If God has made the world a perfect mechanism, He has at least conceded so much to our imperfect intellect that in order to predict little parts of it, we need not solve innumerable differential **equations**, but can use dice with fair success.

"Einstein's Statistical Theories" in

The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to **equations** much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation.

I don't suppose that applies so much to other physicists; I think it’s a peculiarity of myself that I like to play about with **equations**, just looking for beautiful mathematical relations which maybe don’t have any physical meaning at all. Sometimes they do.

Interview with Dr. P. A. M. Dirac by Thomas S. Kuhn at Dirac's home, Cambridge, England, May 7, 1963

In the abstract world of American economists, **equations** run both ways; they believe that by changing the sign of a variable from plus to minus or from minus to plus or the price and quantity of x or y, the direction of historical movement can be reversed.

Chapter Eight, International Finance, p. 336

It is not particularly satisfactory to see **equations** set forth as direct results of observation and experiment, where we used to get long mathematical deductions as apparent proofs of them. Nevertheless, I believe that we cannot, without deceiving ourselves, extract much more from known facts than is asserted in the papers referred to. If we wish to lend more color to the theory, there is nothing to prevent us from supplementing all this and aiding our powers of imagination by concrete representations of the various conceptions as to the nature of electric polarisation, the electric current, etc.

I was appalled to find that the mathematical notation on which I had been raised failed to fill the needs of the courses I was assigned, and I began work on extensions to notation that might serve. In particular, I adopted the matrix algebra used in my thesis work, the systematic use of matrices and higher-dimensional arrays (almost) learned in a course in Tensor Analysis rashly taken in my third year at Queen’s, and (eventually) the notion of Operators in the sense introduced by Heaviside in his treatment of Maxwell’s **equations**.

"Kenneth E. Iverson", autobiographical sketch from an unfinished work (ca. 2004), on his experience at Harvard with "a Masters program in Automatic Data Processing in 1955; in effect, the first computer science program."

The behavior of the economy as a whole, at the aggregate, macro-level, is built up from the individual **equations** at the micro-level.

Part I, Chapter 4, Professional Reservations, p. 79

Baseball players or cricketers do not need to be able to solve explicitly the non-linear differential **equations** which govern the flight of the ball. They just catch it.

Part I, Chapter 5, Mechanistic Modelling, p. 108

Poetry is a sort of inspired mathematics, which gives us **equations**, not for abstract figures, triangles, squares, and the like, but for the human emotions. If one has a mind which inclines to magic rather than science, one will prefer to speak of these **equations** as spells or incantations; it sounds more arcane, mysterious, recondite.

It is clear that the building of models is not a purely mechanical process but requires skill of a high order – not merely mathematical skill but a sensitivity to the relative importance of different factors and a critical, almost an artistic, faculty in the selection of behaviour **equations** which are reasonable, tentative hypotheses in explaining the behaviour of actual economies.

p.16-17 as cited in Andrew Mearman (2011).

I had a hint of this method [of fluxions] from Fermat's way of drawing tangents, and by applying it to abstract **equations**, directly and invertedly, I made it general.

As quoted by Louis Trenchard More,

So far as we know, all the fundamental laws of physics, like Newton’s **equations**, are reversible.

volume I; lecture 46, "Ratchet and Pawl"; section 46-5, "Order and entropy"; p. 46-8

The same **equations** have the same solutions

volume II; lecture 12, "Electrostatic Analogs"; p. 12-1

Any high school boy or girl knows how to calculate the force with which a stone he or she throws will hit someone in the face, but nothing in those **equations** they use will tell them whether or not to throw it…To solve the problem of values we must know what is valuable. Consciousness is the most valuable commodity…To bring values into science, we need to connect science with what is valuable consciousness.

An interview with Ravi Gomatam by Thomas Beardy for

If you have bought one of those T-shirts with Maxwell's **equations** on the front, you may have to worry about its going out of style, but not about its becoming false. We will go on teaching Maxwellian electrodynamics as long as there are scientists.

"The Revolution That Didn't Happen" in

In the abstract world of American economists, **equations** run both ways; they believe that by changing the sign of a variable from plus to minus or from minus to plus or the price and quantity of x or y, the direction of historical movement can be reversed.

The behavior of the economy as a whole, at the aggregate, macro-level, is built up from the individual **equations** at the micro-level.

Baseball players or cricketers do not need to be able to solve explicitly the non-linear differential **equations** which govern the flight of the ball. They just catch it.

The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to **equations** much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation.

"Linear relationships can be captured with a straight line on a graph. Linear relationships are easy to think about....Linear **equations** are solvable... Linear systems have an important modular virtue: you can take them apart, and put them together again the pieces add up."

One of the most frequently mentioned **equations** was Euler 's equation, Respondents called it "the most profound mathematical statement ever written"; "uncanny and sublime"; "filled with cosmic beauty "; and " mind -blowing". Another asked: "What could be more mystical than an imaginary number interacting with real numbers to produce nothing ?" The equation contains nine basic concepts of mathematics once and only once in a single expression. These are: e (the base of natural logarithms); the exponent operation; ?; plus (or minus, depending on how you write it); multiplication; imaginary numbers; equals; one; and zero.

If time is treated in modern physics as a dimension on a par with the dimensions of space, why should we a priori exclude the possibility that we are pulled as well as pushed along its axis? The future has, after all, as much or as little reality as the past, and there is nothing logically inconceivable in introducing, as a working hypothesis, an element of finality, supplementary to the element of causality, into our **equations**. It betrays a great lack of imagination to believe that the concept of "purpose" must necessarily be associated with some anthropomorphic deity.

Arthur Koestler,

Ackoff (1962)... differentiates between iconic models, which use the same materials but involve changes in scale, analogue models which also involve a change in the materials used in building the model, and symbolic models which represent reality by some symbolic system such as a system of mathematical **equations**.

A human being should be able to change a diaper, plan an invasion , butcher a hog, cone a ship, design a building, write a sonnet , balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve **equations**, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly.

I finally understood that the half page of code on the bottom of page 13 of the Lisp 1.5 manual was Lisp in itself. These were “Maxwell’s **equations** of Software!”

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