Article: 32157 of sci.math From: rudolph@cis.umassd.edu (Lee Rudolph) Subject: FROBENIUS: A SESQUILOGUE (was: Simple Question - What's a quaternion?) Keywords: quaternion, Hamilton, Frobenius, calomel, Charm, Truth, Beauty Organization: University of Massachusetts Dartmouth Date: Mon, 23 Aug 1993 22:22:28 GMT This work is copyright 1968, 1990, 1993 by Lee Rudolph. All rights reserved. FROBENIUS: A SESQUILOGUE (GEORG FROBENIUS, exhausted and delirious after proving the uniqueness of the Quaternions, reflects on the philosophy, life, and works of his mentor SIR WILLIAM ROWAN HAMILTON, and thus invokes SIR WILLIAM's ghost) Quod erat demonstrandum, Q. E. D.-- FROBENIUS, his proof SIR WILLIAM would have been so proud of me! completed at last, Now his Quaternions are proved unique, And though some scornful men may cry, "A freak," but fearful of I know that they are good, and useful, too! his detractors, State your theorem: struggle with it: prove it true. What then's more glorious? He said, "Alone, remembers the late Beauty stands naked. After one has shown SIR WILLIAM ROWAN The use of a new theory, tailored clothes HAMILTON's poor For Beauty--not to cover her, but to disclose opinion of Pure New charms beside the old--then one is worth Mathematics, The name of Mathematician." Scorn and mirth Does them ill credit; for they know I've tried, Tried and succeeded. My work is applied, No doubt of it! Can't they let me be? and tries to SIR WILLIAM would have been so proud of me! justify himself, Calm, now; these months of work have warped my mind, Or bent my judgment. Can I really find Justification for a year spent so, without success. Fourteen months squandered on one proof? Say no, SIR WILLIAM: "FROBENIUS, you've put the frosting He imagines his On cake that needed none. One year, exhausting erstwhile mentor Yourself night after night; and, after all, scolding him, What would it matter if it should befall That my i, j, and k were not unique? Would that stop you from using them? You seem to seek Some strange monopoly." Pure mathematics seems At times, alas, the fleetingest of dreams, One it is my damnation to pursue. SIR WILLIAM, are you damned? No news of you, then passes into Nor NEWTON, nor the others, comes this way. a revery in which Feh! you are dead; there's nothing more to say; he reviews the life How shall we judge you, we who are alive, and works of the But by your works? dead Irish knight: So, then: when you were five, his childhood; Hebrew and Latin and Greek; when you were ten, Sanskrit, scrawled Arabic, and Persian; then, At thirteen, that language which transcends all time. his adolescence; CLAIRAUT's Algebre, lacking rhythm, rhyme, And meter, moved you more than HOMER could. Far less than midway through your life, a wood As dark as DANTE's, older than his Creation, Closed you in: and through it lay salvation, And through it you set off, blazing new trails. And, oh! the stories of you! I've read tales-- At seventeen you gave LAPLACE the lie, Corrected his figures. Eighteen: who'd deny, By then, you were the first of Ireland's minds? his young manhood; Your Optics--not since NEWTON (his name winds No longer, broader, better marked a course) Has so much light been shed by one lone source. At twenty-two, professor; and a knight at thirty. No work for your hands; if the nails were dirty, That was just ink. But one idea stuck his long years Fast in your mind; for fifteen years, no luck of searching Nor furious genius could dislodge the thought for an algebra Or solve the problem. (And I said my lot of vectors Was hard? One year? Oh, fie, FROBENIUS, fie!) "Papa, have you learnt yet how to multiply Your `triplets'?" "No, son, I can only add, in physical space Add and subtract'em." of three dimensions. Did they think you mad, Mad for your fifteen years of "wasted time"? Perhaps. I'm certain that they think that I'm FROBENIUS Mad as a hatter. grows frenzied, It's the hatter's trade That drives him mad; do they think I am made Of sterner stuff than hatters? In the felt He makes hats from, are poisons; I have dealt With stronger. It's calomel (I think) they use his frenzy increases, To keep the felt from rotting; if they lose A hatter now and then, because the rot Turned to his mind and kidneys--well, they've got Another, hatters come cheap. And calomel? and he collapses Dug from the earth. Mathematics comes from HELL! with a shriek. * * * "Indeed? Then is this Hell, where I have dreamed SIR WILLIAM's ghost These years that I have slept? What always seemed appears and speaks, To me the hellish waste in mathematics Was `purity'. Why, you've Dynamics, Statics, Optics and Hydraulics--bridges to build, If it comes to that. Why have you got to gild continuing Your lily with false `purity'? A waste of life! the earlier You worry me." scolding. SIR WILLIAM, once your wife FROBENIUS replies, Worried for you fifteen years, unceasing-- reminding the ghost Each day your hopes and prospects were decreasing of its own quest, Until it seemed they could decrease no further, And your dear HELEN told you, "BILL, it's murther, Yer murtherin' yirself." You didn't eat Unless she brought you food; sheet after sheet Of foolscap heaped up on your desk each night; But your equations never worked out right-- fruitless so long, She knew--you had them burnt each morning. Then, one day, it struck you without warning, which was so suddenly As you and she were walking. In the stone and surprisingly Of Brougham Bridge you carved it--not alone: successful. Names of half Dublin's lovers must entwine With that one short, sweet, and immortal line i^2 = j^2 = k^2 = ijk = 1 The QUATERNIONS! Which, written once, can never be erased, Though love and stone shall crumble. All the waste Was hers--her worry. Don't you worry, now. "No waste of my time, GEORG. We'll both allow The ghost is That I am dead; there's nothing more to say. not impressed. Scant news of you, you youngsters, comes this way: How shall we judge you, who are still alive, But by your works?" Works? Don't you think that I've FROBENIUS Worked hard? We've all worked, WILLIAM--sometimes well, contends with More often not; and we've all gone through Hell the ghost. Trying to follow you. We cannot catch you. Yes, some of us, although they could not match you, Ran far, and reached the gates of Paradise; And others (happy men!)--they heard the price CHARON asked for crossing, knew they could not pay, And stopped; but I--I would go all the way, I thought. And we who crossed--how much it cost us! If you played DANTE, WILLIAM, I play FAUSTUS. "Rather a petty one, GEORG; you have sold The ghost, Your soul for a pile of faery gold scornful to the end, That turns to ashes in the light of day, Not true treasure; and you've lit your way With ignis fatuus; and it will fade Sooner than you think, and leave you in the shade." fades away, * * * Your shade, SIR WILLIAM. All of you block our light, leaving FROBENIUS And we cannot see, and we cannot fight Shadows, not shadows dancing on the wall. What would it matter if it should befall That your--MY i j, k are no damned use? Would that make them less beautiful? Bah! I'll seduce Beauty from your workshop; we shall play In the fresh, pure air, in the clean light of day (Damn this dim gaslight!); and she shall go bare, Naked as the newborn--she'll not wear Mechanic's coveralls. We'll live and love Far from this world, never thinking of Utility. I'll follow and let Beauty lead. Knight, if you sleep, you sleep in Hell, indeed. to have the last word. * FINIS * ----- (Lee Rudolph) -----