Left: key section of Scottish engineer William Rankine’s 1874 poem “The Mathematician in Love”, cited by Arthur Eddington in his 1938 The Philosophy of Science lecture, as an example of how, supposedly, it is “easy to introduce mathematical notation”, but difficult to “turn it into useful account”. [2] Right: an image (Ѻ) from a 2011 “Rhyme and Reason” New Scientist article, citing Rankine’s love poem. |
“Those who enjoyed the personal intimacy of the late Professor Rankine—and the circle was not a narrow one—will, it is thought, be glad to have the means of recalling some of the songs which they can no longer hear from him, though his voice and manner lent a charm which the printed page cannot restore. Those who knew him from his graver works only, may be surprised, but it is hoped will not be disappointed, to find that a genius for philosophic research, which made his name known throughout the whole scientific world—and the labors of a life devoted chiefly to directing others, from the chair, and by the press, how to follow his steps—were not incompatible with the playful, genial spirit which brightens the following pages. The first of the Songs may be taken as the meeting point of science and humor:—the last possesses a melancholy interest, from having been written very shortly before his death, when failing health and eyesight seem to have revived a longing for the scenery and simple pleasures of his childhood.”
The equation for stanza six, according to Rankine, is the following:
I. A MATHEMATICIAN fell madly in love
With a lady, young, handsome, and charming:
By angles and ratios harmonic he strove
Her curves and proportions all faultless to prove.
As he scrawled hieroglyphics alarming.
|→ golden ratio
|→ waist-to-hip ratio
|→ Rosetta stoneII. He measured with care, from the ends of a base,
The arcs which her features subtended:
Then he framed transcendental equations, to trace
The flowing outlines of her figure and face,
And thought the result very splendid.
|→ symmetry, averagenessIII. He studied (since music has charms for the fair)
The theory of fiddles and whistles, —
Then composed, by acoustic equations, an air,
Which, when 'twas performed, made the lady's long hair
Stand on end, like a porcupine's bristles.IV. The lady loved dancing: — he therefore applied,
To the polka and waltz, an equation;
But when to rotate on his axis he tried,
His center of gravity swayed to one side,
And he fell, by the earth's gravitation.|→ Paul Dirac (on the puzzle of dancing) V. No doubts of the fate of his suit made him pause,
For he proved, to his own satisfaction,
That the fair one returned his affection; — “because,
“As every one knows, by mechanical laws,
“Re-action is equal to action.”
|→ third law of motion (laws of motion)VI. “Let x denote beauty, — y, manners well-bred, —
“z, fortune, — (this last is essential), —
“Let L stand for love" — our philosopher said, —
“Then L is a function of x, y, and z,
“Of the kind which is known as potential.”
|→ potential energy, thermodynamic potential, human free energyVII. “Now integrate L with respect to dt,
“(t standing for time and persuasion);
“Then, between proper limits, 'tis easy to see,
“The definite integral Marriage must be: —
“(A very concise demonstration).”VIII Said he — “If the wandering course of the moon
“By algebra can be predicted,
“The female affections must yield to it soon” —
— But the lady ran off with a dashing dragoon,
And left him amazed and afflicted.
On this poem segment, Eddington seems dismissive, as though this were a trivial, meaningless, or void poetry diddy:
“At the start there is no essential difference between this example of mathematical notation, and the A, B, C, …, P, Q, R, …, X, Y, Z, …, that we have been discussing. We must find what it is that turns the latter into powerful calculus for scientific purposes, whereas the former has no practical outcome—as the poem goes onto related.”
“This, of course, solves all ticklish problems, past, present and for the future, and all novelists, dramatists and Hollywood scenarists might as well begin right now to fold up their scenarios. However, candor compels the admission that this marvelous mathematical formula was put forth in 1874, but somehow has failed to catch on in spite of the long head start. Whatever success mathematics has achieved in physics, the application of its rigid formulae to the analysis of social phenomena must fail, not only because social phenomena is not susceptible of such formulation, but because its laws can seldom be stated in mathematical language. Neither, for that matter, can that be done about the internal state of the simplest atom. But that does not prevent the physicist and the chemist form making predictions with absolute certainty in their respective fields, and the degree of that certainty is the measure of the successful organization of a particular inquiry.”
“In such accounts, mathematicians feature prominently as exemplars of the dehumanization process. This is comically expressed in W.J.M Rankine’s poem ‘The Mathematician in Love’ (1874). The mathematician is mocked for his inability to related emotionally to the young lady, and his obsession with formulas is duly punished in the living world, where emotions rather than abstractions are the accepted currency.”
S1:L3 – ratios harmonic: harmonic proportion, the relation of three quantities whose reciprocals (inverse relations) are in arithmetical progression.
S2:L7 – subtended: stretched underneath or opposite to.
S2:L8 – transcendental equations: ones resulting only in an infinite series.
S6:L30 – potential: something can be calculated; more amply defined as "a mathematical function or quantity by the differentiation of which the force at any point in space arising from any system of bodies, etc., can be expressed. In the case in which the system consists of separate masses, electrical charges, etc., this quantity is equal to the sum of these, each divided by its distance from the point" (OED "potential" 5).
S7:L31 – integrate: finding a definite integral (cf. line 34) i.e., the numeric difference between the values of a function's indefinite integral for two values of the independent variable.
“Rankine’s ‘The Mathematician in Love’ reveals the absurdity of reducing all the knowledge to science and mathematical equations. There’s more to love than math and science.”
“Professor Rankine was a man of singularly genial spirit and fine intellect, which hardly found adequate expression, notwithstanding that the social instinct was strong in him. This volume of Songs and Fables will suffice to give a hint of the literary possibilities that were in him. There is ready humor, quaint wit, and rare felicity of expression. They are unlaboured jeux d'esprit , but they are finished in their way, and often, in spite of the dash and freedom, show a very delicate point. The Songs are something after the style of Songs from Maga, but are distinctly individual in note. ‘The Mathematician in Love’ is really excellent. The Fables are what they profess to be, genuine fables — but they are ruffled by a stir of real fun.”— Manchester Examiner (1874), review (Ѻ)
“The Editor of these Songs and Fables, by the eminent Glasgow professor of civil engineering, whom the scientific world still laments, fears that belief in a necessary incompatibility between philosophic research and playful humor will prejudice the public against them ; and if one of the objects of the publication was to show the fallacy of such a notion, it will possibly be carried out. . . . The cleverest and most ingenious song in the book is ‘The Mathematician in Love’, of which the Editor scarcely speaks too strongly when he calls it the meeting point of science and humor . . . . The Fables are very short, but some of them are extremely amusing, and the clever illustrations by Mrs. Hugh Blackburn considerably increase the attractiveness of the work.”— Glasgow News (1874), review (Ѻ)