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Who said: “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
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Home > Category Index for Science Quotations > Category Index H > Category: Harmonic

Harmonic Quotes (4 quotes)

Endowed with two qualities, which seemed incompatible with each other, a volcanic imagination and a pertinacity of intellect which the most tedious numerical calculations could not daunt, Kepler conjectured that the movements of the celestial bodies must be connected together by simple laws, or, to use his own expression, by harmonic laws. These laws he undertook to discover. A thousand fruitless attempts, errors of calculation inseparable from a colossal undertaking, did not prevent him a single instant from advancing resolutely toward the goal of which he imagined he had obtained a glimpse. Twenty-two years were employed by him in this investigation, and still he was not weary of it! What, in reality, are twenty-two years of labor to him who is about to become the legislator of worlds; who shall inscribe his name in ineffaceable characters upon the frontispiece of an immortal code; who shall be able to exclaim in dithyrambic language, and without incurring the reproach of anyone, “The die is cast; I have written my book; it will be read either in the present age or by posterity, it matters not which; it may well await a reader, since God has waited six thousand years for an interpreter of his words.”
In 'Eulogy on Laplace', in Smithsonian Report for the year 1874 (1875), 131-132.
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For just as musical instruments are brought to perfection of clearness in the sound of their strings by means of bronze plates or horn sounding boards, so the ancients devised methods of increasing the power of the voice in theaters through the application of the science of harmony.
Vitruvius
In Vitruvius Pollio and Morris Hicky Morgan (trans.), 'Book V: Chapter III', Vitruvius, the Ten Books on Architecture (1914), 139. From the original Latin, “Ergo veteres Architecti, naturae vestigia persecuti, indagationibus vocis scandentes theatrorum perfecerunt gradationes: & quaesiuerunt per canonicam mathematicorum,& musicam rationem, ut quaecunq; vox effet in scena, clarior & suauior ad spectatorum perueniret aures. Uti enim organa in aeneis laminis, aut corneis, diesi ad chordarum sonituum claritatem perficiuntur: sic theatrorum, per harmonicen ad augendam vocem, ratiocinationes ab antiquis sunt constitutae.” In De Architectura libri decem (1552), 175.
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It has just occurred to me to ask if you are familiar with Lissajous’ experiments. I know nothing about them except what I found in Flammarion’s great “Astronomie Populaire.” One extraordinary chapter on numbers gives diagrams of the vibrations of harmonics—showing their singular relation to the geometrical designs of crystal-formation;—and the chapter is aptly closed by the Pythagorian quotation: Ἀεὶ ὁ θεὸς ὁ μέγας γεωμετρεῖ—“God geometrizes everywhere.” … I should imagine that the geometry of a fine opera would—were the vibrations outlined in similar fashion—offer a network of designs which for intricate beauty would double discount the arabesque of the Alhambra.
In letter to H.E. Krehbiel (1887), collected in Elizabeth Bisland The Writings of Lafcadio Hearn (1922), Vol. 14, 8.
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Music may be called the sister of painting, for she is dependent upon hearing, the sense which comes second and her harmony is composed of the union of proportional parts sounded simultaneously, rising and falling in one or more harmonic rhythms.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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