Relevant and resonant extracts from art, science and life and the place where patterns begin to emerge.
Entries in text (6)
Francis Everitt gave a fascinating talk yesterday at the departmental colloquium about the experimental mission - Gravity Probe B, which completed earlier this year, over forty years after its original conception. The aim of the mission was to verify Einstein's Theory of General Relativity, by investigating two extraordinary phenomena predicted by Einstein: the geodesic effect (warping of spacetime due to the Earth) and the frame dragging effect (the extent to which the earth drags its spacetime round with it). The project is a fantastic story of human vision, tenacity and imagination.
Emmy Noether was a great woman mathematician. She created one of the most beautiful and profound theories showing how our most fundamental conservation laws of energy, angular momentum, linear momentum and charge can be derived from corresponding symmetries. Here is Einstein's memorable and thought provoking tribute, published in the New York Times.
Professor Einstein Writes in Appreciation of a Fellow-Mathematician.
To the Editor of The New York Times:
The efforts of most human-beings are consumed in the struggle for their daily bread, but most of those who are, either through fortune or some special gift, relieved of this struggle are largely absorbed in further improving their worldly lot. Beneath the effort directed toward the accumulation of worldly goods lies all too frequently the illusion that this is the most substantial and desirable end to be achieved; but there is, fortunately, a minority composed of those who recognize early in their lives that the most beautiful and satisfying experiences open to humankind are not derived from the outside, but are bound up with the development of the individual's own feeling, thinking and acting. The genuine artists, investigators and thinkers have always been persons of this kind. However inconspicuously the life of these individuals runs its course, none the less the fruits of their endeavors are the most valuable contributions which one generation can make to its successors.
Within the past few days a distinguished mathematician, Professor Emmy Noether, formerly connected with the University of Göttingen and for the past two years at Bryn Mawr College, died in her fifty-third year. In the judgment of the most competent living mathematicians, Fräulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began. In the realm of algebra, in which the most gifted mathematicians have been busy for centuries, she discovered methods which have proved of enormous importance in the development of the present-day younger generation of mathematicians. Pure mathematics is, in its way, the poetry of logical ideas. One seeks the most general ideas of operation which will bring together in simple, logical and unified form the largest possible circle of formal relationships. In this effort toward logical beauty spiritual formulas are discovered necessary for the deeper penetration into the laws of nature.
Born in a Jewish family distinguished for the love of learning, Emmy Noether, who, in spite of the efforts of the great Göttingen mathematician, Hilbert, never reached the academic standing due her in her own country, none the less surrounded herself with a group of students and investigators at Göttingen, who have already become distinguished as teachers and investigators. Her unselfish, significant work over a period of many years was rewarded by the new rulers of Germany with a dismissal, which cost her the means of maintaining her simple life and the opportunity to carry on her mathematical studies. Farsighted friends of science in this country were fortunately able to make such arrangements at Bryn Mawr College and at Princeton that she found in America up to the day of her death not only colleagues who esteemed her friendship but grateful pupils whose enthusiasm made her last years the happiest and perhaps the most fruitful of her entire career.
Princeton University, May 1, 1935.
[New York Times May 5, 1935]
An email from a theoretical physicist friend continued my thinking about butterflies... Chuang-tzu was a Taoist teacher and writer who lived in the fourth century BC.
"Zhuangzi dreamed he was a butterfly" (莊周夢蝶 Zhuāng Zhōu mèng dié).
Once Zhuangzi dreamt he was a butterfly, a butterfly flitting and fluttering around, happy with himself and doing as he pleased. He didn't know he was Zhuangzi. Suddenly he woke up and there he was, solid and unmistakable Zhuangzi. But he didn't know if he was Zhuangzi who had dreamt he was a butterfly, or a butterfly dreaming he was Zhuangzi. Between Zhuangzi and a butterfly there must be some distinction! This is called the Transformation of Things. (2, tr. Burton Watson 1968:49)
Basho created this haiku in response.....
You are the butterfly
And I the dreaming heart
Photographed in a house in Brixton - most probably a Morpho
Freeman Dyson, end. Chap 1, 'Infinite in all Directions'
"This quick tour of the universe will begin with superstrings and end with butterflies. There will be a couple of intermediate stops on the way. Like Dante on his tour of the Inferno, I find at each level some colorful characters to add human interest to an otherwise intimidating scene. I will not explain what butterflies and superstrings are. To explain butterflies is unnecessary because everyone has seen them. To explain superstrings is impossible because nobody has seen them. But please do not think I am trying to mystify you. Superstrings and butterflies are examples illustrating two different aspects of the universe and two different notions of beauty. Super-strings come at the beginning and butterflies at the end because they are extreme examples. Butterflies are at the extreme of concreteness, superstrings at the extreme of abstraction. They mark the extreme limits of the territory over which science claims jurisdiction. Both are, in their different ways, beautiful. Both are, from a scientific point of view, poorly understood. Scientifically speaking, a butterfly is at least as mysterious as a superstring. When something ceases to be mysterious it ceases to be of absorbing concern to scientists. Almost all the things scientists think and dream about are mysterious...................
The last stop on our tour of the universe brings us back to my home in Princeton. We have descended from sky to earth, from abstract and speculative theories to the world of everyday reality. My youngest daughter came back from a music camp in Massachusetts carrying some Monarch caterpillars in a jar. She found them feeding on milkweed near the camp. We also have milkweed growing in Princeton and so she was able to keep the caterpillars alive. After a few days they stopped feeding, hung themselves up by their tails and began to pupate. The process of pupation is delightful to watch. They squeeze themselves up into the skin of the pupa, like a fat boy wriggling into a sleeping bag that is three sizes too small for him. At the beginning you cannot believe that the caterpillar will ever fit inside, and at the end it turns out that the sleeping bag was exactly the right size.
Two or three weeks later the butterflies emerge. The emergence is even more spectacular than the pupation. Out of the sleeping bag crawls the bedraggled remnant of the caterpillar, much reduced in size and with wet black stubs for wings. Then, in a few minutes, the body dries, the legs and antennae stiffen and the wings unfurl. The bedraggled little creature springs to life as a shimmering beauty of orange and white and black. We set her free in a nearby field and she flies high over the trees, disappearing into the sky. We hope that the move from Massachusetts to Princeton will not have disrupted the pattern of her autumn migration. With luck she will find companions to share with her the long journey to the Southwest. She has a long way to go, most of it against the prevailing winds.
The world of biology is full of miracles, but nothing I have seen is as miraculous as this metamorphosis of the Monarch caterpillar. Her brain is a speck of neural tissue a few millimeters long, about a million times smaller than a human brain. With this almost microscopic clump of nerve cells she knows how to manage her new legs and wings, to walk and to fly, to find her way by some unknown means of navigation over thousands of miles from Massachusetts to Mexico. How can all this be done? How are her behavior patterns programmed first into the genes of the caterpillar and then translated into the neural pathways of the butterfly? These are mysteries which our biological colleagues are very far from having understood. And yet, we can be confident that we are on the way toward understanding. Progress is rapid in all the necessary disciplines: biochemistry, genetics, embryology, cytology and neurophysiology. Within twenty or fifty years, we will probably be able to read the message that is written in the DNA of the caterpillar. Then we will see in detail how this message is able to direct the formation of a pupa, of legs and wings, and of a brain capable of long-range navigation. Before long, all these marvels of biochemical technology will be within our grasp. And we shall then be able, if we so choose, to apply the technology of the butterfly to our own purposes.
That is the end of our tour. I have given you brief glimpses of four pieces of the universe with which I have to deal as a scientist. First, the superstrings, our latest attempt to impose a deep mathematical unity on the laws of physics. Second, the black holes, the conceptual laboratories in which we play with the structure of space and time. Third, the Oort Cloud, and the comet showers which we imagine guiding the evolution of life on our planet. Fourth, the Monarch butterfly, which flies up into the summer sky, over the trees and far away, a symbol of evanescent beauty and a living proof that nature's imagination is richer than our own."
Vladimir and Vera Nabokov and a drawing by Nabokov
The lepidopterist and writer, Vladimir Nabokov said of the gap between science and art:
'a mere dimple of a ditch that a small frog could straddle'.
A fleeting 45 second film: 'butterflies are like ideas'. One touch and they are gone.
Source: De Waals - 'The Hare with the Amber Eyes'