January 6, 2011

Dinner at Bernoulli’s

Nikolaus Bernoulli. an apothecary in Basel, Switzerland, in the 17th century, had a nice little spice business going.  He hoped to see it taken over by one of his three sons, but he couldn’t seem to get any of them interested.  So he urged his eldest – Jacob, whose birthday it is today – to study theology, which Jacob dutifully did, although he was also studying mathematics and philosophy on the side.

Jacob Bernoulli

Johann, the youngest, also refused to go into the spice business, so his father bade him study law.  Johann agreed, but followed his older brother instead, studying and collaborating with Jacob.

Nikolaus Junior became a painter and alderman, the only one of his generation not to contriibute a Bernoulli whatsis to either math or physics.  His three nephews, Johann’s sons Daniel, Nikolaus and Johann Jr., on the other hand gave us Bernoulli’s Principle, Distribution and Trial.

So there is Nikolaus the Apothecary at the head of the table grumbling and sulking because his three geniuses are busy arguing probabliity theory, infinitesimal calculus and optics –  and showing no interest at all in spices. It gets even worse when his grandchildren – math prodigies all – show up. Dinner probably wasn’t much fun for Mrs. Bernoulli either.

Helianthus, photo by L. Shyamal

Jacob Bernoulli, the first to formulate inseparable differential calculus and creator of Bernoulli’s theorem, was enthralled by what he called the ‘spira mirabilis’ – the miracle spiral.  Descartes had first identified the logarithmic spiral, but Bernoulli spent much of his intellectual life exploring it.

What is interesting to mathematicians and laymen alike is the appearance of the spiral in nature:  it is the pattern of sunflower seeds. the nerves of the cornea, the flight of a hawk circling its prey, seashells, molluscs, spiral galaxies and you can even see it in the spiral beach form at Half Moon Bay in California.

Gravemarker with wrong spiral. Photo by Wladyslaw Sojka

He once wrote of the spiral that it  “may be used as a symbol, either of fortitude and constancy in adversity, or of the human body, which after all its changes, even after death, will be restored to its exact and perfect self.”

So fond of the spiral was Bernoulli, that he arranged to have it carved on his headstone; he would have been dismayed to find the carver had inscribed an Archimedean spiral instead.



  1. Now this is a mind-expander for me today! I had to look up some photographed examples – the Chambered Nautilus seashell certainly lives up to the “mirabilis” label! This deep-sea survivor from the Pleistocene inspired Oliver Wendell Holmes to describe it as a “ship of pearl” whose “silent toil/That spread his lustrous coil/Still, as the spiral grew/He left the past year’s dwelling for the new.” The spiral form is inspirational indeed!


    Comment by Celia Carroll — January 6, 2011 @ 9:35 am | Reply

  2. This blog really goes to the core of things! Celia knows this too!


    Comment by GALYA TARMU — January 6, 2011 @ 3:37 pm | Reply

  3. very cool post!! interessante… 😉


    Comment by Nina C — January 6, 2011 @ 11:00 pm | Reply



    Comment by avery — January 7, 2011 @ 11:19 am | Reply

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