Differential Quotes
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 of semiordered spaces and operations between them enables us to easily develop a complete theory of such functional equations in abstract form.
Leonid Kantorovich
I have endeavoured, in the following treatise, to convey as complete an account of the present state of knowledge on the subject of Differential Equations, as was consistent with the idea of a work intended, primarily, for elementary instruction. It was my object, first of all, to meet the wants of those who had no previous acquaintance with the subject, but I also desired not quite to disappoint others who might seek for more v advanced information. These distinct, but not inconsistent - aims determined the plan of composition.
George Boole
[Attlee] reminded the delegates that it was vital to reduce costs by greater efficiency, which meant that both employers and employed had to seek in every way to attain it. He did not believe in lowering wages as a means of reducing costs, but equally it was necessary to realize that increases of wages that were not matched by increases of production would gravely impair their chances of getting rapidly over their difficulties. Increased demands for money payments, when there was no increase of goods to meet them led straight away to inflation. There was a danger that when a justifiable advance in wages for an under-paid section of the workers had been granted it resulted in demands from those who had enjoyed higher wages to maintain the same differential. This was bad economics and bad social morality. He had been disturbed at the evidence that some people were abusing the social services in such matters as sickness benefit. They could not have them sabotaged by misuse.
Clement Attlee
When [Born and Heisenberg and the Göttingen theoretical physicists] first discovered matrix mechanics they were having, of course, the same kind of trouble that everybody else had in trying to solve problems and to manipulate and to really do things with matrices. So they had gone to Hilbert for help and Hilbert said the only time he had ever had anything to do with matrices was when they came up as a sort of by-product of the eigenvalues of the boundary-value problem of a differential equation. So if you look for the differential equation which has these matrices you can probably do more with that. They had thought it was a goofy idea and that Hilbert didn't know what he was talking about. So he was having a lot of fun pointing out to them that they could have discovered Schrödinger's wave mechanics six month earlier if they had paid a little more attention to him.
Edward Condon
The science of the age, in short, is physical, chemical, physiological; in all shapes mechanical. Our favourite Mathematics, the highly prized exponent of all these other sciences, has also become more and more mechanical. Excellence in what is called its higher departments depends less on natural genius than on acquired expertness in wielding its machinery. Without undervaluing the wonderful results which a Lagrange or Laplace educes by means of it, we may remark, that their calculus, differential and integral, is little else than a more cunningly-constructed arithmetical mill; where the factors, being put in, are, as it were, ground into the true product, under cover, and without other effort on our part than steady turning of the handle. We have more Mathematics than ever; but less Mathesis.
Thomas Carlyle
If heat were the affecting force, direct indications of its presence could be found which would not make use of geometry as an indirect method. ...direct evidence for the presence of heat is based on the fact that it affects different materials in different ways. ...The forces... which we have introduced... have two properties: (a) They affect all materials in the same way. (b) There are no insulating [or isolating] walls. ...the definition of the insulating wall may be added here: it is a covering made of any kind of material which does not act upon the enclosed object with forces having property a. Let us call the forces which have the properties a and b universal forces; all other forces are called differential forces. Then it can be said that differential forces, but not universal forces, are directly demonstrable.
Hans Reichenbach
If a society insists that warfare is the major occupation for the male sex, it is therefore insisting that all male children display bravery and pugnacity. Even if the insistence upon the differential bravery of men and women is not made articulate, the difference in occupation makes this point implicitly. When, however, a society goes further and defines men as brave and women as timorous, when men are forbidden to show fear and women are indulged in the most flagrant display of fear, a more explicit element enters in. Originally two variations of human temperament, a hatred of fear or willingness to display fear, they have been socially translated into inalienable aspects of the personalities of the two sexes. And to that defined sex-personality every child will be educated, if a boy, to suppress fear, if a girl, to show it.
Margaret Mead
In view of the dramatic effects that alternative representations may produce on search and recognition processes, it may seem surprising that the differential effects on inference appear less strong. Inference is largely independent of representation if the information content of the two sets of inference rules [one operating on diagrams and the other operating on verbal statements] is equivalent-i.e. the two sets are isomorphs as they are in our examples.
Herbert Simon
...nor have I found occasion to depart from the plan... the rejection of the whole doctrine of series in the establishment of the fundamental parts both of the Differential and Integral Calculus. The method of Lagrange... had taken deep root in elementary works; it was the sacrifice of the clear and indubitable principle of limits to a phantom, the idea that an algebra without limits was purer than one in which that notion was introduced. But, independently of the idea of limits being absolutely necessary even to the proper conception of a convergent series, it must have been obvious enough to Lagrange himself, that all application of the science to concrete magnitude, even in his own system, required the theory of limits.
Augustus De Morgan
I am sure that a definite limit exists to the degree of equality which is desirable. We do not want complete equality of incomes, since extra responsibility and exceptional talent require and deserve a differential reward. We are not hostile, as our opponents sometimes foolishly suggest, to 'detached residences in Bournemouth where some elderly woman has obviously more than a thousand a year'. I do not myself want to see all private education disappear; nor the Prime Minister denied an official car, as in one Scandinavian country; nor the Queen riding a bicycle; nor the House of Lords instantly abolished; nor the manufacture of Rolls-Royces banned; nor the Brigade of Guards, nor Oxford and Cambridge, nor Boodle's nor (more doubtfully) the Royal Yacht Squadron, nor even, on a rather lower level, the Milroy Room, lose their present distinctive character; nor anything so dull and colourless as this.
Anthony Crosland
Generally speaking, all the authorities exercising individual control function according to a double mode; that of binary division and branding (mad/sane; dangerous/harmless; normal/abnormal); and that of coercive assignment, of differential distribution (who he is; where he must be; how he is to be characterized' how he is to be recognized' how a constant surveillance is to be exercised over him in a individual way, etc.).
Michel Foucault