Through algebra you easily arrive at equations, but always to pass therefrom to the elegant constructions and demonstrations which usually result by means of the method of porisms is not so easy, nor is one's ingenuity and power of invention so greatly exercised and refined in this analysis.
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.Max Born
What isitthat breathes fire intothe equations and makes a universe for them to describe? Why does the universe go to all the bother of existing?
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.robert gilpin
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.heinrich hertz
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
The behavior of the economy as a whole, at the aggregate, macro-level, is built up from the individual equations at the micro-level.paul ormerod
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.paul ormerod
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.ezra pound
Differential equations won't help you much in the design of aeroplanes — not yet, anyhow.nevil shute
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.kenneth boulding
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.isaac newton
So far as we know, all the fundamental laws of physics, like Newton’s equations, are reversible.richard feynman
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.ravi gomatam
Symmetrical equations are good in their place, but ' vector ' is a useless survival, or offshoot from quaternions, and has never been of the slightest use to any creature.william thomson
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.
The negations of post-structuralism and of certain varieties of deconstruction are precisely as dogmatic, as political as were the positivist equations of archival historicism. The "emptiness of meaning" postulate is no less a priori, no less a case of despotic reductionism than were, say, the axioms of economic and psycho-sociological causality in regard to the generation of meaning in literature and the arts in turn-of-the-century pragmatism and scientism.
The Society for General Systems Theory and its publication General Systems was a mixed bag. Few authors were actually doing research -they philosophized, and many prematurely resolved dilemmas by mathematical equations in a language poorly understood by the empirical investigator.
A human being should be able to change a diaper, plan an invasion, butcher a hog, conn 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, analyse a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects.
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!”alan kay
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!"alan kay