The reason is not to glorify "bit chasing"; a more fundamental issue is at stake here: Numerical subroutines should deliver results that satisfy simple, useful mathematical laws whenever possible. [...] Without any underlying symmetry properties, the job of proving interesting results becomes extremely unpleasant. The enjoyment of one's tools is an essential ingredient of successful work.
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Vol. II, Seminumerical Algorithms, Section 4.2.2 part A, final paragraph [Italics in source]Donald Knuth
Three principles — the conformability of nature to herself, the applicability of the criterion of simplicity, and the "unreasonable effectiveness" of certain parts of mathematics in describing physical reality — are thus consequences of the underlying law of the elementary particles and their interactions. Those three principles need not be assumed as separate metaphysical postulates. Instead, they are emergent properties of the fundamental laws of physics.
Murray Gell-Mann
Heisenberg now approached the problem from a new philosophical angle. He discarded all models, pictures and parables, and made a clear distinction between sure knowledge we gain from observation of nature and the conjectural knowledge we introduce when we use models, pictures and parables. Sure knowledge... can only be numerical, so that Heisenberg's results were inevitably mathematical in form, and could not disclose anything about the true nature of physical properties or entities.
James Jeans
Those who assert that the mathematical sciences say nothing of the beautiful or the good are in error. For these sciences say and prove a great deal about them; if they do not expressly mention them, but prove attributes which are their results or definitions, it is not true that they tell us nothing about them. The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree.
Aristotle
And in November 2012, the day after the election, when we wake up that morning and all the votes are counted, and they declare not only all of the local election results, the statewide election results, the senatorial results, and when we wake up and they declare the presidential results, and Herman Cain has been elected, we'll be able to say: "Free at last, free at last, thank God almighty this nation is free at last again."
Herman Cain
The material which a scientist actually has at his disposal, his laws, his experimental results, his mathematical techniques, his epistemological prejudices, his attitude towards the absurd consequences of the theories which he accepts, is indeterminate in many ways, ambiguous, and never fully separated from the historical background. This material is always contaminated by principles which he does not know and which, if known, would be extremely hard to test.
Paul Karl Feyerabend
Knuth, Donald
Kobayashi, Makoto (physicist)
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