“A certain immense aggregate of operations, is subservient to the production of the commodities useful and agreeable to man. It is of the highest importance that this aggregate should be divided into portions, consisting, each, of as small a number of operations as possible, in order that every operation may be the more quickly and perfectly, performed. If each man could, by the more frequent repetition thus occasioned, perform two of these operations, instead of one, and also perform each of them better, the powers of the community, in producing articles useful and agreeable to them, would, upon this supposition, be more than doubled. Not only would they be doubled in quantity, but a great advantage would be gained in point of quality.
This subject has been fully illustrated by Dr. Smith, in the first chapter of the first book of the "Inquiry into the Nature and Causes of the Wealth of Nations," where the extraordinary effect of the division of labour in increasing its productive powers, in the more complicated cases, is displayed in some very remarkable instances. He states that a boy, who has been accustomed to make nothing but nails, can make-upwards of two thousand three hundred in a day; while a common blacksmith, whose operations are nevertheless so much akin to those of the nailer, cannot make above three hundred, and those very bad ones.”

— James Mill

Ch 1 : Production
Elements of Political Economy (1821)

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James Mill 12

Scottish historian, economist, political theorist and philo… 1773–1836

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“Addition is the combination of any arbitrary repetitions of the above-mentioned simplest act into a single act; from it in a similar way arises multiplication. While the performance of these two operations is always possible, that of the inverse operations, subtraction and division, proves to be limited. Whatever the immediate occasion may have been, whatever comparisons or analogies with experience, or intuition, may have led thereto; it is certainly true that just this limitation in performing the indirect operations has in each case been the real motive for a new creative act; thus negative and fractional numbers have been created by the human mind; and in the system of all rational numbers there has been gained an instrument of infinitely greater perfection. This system, which I shall denote by R, possesses first of all a completeness and self-containedness which I have designated… as characteristic of a body of numbers [Zahlkőrper] and which consists in this, that the four fundamental operations are always performable with any two individuals in R, i. e., the result is always an individual of R, the single case of division by the number zero being excepted.”

Richard Dedekind (1831–1916) German mathematician

p, 125
Stetigkeit und irrationale Zahlen (1872)

“An operation is some action one object performs upon another in order to elicit a reaction.”

Grady Booch (1955) American software engineer

Source: Object-oriented design: With Applications, (1991), p. 80

“Civilization advances by extending the number of important operations which we can perform without thinking about them.”

Alfred North Whitehead (1861–1947) English mathematician and philosopher

Source: 1910s, An Introduction to Mathematics (1911), ch. 5. 
Context: It is a profoundly erroneous truism, repeated by all copy-books and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them. Operations of thought are like cavalry charges in a battle — they are strictly limited in number, they require fresh horses, and must only be made at decisive moments.

“A great surgeon performs operations for stone by a single method; later he makes a statistical summary of deaths and recoveries, and he concludes from these statistics that the mortality law for this operation is two out of five. Well, I say that this ratio means literally nothing scientifically and gives us no certainty in performing the next operation; for we do not know whether the next case will be among the recoveries or the deaths. What really should be done, instead of gathering facts empirically, is to study them more accurately, each in its special determinism…. to discover in them the cause of mortal accidents so as to master the cause and avoid the accidents.”

Claude Bernard (1813–1878) French physiologist

Introduction à l'Étude de la Médecine Expérimentale (1865)

“[T]he navy performed its part of the operations.”

David Dixon Porter (1813–1891) United States Navy admiral

Source: 1880s, Incidents and Anecdotes of the Civil War (1885), p. 214

“To every trend there is a counter-trend. There are a number of pendulums operating and each creates new business opportunities.”

Patrick Dixon book Futurewise

Futurewise (1998)

“Labour, upon whichever of those operations it be bestowed, is productive, because it concurs in the creation of a product. Thus the labour of the philosopher, whether experimental or literary, is productive; the labour of the adventurer or master-manufacturer is productive, although he perform no actual manual work; the labour of every operative workman is productive, from the common day-labourer in agriculture, to the pilot that governs the motion of a ship.”

Jean-Baptiste Say (1767–1832) French economist and businessman

Source: A Treatise On Political Economy (Fourth Edition) (1832), Book I, On Production, Chapter VII, p. 85

“The regulative principles of management along scientific lines include four important elements:
(a) Planning of the processes and operations in detail by a special department organized for this purpose.
(b) Functional organization by which each man superintending the workman is responsible for a single line of effort. This is distinctly opposed to the older type of military organization, where every man in the management is given a combination of executive, legislative and judicial functions.
(c) Training the worker so as to require him to do each job in what has been found to be the best method of operation.
(d) Equable payment of the workers based on quantity and quality of output of each individual. This involves scientific analysis of each operation to determine the proper time that should be required for its accomplishment and also high payment for the worker who obtains the object sought.”

Hugo Diemer (1870–1937) American mechanical engineer

(1921, p. 10); Diemer quotes the ASCM committee
Factory organization and administration, 1910

“There are a number of theorems in ordinary algebra, which, though apparently proved to be true only for symbols representing numbers, admit of a much more extended application. Such theorems depend only on the laws of combination to which the symbols are subject, and are therefore true for all symbols, whatever their nature may be, which are subject to the same laws of combination. The laws with which we have here concern are few in number, and may be stated in the following manner. Let a, b represent two operations, u, v two subjects on which they operate, then the laws are
(1) ab(u) = ba (u),
(2) a(u + v) = a (u) + a (v),
(3) am. an. u = am + n. u.
The first of these laws is called the commutative law, and symbols which are subject to it are called commutative symbols. The second law is called distributive, and the symbols subject to it distributive symbols. The third law is not so much a law of combination of the operation denoted by a, but rather of the operation performed on a, which is indicated by the index affixed to a. It may be conveniently called the law of repetition, since the most obvious and important case of it is that in which m and n are integers, and am therefore indicates the repetition m times of the operation a.”

Duncan Gregory (1813–1844) British mathematician

That these are the laws employed in the demonstration of the principal theorems in Algebra, a slight examination of the processes will easily shew ; but they are not confined to symbols of numbers ; they apply also to the symbol used to denote differentiation.
p. 237 http://books.google.com/books?id=8lQ7AQAAIAAJ&pg=PA237; Highlighted section cited in: George Boole " Mr Boole on a General Method in Analysis http://books.google.com/books?pg=PA225-IA15&id=aGwOAAAAIAAJ&hl," Philosophical Transactions, Vol. 134 (1844), p. 225; Other section (partly) cited in: James Gasser (2000) A Boole Anthology: Recent and Classical Studies in the Logic of George Boole,, p. 52
Examples of the processes of the differential and integral calculus, (1841)

“Each day of those early years in pediatric surgery I felt I was on the cutting edge. Some of the surgical problems that landed on the operating table at Children's had not even been named. Many of the operations I performed had never been done before. It was an exuberant feeling, but also a little scary. At times I was troubled by fears that I wasn't doing things the right way, that I would have regrets, or that someone else had performed a certain procedure successfully but had never bothered to write it up for the medical journals, or if they had I couldn't find it.”

C. Everett Koop (1916–2013) American pediatric surgeon and public health administrator

Koop: The Memoirs of America's Family Doctor (1993), p. 127.

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James Mill 12

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