On Logarithms (1900-1949)

"The invention of logarithms and the calculation of the earlier tables form a very striking episode in the history of exact science, and, with the exception of the Principia of Newton, there is no mathematical work published in the country which has produced such important consequences, or to which so much interest attaches as to Napier's Descriptio." (James W L Glaisher, "Logarithms", Encyclopedia Britannica 9th Ed., 1914)

"The invention of logarithms came on the world as a bolt from the blue. No previous work had led up to it, nothing had foreshadowed it or heralded its arrival. It stands isolated, breaking in upon human thought abruptly without borrowing from the work of other intellects or following known lines of mathematical thought. It reminds me of those islands in the ocean which rise up suddenly from great depths and which stand solitary with deep water close around all their shores. In such cases we may believe that some cataclysm has thrust them up suddenly with earth-rending force. But can it be so with human thought?" (Lord John F Moulton, "The Invention of Logarithms, Its Genesis and Growth", [address in "The Napier Tercentenary"] 1914)

"To summarize - with the ordinary arithmetical scale, fluctuations in large factors are very noticeable, while relatively greater fluctuations in smaller factors are barely apparent. The logarithmic scale permits the graphic representation of changes in every quantity without respect to the magnitude of the quantity itself. At the same time, the logarithmic scale shows the actual value by reference to the numbers in the vertical scale. By indicating both absolute and relative values and changes, the logarithmic scale combines the advantages of both the natural and the percentage scale without the disadvantages of either." (Willard C Brinton, "Graphic Methods for Presenting Facts", 1919)

"With the ordinary scale, fluctuations in large factors are very noticeable, while relatively greater fluctuations in smaller factors are barely apparent. The semi-logarithmic scale permits the graphic representation of changes in every quantity on the same basis, without respect to the magnitude of the quantity itself. At the same time, it shows the actual value by reference to the numbers in the scale column. By indicating both absolute and relative value and changes to one scale, it combines the advantages of both the natural and percentage scale, without the disadvantages of either." (Allan C Haskell, "How to Make and Use Graphic Charts", 1919)

"The definition of e is usually, in imitation of the French models, placed at the very beginning of the great text books of analysis, and entirely unmotivated, whereby the really valuable element is missed, the one which mediates the understanding, namely, an explanation of why precisely this remarkable limit is used as base and why the resulting logarithms are called natural." (Felix Klein, "Elementary Mathematics from an Advanced Standpoint", 1924)

"The piano keyboard is really a rather inaccurate table of logarithms, a fact which I believe is equally ignored in the teaching of mathematics and of music." (John B S Haldane, "Possible Worlds and Other Essays", 1928)

"Mathematics, indeed, is the very example of brevity, whether it be in the shorthand rule of the circle, c = πd, or in that fruitful formula of analysis, e^iπ = -1, - a formula which fuses together four of the most important concepts of the science - the logarithmic base, the transcendental ratio π, and the imaginary and negative units." (David E Smith, "The Poetry of Mathematics", The Mathematics Teacher, 1926)