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March 30, 2005

A Story

Galileo, Marin Mersenne, Honore Fabri, and Christian Huygens were on a fishing excursion on the Arno River one day, and Galileo was relating his ingenious reasoning on ballistics.  The others were congratulating Galileo on the profound mathematical and physical insights that in one fell swoop allowed him, and every man coming after, to exactly know the path of an object flung through the air. 

Fabri:  Indeed professor.  By simple geometry you have shown us what Aristotle had missed, and now we can predict the impact point, the struck target, of anything a man can throw, loose, or a cannon can shoot, windage excepted.

Their fishing guide, Victorio, fisherman that he was, though he would bait them with a problem.

Victorio:  You mean I can fling this oar, hard as I might, and you can by dint of calculations tell me where it will land?

Galileo:  But of course.  By simply knowing the angle at which you throw it, from the north and from the vertical, and with what degree of speed you hurl it, we can plot the parabolic path and tell you exactly where it shall land, with some errors due to the resistance of the air, which we can also put into our calculations to a degree.

Huygens:  Indeed, and that this is repeatable by any number of men is what makes it science as opposed to the mere speculations of the uneducated.  We know the physics of t he thing.

Victorio:  I'll bet you twenty bottles of ale that you're wrong, and can't tell me where the oar will land.

Fabri:  You're on.

The intrepid fishing guide then flung his oar high and far, sending it spinning into the heavens, tumbling and twirling until it made a big splash right in the middle of the river.

Fabri: Twill be a dry night for you, as you haven't given us any time to calculate, nor a measure of the angles and velocities of the oar when it was loosed.

Victorio: You have all the time in the world.  For you see, the oar hasn't landed yet.  It's still floating.  I'm betting it beaches upon the left bank, down just past that large oak.  What say you fine scientists?

Galileo:  Ah, a most fascinating problem you've posed to us.  Where lands the oar, given the currents, the tides, the winds, and the swirls and eddies.  This is a fascinating problem indeed.

What followed was hours of learned debate. They proposed models of currents and engaged in discussions about the formation and dynamics of eddies and whether these would enhance or subtract from the shoreward drift of the oar.  They put forth long deep thoughts on the mass, buoyancy, and drag forces on the oar; the relations between the oar's drag due to the winds versus the currents, and how much the surface currents are pushed by those winds.  That brought up predictions of the winds, since they would shift throughout the day.  Indeed it seemed that to predict the oar's landing required a prediction of the very weather, since the wind and current were set by the rains.

In exasperation Huygens suggested they observe the shore to see where floating limbs have historically accumulated, but Fabri noted that this would also be a function of where they entered the river.  Galileo correct him to say it would be a function of their relative position, from bank to bank, as they passed particular bends.  Mersenne added that these limbs would probably accumulate during high water periods, or when the flow was starting to drop, as opposed to the current conditions, so that the past record wasn't a completely sound predictor of the problem as posed.

During their long and reasoned debate a turtle bumped the oar, creating ripples in the flow of the river and the discussion.  If the influence of such chance events must be included then all sorts of additional effects are in play, causing doubt as to whether a true mathematical solution was even possible, especially on a problem dependent on the flick of a fish's tail.   But Huygens pointed to the mathematical theories of chance as put forth in his own book on the subject, along with the statisticalworks of Galileo, Fermat, Cardano, and others.  If the problem of the oar depended on odds and probabilities then science could encompass that too.

The debate raged back and forth, discussing the forces driving the oar toward the left bank versus those driving it toward the right.  Since the oar stayed stubbornly toward the middle it seemed the bulk of these forces were balanced, and that the final outcome might come down to the error terms that everyone ignores.  After several hours of this the boat and oar had drifted close to the old oak the fishing guide had firsts picked, and it looked certain that the oar would drift right past.

Victorio:  You have put forth many complicated reasons why the oar might do this or that.  How am I to know which one of you is right, and when your answer is correct?

Mersenne:  You can put faith in our answer when we are in agreement amongst ourselves, having thought about the subject sufficiently to convince each other of the soundness of the theory we have produced.

Victorio:  Ah, I see.  So when a boatload of enlightened and astute men have reached consensus then their answer can be trusted.

Mersenne:  Quite so it is.

Victorio: Would this be the same boatload of learned consensus, the convictions of the captain, officers, and navigators, which produced all the shipwrecks dotting our shores?  You esteemed gentlemen have certainly spent much great reasoning on this question, but as you can see this problem, though governed by the laws you discovered, depends on them in such complex ways that you are guessing as much as any other boatload of sailors, idling speculating away on a lazy afternoon.  I bet that my oar would land near the old oak, and now behold.

Victorio stood up and cupped his hands to his mouth, hollering "Eligio!  Eligio!  Come quickly! I've dropped my oar in the water.  Can you wade out and get it?"  And from a cabin tucked behind the tree a man broke from his sawing and waded out, retrieving the oar and winning Victorio the gambled ale.

Victorio: You forgot to include my cunning thirst in your calculations, though I did find your idle but reasoned speculations most informative.  Never forget to include mans' free will and dripping wet Eligio in your models.  It sometimes saves a lot of mathematical argumentation.

Mersenne:  But your bet was rigged from the beginning!

Victorio (laughing): The future often is, and only fools, tricksters, and fishermen bet on it.  Your esteemed physics may be astoundingly good for cannon balls and planets, but when it comes to problems that depend on the battles between the tiniest of nature's whims your predictions grow quite uncertain.

March 30, 2005 in Science | Permalink | Comments (24) | TrackBack