[797] Big Whorls Have Little Whorls

Big whorls have little whorls
  That feed on their velocity,
And little whorls have lesser whorls
  And so on to viscosity.

 	-- Lewis F. Richardson

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
    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

From: Abraham Thomas <Thomas@>

In addition to his work on meteorology, Richardson was a pioneer in the
field of computational mathematics, specifically, the design of numerical
algorithms for the solution of ordinary and partial differential equations -
algorithms which came into their own with the advent of electronic
computers. Later in his career, he turned to the study of war and conflict,
and was one of the first mathematicians to apply statistical tools to
sociological analysis. 

http://world.std.com/~jlr/comment/statistics.htm has a fairly detailed
review of "The Statistics of Deadly Quarrels", Richardson's seminal work on
war.

http://www.siam.org/siamnews/bookrevs/weather.htm has a Richardson biography
that's a lot more comprehensive than EB's. Skip the first 5 or 6 paragraphs,
they're about something else. 

Incidentally, the final episode of Carl Sagan's wonderful TV series "Cosmos"
(and the final chapter of his equally wonderful book of the same name),
titled "Who Speaks For Earth?" has quite a bit about Richardson and his
analysis of conflict.