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.
'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
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.jean-baptiste say
The whole of arithmetic now appeared within the grasp of mechanism.Charles Babbage
No man acquires property without acquiring with it a little arithmetic , also.
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.
Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin. For, as has been pointed out several times, there is no such thing as a random number there are only methods to produce random numbers, and a strict arithmetic procedure of course is not such a method.
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.
A class in arithmetic will be pleased to hear about the Hindoos and their invention of the "Arabic notation;" they will marvel at the thousands of years which elapsed before people had even thought of introducing into the numeral notation that Columbus-egg -- the zero; they will find it astounding that it should have taken so long to invent a notation which they themselves can now learn in a month.
The second [Babylonian] tablet records the magnitude of the illuminated portion of the moon's disc for every day from new to full moon, the whole disc being assumed to consist of 240 parts. ...This table not only exhibits the use of the sexagesimal system but also indicates the acquaintance of the Babylonians with [ geometric and arithmetic ] progressions.
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.
"Music is a hidden arithmetic exercise of the soul, which doesn't know that it is counting."
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 .
"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