Quotes About Abstraction

It has been said that geometry is the art of applying good reasoning to bad diagrams.

Generalization can allow us to reduce a problem to something more essential, resulting in an approach that embodies regularity across known examples, a regularity that is crisp, concise, and well grounded. However, too often generalization becomes a work item in itself, pulling in the opposite direction, adding to the complexity rather than reducing it.

The problem with traditional approaches to abstraction and encapsulation is that they aim at complete information hiding. This characteristic anticipates being able to eliminate programming from parts of the software development process, those parts contained within module boundaries. As we've seen, though, the need to program is never eliminated because customization, modification, and maintenance are always required-that is, piecemeal growth.

If you cannot grok the overall structure of a program while taking a shower, e.g., with no external memory aids, you are not ready to code it.

We seem to have this tendency to want to make things simple with formulas-and yet our formulas consistently make them more complex.

Numbers larger than ten are no longer human: they fly from the hand into the imaginary sky we call hypothesis.

The function of generalizations is quite simple. Without generalizations we could not explain anything. Things would occur around us for no reason that we could fathom. We would stand around in a stupor, unable to relate anything to anything else, for a generalization is simply a way to take some set of things (that we don't understand) and compare them with something we do understand by means of some "abstract" words.

Acting per se, like all art, is a process of abstracting, of retaining only significant detail. But in impersonation any detail can be significant.

Ownership is a sophisticated abstraction, a mystical relationship.

These pretty pictures and bright medallions were not money; they were symbols for an idea which spread through these people, all through their world. But things were not money, any more than water shared was growing-closer. Money was an idea, as abstract as an Old-One's thoughts--money was a great structured symbol for balancing and healing and growing closer.

All 'nows' are equal; that is the basic theorem of time travel. They don't disappear; both 'past' and 'future' are mathematical abstractions; the 'now' is always all there is.

If you hypnotized somebody and told him not to use the word "nose," and then asked him to explain the sense of smell, you would get the same kind of drifting linguistic snow banks in his answers. Intellectuals, who have more abstractions stored in their biocomputers, are more skilled at this than most, but all can do it to some extent.

Which would you consider more real — the abstract Architect's floor plan — which shows something nobody ever sees in experience but which all can agree serves a useful function — or the various drawings from individual perspectives, which show the plural realities that people actually see, but which have no practical function?

Of course. Chaos and the Abyss are metaphors, of the special kind that we have called metaphors about metaphors. They attempt to describe what is left when abstractions like the leaf and the average — linguistic reality-tunnels — are dropped from our minds.

For leveling really to come about a phantom must first be provided, its spirit, a monstrous abstraction, an all-encompassing something that is nothing, a mirage -- this phantom is the public . Only a passionless but reflective age can spin this phantom out, with the help of the press when the press itself becomes an abstraction ... [and] the only thing that can keep life going in the prevailing torpor.

The less there is to look at, the more important it is that we look at it closely and carefully. This is critical to abstract art. Small differences make all the difference.

People react primarily to direct experience and not to abstractions; it is very rare to find anyone who can become emotionally involved with an abstraction. The longer the bomb is around without anything happening, the better the job that people do in psychologically denying its existence. It has become as abstract as the fact that we are all going to die someday, which we usually do an excellent job of denying.

One cannot understand... the universality of laws of nature, the relationship of things, without an understanding of mathematics. There is no other way to do it.

Words are a medium that reduces reality to abstraction for transmission to our reason, and in their power to corrode reality inevitably lurks the danger that the words themselves will be corroded too.

The only real flesh was the flesh that existed in his imagination. Since, therefore, he regarded the flesh as an ideal abstraction, rather than as a physical fact, he had relied on his spiritual strength to subjugate it.

Words are a medium that reduces reality to abstraction for transmission to our reason, and in their power to corrode reality inevitably lurks the danger that the words will be corroded too.

Yet how strange a thing is the beauty of music! The brief beauty that the player brings into being transforms a given period of time into pure continuance; it is certain never to be repeated; like the existence of dayflies and other such short-lived creatures, beauty is a perfect abstraction and creation of life itself. Nothing is so similar to life as music.

Mathematics doesn't care about those beyond the numbers.

It is easier to take a position in the abstract than when it hits home.