http://wonderingminstrels.blogspot.com/2001/05/big-whorls-have-little-whorls-lewis-f.html wrote:
- " Big whorls have little whorls
That feed on their velocity,
And little whorls have lesser whorls
And so on to viscosity."
-- Lewis F Richardson
I first encountered this wonderful verselet in James Gleick's 'Chaos'
(highly recommended, incidentally - a very understandable and well-written
introduction to the topic), and was instantly captivated. The poem works on
two levels - both as a delightfully well-done parody of DeMorgan's famous
paraphrase of Swift, and as as nice a summation of the fractal nature of
turbulence as any I've seen. - martin
Biography:
Richardson, Lewis Fry
b. Oct. 11, 1881, Newcastle upon Tyne, Northumberland, Eng.
d. Sept. 30, 1953, Kilmun, Argyll, Scot.
British physicist and psychologist who was the first to apply mathematical
techniques to predict the weather accurately.
Richardson made major contributions to methods of solving certain types of
problems in physics, and from 1913 to 1922 he applied his ideas to
meteorology. His work, published in Weather Prediction by Numerical
Process (1922), was not entirely successful at first. The main drawback to
his mathematical technique for systematically forecasting the weather was
the time necessary to produce such a forecast. It generally took him three
months to predict the weather for the next 24 hours. With the advent of
electronic computers after World War II, his method of weather prediction,
somewhat altered and improved, became practical. The Richardson number,
a fundamental quantity involving the gradients (change over a distance)
of temperature and wind velocity, is named after him.
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http://en.wikipedia.org/wiki/Ad_infinitum wrote:
The 17th century writer Jonathan Swift mocked the idea of self-similarity in natural philosophy with the following lines in his poem 'On Poetry: A Rhapsody':
- "So nat'ralists observe, a flea
Hath smaller fleas that on him prey,
And these have smaller fleas that bite 'em,
And so proceed ad infinitum."
The Victorian era mathematician Augustus De Morgan expanded on this with a similar verse:
- "Great fleas have little fleas upon their backs to bite 'em,
And little fleas have lesser fleas, and so ad infinitum.
And the great fleas themselves, in turn, have greater fleas to go on,
While these again have greater still, and greater still, and so on."