Painting - Logarithms

This painting illustrates two different kinds of mathematical progressions, the geometric (on the top) and the arithmetic (on the bottom). Going across the top from left to right each section is twice as wide as the previous one, as in a geometric progression. Going across the bottom from right to left, each section is 1 unit wider than the previous one, as in an arithmetic progression.

If the width of the top sections, considered going from left to right, represents the numbers a, 2a, 4a, and 8a in a geometric progression, then the width of the bottom sections, going right to left, can represent logarithms of these numbers, b = log a, 2b =2 log a, 3b = 3 log a, and 4b =4 log a. Crockett Johnson may have sought to illustrate an account of logarithms given in an article by H. W. Turnbull in Newman's Men of Mathematics. This painting does not represent the traditional divisions of either a slide rule or a ruler.

The Scottish nobleman John Napier published his discovery of logarithms in 1614. The painting suggests how logarithms allow one to reduce multiplication (as in the terms of a geometric progression) to addition (as in the terms of an arithmetic progression). As addition is far simpler than multiplication, logarithms were widely used by people carrying out calculations from the seventeenth century onward.

The painting is #37 in the series. It is in oil or acrylic on masonite, and is signed: CJ66. There is a gray wooden frame.

Reference: H. W. Turnbull, “The Great Mathematicians,” in James R. Newman, The World of Mathematics, (1956), p. 124. This volume was in Crockett Johnson's library, but the figure is not annotated.

Currently not on view