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.
CLAIRAUT's Algèbre, lacking rhythm, rhyme,
And meter, moved you more than HOMER could.	his adolescence;
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!)
"Papà, 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
i2 = j2 = i2 = 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 faëry 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.	to have
Knight, if you sleep, you sleep in Hell, indeed.	the last word.
FINIS & Q.E.D.