Sylvester, poetaster

Delivered before the Oxford University Invariant Society by Owen Massey on 16 February 1999

The intersection of mathematics and poetry is not large. For a long time I'd thought it confined to the limerick which goes:

A graduate student at Trinity
Computed the square of infinity
But it gave him the fidgets
To write down the digits
So he dropped maths and took up divinity.

At last year's Members' Papers, Nick Fortescue recited a poem by Coleridge which was called 'A mathematical problem'. This was a geometrical construction in rather random metre, and basically confirmed that mathematics is no subject for poetry and poetry no form in which to write mathematics. I hope my talk this evening will give further evidence of this.

James Joseph Sylvester (1814-1897) was a Victorian algebraist who disagreed with me:

The incongruity between advanced mathematics and verse composition is more apparent than real - Mathematic commencing as a practical art, thence passing into the form of a science, having again emerged into an art of a higher order - a fine art - plastic in the hands of the Mathematician, obedient to and taking shape from his will, and almost admitting of the free play of fancy upon it ...

Sylvester was educated at Cambridge, where he came second in the mathematical Tripos but couldn't receive his degree because of his Jewish faith. He became a professor at University College, London, which was founded in part to combat the legal religious discrimination of Oxford and Cambridge. However, after the requirement to subscribe to the Thirty-Nine Articles of the Church of England was dropped fifty years later, Sylvester became the first Jew to hold a Professorship at Oxford, which was the office of Savilian Professor of Geometry. The title is rather misleading because Sylvester always concentrated his mathematical efforts on algebra. He worked hand in hand with Arthur Cayley, of the Cayley-Hamilton theorem.

The article in the Oxford Magazine [2nd Week Trinity 1997] which inspired this talk is written by Ioan James, who I think is the current Savilian Professor of Geometry. He quotes a poem of Sylvester's which I have unfortunately not been able to trace in the Bodleian. It is called 'To a missing member of a family of terms in an algebraical formula':

Lone and discarded one! divorced by fate,
From thy wished-for fellows--whither art flown?
Where lingerest thou in thy bereaved estate,
Like some lost star or buried meteor stone?
Thou mindst me much of that presumptuous one
Who loth, aught less than greatest, to be great,
From Heaven's immensity fell headlong down
To live forlorn, self-centred, desolate;
Or who, new Heraclid, hard exile bore,
Now buoyed by hope, now stretched on rack of fear
Till throned Astraea, wafting to his ear
Works of dim portent through the Atlantic roar,
Bade him the sanctuary of the Muse revere
And strew with flame the dust of Isis' shore.

One reference I was able to confirm is to a pamphlet Sylvester had privately printed in 1876. The pamphlet is called 'Fliegende Blaetter', which may be roughly translated as 'Fugitive leaves'. It contains a mock-heroic poem, an ode to an actress who played Rosalind in a production of 'As you like it'. The poem is over 250 lines long, and every single one of those lines ends in the same syllable. To give you a taste of it, I'll quote the closing lines:

With each mortal thing unkinned
Heaven's light comforting the blind
To those tones of Orpheus twinned
That could death's decrees rescind,
Soft as notes of Jenny Lind
Ere by Time's harsh sickle thinned,
Thy swéet name, déar Rosalind!
Rose smells sweet and soft spells 'lind',
Soft, smooth, sweet, spell Rosalind.

(The monotony is slightly relieved by 'ind' and 'eind', but not much.) One is reminded of Dr Johnson's remark about a dog standing on its hind legs -- the impressive thing is not that it is done well, but that it is done at all. A contemporary commentator wrote:

Language all is Sylvestr'ined,
In the light of Rosalind.

It's hard to tell, but Sylvester does seem to have a high opinion of his own poetry. He insists on smothering his poems with footnotes explaining any slightly imaginative word or phrase. For instance:

'Twin-lit', 'unshape', and 'whirls-in-one' are, I imagine, additions, and faultless ones, to our current speech, and destined, I venture to believe, to take rank with 'invariant', 'covariant' [&] 'contravariant' ... which have been struck at the same mint, and have met with universal recognition and acceptance.

Yes, Sylvester was responsible for the first mathematical use of the word 'invariant', though not in the adjectival sense but in the context of quadratic forms, as touched on by the present Mods syllabus.

Sylvester had grander ambitions than merely writing verse; he wanted to apply scientific principles to poetry to determine its rules. He laid out his ideas in a thin book called 'The laws of verse'. It's rather puzzling to read, partly because of Sylvester's extremely discursive style which is characterised by innumerate subordinate clauses, classical allusions and, once again, footnotes.

Coleridge defined poetry as 'The best words in their best order'. Sylvester couldn't express himself so succinctly, and defined poetry quite romantically as:

the junction of words, the laying of them duly alongside one another (like drainage pipes set end to end, or the capillary terminations of the veins and arteries) so as to provide for the easy transmission and flow of breath ... from one into the other.

The only aspect of poetry he examines closely in 'The laws of verse' is rhythm, this being most tractable to a mathematical, or at least formal, analysis. He writes:

As regards metre, let us denote a spondee, the first epitrite, a dactyl and a trochee, by A, B, C, D respectively : then the construction of the Alcaic stanza, as commonly practised by Horace ... will be represented by the scheme, (or as, say, in determinants, the square matrix) -
which (as is apparent) has a pure algebraical or tactical deep-seated harmony of its own. Denoting the lines of symbols by single letters, and reading the square upwards, the scheme assumes the type L M N N, which is homeomorphic with the upper two lines of the square. And again, using α, β, γ to denote the duads AB, CC, DD respectively, and counting only as one the repeated uppermost horizontal line, we obtain the complete combination system -
... evidence of the strong mathematical bias of Horace's mind, wherein perhaps is to be sought the secret of the peculiar incisive power and diamond-like glitter of his verse.

Here we see all the trademarks of the crackpot: numerology (albeit with letters), arbitrary disposal of anything which doesn't fit the theory, and an insistence on the inevitability of the process leading to the revelation of hidden truths. Sylvester was a great mathematician, who should have been aware of these traps, but perhaps not; it seems he carried the same style into his mathematical writing. His entry in the Dictionary of National Biography says:

He was wont to write with eager haste in a style as stimulating as it was excited, in flowery language enriched by poetical imagination, and by illustration boldly drawn from themes alien to pure science.

I have found some verses written about Sylvester, by an unnamed lecturer:

What though in every clime or land
Where symbolled truths are shown,
Entwined in curly-curious type,
Sylvester's name is known?

What though he sees with awestruck gaze
The endless series' limit,
And round him n-dimensioned space,
With whirling vectors in it?

What though the gay determinant
For him its rows exchanges,
While Hamilton's weird Delta turned
O'er all the symbols ranges?

What though he can imagine points
Where points can never be,
And circles at infinity
Can measure, touch, and see?

I think this nicely suggests the imaginative worlds that all mathematicians roam in, whether or not they descend to write poetry. Thank you.