Operations Quotes - page 11
The Hindus introduced negative numbers... The first known use is Brahmagupta about 628; he also states the rules for the four operations with negative numbers. Bhāskara points out that the square root of a positive number is twofold, positive and negative. He brings up the matter of the square root of a negative number but says that there is no square root because a negative number is not a square. No definitions, axioms, or theorems are given.
The Hindus did not unreservedly accept negative numbers. Even Bhāskara, while giving 50 and -5 as two solutions of a problem, says, "The second value is in this case not to be taken, for it is inadequate; people do not approve of negative solutions."
Morris Kline
The chief innovator of symbolism in algebra was François Viète... an amateur in the sense that his professional life was devoted to the law... John Wallis... says that Viète, in denoting a class of numbers by a letter, followed the custom of lawyers who discussed legal cases by using arbitrary names [for the litigants]... and later the abbreviations... and still more briefly A, B, and C. Actually, letters had been used occasionally by the Greek Diophantus and by the Hindus. However, in these cases letters were confined to designating a fixed unknown number, powers of that number, and some operations. Viète recognized that a more extensive use of letters, and, in particular, the use of letters to denote classes of numbers, would permit the development of a new kind of mathematics; this he called logistica speciosa in distinction from logistica numerosa.
Morris Kline
Cage took it to work in his way of making compositions then; and he used the idea of 64-the number of the hexagrams -to say that you had 64, for example, sounds; then you could cast, by chance, to find which sound first appeared, cast again, to say which sound came second, cast again, so that it's done by, in that sense, chance operations. Instead of finding out what you think should follow-say a particular sound-what did the I Ching suggest? Well, I took this also for dance.
Merce Cunningham
I regard the whole of arithmetic as a necessary, or at least natural, consequence of the simplest arithmetic act, that of counting, and counting itself as nothing else than the successive creation of the infinite series of positive integers in which each individual is defined by the one immediately preceding; the simplest act is the passing from an already-formed individual to the consecutive new one to be formed. The chain of these numbers forms in itself an exceedingly useful instrument for the human mind; it presents an inexhaustible wealth of remarkable laws obtained by the introduction of the four fundamental operations of arithmetic.
Richard Dedekind
The U. S. policy on Iraq, not just from Bill Clinton to Bush to Obama and beyond, has been consistent but that it's been consistent for six decades through eleven presidents. That included covert CIA operations, regime change, support for Saddam Hussein and a merciless policy of targeting the Iraqi civilian population.
Jeremy Scahill
As the war rages on in Afghanistan and-despite spin to the contrary-in Iraq as well, US Special Operations Forces and the Central Intelligence Agency are engaged in parallel, covert, shadow wars that are waged in near total darkness and largely away from effective or meaningful Congressional oversight or journalistic scrutiny. The actions and consequences of these wars is seldom discussed in public or investigated by the Congress. The current US strategy can be summed up as follows: We are trying to kill our way to peace. And the killing fields are growing in number.
Jeremy Scahill
Starting in 1918 at General Motors I found to my surprise] that if I followed the prevailing practice of intercorporate relations I would no longer be able to determine the rate of return on investment for these accessory divisions individually or as a group. This would necessarily mean that I would lose some degree of managerial control over my area of operations. At that time, material within General Motors was passing from one operating division to another at cost, or at cost plus some predetermined percentage. My divisions in the United Motors Corporation had sold both to outside customers and to their allied divisions at the market price. I knew that I operated a profit-making group, and I wished to continue to be able to demonstrate this performance to the general management, rather than to have my operating results on interdivisional business swallowed up in the extra bookkeeping profits of some other division. It was a case of keeping the information clear.
Alfred P. Sloan
Ahmud Shah, without waiting to besiege the Hindoo capital, overran the open country; and wherever he went put to death men, women, and children, without mercy, contrary to the compact made between his uncle and predecessor, Mahomed Shah, and the Rays of Beejanuggur. Whenever the number of slain amounted to twenty thousand, he halted three days, and made a festival celebration of the bloody event. He broke down, also, the idolatrous temples, and destroyed the colleges of the bramins. During these operations, a body of five thousand Hindoos, urged by desperation at the destruction of their religious buildings, and at the insults offered to their deities, united in taking an oath to sacrifice their lives in an attempt to kill the King, as the author of all their sufferings...
Firishta
It is interesting to note that in nearly all the economics courses it is taught that the income tax is the proper instrument for the regulation of the country's economy; that private property is not an inalienable right (in fact, there are no inalienable rights); that the economic ills of the country are traceable to the remnants of free enterprise; that the economy of the nation can be sound only when the government manages prices, controls wages, and regulates operations. This was not taught in the colleges before 1913.
Frank Chodorov
