The Mathematician in Love

Rankine love poem (segment) Eddington
loved math (image)
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.
In poetry, “The Mathematician in Love” is a circa 1845 posthumously-published (1874) eight stanza, five line poem, or song, depending, by Scottish mathematical physicist and engineer William Rankine (1820-1872) — sometimes referred to as the Rankine love poem — in which one of the earliest known equations of love, or “marvelous mathematical formula”, as American physical historian Morris Zucker describe things, is found, and in which, incredibly, he discusses, in his poetic humor view, the hypothesis that love is type of thermodynamic potential, a very honed discernment, particularly coming from the 1853 coiner of the term “potential energy”.

The following is the abstract of the collected "songs" of Rankine, from the 1874 posthumously-published collected works set, of which "The Mathematician in Love" is listed first: [1]

“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.”

It would seem, therefore, approximately correct to estimate the writing of this poetry song to circa 1845 (age 25±), or somewhere between age 16 to 28, specifically from the year 1836, when Rankine (age 16) began to study a spectrum of scientific topics at the University of Edinburgh, including natural history under Robert Jameson and natural philosophy under James Forbes, to 1842 (age 22), when he attempted to reduce the phenomena of heat to a mathematical form but he was frustrated by his lack of experimental data, to age 1848 (age 28), when he switched careers to study mathematical physics, thermodynamics, and applied mechanics, the year after which (1849) he was elected to the Royal Society of Edinburgh. This is an estimate in line with the ages at which other human chemical thermodynamics pioneers penned their thermodynamics of love theories (Christopher Hirata, age 18-20; David Hwang, age 22; Libb Thims, age 24; Surya Pati, age 26).

The following is Rankine’s “The Mathematician in Love” poem, from his 1874 Songs and Fables, listed in his table of contents as the first song or “clever little ditty” as Morris Zucker refers to it:

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 stone

II. 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, averageness

III. 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 energy

VII. “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).”

VIIISaid 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.

The equation for stanza six, according to Rankine, is the following:

Eq S6

The equation for stanza seven, according to Rankine, is the following:

Eq S7

(add discussion)

In 1938, English astronomer Arthur Eddington, in his “The Philosophy of Physical Science”, Tarner Lecture series, delivered Easter term at Trinity College, Cambridge, being a general discussion of principles of philosophical thought associated with advances in physical science, developing the ideas contained in earlier titles such as The Nature of the Physical World (1928) in line with discoveries in quantum mechanics and group theory, in his discussion of how it is easy to introduce mathematical notation, to explain something, but difficult to turn the notation into useful account, cites the cites the following poem segment: [2]

Rankine love poem (segment) Eddington
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.”

Here, in this “no practical outcome” conclusion, we are reminded of Japanese chemical engineer Tominaga Keii’s 2004 chemical thermodynamics of reactions chapter section Chemical Affinity in 1806 wherein he, like Eddington, dismisses Goethe’s physical chemistry based Elective Affinities, as having not added “any scientific knowledge”. Both are examples of two cultures blindness (see: forest blind).

In 1945, American physical historian Morris Zucker, in his Causality or Indeterminacy in History chapter, subsection: “Probability Statistics Applied to Social Phenoomena”, citing Eddington, quotes stanza six, and, like Eddington, seems to at the same time glorify and deride the premise of the poem, namely that love or the passions running society can be formulated and hence thereby predicted: [3]

“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.”

All of this is very odd indeed, being that Zucker seems to devote nearly the entirety of volume one, of this two-volume A Field Theory of History, the previous 578-pages up to this poem love formula citation in fact, to a pronged effort to prove and or substantiate that the “laws of social motion” and or “laws of economic motion”, a Karl Marx phrase he employs repetitively, can be formulated; but then, above, negating all of his previous argument, states his seemingly hidden views explicitly, namely that “social phenomena is not susceptible to such formulation”, and shockingly that the application of the rigid formula of physics to social phenomena “must fail”?

These concluding remarks are very strange indeed, particularly coming from someone who has put so much effort into collecting and discussing all of the various “physical historian” points of view, and for someone who is attempting to formulate some type of Maxwell-Einstein like “field theory of history”? The only supposition offered here, with Zucker’s passing seemingly innocuous mentions of God, his Heisenberg uncertainty principle discussions, etc., is that he is some type of closet ontic opening theorist, i.e. attempting to formulate a "scientific" version of history, yet at the same retaining belief in free will, and hence some type of hidden agenda soul weight afterlife theory, or something along these lines.

In 1994, Australian science and literature scholar Roslynn Haynes, in her From Faust to Strangelove, comments the following incorrect take on the poem: [6]

“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.”

Here, Roslynn, not being a mathematician herself—her degrees being in biochemistry (BS) and literature (BA and MA)—falters in her take on Rankine’s poem.

Firstly, she thinks Rankine is mocking himself? This is incorrect. Correctly, Rankine wants to understand the process of falling in love as Newton understood the process of a body falling to the earth, via the force of gravity; and he wants to do so formulaically, i.e. with precision—but he cannot quite see the clear picture, hence he must take recourse to rhyme and poetry, which, according to Goethe, is a tool that helps one to work out frustration and or confusion in thought. Yet, he is prescient: one day the wandering course of male and female affections “must yield soon” to prediction, as has been shown in celestial mechanics.

Secondly, her jibe about how his “obsession with formulas” results in him being “duly punished” in the “living world”, as compared, supposedly, to the abstract world of mathematical physics, where “emotions” are the accepted currency, is off—Goethe explained the currency of emotions correctly in terms reaction of affinities (see: Goethe timeline, 1799) and at the abstractions of Cullen reaction diagrams; Rankine was but expanding and elaborating in this direction is precursory human chemical thermodynamics logic.

Thirdly, her idea that "mathematicians feature prominently as exemplars of the dehumanization process", this in the Rankine love poem example, is not the case. In fact, it is the exact opposite: Rankine above is working out the details of the "rehumanization process", namely that when belief systems behind the explanation human ideals begins to falter in logic, the passions begin to suffer, owing to misdirection, and thereby only through rehumanization process (clearly direction) can the passions again "come alive", so to say, in defunct terminology, in the source of social progress.

In 2003, Canadian poem collector Ian Lancashire, an English professor at the University of Toronto, posted the Rankine poem online, with a few analysis points or notes, labeled in a Stanza/Line citation method: [4]

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.

(add discussion)

In 2005, American religion apologist Paul Copan, in his How Do You Know You’re Not Wrong?: Responding to Objections that Leave Christians Speechless, referred to the Rankine love poem, naturally enough, as follows: [5]

“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.”

This religious belief system based objection, naturally enough, is followed by something about how “just as one scientific discipline can’t rule out theism, stacking them all up together can’t do so either”, followed by citation of Edward Wilson's "consilience" of all things theory.

On 1 Feb 2013, Peter Mander, in his “Rankine on Entropy, Love and Marriage” (Ѻ), blogged on firstly on Rankine’s version of the new heat function, a variant of what Clausius would eventually call entropy, and secondly on Rankine’s circa 1845 “The Mathematician in Love”, about which he commented: “Rankine never found the time to test this theory in practice. He died a bachelor on Christmas Eve 1872, at the age of 52, of overwork.”

Hmolpedia | Thims
On 29 Nov 2013, Libb Thims discovered the Rankine love poem. One aspect, about the Rankine love poem, which comes to mind, is that knowing that this page is Hmolpedia article #3,086, started two days following the 29 Nov 2013 discovery of the Rankine poem, via the Zucker 1945 citation, which in turn cited the 1938 Eddington lecture, is the buried underground hiddenness of these types of suppositional arguments, i.e. that love or equivalently the passions can be quantified formulaically as a thermodynamic potential amenable to evolutionary psychology analysis.

In plain speak, it has taken American electrochemical engineer Thims 18-years, since his 1995 seeded reverse engineering puzzle, to dig this poem out of the matrix of buried and archived scientific knowledge; which can be compared to the 2006 discovery of Goethe's Elective Affinities via footnote 2.5 of Ilya Prigogine's mention of Mittler the mediator, something which took 11-years to find. The fact that there is such a large disjunct between the two cultures is a mar to the mind of the growing erudition.

The following are news paper clipping reviews:

“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)

The poem has a 6.2 out of 10 rating (12 votes) at (Ѻ).

See also
● The World Ways (Friedrich Schiller, 1795) | Freud-Schiller drive theory
A Paradoxical Ode (James Maxwell, 1874)
Mala Radhakrishnan

1. (a) Rankine, William. (1874). “The Mathematician in Love” (Ѻ), Songs and Fables (§Song 1, pgs. 3-6). Glasgow: James Maclehose.
(b) Rankine, William. (1908), “The Mathematician in Love”, The Michigan Technic, 19(21):95-96.
(c) Eddington, Arthur. (1938). The Philosophy of Physical Science (pg. 138). Cambridge University Press.
(d) Zucker, Morris. (1945). The Philosophy of American History: The Historical Field Theory (pg. 579). Arnold-Howard Publishing Co.
2. (a) Eddington, Arthur. (1938). The Philosophy of Physical Science (pg. 138). Cambridge University Press.
(b) Tarner Lectures – Wikipedia.
3. Zucker, Morris. (1945). The Philosophy of American History: The Historical Field Theory (pg. 579). Arnold-Howard Publishing Co.
4. (a) Rankine, William. (1874) “The Mathematician in Love” (analysis: Ian Lancashire), University of Toronto, 2003.
(b) Ian Lancashire (faculty) – University of Toronto.
5. (a) Copan, Paul. (2005). How Do You Know You’re Not Wrong?: Responding to Objections that Leave Christians Speechless (pg. 74). Baker Books.
(b) Paul Copan – Wikipedia.
6. Haynes, Roslynn. (1994). From Faust to Strangelove: Representations of the Scientist in Western Literature (pg. 85). John Hopkins University Press.

Further reading
● Fadiman, Clifton. (1997). The Mathematical Magpie: being more stories, mainly transcendental, plus subjects of essays, rhymes, music, anecdotes, epigrams, and other prime oddments and diversions, rational and irrational, all derived from the infinite domain of mathematics (pg. 276-77). Copernicus.
● Gaither, Carl C. and Cavazos-Gaither, Alma E. (2012). Gaither’s Dictionary of Scientific Quotations (pg. 835). Springer.

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