The Precious Beaver Testicles of Gerald Of Wales

History remembers the killer apps which remade the world--the printing presses, the cotton gins, the fire.  The conquering army, the victorious legislator, the trailblazing poet--these are the names that will live on forever.

And you're not one of them.  And I'm not one of them.  And nobody you've ever met is one of them.  (Probably.)

Clio, muse of history, probably doesn't even know your goddamn name.

No, our world is rich in folly and failure.  Medical researchers calculated the half life of a given truth to be 45 years.  That is, of any given set of facts (all things being equal) half will be disproved in a little less than half a century.  So in forty-five years, half of everything you think is true will be proven wrong.  No wonder old people get so cranky.

Brilliance, humility and genius prove no antidote to failure.  Take the ebullient medieval scholar Gerald of Wales, who lived in the 12th Century.  Tall and fearsome and erudite, Gerald became a churchman and a politician.  The undisputed 'universal scholar' of his age travelled to the peripheries of the British Isles.  These trips resulted in exemplary, entertaining and learned histories of Ireland and Wales which remain go-to historical sources.  In addition to these travelogues Gerald published about twenty other tomes on topics ranging from theology to hagiography to biography.  (It was the 12th Century:  there wasn't really any wiggle room about genre).  Gerald of Wales combined his era's best learning with keen empirical observation.  If anyone should have avoided folly, it would have been Gerald of Wales.

But even poor Gerald fell prone to mistake.  Here's just one.  Nestled at the end of a fine description of a European beaver colony, Gerald goes off on a tangent about how when beavers are frightened they bite off their own testicles.

Wait, what?

Yes, you read right.  Gerald of Wales thought that when hunted, male beavers chomped off their own balls with their sharp sharp teeth.

Gerald's peculiar observation has some source.  He is going off a description of beavers in Aesop's fables, in which the beavers, hunted for their useful testicles, wisely detached their gonads from their bodies and offered them to the slavering dogs--gratis--so that they could go on their merry way, alive but gelded.  This is backed up in Pliny's Natural history which tells pretty much the same story.

Now you can wear the unmistakable scent of beaver anal glands!

And even this is not as crazy as it seems at first blush.  Beavers were hunted for a thing called castoreum--which Pliny, Aesop, and Gerald all misidentified as the beaver's balls.  Actually castoreum comes from glands in the beaver's anus and it proves incredibly useful--it remains in use today as a perfume base (giving 'animal notes') and a food additive.  A Scandinavian schnaps called Bäverhojt is flavored with castor.

Now you can taste the unmistakeable relish of beaver anal glands!

So the myth of beaver's self-castrating self-preservation is explained, if not excused.

And this is how the parade of folly makes its march down the avenue of history:  a misheard word, a bad joke, a good guess that turns out wrong--repeated again and again until it assumes the air of truth.  And in forty-five years, if the scientists have it right, half of what I've written here will also be filed away in the ignoble archives of idiocy.

This post was inspired by the always-inspiring In Our Time with Melvyn Bragg, which recently ran an episode on Gerald of Wales.

Letters, Lies and Calculus

In 1696 Guillaume de l'Hôpital published one of the first calculus textbooks, euphoniously entitled Analysis of the Infinitely Small for the Understanding of Curved Lines--or the Analyse for short.  In the Analyse's pages l'Hôpital laid out a method of figuring out the limits of indeterminate forms that was a huge deal in the burgeoning field of calculus.  It made L'Hôpital a star.

With all the linguistic verve of mathematicians, the rule was dubbed l'Hôpital's Rule, and ever since it has been rammed into the heads of calculus students, where it remains, a bit of discarded fact lodged somewhere between first girlfriend's middle name and capital of Peru.

As you can probably tell from the de appended to l'Hôpital's name (and the frothy wig perched on his head) good old Guillaume was a nobleman.  More than that, he mixed a genuine mathematical curiosity with the ability to straightforwardly explain the stuff he was interested in.  But while l'Hôpital was undoubtably a very good mathematician, and his textbook remained required reading for a hundred years, it turns out that all of the great discoveries that l'Hôpital is known for--including the eponymous rule--weren't actually discovered by l'Hôpital.  He merely owned them.

It all started in the salon of Malebranche, where the aristocratic thirty-something savant l'Hôpital met the 24-year old wannabe math nerd Johann (sometimes John) Bernoulli.  At some point in the night Bernoulli whipped out his 'secret weapon'--an unpublished forumla on how to figure out the radius of the curvature of a curve.   L'Hôpital, impressed, signed Bernoulli up to be his calculus tutor for ten months.  In 1694 l'Hôpital offered Bernoulli a further three hundred francs a year if he would tell him everything he could about this new-fangled calculus--and not tell anyone else.  Bernoulli agreed, and produced a series of brilliant letters explaining everything l'Hôpital could hope to know--and then some.  L'Hôpital would then take the insights Bernoulli told him and pass them off as his own, reaping the fame.

When l'Hôpital died, Johann Bernoulli claimed much of the content of l'Hôpital's work.  The famous textbook?  Actually that amounted to the ten-month course Bernoulli taught l'Hôpital.  The rule?  It should be Bernoulli's Rule.  L'Hôpital's work on conic sections?  That was Bernoulli's work.  But no one believed him.

There was good reason for this.  Johann Bernoulli was an irascible  thin-skinned man who involved himself in quite a few mathematical kerfuffles.  One acrimonious struggle was with his own son Daniel.  To win the argument (against his own son!) over who came up with some principle of hydrodynamics first, Johann resorted to forgery.

So clearly Bernoulli was jealous of his reputation.  Since he didn't claim l'Hôpital's discoveries with any special grievance, people just thought Johann's claim was just Johann being Johann again.

But Johann Bernoulli was right.  And nobody realized until 1922, when Bernoulli's first calculus lectures were discovered in a musty archive somewhere.   They were written before l'Hôpital's textbook.  And they were undoubtedly l'Hôpital's inspiration for the Analyse.  The L'Hôpital's Rule is really Bernoulli's Rule.

But I suspect that renaming l'Hôpital's Rule is just plain greedy.  The Bernoullis claim a menagerie of grey matter so quirky and brilliant that the three generations of genius could easily make up the cast of a Wes Anderson film.  (Bill Murray as Johann Bernoulli; Jason Schwartzman as Daniel Bernoulli.  Right?)  Because of this tons of stuff is already named after them.  There's the Bernoulli Effect.  The Bernoulli Principle.  The Bernoulli Distribution.  The Bernoulli Theorem.  These range over the domains of statistics, fluid dynamics, and calculus--and they are only a small sampling of the discoveries pinned with the Bernoulli name.  Do we really need a Bernoulli Rule?  Really?  The rule itself is confusing enough as it is.  We don't need to go messing around with its name.

My primary source for this story is an article by C. Truesdale.  I learned about l'Hôpital's Rule in Mark Hansen's math for social scientists class.