A Quote by Kim Stanley
Logic was to cognition as geometry was to landscape
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Intuitive cognition of a thing is cognition that enables us to know whether the thing exists or does not exist, in such a way that, if the thing exists, then the intellect immediately judges that it exists and evidently knows that it exists, unless the judgment happens to be impeded through the imperfection of this cognition.
The concept of congruence in Euclidean geometry is not exactly the same as that in non-Euclidean geometry. ..."Congruent" means in Euclidean geometry the same as "determining parallelism," a meaning which it does not have in non-Euclidean geometry.
Analytical geometry has never existed. There are only people who do linear geometry badly, by taking coordinates, and they call this analytical geometry. Out with them!
Metrical geometry is thus a part of descriptive geometry, and descriptive geometry is all geometry.
But though cognition is not an element of mental action, nor even in any real sense of the word an aspect of it, the distinction of cognition and conation has if properly defined a definite value.
The psychoanalytic liberation of memory explodes the rationality of the repressed individual. As cognition gives way to re-cognition, the forbidden images and impulses of childhood begin to tell the truth that reason denies.
If, in a democracy, the cognition of the majority is not much better than the cognition of the sheep, democracy will surely fail.
We are not talking about a new cognition in relation to abstract art, rather a new area of cognition.
The purely formal language of geometry describes adequately the reality of space. We might say, in this sense, that geometry is successful magic. I should like to state a converse: is not all magic, to the extent that it is successful, geometry?
The want of logic annoys. Too much logic bores. Life eludes logic, and everything that logic alone constructs remains artificial and forced.
The world of shapes, lines, curves, and solids is as varied as the world of numbers, and it is only our long-satisfied possession of Euclidean geometry that offers us the impression, or the illusion, that it has, that world, already been encompassed in a manageable intellectual structure. The lineaments of that structure are well known: as in the rest of life, something is given and something is gotten; but the logic behind those lineaments is apt to pass unnoticed, and it is the logic that controls the system.
Over against any cognition, there is an unknown but knowable reality; but over against all possible cognition, there is only the self-contradictory. In short, cognizability (in its widest sense) and being are not merely metaphysically the same, but are synonymous terms.
In fact, Gentlemen, no geometry without arithmetic, no mechanics without geometry... you cannot count upon success, if your mind is not sufficiently exercised on the forms and demonstrations of geometry, on the theories and calculations of arithmetic ... In a word, the theory of proportions is for industrial teaching, what algebra is for the most elevated mathematical teaching.
if we can control the environment in which rapid cognition takes place, then we can control rapid cognition
Whenever humanity seems condemned to heaviness, I think I should fly like Perseus into a different space. I don't mean escaping into dreams or into the irrational. I mean that I have to change my approach, look at the world from a different perspective, with a different logic and with fresh methods of cognition and verification.
Geometry enlightens the intellect and sets one's mind right. All of its proofs are very clear and orderly. It is hardly possible for errors to enter into geometrical reasoning, because it is well arranged and orderly. Thus, the mind that constantly applies itself to geometry is not likely to fall into error. In this convenient way, the person who knows geometry acquires intelligence.
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