A Quote by Keith Devlin
The increased abstraction in mathematics that took place during the early part of this century was paralleled by a similar trend in the arts. In both cases, the increased level of abstraction demands greater effort on the part of anyone who wants to understand the work.
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To criticize mathematics for its abstraction is to miss the point entirely. Abstraction is what makes mathematics work. If you concentrate too closely on too limited an application of a mathematical idea, you rob the mathematician of his most important tools: analogy, generality, and simplicity. Mathematics is the ultimate in technology transfer.
If the demand for home commodities should be diminished, because of the fall of rent on the part of the landlords, it will be increased in a far greater degree by the increased opulence of the commercial classes.
Increased demands on the members of the Iowa National Guard often means increased time away from home and increased responsibility for those left behind.
I have tried, with little success, to get some of my friends to understand my amazement that the abstraction of integers for counting is both possible and useful. Is it not remarkable that 6 sheep plus 7 sheep makes 13 sheep; that 6 stones plus 7 stones make 13 stones? Is it not a miracle that the universe is so constructed that such a simple abstraction as a number is possible? To me this is one of the strongest examples of the unreasonable effectiveness of mathematics. Indeed, I find it both strange and unexplainable.
In past times when one lived in contact with nature, abstraction was easy; it was done unconsciously. Now in our denaturalized age abstraction becomes an effort.
What does the public want? It wants a vested interest in its own energy provision - driving more efficient behaviour. It wants greater choice and responsibility at a local level. And it wants increased use of renewables to protect the environment.
Man is still by instinct a predatory animal given to devilish aggression. The discoveries of science have immensely increased productivity of material things. They have increased the standards of living and comfort. They have eliminated infinite drudgery. They have increased leisure. But that gives more time for devilment. The work of science has eliminated much disease and suffering. It has increased the length of life. That, together with increase in productivity, has resulted in vastly increased populations. Also it increased the number of people engaged in devilment.
The point of mathematics is that in it we have always got rid of the particular instance, and even of any particular sorts of entities. So that for example, no mathematical truths apply merely to fish, or merely to stones, or merely to colours. So long as you are dealing with pure mathematics, you are in the realm of complete and absolute abstraction. . . . Mathematics is thought moving in the sphere of complete abstraction from any particular instance of what it is talking about.
Yes, there was an element of abstraction and unreality in misfortune. But when an abstraction starts to kill you, you have to get to work on it.
My work has the abstraction underneath it all now & what I deliberately set out to do down here, for this is the perfect realistic abstraction in landscape.
Only since the turn of the century has abstraction again become recognized as an artistic means of representation. It was then that one returned to the recognition of the immense role abstraction plays in the human mind by its power of concentration upon absolute essentials.
The first type of abstraction from objects I shall refer to as simple abstraction, but the second type I shall call reflective abstraction, using this term in a double sense.
Here is a quilted book about mathematical practice, each patch wonderfully prepared. Part invitation to number theory, part autobiography, part sociology of mathematical training, Mathematics without Apologies brings us into contemporary mathematics as a living, active inquiry by real people. Anyone wanting a varied, cultured, and penetrating view of today's mathematics could find no better place to engage.
More and more people are becoming aware that government has nothing to give them without first taking it away from somebody else-or from themselves. Increased handouts to selected groups mean merely increased taxes, or increased deficits and increased inflation.
As was the case for Nobel's own invention of dynamite, the uses that are made of increased knowledge can serve both beneficial and potentially harmful ends. Increased knowledge clearly implies increased responsibility. We reject the notion advocated in some quarters that man should stop eating from the tree of knowledge, as if that were humanly possible.
The subject for which I am asking your attention deals with the foundations of mathematics. To understand the development of the opposing theories existing in this field one must first gain a clear understnding of the concept "science"; for it is as a part of science that mathematics originally took its place in human thought.
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