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?
all the standard equations of mathematical physics can be separated and solved in Kerr geometry.subrahmanyan chandrasekhar
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.paul dirac
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.paul dirac
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
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
My algebra was relatively poor. I found it very difficult to use equations that substituted numbers — to which I had a synesthetic and emotional response — for letters, to which I had none. It was because of this that I decided not to continue math at Advanced level, but chose to study history, French and German instead.daniel tammet
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
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
The equations at which we arrive must be such that a person of any nation, by substituting the numerical values of the quantities as measured by his own national units, would obtain a true result.james clerk maxwell
Think of Adam and Eve like an imaginary number, like the square root of minus one: you can never see any concrete proof that it exists, but if you include it in your equations, you can calculate all manner of things that couldn’t be imagined without it.philip pullman
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.steven weinberg
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.
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.
"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
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