Steckt keine Poesie in der Lokomotive, die brausend durch die Nacht zieht und über die zitternde Erde hintobt, als wollte sie Raum und Zeit zermalmen, in dem hastigen, aber wohl geregelten Zucken und Zerren ihrer gewaltigen Glieder, in dem stieren, nur auf ein Ziel losstürmenden Blick ihrer roten Augen, in dem emsigen, willenlosen Gefolge der Wagen, die kreischend und klappernd, aber mit unfehlbarer Sicherheit dem verkörperten Willen aus Eisen und Stahl folge leisten?
Is there no poetry in the locomotive roaring through the night and charging over the quivering earth as if it wanted to crush time and space? Is there no poetry in the hasty but regular jerking and tugging of its powerful limbs, in the stare of its red eyes that never lose sight of their goal? Is there no poetry in the bustling, will-less retinue of cars that follow, screeching and clattering with unmistakable surety, the steel and iron embodiment of will?

Euclid alone has looked on Beauty bare.
Let all who prate of Beauty hold their peace,
And lay them prone upon the earth and cease
To ponder on themselves, the while they stare
At nothing, intricately drawn nowhere
In shapes of shifting lineage; let geese
Gabble and hiss, but heroes seek release
From dusty bondage into luminous air.
O blinding hour, O holy, terrible day,
When first the shaft into his vision shone
Of light anatomized! Euclid alone
Has looked on Beauty bare. Fortunate they
Who, though once only and then but far away,
Have heard her massive sandal set on stone.

Euclid alone
Has looked on Beauty bare.
He turned away at once;
Far too polite to stare.

Forty years as an astronomer have not quelled my enthusiasm for lying outside after dark, staring up at the stars. It isn’t only the beauty of the night sky that thrills me. It’s the sense I have that some of those points of light—which ones I can’t even guess—are the home stars of beings not so different from us, daily cares and all, who look across space and wonder, just as we do.

He saw virus particles shaped like snakes, in negative images. They were white cobras tangled among themselves, like the hair of Medusa. They were the face of nature herself, the obscene goddess revealed naked. This life form thing was breathtakingly beautiful. As he stared at it, he found himself being pulled out of the human world into a world where moral boundaries blur and finally dissolve completely. He was lost in wonder and admiration, even though he knew that he was the prey.

I find sitting at a specially equipped desk in front of some pretty ugly plastics and staring at a little window is a very unnatural event.

Most, if not all, of the great ideas of modern mathematics have had their origin in observation. Take, for instance, the arithmetical theory of forms, of which the foundation was laid in the diophantine theorems of Fermat, left without proof by their author, which resisted all efforts of the myriad-minded Euler to reduce to demonstration, and only yielded up their cause of being when turned over in the blow-pipe flame of Gauss’s transcendent genius; or the doctrine of double periodicity, which resulted from the observation of Jacobi of a purely analytical fact of transformation; or Legendre’s law of reciprocity; or Sturm’s theorem about the roots of equations, which, as he informed me with his own lips, stared him in the face in the midst of some mechanical investigations connected (if my memory serves me right) with the motion of compound pendulums; or Huyghen’s method of continued fractions, characterized by Lagrange as one of the principal discoveries of that great mathematician, and to which he appears to have been led by the construction of his Planetary Automaton; or the new algebra, speaking of which one of my predecessors (Mr. Spottiswoode) has said, not without just reason and authority, from this chair, “that it reaches out and indissolubly connects itself each year with fresh branches of mathematics, that the theory of equations has become almost new through it, algebraic geometry transfigured in its light, that the calculus of variations, molecular physics, and mechanics” (he might, if speaking at the present moment, go on to add the theory of elasticity and the development of the integral calculus) “have all felt its influence”.

The worst primary school scolding I ever received was for ridiculing a classmate who asked, ‘What’s an atom?’ To my third grader’s mind, the question betrayed a level of ignorance more befitting a preschooler, but the teacher disagreed and banned me from recess for a week. I had forgotten the incident until a few years ago, while sitting in on a quantum mechanics class taught by a Nobel Prizewinning physicist. Midway through a brutally abstract lecture on the hydrogen atom, a plucky sophomore raised his hand and asked the very same question. To the astonishment of all, our speaker fell silent. He stared out the window for what seemed like an eternity before answering, ‘I don’t know.’

We dissect nature along lines laid down by our native languages. The categories and types that we isolate from the world of phenomena we do not find there because they stare every observer in the face; on the contrary, the world is presented in a kaleidoscopic flux of impressions which has to be organized by our minds—and this means largely by the linguistic systems in our minds.