On Logarithms (1950 - 1999)

"Just as entropy is a measure of disorganization, the information carried by a set of messages is a measure of organization. In fact, it is possible to interpret the information carried by a message as essentially the negative of its entropy, and the negative logarithm of its probability. That is, the more probable the message, the less information it gives. Clichés, for example, are less illuminating than great poems." (Norbert Wiener, "The Human Use of Human Beings", 1950)

"The efforts of computer engineers have already produced a mechanical Briggs (who spent his lifetime computing logarithms) and a mechanical Barlow (whose famous Tables were a life’s work), but no one has ever conceived of a mechanical Napier (for he invented logarithms)." (Bertram V Bowden, "Faster than Thought", 1953)

"In form, the ratio chart differs from the arithmetic chart in that the vertical scale is not divided into equal spaces to represent equal amounts, but is divided logarithmically to represent percentages of gain or loss. On the arithmetic chart equal vertical distances represent equal amounts of change; on the ratio chart equal vertical distances represent equal percentages of change." (Walter E Weld, "How to Chart; Facts from Figures with Graphs", 1959)

So we now have to talk about what we mean by disorder and what we mean by order.[...] Suppose we divide the space into little volume elements. If we have black and white molecules, how many ways could we distribute them among the volume elements so that white is on one side and black is on the other? On the other hand, how many ways could we distribute them with no restriction on which goes where? Clearly, there are many more ways to arrange them in the latter case. We measure 'disorder' by the number of ways that the insides can be arranged, so that from the outside it looks the same. The logarithm of that number of ways is the entropy. The number of ways in the separated case is less, so the entropy is less, or the 'disorder' is less." (Richard P Feynman et al, "Feynman Lectures on Physics" Vol. 1, 1963)

"Since logarithms are clearly part of pure mathematics it may well be surprising to learn that they have been until now the subject of an embarrassing controversy in which whatever side is taken contradictions appear that seem completely impossible to resolve. Meanwhile if truth is to be universal there can be no doubt that these contradictions, [...], however unresolved they seem can only be apparent. [...] I will bring out fully all the contradictions involved so that it may be seen how difficult it is to discover truth and to guard against inconsistency even when two great men are working on the problem." (Morris Kline, "Mathematical Thought from Ancient to Modern Times", 1972)

"Logging skewed variables also helps to reveal the patterns in the data. […] the rescaling of the variables by taking logarithms reduces the nonlinearity in the relationship and removes much of the clutter resulting from the skewed distributions on both variables; in short, the transformation helps clarify the relationship between the two variables. It also […] leads to a theoretically meaningful regression coefficient." (Edward R Tufte, "Data Analysis for Politics and Policy", 1974)

"It is common for positive data to be skewed to the right: some values bunch together at the low end of the scale and others trail off to the high end with increasing gaps between the values as they get higher. Such data can cause severe resolution problems on graphs, and the common remedy is to take logarithms. Indeed, it is the frequent success of this remedy that partly accounts for the large use of logarithms in graphical data display." (William S Cleveland, "The Elements of Graphing Data", 1985) 

"The logarithm is one of many transformations that we can apply to univariate measurements. The square root is another. Transformation is a critical tool for visualization or for any other mode of data analysis because it can substantially simplify the structure of a set of data. For example, transformation can remove skewness toward large values, and it can remove monotone increasing spread. And often, it is the logarithm that achieves this removal." (William S Cleveland, "Visualizing Data", 1993)

"Great inventions generally fall into one of two categories: some are the product of a single person's creative mind, descending on the world suddenly like a bolt out of the blue; others - by far the larger group - are the end product of a long evolution of ideas that have fermented in many minds over decades, if not centuries. The invention of logarithms belongs to the first group, that of the calculus to the second." (Eli Maor, "e: The Story of a Number", 1994)

"If you want to show the growth of numbers which tend to grow by percentages, plot them on a logarithmic vertical scale. When plotted against a logarithmic vertical axis, equal percentage changes take up equal distances on the vertical axis. Thus, a constant annual percentage rate of change will plot as a straight line. The vertical scale on a logarithmic chart does not start at zero, as it shows the ratio of values (in this case, land values), and dividing by zero is impossible." (Herbert F Spirer et al, "Misused Statistics" 2nd Ed, 1998)