“In my essay I refuted the Hayek-Robbins argument by showing how a market mechanism could be established in a socialist economy which would lead to the solution of the simultaneous equations by means of an empirical procedure of trial and error. […] Were I to rewrite my essay today my task would be much simpler. My answer to Hayek and Robbins would be: so what’s the trouble?
Let us put the simultaneous equations on an electronic computer and we shall obtain the solution in less than a second. The market process with its cumbersome tatonnements appears old-fashioned. Indeed, it may be considered as a computing device of the preelectronic age.”

"The computer and the market" (1967)

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Oskar R. Lange3

Polish economist 1904–1965

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“The total number of multiplications involved in the practical solution of our problem exceeds 450,000. This task alone would mean a two-year job, at 120 multiplications per hour. Fortunately, the recent invention of the Simultaneous Calculator by Professor Wilbur of the Massachusetts Institute of Technology has made it possible to perform all the necessary computations in a small fraction of the time they otherwise would have required. This apparatus solves nearly automatically a system of nine simultaneous linear equations.”

Wassily Leontief (1906–1999) Russian economist

Source: Structure of American economy, 1919-1929, 1941, p. 74.

“It may be in some measure due to the defects of notation in his time that Diophantos will have in his solutions no numbers whatever except rational numbers, in [the non-numbers of] which, in addition to surds and imaginary quantities, he includes negative quantities. …Such equations then as lead to surd, imaginary, or negative roots he regards as useless for his purpose: the solution is in these cases ὰδοπος, impossible. So we find him describing the equation 4=4x+20 as ᾰτοπος because it would give x=-4. Diophantos makes it throughout his object to obtain solutions in rational numbers, and we find him frequently giving, as a preliminary, conditions which must be satisfied, which are the conditions of a result rational in Diophantos' sense. In the great majority of cases when Diophantos arrives in the course of a solution at an equation which would give an irrational result he retraces his steps and finds out how his equation has arisen, and how he may by altering the previous work substitute for it another which shall give a rational result. This gives rise, in general, to a subsidiary problem the solution of which ensures a rational result for the problem itself. Though, however, Diophantos has no notation for a surd, and does not admit surd results, it is scarcely true to say that he makes no use of quadratic equations which lead to such results. Thus, for example, in v. 33 he solves such an equation so far as to be able to see to what integers the solution would approximate most nearly.”

Thomas Little Heath (1861–1940) British civil servant and academic

Diophantos of Alexandria: A Study in the History of Greek Algebra (1885)

“Hayek’s essential gist in capital theory was that capital is heterogeneous, that it cannot be put to many uses simultaneously or at different times. If these empirical assumptions as to capital’s heterogeneity are false, then his theoretical system of economic activity falls. Hayek never established that changes in interest rates primarily and predominantly influence capital production of goods of higher order and their prices.”

Alan O. Ebenstein (1959) American political scientist, educator and author

Hayek's Journey: The Mind of Friedrich Hayek (2003)

“L. Walras first formulated the state of the economic system at any point of time as the solution of a system of simultaneous equations representing the demand for goods by consumers, the supply of goods by producers and the equilibrium condition that supply equal demand on every market.”

Gérard Debreu (1921–2004) French economist and mathematician

Arrow, Kenneth J., and Gerard Debreu. " Existence of an equilibrium for a competitive economy http://cowles.econ.yale.edu/P/cp/p00b/p0087.pdf." Econometrica: Journal of the Econometric Society (1954): p. 265

Kenneth Arrow (1921–2017) American economist

Source: 1950s-1960s, "Existence of an equilibrium for a competitive economy." 1954, p. 265

“Someone told me that each equation I included in the book would halve the sales. I therefore resolved not to have any equations at all. In the end, however, I did put in one equation, Einstein's famous equation, E = mc^2. I hope that this will not scare off half of my potential readers.”

Stephen Hawking book A Brief History of Time

A Brief History of Time (1988)

“I would be dishonest if I did not state quite clearly that the proposals which were put to us in Pretoria do not represent what in our view would be the best solution to Rhodesia's problems.”

Ian Smith (1919–2007) Prime Minister of Rhodesia

Michael Knipe, "Mr Smith agrees to majority rule coming within two years", The Times, September 25, 1976, p. 1.
Statement (September 24, 1976) on negotiations in South Africa which proposed a phased transition to majority rule.

“The method of successive approximations is often applied to proving existence of solutions to various classes of functional equations; moreover, the proof of convergence of these approximations leans on the fact that the equation under study may be majorised by another equation of a simple kind. Similar proofs may be encountered in the theory of infinitely many simultaneous linear equations and in the theory of integral and differential equations. Consideration ofjkbni semiordered spaces and operations between them enables us to easily develop a complete theory of such functional equations in abstract form.”

Leonid Kantorovich (1912–1986) Russian mathematician

"On one class of functional equations" (1936), as cited in: O'Connor, John J.; Robertson, Edmund F., " Leonid Kantorovich http://www-history.mcs.st-andrews.ac.uk/Biographies/Kantorovich.html", MacTutor History of Mathematics archive, University of St Andrews

“If I were asked to answer the following question: What is slavery? and I should answer in one word, It is murder, my meaning would be understood at once. No extended argument would be required to show that the power to take from a man his thought, his will, his personality, is a power of life and death; and that to enslave a man is to kill him. Why, then, to this other question: What is property! may I not likewise answer, It is robbery, without the certainty of being misunderstood; the second proposition being no other than a transformation of the first?”

Pierre Joseph Proudhon (1809–1865) French politician, mutualist philosopher, economist, and socialist

Source: What is Property? (1840), Ch. I: "Method Pursued in this Work. The Idea of a Revolution"
Context: If I were asked to answer the following question: What is slavery? and I should answer in one word, It is murder, my meaning would be understood at once. No extended argument would be required to show that the power to take from a man his thought, his will, his personality, is a power of life and death; and that to enslave a man is to kill him. Why, then, to this other question: What is property! may I not likewise answer, It is robbery, without the certainty of being misunderstood; the second proposition being no other than a transformation of the first?
I undertake to discuss the vital principle of our government and our institutions, property: I am in my right. I may be mistaken in the conclusion which shall result from my investigations: I am in my right. I think best to place the last thought of my book first: still am I in my right.

“I'd written personal essays before, but never on this scale -- never so often and with such, er, honesty. (If by honesty I mean slashing my wrists and hemorrhaging all over the computer screen).”

Ayelet Waldman (1964) American- Israeli writer

Blog post http://bad-mother.blogspot.com/2005/02/end.html<br>Regarding blogging

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Oskar R. Lange3

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