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[Phys-L] Kepler, Raleigh, Cannon-balls and Oranges



Keith S. Taber wrote on Wed, Jul 6 at 11:18 AM
I've just found the book ('On the six-cornered snowflake') and as far as
I can see his example was the 'pellets' (the terms used in the English
translation I have - is that what they are normally called?) in the
pomegranate, then he switches to non-specific 'balls' - perhaps he later
applied his theory more specifically to cannon balls-  /snip/

Keith

There seems to be some doubt about the temporal sequence of the historical record.....
Phillip Ball wrote in Nature:“There must be a cause why snow has the shape of a six-cornered starlet,” Kepler wrote in De nive sexangula. “It cannot be chance. Why always six? The cause is not to be looked for in the material, for vapour is formless and flows, but in an agent.” This 'agent', he suspected, might be mechanical: the orderly stacking of frozen 'globules' that represent “the smallest natural unit of a liquid like water” — not explicitly atoms, but as good as.        Here he was indebted to the English mathematician Thomas Harriot, who acted as a navigator for Walter Raleigh's voyages to the New World in 1584–5. Raleigh sought Harriot's advice on the most efficient way to stack cannonballs on the ship's deck, prompting the ingenious Harriot to theorize about the close-packing of spheres. Around 1606–8, Harriot communicated his thoughts to Kepler, who returned to the issue in De nive sexangula.       A booklet of just 24 pages, it was written in 1611     [ Ball, P. In retrospect: On the Six-Cornered Snowflake. Nature 480, 455 (2011). https://doi.org/10.1038/480455a ;]


There is another source not so sure about the Raleigh/Harriot/Kepler connection, however.   Roberto Cardil (matematicasVisuales) wrote in Mathematical Association of America (on-line):

"Kepler may have become interested in the question of the stacking of spheres through Thomas Harriot (ca 1560–1621). Harriot was an English mathematician, astronomer, and a friend and adviser to Sir Walter Raleigh (ca 1552–1618). Raleigh asked Harriot to solve several problems about the stacking of cannonballs because, as a sea explorer, he needed to deal with the issue on a practical level.  /snip/
It is not known whether Harriot shared the problem of the best way to pack cannonballs with Kepler. We do know that they exchanged a few letters, with optics as the main subject of their correspondence"    [ https://www.maa.org/press/periodicals/convergence/kepler-and-the-rhombic-dodecahedron-stacking-cannonballs ;]


Finally, a detail: The Kepler  monograph contains a pun which is explained in the letter of dedication to Kepler’s friend Matthias Wacker. Due to his great modesty, Wacker wants only a very tiny New Year's gift. Now he receives nix, which can be interpreted not only as the Latin word for “snow”, but also as the German word for "nothing".[ https://wiki.uibk.ac.at/noscemus/De_nive_sexangula ;]