31 January 2021

On Manifold VI (Trivia III)

"In her manifold opportunities Nature has thus helped man to polish the mirror of [man’s] mind, and the pro￾cess continues. Nature still supplies us with abundance of brain-stretching theoretical puzzles and we eagerly tackle them; there are more worlds to conquer and we do not let the sword sleep in our hand; but how does it stand with feeling? Nature is beautiful, gladdening, awesome, mysterious, wonderful, as ever, but do we feel it as our forefathers did?" (J Arthur Thomson, "The System of Animate Nature" Vol. 1, 1920)

"The mystery that clings to numbers, the magic of numbers, may spring from this very fact, that the intellect, in the form of the number series, creates an infinite manifold of well distinguishable individuals. Even we enlightened scientists can still feel it e.g. in the impenetrable law of the distribution of prime numbers." (Hermann Weyl, "Philosophy of Mathematics and Natural Science", 1927)

"To the grand primary impression of the world power, the immensities, the pervading order, and the universal flux, with which the man of feeling has been nurtured from the old, modern science has added thrilling impressions of manifoldedness, intricacy, uniformity, inter-relatedness, and evolution. Science widens and clears the emotional window. There are great vistas to which science alone can lead, and they make for elevation of mind." (J Arthur Thomson, "The Outline of Science" Vol. 4, 1937)

"The scientist takes off from the manifold observations of predecessors, and shows his intelligence, if any, by his ability to discriminate between the important and the negligible, by selecting here and there the significant stepping-stones that will lead across the difficulties to new understanding. The one who places the last stone and steps across the terra firma of accomplished discovery gets all the credit. Only the initiated know and honor those whose patient integrity and devotion to exact observation have made the last step possible." (Hans Zinsser, As I Remember Him: The Biography of R.S., 1940)

"Although it is true that it is the goal of science to discover rules which permit the association and foretelling of facts, this is not its only aim. It also seeks to reduce the connections discovered to the smallest possible number of mutually independent conceptual elements. It is in this striving after the rational unification of the manifold that it encounters its greatest successes, even though it is precisely this attempt which causes it to run the greatest risk of falling a prey to illusion. But whoever has undergone the intense experience of successful advances made in this domain, is moved by profound reverence for the rationality made manifest in existence." (Albert Einstein, "Ideas and Opinions", 1954)

"There is a fact, or if you wish, a law governing all natural phenomena that are known to date. There is no known exception to this law - it is exact as far as we know. The law is called the conservation of energy. It states that there is a certain quantity, which we call energy, that does not change in the manifold changes which nature undergoes. That is a most abstract idea, because it is a mathematical principle; it says that there is a numerical quantity which does not change when something happens." (Richard P Feynman et al, "The Feynman Lectures on Physics" Vol. 1, 1983)

"My aim is to show that the heavenly machine is not a kind of divine, live being, but a kind of clockwork, insofar as nearly all the manifold motions are caused by a most simple, magnetic, and material force, just as all motions of the clock are caused by a simple weight. And I also show how these physical causes are to be given numerical and geometrical expression." (Johannes Kepler)

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