"A logarithm is a mapping that allows you to multiply by adding." (George Lakoff & Rafael E Nuñez, "Where Mathematics Come From: How the Embodied Mind Brings Mathematics into Being", 2000)
"As an abstract mathematical function, log maps every positive real number onto a corresponding real number, and maps every product of positive real numbers onto a sum of real numbers. Of course, there can be no table for such a mapping, because it would be infinitely long. But abstractly, such a mapping can be characterized as outlined here. These constraints completely and uniquely determine every possible value of the mapping. But the constraints do not in provide an algorithm for computing such mappings for al1 the real numbers. Approximations to values for real numbers can be made to any degree of accuracy required by doing arithmetic operations on rational numbers." (George Lakoff & Rafael E Nuñez, "Where Mathematics Come From: How the Embodied Mind Brings Mathematics into Being", 2000)
"The mathematics of physics resides in physical phenomena themselves - there are ellipses in the elliptical orbits of the planets, fractals in the fractal shapes of leaves and branches, logarithms in the logarithmic spirals of snails. This means that 'the books of nature is written in mathematics', which implies that the language of mathematics is the language of nature and that only those who lznow mathematics can truly understand nature."
"Information entropy has its own special interpretation and is defined as the degree of unexpectedness in a message. The more unexpected words or phrases, the higher the entropy. It may be calculated with the regular binary logarithm on the number of existing alternatives in a given repertoire. A repertoire of 16 alternatives therefore gives a maximum entropy of 4 bits. Maximum entropy presupposes that all probabilities are equal and independent of each other. Minimum entropy exists when only one possibility is expected to be chosen. When uncertainty, variety or entropy decreases it is thus reasonable to speak of a corresponding increase in information." (Lars Skyttner, "General Systems Theory: Ideas and Applications", 2001)
"If the intensity of the material world is plotted along the horizontal axis, and the response of the human mind is on the vertical, the relation between the two is represented by the logarithmic curve. Could this rule provide a clue to the relationship between the objective measure of information, and our subjective perception of it?" (Hans Christian von Baeyer, "Information, The New Language of Science", 2003)
"The revelation that the graph appears to climb so smoothly, even though the primes themselves are so unpredictable, is one of the most miraculous in mathematics and represents one of the high points in the story of the primes. On the back page of his book of logarithms, Gauss recorded the discovery of his formula for the number of primes up to N in terms of the logarithm function. Yet despite the importance of the discovery, Gauss told no one what he had found. The most the world heard of his revelation were the cryptic words, 'You have no idea how much poetry there is in a table of logarithms.'" (Marcus du Sautoy, "The Music of the Primes", 2003)
"Mathematics is sometimes described as the science which generates eternal notions and concepts for the scientific method: derivatives‚ continuity‚ powers‚ logarithms are examples. The notions of chaos‚ fractals and strange attractors are not yet mathematical notions in that sense‚ because their final definitions are not yet agreed upon." (Heinz-Otto Peitgen et al, "Chaos and Fractals: New Frontiers of Science", 2004)
"In a time of great mathematical ignorance, John Napier made an outstanding contribution through his discovery of the logarithm. Not only did this discovery provide an algorithm that simplified arithmetical computation, but it also presented a transcendental function that has fascinated mathematicians for centuries." (Tucker McElroy, "A to Z of Mathematicians", 2005)
"Use a logarithmic scale when it is important to understand percent change or multiplicative factors. […] Showing data on a logarithmic scale can cure skewness toward large values." (Naomi B Robbins, "Creating More effective Graphs", 2005)
"[…] the symmetry group of the infinite logarithmic spiral is an infinite group, with one element for each real number . Two such transformations compose by adding the corresponding angles, so this group is isomorphic to the real numbers under addition." (Ian Stewart, "Symmetry: A Very Short Introduction", 2013)
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