Quaternion Quotes
A curated collection of the best quotes about Quaternion.
Top Quotes
“Mathematics”
“History of mathematics”
“William Rowan Hamilton”
“Wikipedia: Quaternion”
“The next grand extensions of mathematical physics will, in all likelihood, be furnished by quaternions.”
“'(2). But the question arises, what special connexion has the number Four with mathematics generally, or with that branch of mathematical science in particular, to which the "Lectures on Quaternions" relate?”
“Here as he walked by,
on the 16th of October 1843
Sir William Rowan Hamilton
in a flash of genius discovered
the fundamental formula for
quaternion multiplication
& cut it on a stone of this bridge.”
“I have not been exclusively occupied by my Quaternions, but confess that they have been growing in interest upon me, and that I more and more believe they will one day justify a hope which I ventured to express... that they will constitute nothing less than "a new algebraical geometry."”
“While translations are well animated by using vectors, rotation animation can be improved by using the progenitor of vectors, quaternions. ...By an odd quirk of mathematics, only systems of two, four, or eight components will multiply as Hamilton desired; triples had been his stumbling block.”
“Frobenius' Theorem. Over the real number field there exist precisely three associative division algebras, namely the real numbers, the complex numbers, and the real quaternions.”
“[O]f possible quadruple algebras the one... by far the most beautiful and remarkable was practically identical with quaternions, and... it [is] most interesting that a calculus which so strongly appealed to the human mind by its intrinsic beauty and symmetry should prove to be especially adapted to the study of natural phenomena. The mind of man and that of Nature’s God must work in the same channels.”
“'(1). The word "Quaternion" requires no explanation, since... it occurs in the Scriptures and in Milton. Peter was delivered to "four quaternions of soldiers" to keep him; Adam, in his morning hymn, invokes air and the elements, "which in quaternion run." The word (like, the Latin "quaternio," from which it is derived) means simply a set of four, whether those "four" be persons or things.”
“The real numbers are the dependable breadwinner of the family, the complete ordered field we all rely on. The complex numbers are a slightly flashier but still respectable younger brother: not ordered, but algebraically complete. The quaternions, being noncommutative, are the eccentric cousin who is shunned at important family gatherings. But the octonions are the crazy old uncle nobody lets out of the attic: they are nonassociative.”
“I see no possible objection to your now publishing the deferred "scrap" if you yourself approve of what is said in it in favour of quaternions.
I think you are right in your use of the word "Volapuk," but I don't think you should confine it to the vector part of quaternions. The whole affair has in respect to mathematics a value not inferior to that of "Volapuk" in respect to language.”
“It is a curious fact in the history of mathematics that discoveries of the greatest importance were made simultaneously by different men of genius. The classical example is the... development of the infinitesimal calculus by Newton and Leibniz. Another case is the development of vector calculus in Grassmann's Ausdehnungslehre and Hamilton's Calculus of Quaternions. In the same way we find analytic geometry simultaneously developed by Fermat and Descartes.”
“I do think... that you would find it would lose nothing by omitting the word "vector" throughout. It adds nothing to the clearness or simplicity of the geometry, whether of two dimensions or three dimensions. Quaternions came from Hamilton after his really good work had been done; and, though beautifully ingenious, have been an unmixed evil to those who have touched them in any way, including Clerk Maxwell.”
“all the numbers that have been derived from the genus are four; but number is the indefinite genus, from which was constituted, according to them, the perfect number, viz. the decade. For one, two, three, four, become ten, if its proper denomination be preserved essentially for each of the numbers. Pythagoras affirmed this to be a sacred quaternion, source of everlasting nature, having, as it were, roots in itself; and that from this number all the numbers receive their originating principle.”
“Symmetrical equations are good in their place, but "vector" is a useless survival, or offshoot, from quaternions, and has never been of the slightest use to any creature. Hertz wisely shunted it, but unwisely he adopted temporarily Heaviside’s nihilism. He even tended to nihilism in dynamics, as I warned you soon after his death. He would have grown out of all this, I believe, if he had lived. He certainly was the opposite pole of nature to a nihilist in his experimental work, and in his Doctorate Thesis on the impact of elastic bodies.”
“[Q]uaternions form the appropriate algebraic basis for a description of nature whenever we have to deal either with pseudoreal group representations or with co-representations of Wigner's Type II. The context in which quaternions arose historically, in a study of the three-dimensional rotation group, can now be seen to be an extremely special case of this general principle. Every group which admits pseudoreal representations equally admits a natural description in terms of real quaternions.”
“[T]he common solution, using three Euler's angles interpolated independently, is not ideal. The more recent (1843) notation of quaternions is proposed instead, along with interpolation on the quaternion unit sphere. Although quaternions are less familiar, conversion to quaternions and generation of in-between frames can be completely automatic, no matter how key frames were originally specified, so users don't need to know—or care—about inner details. The same cannot be said for Euler's angles, which are more difficult to use.”