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Best Mathematical Writing - Wislawa Szymborska

In several of her poems, the Polish Nobel Laureate Wislawa Szymborska (1923-2012) shared her fascination for the infinite realm of numbers. Here she sings the praises of the mathematical constant Pi:

The admirable number pi:
three point one four one.
All the following digits are also initial,
five nine two because it never ends.
It can't be comprehended six five three five at a glance,
eight nine by calculation,
seven nine or imagination,
not even three two three eight by wit, that is, by comparison
four six to anything else
two six four three in the world.
The longest snake on earth calls it quits at about forty feet.
Likewise, snakes of myth and legend, though they may hold out a bit longer.
The pageant of digits comprising the number pi
doesn't stop at the page's edge.
It goes on across the table, through the air,
over a wall, a leaf, a bird's nest, clouds, straight into the sky,
through all the bottomless, bloated heavens.
Oh how brief - a mouse tail, a pigtail - is the tail of a comet!
How feeble the star's ray, bent by bumping up against space!
While here we have two three fifteen three hundred nineteen
my phone number your shirt size the year
nineteen hundred and seventy-three the sixth floor
the number of inhabitants sixty-five cents
hip measurement two fingers a charade, a code,
in which we find hail to thee, blithe spirit, bird thou never wert
alongside ladies and gentlemen, no cause for alarm,
as well as heaven and earth shall pass away,
but not the number pi, oh no, nothing doing,
it keeps right on with its rather remarkable five,
its uncommonly fine eight,
its far from final seven,
nudging, always nudging a sluggish eternity
to continue.

To learn more about Wislawa Szymborska: http://www.nobelprize.org/nobel_prizes/literature/laureates/1996/szymborska-poetry.html

Best Mathematical Writing - Henri Poincaré

Mathematical writing, I want to show, can be as rich and rewarding as any 'fiction'. Today's example comes from the great French mathematician Henri Poincaré (1854-1912) and his book Science and Method:

Tolstoy explains somewhere in his writings why, in his opinion, "Science for Science's sake" is an absurd conception. We cannot know all the facts, since they are practically infinite in number. We must make a selection; and that being so, can this selection be governed by the mere caprice of our curiosity? Is it not better to be guided by utility, by our practical, and more especially our moral, necessities? Have we not some better occupation than counting the number of ladybirds in existence on this planet? ...

A selection [of facts] must be made: however great our activity, facts outstrip us, and we can never overtake them; while the scientist is discovering one fact, millions and millions are produced in every cubic inch of his body ...

But scientists believe that there is a hierarchy of facts ... they are right, for otherwise there would be no science ...

The most interesting facts are those which can be used several times, those which have a chance of recurring ... What we must aim at is not so much to ascertain resemblances and differences, as to discover similarities hidden under apparent discrepancies ... on looking closer we can generally detect a resemblance; though differing in matter, they approximate in form and in the order of their parts. When we examine them from this point of view, we shall see them widen and tend to embrace everything. This is what gives value to certain facts that come to complete a whole, and show that it is the faithful image of other known wholes.

Best Mathematical Writing - J. B. S. Haldane

In the right hands, 'non-fiction' prose can be just as creative, imaginative, stylish, and fun as 'fiction'. The best maths-inspired writing provides a shining example. Over the coming days I will introduce you to some of my favourite mathematical writers: scientists and philosophers, novelists and poets, including short excerpts from their finest work.

Today's pick is the British biologist J. B. S. Haldane (1892-1964) and his wonderful essay 'On Being the Right Size':

The most obvious differences between different animals are differences of size, but for some reason the zoologists have paid singularly little attention to them. In a large textbook of zoology before me I find no indication that the eagle is larger than the sparrow, or the hippopotamus bigger than the hare, though some grudging admissions are made in the case of the mouse and the whale. But yet it is easy to show that a hare could not be as large as a hippopotamus, or a whale as small as a herring. For every type of animal there is a most convenient size, and a large change in size inevitably carries with it a change of form.

Let us take the most obvious of possible cases, and consider a giant man sixty feet high—about the height of Giant Pope and Giant Pagan in the illustrated Pilgrim’s Progress of my childhood. These monsters were not only ten times as high as Christian, but ten times as wide and ten times as thick, so that their total weight was a thousand times his, or about eighty to ninety tons. Unfortunately the cross sections of their bones were only a hundred times those of Christian, so that every square inch of giant bone had to support ten times the weight borne by a square inch of human bone. As the human thigh-bone breaks under about ten times the human weight, Pope and Pagan would have broken their thighs every time they took a step. This was doubtless why they were sitting down in the picture I remember. But it lessens one’s respect for Christian and Jack the Giant Killer ...

Gravity, a mere nuisance to Christian, was a terror to Pope, Pagan, and Despair. To the mouse and any smaller animal it presents practically no dangers. You can drop a mouse down a thousand-yard mine shaft; and, on arriving at the bottom, it gets a slight shock and walks away, provided that the ground is fairly soft. A rat is killed, a man is broken, a horse splashes.

You can read Haldane's essay in full here: http://irl.cs.ucla.edu/papers/right-size.html

Video for Thinking in Numbers!

What was Count von Count's favourite number?

Apparently it was 34,969. For those who have never seen Sesame Street, here's a quick video of the count in his prime: http://www.youtube.com/watch?v=TJxKvwMIVtA Btw 34,969 is divisible by 17 (it's 187 squared, or ((17 x 17) x (11 x 11)). The BBC website has more: http://www.bbc.co.uk/news/magazine-19409960