Logarithm Quotes (9 quotes)

Are the humanistic and scientific approaches different? Scientists can calculate the torsion of a skyscraper at the wing-beat of a bird, or 155 motions of the Moon and 500 smaller ones in addition. They move in academic garb and sing logarithms. They say, The sky is ours, like priests in charge of heaven. We poor humanists cannot even think clearly, or write a sentence without a blunder, commoners of common sense. We never take a step without stumbling; they move solemnly, ever unerringly, never a step back, and carry bell, book, and candle.

Imagine a person with a gift of ridicule [He might say] First that a negative quantity has no logarithm; secondly that a negative quantity has no square root; thirdly that the first non-existent is to the second as the circumference of a circle is to the diameter.

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.
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.
The science of calculation
is indispensable as far as the extraction of the square and cube roots: Algebra as far as the quadratic equation and the use of logarithms are often of value in ordinary cases: but all beyond these is but a luxury; a delicious luxury indeed; but not to be indulged in by one who is to have a profession to follow for his subsistence.

The spectacular thing about Johnny [von Neumann] was not his power as a mathematician, which was great, or his insight and his clarity, but his rapidity; he was very, very fast. And like the modern computer, which no longer bothers to retrieve the logarithm of 11 from its memory (but, instead, computes the logarithm of 11 each time it is needed), Johnny didnt bother to remember things. He computed them. You asked him a question, and if he didnt know the answer, he thought for three seconds and would produce and answer.

Thought-economy is most highly developed in mathematics, that science which has reached the highest formal development, and on which natural science so frequently calls for assistance. Strange as it may seem, the strength of mathematics lies in the avoidance of all unnecessary thoughts, in the utmost economy of thought-operations. The symbols of order, which we call numbers, form already a system of wonderful simplicity and economy. When in the multiplication of a number with several digits we employ the multiplication table and thus make use of previously accomplished results rather than to repeat them each time, when by the use of tables of logarithms we avoid new numerical calculations by replacing them by others long since performed, when we employ determinants instead of carrying through from the beginning the solution of a system of equations, when we decompose new integral expressions into others that are familiar,we see in all this but a faint reflection of the intellectual activity of a Lagrange or Cauchy, who with the keen discernment of a military commander marshalls a whole troop of completed operations in the execution of a new one.

When he had a few moments for diversion, he [Napoleon] not unfrequently employed them over a book of logarithms, in which he always found recreation.

by shortening the labours doubled the life of the astronomer.

*On the benefit of Napiers logarithms.*