Music is the arithmetic of sounds as optics is the geometry of light.
If scientific reasoning were limited to the logical processes of arithmetic, we should not get far in our understanding of the physical world. One might as well attempt to grasp the game of poker entirely by the use of the mathematics of probability. The abacus, with its beads strung on parallel wires, led the Arabs to positional numeration and the concept of zero many centuries before the rest of the world; and it was a useful tool so useful that it still exists.
I do hate sums, There is no greater mistake than to call arithmetic an exact science. There are Permutations and Aberrations discernible to minds entirely noble like mine; subtle variations which ordinary accountants fail to discover; hidden laws of Numbers which it requires a mind like mine to perceive. For instance, if you add a sum from the bottom up, and then again from the top down, the result is always different.
It is noteworthy that modern Platonists , almost without exception, are ignorant of mathematics, in spite of the immense importance that Plato attached to arithmetic and geometry, and the immense influence that they [these studies] had on his philosophy. This is an example of the evils of specialization: a man must not write on Plato unless he has spent so much of his youth on Greek as to have no time for the things that Plato thought important.
It seems probable that the early Greeks were largely indebted to the Phoenicians for their knowledge of practical arithmetic or the art of calculation, and perhaps also learnt from them a few properties of numbers. It may be worthy of note that Pythagoras was a Phoenician; and according to Herodotus , but this is more doubtful, Thales was also of that race.
Legitimized love always despises its easygoing brother Like all women, being very fond of indigestible things Presence of a woman, that sovereign inspiration Spirit of order and arithmetic in the business house Subtleties of expression to describe the most improper things Thin veneer of modesty of every woman Thrill of furious and bestial anger which urges on a mob to massacre .
'I only took the regular course.' 'What was that?' inquired Alice. 'Reeling and Writhing, of course, to begin with, 'the Mock Turtle replied; 'and then the different branches of arithmetic -- Ambition, Distraction, Uglification, and Derision.'Lewis Carroll
The desire to economize time and mental effort in arithmetical computations, and to eliminate human liability to error is probably as old as the science of arithmetic itself.howard h. aiken
The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic. It has engaged the industry and wisdom of ancient and modern geometers to such an extent that it would be superfluous to discuss the problem at length. ...Further, the dignity of the science itself seems to require that every possible means be explored for the solution of a problem so elegant and so celebrated.
Problema, numeros primos a compositis dignoscendi, hosque in factores suos primos resolvendi, ad gravissima ac utilissima totius arithmeticae pertinere, et geometrarum tum veterum tum recentiorum industriam ac sagacitatem occupavisse, tam notum est, ut de hac re copiose loqui superfluum foret. ... [P]raetereaque scientiae dignitas requirere videtur, ut omnia subsidia ad solutionem problematis tam elegantis ac celebris sedulo excolantur.
The whole of arithmetic now appeared within the grasp of mechanism.Charles Babbage
The hardest arithmetic to master is that which enables us to count our blessings.Eric Hoffer
In the metaphor of arithmetic , the dyad reveals itself as the door between the One and the Many, between monad and all other numbers.
We know, and we feel, that the vast business of our redemption, arranged in the councils of the far-back eternity, and acted out amid the wonderings and throbbings of the universe, could not have been that stupendous transaction which gave God glory by giving sinners safety, if the inspired account brought its dimensions within the compass of a human arithmetic, or denned its issues by the lines of a human demarcation.
No man acquires property without acquiring with it a little arithmetic, also.
I hope I may claim in the present work to have made it probable that the laws of arithmetic are analytic judgments and consequently a priori. arithmetic thus becomes simply a development of logic, and every proposition of arithmetic a law of logic, albeit a derivative one. To apply arithmetic in the physical sciences is to bring logic to bear on observed facts; calculation becomes deduction.
If I compare arithmetic with a tree that unfolds upward into a multitude of techniques and theorems while its root drives into the depths, then it seems to me that the impetus of the root.
Some writers maintain arithmetic to be only the only sure guide in political economy; for my part, I see so many detestable systems built upon arithmetical statements, that I am rather inclined to regard that science as the instrument of national calamity.
Unfortunately for Pythagoras, his theorem led at once to the discovery of incommensurables , which appeared to disprove his whole philosophy. So long as no adequate arithmetical theory on incommensurables existed, the method of Euclid was the best that was possible in geometry. When Descartes introduced co-ordinate geometry, thereby again making arithmetic supreme, he [Descartes] assumed the possibility of a solution of the problem of incommensurables, though in his day no such solution had been found.
Mystical doctrines as to the relation of time to eternity are also reinforced by pure mathematics, for the mathematical objects, such as numbers, if real at all, are eternal and not in time. Such eternal objects can be conceived as God's thoughts. Hence Plato's doctrine that God is a geometer, and Sir James Jeans' belief that He is addicted to arithmetic.
The Eudemian Summary says that "Pythagoras changed the study of geometry into the form of a liberal education, for he examined its principles to the bottom, and investigated its theorems in an immaterial and intellectual manner." His geometry was connected closely with his arithmetic. He was especially fond of those geometrical relations which admitted of arithmetical expression.
( Ptolemy ) left in his Optics , the earliest surviving table of angles of refraction from air to water. ...This table, quoted and requoted until modern times, has been admired... A closer glance at it, however, suggests that there was less experimentation involved in it than originally was thought, for the values of the angles of refraction form an arithmetic progression of second order... As in other portions of Greek Science, confidence in mathematics was here greater than that in the evidence of the senses, although the value corresponding to 60° agrees remarkably well with experience.
Music is the arithmetic of sounds as optics is the geometry of light.
"Reeling and Writhing, of course, to begin with," the Mock Turtle replied, "and the different branches of arithmetic, Ambition, Distraction, Uglification, and Derision."Lewis Carroll