Notes

The poem summarises Richardson’s 1920 paper ‘The supply of energy from and to Atmospheric Eddies’

The LFR homepage quotes line 3 as ‘Little whorls have smaller whorls’; however, practically everywhere else has it as ‘lesser’, and this is more faithful to DeMorgan’s original. Also (and I’m being a trifle inconsistent here) the homepage has it in two lines rather than the more familiar quatrain format; this is actually the way DeMorgan had it, but the four line version is more popular and flows better IMO; I compromised by indenting the even lines.

The poem is untitled; I’ve merely followed the popular convention of using the first line as a title.

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.

Original:

From Bartlett’s Quotations,

AUTHOR: Jonathan Swift (1667-1745)

    QUOTATION:  So, naturalists observe, a flea
                Has smaller fleas that on him prey;
                And these have smaller still to bite 'em;
                And so proceed ad infinitum.

ATTRIBUTION: Poetry, a Rhapsody.

And as an addendum

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.

– Augustus De Morgan: A Budget of Paradoxes, p. 377.

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.

– EB

See also http://maths.paisley.ac.uk/LfR/Biography.htm for a timeline

Links

The LFR homepage:

http://maths.paisley.ac.uk/LfR/home.htm

Some quotations by DeMorgan

http://www-groups.dcs.st-andrews.ac.uk/~history/Quotations/De_Morgan.html

  For a nice if confusingly laid out introduction to turbulence
    [broken link] http://www.weizmann.ac.il/lvov/Lect/index.html

And one on fractals

http://math.rice.edu/~lanius/frac/

Chaos

http://www.pha.jhu.edu/~ldb/seminar/index.html

And so on to viscosity…

http://www.susqu.edu/facstaff/b/brakke/complexity/hagey/chaos.htm

The ‘science poems by scientists’ theme began at poem #795

Further reading: http://newton.ex.ac.uk/aip/catagories/chaos.html

— Martin