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William Rowan Hamilton
6 quotes
“The Study of Algebra may be pursued in three very different schools, the Practical, the Philological, or the Theoretical, according as Algebra itself is accounted an Instrument, or a Language, or a Contemplation; according as ease of operation, or symmetry of expression, or clearness of thought, (the agere, the fari, or the sapere,) is eminently prized and sought for.”
William Rowan Hamilton (1805–1865) first seen 1833 wikiquote, CC BY-SA 4.0 source
Recorded in: Theory of Conjugate Functions, or Algebraic Couples; with a Preliminary and Elementary Essay on Algebra as the Science of Pure Time" (1837) Transactions of the Royal Irish Academy, Vol. 17, pp. 293–422. Read November 4t…
“To admire is, to me, questionless, the highest pleasure of life.”
William Rowan Hamilton (1805–1865) first seen 1838 wikiquote, CC BY-SA 4.0 source
Recorded in: Letter to the Marquess of Northampton (June 17, 1838), in Robert Perceval Graves, Life of Sir William Rowan Hamilton Vol. 2 (1885), pp. 260-261.
“Time is said to have only one dimension, and space to have three dimensions. ... The mathematical quaternion partakes of both these elements; in technical language it may be said to be 'time plus space', or 'space plus time': and in this sense it has, or at least involves a reference to, four dimensions. And how the One of Time, of Space the Three, Might in the Chain of Symbols girdled be.”
William Rowan Hamilton (1805–1865) said by 1865 at the latest wikiquote, CC BY-SA 4.0 source
Recorded in: Quoted in Robert Percival Graves' "Life of Sir William Rowan Hamilton" (3 volumes, 1882, 1885, 1889))
“The difficulties which so many have felt in the doctrine of Negative and Imaginary Quantities in Algebra forced themselves long ago on my attention... And while agreeing with those who had contended that negatives and imaginaries were not properly quantities at all, I still felt dissatisfied with any view which should not give to them, from the outset, a clear interpretation and meaning... It early appeared to me that these ends might be attained by our consenting to regard Algebra as being no mere Art, nor Language, nor primarily a Science of Quantity; but rather as the Science of Order in Progression. It was, however, a part of this conception, that the progression here spoken of was understood to be continuous and unidimensional: extending indefinitely forward and backward, but not in any lateral direction. And although the successive states of such a progression might (no doubt) be represented by points upon a line, yet I thought that their simple successiveness was better conceived by comparing them with moments of time, divested, however, of all reference to cause and effect; so that the "time" here considered might be said to be abstract, ideal, or pure, like that "space" which is the object of geometry. In this manner I was led, many years ago, to regard Algebra as the Science of Pure Time: and an Essay, containing my views respecting it as such, was published in 1835. ...[I]f the letters A and B were employed as dates, to denote any two moments of time, which might or might not be distinct, the case of the coincidence or identity of these two moments, or of equivalence of these two dates, was denoted by the equation,B = Awhich symbolic assertion was thus interpreted as not involving any original reference to quantity, nor as expressing the result of any comparison between two durations as measured. It corresponded to the conception of simultaneity or synchronism; or, in simpler words, it represented the thought of the present in time. Of all possible answers to the general question, "When," the simplest is the answer, "Now:" and it was the attitude of mind, assumed in the making of this answer, which (in the system here described) might be said to be originally symbolized by the equation above written.”
William Rowan Hamilton (1805–1865) first seen 1833 wikiquote, CC BY-SA 4.0 source
Recorded in: Preface, Lectures on Quaternions: Containing a Systematic Statement of a New Mathematical Method of which the Principles were Communicated in 1843 to the Royal Irish Academy... (1853) pp. 1-4. Hamilton makes reference t…
“It may not sound very consistent with any such professed humility on my part, if I say to you that, after having served for the Quaternions during fourteen years, and having (as America seems to think) won my Rachel—to be my own by an intellectual marriage—I now wish to wind up several scientific projects, from which those quaternions had for a long time diverted me; and feel as if I were entering, or had already entered, on a new harvest of labour and reputation. As to Fame, if it have not been won or earned already, it is not likely that any future exertion will make it mine. But as to the Labour; that is a thing within everybody's power to judge of, even for himself. I have very long admired Ptolemy's description of his great astronomical Master, Hipparchus... "a labour-loving and truth-loving man."—Be such my epitaph!”
William Rowan Hamilton (1805–1865) first seen 1858 wikiquote, CC BY-SA 4.0 source
Recorded in: Letter to Mrs. Wilde, (February 11, 1858) as quoted by Robert Perceval Graves, Life of Sir William Rowan Hamilton (1889) Vol.3, p. 230
“… an undercurrent of thought was going on in my mind which gave at last a result, whereof it is not too much to say that I felt at once the importance. An electric circuit seemed to close; and a spark flashed forth the herald (as I foresaw immediately) of many long years to come of definitely directed thought and work by myself, if spared, and, at all events, on the part of others if I should even be allowed to live long enough distinctly to communicate the discovery. Nor could I resist the impulse - unphilosophical as it may have been - to cut with a knife on a stone of Brougham Bridge, as we passed it, the fundamental formula which contains the Solution of the Problem, but of course, as an inscription, has long since mouldered away.”
William Rowan Hamilton (1805–1865) first seen 1843 wikiquote, CC BY-SA 4.0 source
Recorded in: in a letter to his son (dated August 5, 1865), describing his discovery of quaternions on October 16, 1843, in Robert Perceval Graves, Life of Sir William Rowan Hamilton Vol. 2 (1885), pp. 434-435.