as an undergrad (and which has actually proven useful to me in my career, since computers are not unmatched along that dimension). But the truly and surprisingly beautiful portion of the book of tables turned out to be the Foreword, written by one H. T. Davis of northwestern university.

I highly recommend clicking on the link above and reading the entire text (don’t miss the “note” at the end!), which is only about two pages. But if you are in a rush (or just need a teaser to spur your interest), here are some highlights:

- …discovery and measurement have gone hand in hand.
- The mathematical functions’ origin in some universal principle has endowed them with a kind of immortality, and hence they appear over and over again in disciplines [including economics!] far removed from the one in which historically they first appeared.
- The figures seen on the printed page may appear dull reading to the uninitiated, but behind them there is a realm that challenges the imagination … usually there is a long story of scientific achievement.
- Even the old table of chords, computed probably by Hipparchus in the second century BC and transmitted to us through Claudius Ptolemy, could be adapted readily to the use of modern students of trigonometry.
- The present volume … adds another pillar to this great monument of science, which, in the words of Horace, “is more enduring than bronze.”

It is marvelous to me to imagine the concentrated time and effort, stretching back continuously over centuries, that fed these and similar tables — and to imagine the many discoveries and adventures that would not have been possible without them.…