# Happy Quaternions Day

“Here as he walked by [in Dublin] on the 16th of October 1843 Sir William Rowan Hamilton in a flash of genius discovered the fundamental formula for quaternion multiplication i2 = j2 = k2 = ijk = -1 & cut it on a stone of this bridge.”

It’s the 175th anniversary.

1. Lee Rudolph says

FROBENIUS, A SESQUILOGUE

(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.—                          [1]
SIR WILLIAM would have been so proud of me!
Now his Quaternions are proved unique,
And though some scornful men may cry, “A freak,”      [2]
I know that they are good, and useful, too!
To state your theorem, struggle, prove it true:
What then’s more glorious? He said, “Alone,               [3]
Beauty stands naked. After one has shown
The use of a new theory, tailored clothes
For Beauty—not to cover her, but to disclose
New charms beside the old—then one is worth
The name of Mathematician.”
Scorn and mirth
Do them ill credit; for they know I’ve tried,
Tried and succeeded. My work is applied,
No doubt about it! Can’t they let me be?                     [4]
SIR WILLIAM would have been so proud of me!

Calm, now; these months of work have warped my rnind,
Or bent my judgment. Can I really find
Justification for a year spent so,                                  [5]
Fourteen months squandered on one proof? Say no,
SIR WILLIAM: “FROBENIUS, you’ve put the frosting  [6]
On cake that needed none. One year, exhausting
Yourself night after night; and, after all,
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
A 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,   [7]
Nor NEWTON, nor the others, comes this way.
Feh! you are dead; there’s nothing more to say;
How shall we judge you, we who are alive,
So, then: when you were five,    [8]
Hebrew and Latin and Greek; when you were ten,
Sanskrit, scrawled Arabic, and Persian; then,
At thirteen, that language which transcends ail time.  [9]
CLAIRAUT’s Algèbre, 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?
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; knight at thirty.
No work for your hands; if the nails were dirty,
That was just ink.
But one idea stuck         [10]
Fast in your mind; for fifteen years, no luck
Nor furious genius could dislodge the thought
Or solve the problem. (And I said my lot
Was hard? One year? Oh, fie, FROBENIUS, fie!)
“Papà, have you learnt yet how to multiply
Perhaps. I’m certain that they think that I‘m       [12]
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      [13]
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?
Dug from the earth. Mathematics comes from HELL! [14]

*  *  *

“Indeed? Then is this Hell, where I have dreamed      [15]
These years that I have slept? What always seemed
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
The lily with ‘purity’? A waste of life!
You worry me.”                                                          [16]
SIR WILLIAM, once your wife          [17]
Worried for you fifteen years, unceasing—
Each day your hopes and prospects were decreasing
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—          [18]
She knew it, for you had them burnt each morning.

Then, one day, it struck you without warning,         [19]
As you and she were walking. In the stone
Of Brougham Bridge you carved it—not alone:
Names of half Dublin’s lovers must entwine
With that one short, sweet, and immortal line
i²=j²=k²=ijk=–1                                              [20]
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       [21]
That I am dead; there’s nothing more to say.
Scant news of you, you youngsters, comes this way:
How shall we judge you, who are still alive,
Works? Don’t you think that I’ve    [22]
Worked hard? We’ve all worked, WILLIAM—sometimes well,
More often not; and we’ve all gone through Hell
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               [23]
Your soul for a pile of faëry gold
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                                  [24]
Sooner than you think, and leave you in the shade.”
*  *  *
So that we cannot see, and cannot fight
What would it matter if it should befall
That your—my i, j, k are no damned use?
Would that make them less beautiful? 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