Degenerate Quotes (14 quotes)

After innumerable dynasties of giant creatures, after endless generations of fish and families of molluscs, man finally arrives, the degenerate product of a grandiose type, his mould perhaps broken by his Creator. Fired by his retrospection, these timid humans, born but yesterday, can now leap across chaos, sing an endless hymn, and configure the history of the universe in a sort of retrograde Apocalypse.

An autocratic system of coercion, in my opinion, soon degenerates. For force always attracts men of low morality, and I believe it to be an invariable rule that tyrants of genius are succeeded by scoundrels. For this reason I have always been passionately opposed to systems such as we see in Italy and Russia to-day.

Definition of Mathematics.—It has now become apparent that the traditional field of mathematics in the province of discrete and continuous number can only be separated from the general abstract theory of classes and relations by a wavering and indeterminate line. Of course a discussion as to the mere application of a word easily degenerates into the most fruitless logomachy. It is open to any one to use any word in any sense. But on the assumption that “mathematics” is to denote a science well marked out by its subject matter and its methods from other topics of thought, and that at least it is to include all topics habitually assigned to it, there is now no option but to employ “mathematics” in the general sense of the “science concerned with the logical deduction of consequences from the general premisses of all reasoning.”

Early Greek astronomers, derived their first knowledge from the Egyptians, and these from the Chaldeans, among whom the science was studied, at a very early period. Their knowledge of astronomy, which gave their learned men the name of Magi, wise men, afterwards degenerated into astrology, or the art of consulting the position of the stars to foretel events—and hence sprung the silly occupation of sooth saying, for which the Chaldeans were noted to a proverb, in later ages.

Generality of points of view and of methods, precision and elegance in presentation, have become, since Lagrange, the common property of all who would lay claim to the rank of scientific mathematicians. And, even if this generality leads at times to abstruseness at the expense of intuition and applicability, so that general theorems are formulated which fail to apply to a single special case, if furthermore precision at times degenerates into a studied brevity which makes it more difficult to read an article than it was to write it; if, finally, elegance of form has well-nigh become in our day the criterion of the worth or worthlessness of a proposition,—yet are these conditions of the highest importance to a wholesome development, in that they keep the scientific material within the limits which are necessary both intrinsically and extrinsically if mathematics is not to spend itself in trivialities or smother in profusion.

I have found no better expression than ‘religious’ for confidence in the rational nature of reality, insofar as it is accessible to human reason. Whenever this feeling is absent, science degenerates into uninspired empiricism.

If I were a comet, I should consider the men of our present age a degenerate breed. In former times, the respect for comets was universal and profound.

In degenerating programmes, however, theories are fabricated only in order to accommodate known facts.

Mathematics is distinguished from all other sciences except only ethics, in standing in no need of ethics. Every other science, even logic—logic, especially—is in its early stages in danger of evaporating into airy nothingness, degenerating, as the Germans say, into an anachrioid [?] film, spun from the stuff that dreams are made of. There is no such danger for pure mathematics; for that is precisely what mathematics ought to be.

Order is not sufficient. What is required, is something much more complex. It is order entering upon novelty; so that the massiveness of order does not degenerate into mere repetition; and so that the novelty is always reflected upon a background of system.

Religion now has degenerated and it has turned into a wolf; it has opened its mouth to show his ugly teeth; its spreading fear instead of love; and science has hidden in a corner like a lamb, trembling with fear!

Scientists have long been baffled by the existence of spontaneous order in the universe. The laws of thermodynamics seem to dictate the opposite, that nature should inexorably degenerate toward a state of greater disorder, greater entropy. Yet all around

Study actively. Don’t just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?

The pursuit of pretty formulas and neat theorems can no doubt quickly degenerate into a silly vice, but so can the quest for austere generalities which are so very general indeed that they are incapable of application to any particular.