Wednesday, March 19, 2008

I am the very Model for a Student Mathematical

I am the very model for a student mathematical;
I’ve information rational, and logical and practical.
I know the laws of algebra, and find them quite symmetrical,
And even know the meaning of ‘a variate antithetical’.
I’m extremely well acquainted, with all things mathematical.
I understand equations, both the simple and quadratical.
About binomial theorems I’m teeming with a lot o’news,
With many cheerful facts about the square of the hypotenuse.
I’m very good at integral and differential calculus,
And solving paradoxes that so often seem to rankle us.
In short in matters rational, and logical and practical,
I am the very model for a student mathematical.
I know the singularities of equations differential,
And some of these are regular, but the rest are quite essential.
I quote the results of giants; with Euler, Newton, Gauss, Laplace,
And can calculate an orbit, given a centre, force and mass.
I can reconstruct equations, both canonical and formal,
And write all kinds of matrices, orthogonal, real and normal.
I show how to tackle problems that one has never met before,
By analogy or example, or with some clever metaphor.
I seldom use equivalence to help decide upon a class,
But often find an integral, using a contour o’er a pass.
In short in matters rational, and logical and practical,
I am the very model for a student mathematical.
When you have learnt just what is meant by ‘Jacobian’ and ‘Abelian’;
When you at sight can estimate, for the modal, mean and median;
When describing normal subgroups is much more than recitation;
When you understand precisely what is ‘quantum excitation’;
When you know enough statistics that you can recognise RV;
When you have learnt all advances that have been made in SVD;
And when you can spot the transform that solves some tricky PDE,
You will feel no better student has ever sat for a degree.
Your accumulated knowledge, whilst extensive and exemplary,
Will have only been brought down to the beginning of last century,
But still in matters rational, and logical and practical,
You’ll be the very model of a student mathematical.

*KFR, with apologies to W.S. Gilbert

Friday, March 14, 2008

XVII. The Hunting of Pau-Puk-Keewis

Full of wrath was Hiawatha
When he came into the village,
Found the people in confusion,
Heard of all the misdemeanors,
All the malice and the mischief,
Of the cunning Pau-Puk-Keewis.
Hard his breath came through his nostrils,
Through his teeth he buzzed and muttered
Words of anger and resentment,
Hot and humming, like a hornet.
"I will slay this Pau-Puk-Keewis,
Slay this mischief-maker!" said he.
"Not so long and wide the world is,
Not so rude and rough the way is,
That my wrath shall not attain him,
That my vengeance shall not reach him!"
Then in swift pursuit departed
Hiawatha and the hunters
On the trail of Pau-Puk-Keewis,
Through the forest, where he passed it,
To the headlands where he rested;
But they found not Pau-Puk-Keewis,
Only in the trampled grasses,
In the whortleberry-bushes,
Found the couch where he had rested,
Found the impress of his body.
From the lowlands far beneath them,
From the Muskoday, the meadow,
Pau-Puk-Keewis, turning backward,
Made a gesture of defiance,
Made a gesture of derision;
And aloud cried Hiawatha,
From the summit of the mountains:
"Not so long and wide the world is,
Not so rude and rough the way is,
But my wrath shall overtake you,
And my vengeance shall attain you!"
Over rock and over river,
Through bush, and brake, and forest,
Ran the cunning Pau-Puk-Keewis;
Like an antelope he bounded,
Till he came unto a streamlet
In the middle of the forest,
To a streamlet still and tranquil,
That had overflowed its margin,
To a dam made by the beavers,
To a pond of quiet water,
Where knee-deep the trees were standing,
Where the water lilies floated,
Where the rushes waved and whispered.
On the dam stood Pau-Puk-Keewis,
On the dam of trunks and branches,
Through whose chinks the water spouted,
O'er whose summit flowed the streamlet.
From the bottom rose the beaver,
Looked with two great eyes of wonder,
Eyes that seemed to ask a question,
At the stranger, Pau-Puk-Keewis.
On the dam stood Pau-Puk-Keewis,
O'er his ankles flowed the streamlet,
Flowed the bright and silvery water,
And he spake unto the beaver,
With a smile he spake in this wise:
"O my friend Ahmeek, the beaver,
Cool and pleasant Is the water;
Let me dive into the water,
Let me rest there in your lodges;
Change me, too, into a beaver!"
Cautiously replied the beaver,
With reserve he thus made answer:
"Let me first consult the others,
Let me ask the other beavers."
Down he sank into the water,
Heavily sank he, as a stone sinks,
Down among the leaves and branches,
Brown and matted at the bottom.
On the dam stood Pau-Puk-Keewis,
O'er his ankles flowed the streamlet,
Spouted through the chinks below him,
Dashed upon the stones beneath him,
Spread serene and calm before him,
And the sunshine and the shadows
Fell in flecks and gleams upon him,
Fell in little shining patches,
Through the waving, rustling branches.
From the bottom rose the beavers,
Silently above the surface
Rose one head and then another,
Till the pond seemed full of beavers,
Full of black and shining faces.
To the beavers Pau-Puk-Keewis
Spake entreating, said in this wise:
"Very pleasant Is your dwelling,
O my friends! and safe from danger;
Can you not, with all your cunning,
All your wisdom and contrivance,
Change me, too, into a beaver?"
"Yes!" replied Ahmeek, the beaver,
He the King of all the beavers,
"Let yourself slide down among us,
Down into the tranquil water."
Down into the pond among them
Silently sank Pau-Puk-Keewis;
Black became his shirt of deer-skin,
Black his moccasins and leggings,
In a broad black tail behind him
Spread his fox-tails and his fringes;
He was changed into a beaver.
"Make me large," said Pau-Puk-Keewis,
"Make me large and make me larger,
Larger than the other beavers."
"Yes," the beaver chief responded,
"When our lodge below you enter,
In our wigwam we will make you
Ten times larger than the others."
Thus into the clear, brown water
Silently sank Pau-Puk-Keewis:
Found the bottom covered over
With the trunks of trees and branches,
Hoards of food against the winter,
Piles and heaps against the famine;
Found the lodge with arching doorway,
Leading into spacious chambers.
Here they made him large and larger,
Made him largest of the beavers,
Ten times larger than the others.
"You shall be our ruler," said they;
"Chief and King of all the beavers."
But not long had Pau-Puk-Keewis
Sat in state among the beavers,
When there came a voice, of warning
From the watchman at his station
In the water-flags and lilies,
Saying, "Here Is Hiawatha!
Hiawatha with his hunters!"
Then they heard a cry above them,
Heard a shouting and a tramping,
Heard a crashing and a rushing,
And the water round and o'er them
Sank and sucked away in eddies,
And they knew their dam was broken.
On the lodge's roof the hunters
Leaped, and broke it all asunder;
Streamed the sunshine through the crevice,
Sprang the beavers through the doorway,
Hid themselves in deeper water,
In the channel of the streamlet;
But the mighty Pau-Puk-Keewis
Could not pass beneath the doorway;
He was puffed with pride and feeding,
He was swollen like a bladder.
Through the roof looked Hiawatha,
Cried aloud, "O Pau-Puk-Keewis
Vain are all your craft and cunning,
Vain your manifold disguises!
Well I know you, Pau-Puk-Keewis!"
With their clubs they beat and bruised him,
Beat to death poor Pau-Puk-Keewis,
Pounded him as maize is pounded,
Till his skull was crushed to pieces.
Six tall hunters, lithe and limber,
Bore him home on poles and branches,
Bore the body of the beaver;
But the ghost, the Jeebi in him,
Thought and felt as Pau-Puk-Keewis,
Still lived on as Pau-Puk-Keewis.
And it fluttered, strove, and struggled,
Waving hither, waving thither,
As the curtains of a wigwam
Struggle with their thongs of deer-skin,
When the wintry wind is blowing;
Till it drew itself together,
Till it rose up from the body,
Till it took the form and features
Of the cunning Pau-Puk-Keewis
Vanishing into the forest.
But the wary Hiawatha
Saw the figure ere it vanished,
Saw the form of Pau-Puk-Keewis
Glide into the soft blue shadow
Of the pine-trees of the forest;
Toward the squares of white beyond it,
Toward an opening in the forest.
Like a wind it rushed and panted,
Bending all the boughs before it,
And behind it, as the rain comes,
Came the steps of Hiawatha.
To a lake with many islands
Came the breathless Pau-Puk-Keewis,
Where among the water-lilies
Pishnekuh, the brant, were sailing;
Through the tufts of rushes floating,
Steering through the reedy Islands.
Now their broad black beaks they lifted,
Now they plunged beneath the water,
Now they darkened in the shadow,
Now they brightened in the sunshine.
"Pishnekuh!" cried Pau-Puk-Keewis,
"Pishnekuh! my brothers!" said he,
"Change me to a brant with plumage,
With a shining neck and feathers,
Make me large, and make me larger,
Ten times larger than the others."
Straightway to a brant they changed him,
With two huge and dusky pinions,
With a bosom smooth and rounded,
With a bill like two great paddles,
Made him larger than the others,
Ten times larger than the largest,
Just as, shouting from the forest,
On the shore stood Hiawatha.
Up they rose with cry and clamor,
With a whir and beat of pinions,
Rose up from the reedy Islands,
From the water-flags and lilies.
And they said to Pau-Puk-Keewis:
"In your flying, look not downward,
Take good heed and look not downward,
Lest some strange mischance should happen,
Lest some great mishap befall you!"
Fast and far they fled to northward,
Fast and far through mist and sunshine,
Fed among the moors and fen-lands,
Slept among the reeds and rushes.
On the morrow as they journeyed,
Buoyed and lifted by the South-wind,
Wafted onward by the South-wind,
Blowing fresh and strong behind them,
Rose a sound of human voices,
Rose a clamor from beneath them,
From the lodges of a village,
From the people miles beneath them.
For the people of the village
Saw the flock of brant with wonder,
Saw the wings of Pau-Puk-Keewis
Flapping far up in the ether,
Broader than two doorway curtains.
Pau-Puk-Keewis heard the shouting,
Knew the voice of Hiawatha,
Knew the outcry of Iagoo,
And, forgetful of the warning,
Drew his neck in, and looked downward,
And the wind that blew behind him
Caught his mighty fan of feathers,
Sent him wheeling, whirling downward!
All in vain did Pau-Puk-Keewis
Struggle to regain his balance!
Whirling round and round and downward,
He beheld in turn the village
And in turn the flock above him,
Saw the village coming nearer,
And the flock receding farther,
Heard the voices growing louder,
Heard the shouting and the laughter;
Saw no more the flocks above him,
Only saw the earth beneath him;
Dead out of the empty heaven,
Dead among the shouting people,
With a heavy sound and sullen,
Fell the brant with broken pinions.
But his soul, his ghost, his shadow,
Still survived as Pau-Puk-Keewis,
Took again the form and features
Of the handsome Yenadizze,
And again went rushing onward,
Followed fast by Hiawatha,
Crying: "Not so wide the world is,
Not so long and rough the way Is,
But my wrath shall overtake you,
But my vengeance shall attain you!"
And so near he came, so near him,
That his hand was stretched to seize him,
His right hand to seize and hold him,
When the cunning Pau-Puk-Keewis
Whirled and spun about in circles,
Fanned the air into a whirlwind,
Danced the dust and leaves about him,
And amid the whirling eddies
Sprang into a hollow oak-tree,
Changed himself into a serpent,
Gliding out through root and rubbish.
With his right hand Hiawatha
Smote amain the hollow oak-tree,
Rent it into shreds and splinters,
Left it lying there in fragments.
But in vain; for Pau-Puk-Keewis,
Once again in human figure,
Full in sight ran on before him,
Sped away in gust and whirlwind,
On the shores of Gitche Gumee,
Westward by the Big-Sea-Water,
Came unto the rocky headlands,
To the Pictured Rocks of sandstone,
Looking over lake and landscape.
And the Old Man of the Mountain,
He the Manito of Mountains,
Opened wide his rocky doorways,
Opened wide his deep abysses,
Giving Pau-Puk-Keewis shelter
In his caverns dark and dreary,
Bidding Pau-Puk-Keewis welcome
To his gloomy lodge of sandstone.
There without stood Hiawatha,
Found the doorways closed against him,
With his mittens, Minjekahwun,
Smote great caverns in the sandstone,
Cried aloud in tones of thunder,
"Open! I am Hiawatha!"
But the Old Man of the Mountain
Opened not, and made no answer
From the silent crags of sandstone,
From the gloomy rock abysses.
Then he raised his hands to heaven,
Called imploring on the tempest,
Called Waywassimo, the lightning,
And the thunder, Annemeekee;
And they came with night and darkness,
Sweeping down the Big-Sea-Water
From the distant Thunder Mountains;
And the trembling Pau-Puk-Keewis
Heard the footsteps of the thunder,
Saw the red eyes of the lightning,
Was afraid, and crouched and trembled.
Then Waywassimo, the lightning,
Smote the doorways of the caverns,
With his war-club smote the doorways,
Smote the jutting crags of sandstone,
And the thunder, Annemeekee,
Shouted down into the caverns,
Saying, "Where is Pau-Puk-Keewis!"
And the crags fell, and beneath them
Dead among the rocky ruins
Lay the cunning Pau-Puk-Keewis,
Lay the handsome Yenadizze,
Slain in his own human figure.
Ended were his wild adventures,
Ended were his tricks and gambols,
Ended all his craft and cunning,
Ended all his mischief-making,
All his gambling and his dancing,
All his wooing of the maidens.
Then the noble Hiawatha
Took his soul, his ghost, his shadow,
Spake and said: "O Pau-Puk-Keewis,
Never more in human figure
Shall you search for new adventures'
Never more with jest and laughter
Dance the dust and leaves in whirlwinds;
But above there in the heavens
You shall soar and sail in circles;
I will change you to an eagle,
To Keneu, the great war-eagle,
Chief of all the fowls with feathers,
Chief of Hiawatha's chickens."
And the name of Pau-Puk-Keewis
Lingers still among the people,
Lingers still among the singers,
And among the story-tellers;
And in Winter, when the snow-flakes
Whirl in eddies round the lodges,
When the wind in gusty tumult
O'er the smoke-flue pipes and whistles,
"There," they cry, "comes Pau-Puk-Keewis,
He is dancing through the village,
He is gathering in his harvest!"

Henry Wadsworth Longfellow
(The Song of Hiawatha)

Tuesday, March 11, 2008

My Last Duchess


That's my last Duchess painted on the wall,
Looking as if she were alive. I call
That piece a wonder, now: Frà Pandolf's hands
Worked busily a day, and there she stands.
Will 't please you sit and look at her? I said
"Frà Pandolf" by design, for never read
Strangers like you that pictured countenance,
The depth and passion of its earnest glance,
But to myself they turned (since none puts by
The curtain I have drawn for you, but I)
And seemed as they would ask me, if they durst,
How such a glance came there; so, not the first
Are you to turn and ask thus. Sir, 'twas not
Her husband's presence only, called that spot
Of joy into the Duchess' cheek: perhaps
Frà Pandolf chanced to say, "Her mantle laps
Over my Lady's wrist too much," or "Paint
Must never hope to reproduce the faint
Half-flush that dies along her throat"; such stuff
Was courtesy, she thought, and cause enough
For calling up that spot of joy. She had
A heart . . . how shall I say? . . . too soon made glad,
Too easily impressed; she liked whate'er
She looked on, and her looks went everywhere.
Sir, 'twas all one! My favour at her breast,
The dropping of the daylight in the West,
The bough of cherries some officious fool
Broke in the orchard for her, the white mule
She rode with round the terrace--all and each
Would draw from her alike the approving speech,
Or blush, at least. She thanked men,--good; but thanked
Somehow . . . I know not how . . . as if she ranked
My gift of a nine-hundred-years-old name
With anybody's gift. Who'd stoop to blame
This sort of trifling? Even had you skill
In speech--(which I have not)--to make your will
Quite clear to such an one, and say, "Just this
Or that in you disgusts me; here you miss,
Or there exceed the mark"--and if she let
Herself be lessoned so, nor plainly set
Her wits to yours, forsooth, and made excuse,
--E'en then would be some stooping; and I chuse
Never to stoop. Oh, sir, she smiled, no doubt,
Whene'er I passed her; but who passed without
Much the same smile? This grew; I gave commands;
Then all smiles stopped together. There she stands
As if alive. Will 't please you rise? We'll meet
The company below, then. I repeat,
The Count your Master's known munificence
Is ample warrant that no just pretence
Of mine for dowry will be disallowed;
Though his fair daughter's self, as I avowed
At starting, is my object. Nay, we'll go
Together down, Sir! Notice Neptune, though,
Taming a sea-horse, thought a rarity,
Which Claus of Innsbruck cast in bronze for me.

Robert Browning (1812-1889)

Tuesday, March 4, 2008


Sound the flute!
Now it's mute!
Birds delight,
Day and night,
In the dale,
Lark in sky, -
Merrily, merrily to welcome in the year.

Little boy,
Full of joy;
Little girl,
Sweet and small;
Cock does crow,
So do you;
Merry voice,
Infant noise;
Merrily, merrily to welcome in the year.

Little lamb,
Here I am;
Come and lick
My white neck;
Let me pull
Your soft wool;
Let me kiss
Your soft face;
Merrily, merrily we welcome in the year.

by William Blake

Monday, March 3, 2008


THAT for seven lusters I did never come
To do the rites to thy religious tomb ;
That neither hair was cut, or true tears shed
By me, o'er thee, as justments to the dead,
Forgive, forgive me ; since I did not know
Whether thy bones had here their rest or no.
But now 'tis known, behold! behold, I bring
Unto thy ghost th' effused offering :
And look what smallage, night-shade, cypress, yew,
Unto the shades have been, or now are due,
Here I devote ; and something more than so ;
I come to pay a debt of birth I owe.
Thou gav'st me life, but mortal ; for that one
Favour I'll make full satisfaction ;
For my life mortal rise from out thy herse,
And take a life immortal from my verse.

Seven lusters, five and thirty years.
Hair was cut, according to the Greek custom.
Justments, dues.
Smallage, water parsley.


Herrick, Robert.



O sweet illusions of Song,
That tempt me everywhere,
In the lonely fields, and the throng
Of the crowded thoroughfare!

I approach, and ye vanish away,
I grasp you, and ye are gone;
But ever by nigh an day,
The melody soundeth on.

As the weary traveller sees
In desert or prairie vast,
Blue lakes, overhung with trees,
That a pleasant shadow cast;

Fair towns with turrets high,
And shining roofs of gold,
That vanish as he draws nigh,
Like mists together rolled,--

So I wander and wander along,
And forever before me gleams
The shining city of song,
In the beautiful land of dreams.

But when I would enter the gate
Of that golden atmosphere,
It is gone, and I wander and wait
For the vision to reappear.

Poetry of Henry Wadsworth Longfellow
Birds of Passage