Mathematics of waving wheat

Here on the Yorkshire Wolds Way, we’ve walked by many fields of wheat waving in the breeze. It’s beautiful how at any given moment, twenty patches are waving left and another twenty are waving right. Back and forth, forth and back, each plant coupled to some friends nearby but uncoupled to those ten feet away.

What makes this possible is that each stem of wheat, viewed as an oscillator, is in the underdamped regime. If the damping were stronger, we’d see much less motion, with the plants bending placidly in proportion to the local wind speed. The waving back and forth reveals that the damping is subcritical.

[25 August 2019]

Mathematical prerequisites for public office (II)

Yesterday Boris Johnson announced an additional one billion pounds to prepare for a possible no-deal Brexit.

Today he stated that the chances against a no-deal Brexit were “a million to one”. When asked for clarification, he repeated that this was his estimate “exactly”.

Combining these figures, we see that Johnson’s estimate of the costs associated with a no-deal Brexit is on the order of one quadrillion (1,000,000,000,000,000) pounds.

[29 July 2019]

The end of Oxford’s science library

The humanities and the sciences differ all over the world, but at Oxford the gulf is especially wide. Science students and faculty spend their time mainly in departments, while humanities people are mainly in colleges. With a wife in English Literature, I see this up close and personal.

And now the gulf is to be widened further. The university has long had far better libraries for the humanities than for the sciences. But now it has been decided that scientists do not use books, and the Radcliffe Science Library will be merged into a new science-oriented Parks College. Most of the books will be shipped away to a site in another city.

One could take two opposing views of this transition. Lovers of the past might say, Oxford’s already dim science library provision is being made dimmer. Apostles of the future might say, the difference between humanities and sciences is a real one, and Oxford is showing world leadership in optimizing both sides independently. I’m in the first camp, but I realize I may be mistaken.

[12 June 2019]

Social change on display at WHSmith

I went to WHSmith this morning to buy a magazine. They’ve moved! Magazines are no longer in the entrance, but tucked away out of sight in the back. The entrance is now given over to greeting cards.

But not entirely. Along with the greeting cards, WHSmith now devotes its prime retail area to plastic water bottles. I saw stacks, rows, cases of 15, more cases, more rows, here there and around every corner. I counted. As of 8:30 this morning, WHSmith Oxford has 1570 plastic water bottles on display.

[14 June 2019]

One day in Zimbabwe

On April 1 André and Marí Weideman and I spent a few hours is a hide around dawn, then a few more hours in the Stanley and Livingstone game reserve around sunset. In what will surely be my most remarkable wildlife day ever we saw

baboon, black rhinoceros, buffalo, bush buck, crocodile, elephant, giraffe, hippopotamus, impala, kudu, leopard tortoise, lion, squirrel, warthog, zebra

and

bee eater, double-banded sand grouse, drongo, emerald dove, egret, Egyptian goose, fish eagle, francolin, grey heron, grey lourie, guinea fowl, hammerhead, hornbill, lapwing, marabou, open-billed stork, pied kingfisher, red-billed oxpecker, strand kiewiet, thickhead, turtle dove, weaver, white-headed vulture.

[12 June 2019]

Turing Awards and Numerical Analysis

Numerical analysts played a leading role in creating the field of computer science in the 1960s. There were Gautschi and Rice at Purdue, Forsythe and Golub at Stanford, Bauer in Munich, Stiefel and Rutishauser in Zurich, Bennett in Sydney, Fox at Oxford, Gear at Illinois, Dahlquist in Stockholm,….

Half a century on, there have been 70 winners of the Turing Award, computer science’s highest honor. How many have been numerical analysts? The answer is three, if you include Richard Hamming (1968). Wilkinson (1970) and Kahan (1989) were the other two, 30+ years ago.

[4 June 2019]

Many-worlds interpretation of rounding errors

Every floating-point rounding error, Wilkinson teaches us, can be interpreted by backward error analysis: it’s the exact result, but for slightly perturbed data.

Every quantum mechanical measurement, Everett teaches us, can be interpreted as the splitting of two universes: one where this choice happens, the other with the other.

I like to imagine a kind of Everett–Wilkinson interpretation. Every floating-point operation is exact, hooray! — but each time one happens, we are jiggled ever so slightly, just one part in 1016, into a neighboring universe.

[17 February 2015]