52 Abstraction Quotes

Do not imagine that mathematics is hard and crabbed, and repulsive to common sense. It is merely the etherealization of common sense.

The psychological profiling [of a programmer] is mostly the ability to shift levels of abstraction, from low level to high level. To see something in the small and to see something in the large.

Users do not care about what is inside the box, as long as the box does what they need done.

A name indicates what we seek. An address indicates where it is. A route indicates how we get there.

Before abstraction everything is one, but one like chaos; after abstraction everything is united again, but this union is a free binding of autonomous, self-determined beings. Out of a mob a society has developed, chaos has been transformed into a manifold world.

Mark Tobey fills his canvases with elliptical, calligraphic lines, beautiful whirls that seem at first glance to be completely abstract and to come from nowhere at all except his own subjective musing. But I shall never forget how struck I was, on visiting Tobey's studio one day, to see strewn around books on astronomy and photographs of the Milky Way. I knew then that Tobey experiences the movement of the stars and solar constellations as the external pole of his encounter.

For the only way one can speak of nothing is to speak of it as though it were something, just as the only way one can speak of God is to speak of him as though he were a man, which to be sure he was, in a sense, for a time, and as the only way one can speak of man, even our anthropologists have realized that, is to speak of him as though he were a termite.

Government is as unreal, as intangible, as unapproachable as God. Try it, if you don't believe it. Seek through the legislative halls of America and find, if you can, the Government. In the end you will be doomed to confer with the agent, as before.

Abstraction is an exercise in a pre-assured failure. It is a futile attempt to communicate the non-communicable.

Genius is the ability to see things invisible, to manipulate things intangible, to paint things that have no features.

Denotation by means of sounds and markings is a remarkable abstraction. Three letters designate God for me; several lines a million things. How easy becomes the manipulation of the universe here, how evident the concentration of the intellectual world! Language is the dynamics of the spiritual realm. One word of command moves armies; the word Liberty entire nations.

'None of the abstract concepts comes closer to fulfilled utopia than that of eternal peace.'

He tried to recall what he had read about the disease. Figures floated across his memory, and he recalled that some thirty or so great plagues known to history had accounted for nearly a hundred million deaths. But what are a hundred million deaths? When one has served in a war, one hardly knows what a dead man is, after a while. And since a dead man has no substance unless one actually sees him dead, a hundred million corpses broadcast through history are no more than a puff of smoke in the imagination.

Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true ... If our hypothesis is about anything, and not about some one or more particular things, then our deductions constitute mathematics. Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. People who have been puzzled by the beginnings of mathematics will, I hope, find comfort in this definition, and will probably agree that it is accurate.

History, like a vast river, propels logs, vegetation, rafts, and debris; it is full of live and dead things, some destined for resurrection; it mingles many waters and holds in solution invisible substances stolen from distant soils. Anything may become part of it; that is why it can be an image of the continuity of mankind. And it is also why some of its freight turns up again in the social sciences: they were constructed out of the contents of history in the same way as houses in medieval Rome were made out of stones taken from the Coliseum. But the special sciences based on sorted facts cannot be mistaken for rivers flowing in time and full of persons and events. They are systems fashioned with concepts, numbers, and abstract relations. For history, the reward of eluding method is to escape abstraction.

The tendency has always been strong to believe that whatever received a name must be an entity or thing, having an independent existence of its own; and if no real entity answering to the name could be found, men did not for that reason suppose that none existed, but imagined that it was something peculiarly abstruse and mysterious, too high to be an object of sense. The meaning of all general, and especially of all abstract terms, became in this way enveloped in a mystical base...

It was _such_ a relief to program in user mode for a change. Not having to care about the small stuff is wonderful.

Mathematics takes us still further from what is human, into the region of absolute necessity, to which not only the world, but every possible world, must conform.

We may assume the existence of an aether; only we must give up ascribing a definite state of motion to it, i.e. we must by abstraction take from it the last mechanical characteristic which Lorentz had still left it.

There is discontinuity between my former paintings and my cut-outs,only with more absloluteness and more abstraction.

Les mathematiciens n'etudient pas des objets, mais des relations entre les objets; il leur est donc indifferent de remplacer ces objets par d'autres, pourvu que les relations ne changent pas. La matiere ne leur importe pas, la forme seule les interesse.

We are to remember, in the first place, that the arrangement of colours and lines is an art analogous to the composition of music, and entirely independent of the representation of facts. Good colouring does not necessarily convey the image of anything but itself. It consists of certain proportions and arrangements of rays of light, but not in likeness to anything. A few touches of certain greys and purples laid by a master's hand on white paper will be good colouring; as more touches are added beside them, we may find out that they were intended to represent a dove's neck, and we may praise, as the drawing advances, the perfect imitation of the dove's neck. But the good colouring does not consist in that imitation, but in the abstract qualities and relations of the grey and purple.

Well, enough clowning around. Perl is, in intent, a cleaned up and summarized version of that wonderful semi-natural language known as 'Unix'.

Well, that's more-or-less what I was saying, though obviously addition is a little more cosmic than the bitwise operators.

The concrete is a combination of abstractions - not an arbitrary or subjective combination but one that corresponds to the laws of the movement of a given phenomenon.

It must be visible or invisible, Invisible or visible or both: A seeing and unseeing in the eye. The weather and the giant of the weather, Say the weather, the mere weather, the mere air: An abstraction blooded, as a man by thought.

In being more than an exception, part, Though an heroic part, of the commonal. The major abstraction is the commonal, The inanimate, difficult visage.

I more or less dissolved the objects(in my improvisations) so that not all of them could be recognised at once,so that the spiritual overtones could be gradually experienced by the viewer one after the other...and here and there even purely abstract forms came in of their own accord,in other words,that had to have a purely painterly effect.

Gould's argument on reification purports to get at the philosophical foundation of the field. He claims that general intelligence, defined as the factor common to different cognitive abilities, is merely a mathematical abstraction; hence if we consider it a measurable attribute we are reifying it, falsely converting an abstraction into an 'entity' or a 'thing'-variously referred to as 'a hard, quantifiable thing,' 'a quantifiable fundamental particle,' 'a thing in the most direct, material sense.' Here he has dug himself a deep hole.: Indeed, this whole argument is fantastic. The scientist does not measure 'material things': He measures properties (such as length or mass), sometimes of a single 'thing' (however defined), and sometimes of an organized collection of things, such as a machine, a biological organ, or an organism. In a particularly complex collection, the brain, some properties (i.e., specific functions) have been traced to narrowly-localized regions (such as the sensory or motor nuclei connected to particular parts of the body).

The major abstraction is the idea of man And major man is its exponent, abler In the abstract than in his singular, More fecund as principle than particle

The study of mathematics is apt to commence in disappointment... We are told that by its aid the stars are weighed and the billions of molecules in a drop of water are counted. Yet, like the ghost of Hamlet's father, this great science eludes the efforts of our mental weapons to grasp it.

I should like to take the wind and water and sand as a motif and work with them, but it has to be simplified in most cases to colour and force lines, just as music has done with sound.

There's no such thing as abstraction, it is extraction, gravitation and minding your own business.

To the pure geometer the radius of curvature is an incidental characteristic - like the grin of the Cheshire cat. To the physicist it is an indispensable characteristic. It would be going too far to say that to the physicist the cat is merely incidental to the grin. Physics is concerned with interrelatedness such as the interrelatedness of cats and grins. In this case the 'cat without a grin' and the 'grin without a cat' are equally set aside as purely mathematical phantasies.

Science aims at constructing a world which shall be symbolic of the world of commonplace experience. It is not at all necessary that every individual symbol that is used should represent something in common experience or even something explicable in terms of common experience. The man in the street is always making this demand for concrete explanation of the things referred to in science; but of necessity he must be disappointed. It is like our experience in learning to read. That which is written in a book is symbolic of a story in real life. The whole intention of the book is that ultimately a reader will identify some symbol, say BREAD, with one of the conceptions of familiar life. But it is mischievous to attempt such identifications prematurely, before the letters are strung into words and the words into sentences. The symbol A is not the counterpart of anything in familiar life.

The eternal is omniembracing and permeative; and the temporal is linear. This opens up a very high order of generalizations of generalizations. The truth could not be more omni-important, although it is often manifestly operative only as a linear identification of a special-case experience on a specialized subject.

The venerability, reliability, and utility of truth is something which a person demonstrates for himself from the contrast with the liar, whom no one trusts and everyone excludes. As a 'rational' being, he now places his behavior under the control of abstractions. He will no longer tolerate being carried away by sudden impressions, by intuitions.

'It is the transcendent (or 'abstract' or 'self-contained') nature of music that the new so called concretism--Pop Art, eighteen-hour slices-of-reality films, musique concrete--opposes. But instead of bringing art and reality closer together, the new movement merely thins out the distinction.'

Abstract painting is abstract. It confronts you. There was a reviewer a while back who wrote that my pictures didn't have any beginning or any end. He didn't mean it as a compliment, but it was.

Abstract propositions should never be discussed by a legislative body.

I sat reading in these chairs and felt somehow, in an abstract rather than a religious way, that suffering shapes you. Not only my own religious thought, but that of my ancestors, affected me in some way. The thing we have as Jews is that it's a wonderfully abstract religion. Images are not allowed, so it's welcome to abstract thought.

I summed up all systems in a phrase, and all existence in an epigram.

Plato finds it necessary to separate, for example, 'horseness' from 'horse' and say that horseness is real and fixed and true and unmoving, while the horse is a mere, unimportant, transitory phenomenon. Horseness is pure Idea. The horse that one sees is a collection of changing Appearances, a horse that can flux and move around all it wants to and even die on the spot without disturbing horseness, which is the Immortal Principle and can go on forever in the path of the Gods of old.

Metaphysics is a restaurant where they give you a thirty thousand page menu, and no food.