[Image: “Golden Rectangle,” by “Greg” (user “sightrays”) on Flickr. (Used here under a Creative Commons license; thank you!) The explanation at that page provides much more detail than I can here. The gist, though, is that a “golden spiral” appears to home in on a particular point — where the diagonals of the two rectangles making a golden rectangle intersect — but in fact, never really reaches that point: the spiral is infinite in length.]
Not from whiskey river:
Nature Knows Its Math
the snow then
(Joan Graham [source])
[Let us consider] the common idea that mathematics is a dull subject, whereas the testimony of all those who have any dealing with it shows that it is one of the most thrilling and tantalising and enchanting subjects in the world. It is abstract, but so, to all appearance, is theology. Men have hurled themselves on the spears of their enemies rather than admit that the second person of the Trinity was not co-eternal with the first. Men have been burned by inches rather than allow that the charge to Peter was to be a charge to him as an individual rather than to him as a representative of the Apostles. Of such questions as these it is perfectly reasonable for anyone to say that, in his opinion, they are preposterous and fanatical questions. And what men have before now done for the abstractions of theology I have little doubt that they would, if necessary, do for the abstractions of mathematics. If human history and human variety teach us anything at all, it is supremely probable that there are men who would be stabbed in battle or burnt at the stake rather than admit that three angles of a triangle could be together greater than two right angles.
The truth surely is that it is perfectly permissible and perfectly natural to become bored with a subject just as it is perfectly permissible and perfectly natural to be thrown from a horse or to miss a train or to look up the answer to a puzzle at the end of a book. But it is not a triumph if it is anything at all, it is a defeat. We have certainly no right to assume offhand that the fault lies with the horse or with the subject.
(G.K. Chesterton [source])
For knowledge, says the Old Sage, add; for wisdom,
subtract. My head in a surgeon’s chair, checking
Lao Tsu’s math as these teeth I barely knew
I had (mumbled of as wisdom) introduced
themselves—rude party guests—right as they had
to go, their pinched goodbye-hello. Like learning
you’ve been speaking your whole life in prose,
or my late eighth-grade astonishment that I—
confirmed a Gentile in almost all respects—
had hung so long among the circumcised.
Hard to know what you have, I’ll have you know.
Harder to know what you haven’t. Knowledge! The nerve!
Hushed up like a gulp behind the tongue,
shrewdly shooting roots down at an age
my gums were smug from rolling words around,
when my morals (like my molars) proved
basically interchangeable. Wise
I wasn’t, but I wanted it so painfully then.
Now I’ve had it—you have it, doc. You know
the drill, or whatever you’ve got. Take it away…
(Kevin McFadden [source])
For the mathematician Henri Poincaré, beauty was classical, not baroque, a simple purity of line and idea, the absence of ambiguity. Nature doesn’t always reveal itself that simply, but when it does, it strikes a mental chord. Doing creative mathematics meant discovering the rare “unsuspected kinship between… facts, long known, but wrongly believe to be strangers to one another.” For Poincaré, to invent was to choose. He remembered vividly when the solution to a particularly stubborn problem came to him:
Just at this time I left Caen, where I was then living, to go on a geological excursion under the auspices of the school of mines. The changes of travel made me forget my mathematical work. Having reached Coutances, we entered an omnibus to go some place or other. At the moment when I put my foot on the step the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Euclidean geometry.
Where did the sudden illumination come from? The subliminal self, including long spells of unconscious toil beforehand, priming the pump, laying down a bedrock of memories. And afterward, the work of shaping, deducing, verifying. Any great lightning-bolt insight requires a before and after.
(Diane Ackerman [source])
…and, from whiskey river (the poem’s last stanza), the trigger for my own weekly wandering around the Web:
Just before she flew off like a swan
to her wealthy parents’ summer home,
Bruce’s college girlfriend asked him
to improve his expertise at oral sex,
and offered him some technical advice:
Use nothing but his tonguetip
to flick the light switch in his room
on and off a hundred times a day
until he grew fluent at the nuances
of force and latitude.
Imagine him at practice every evening,
more inspired than he ever was at algebra,
beads of sweat sprouting on his brow,
thinking, thirty-seven, thirty-eight,
seeing, in the tunnel vision of his mind’s eye,
the quadratic equation of her climax
yield to the logic
of his simple math.
Maybe he unscrewed
the bulb from his apartment ceiling
so that passersby would not believe
a giant firefly was pulsing
its electric abdomen in 13 B.
Maybe, as he stood
two inches from the wall,
in darkness, fogging the old plaster
with his breath, he visualized the future
as a mansion standing on the shore
that he was rowing to
with his tongue’s exhausted oar.
Of course, the girlfriend dumped him:
met someone, apres-ski, who,
using nothing but his nose
could identify the vintage of a Cabernet.
Sometimes we are asked
to get good at something we have
no talent for,
or we excel at something we will never
have the opportunity to prove.
Often we ask ourselves
to make absolute sense
out of what just happens,
and in this way, what we are practicing
which everybody practices,
but strangely few of us
grow graceful in.
The climaxes of suffering are complex,
costly, beautiful, but secret.
Bruce never played the light switch again.
So the avenues we walk down,
full of bodies wearing faces,
are full of hidden talent:
enough to make pianos moan,
streetlights deliriously flicker.
(Tony Hoagland [source])