For decades it seems, I’ve been coming across a small shop on St.-Denis Street called Pierres d’ailleurs. It is located in a semi-basement, south of Mount Royal Avenue and I’ve always been drawn to the diversity of shapes and colors displayed in its modest window. But, on fine days, what strikes you most is one enormous troll – at least a meter high – leaning on his stick.

In this shop, we can find stones with special properties, dream-catcher necklaces, garden trolls and various items whose « disneyesque » aspect definitely belongs to another era, perhaps even to a different continent, as far as our thinking is concerned.

From Potions to Pharmacology; from Astrology to Statistics

Sorcerers and magicians pretended they could throw curses from a distance by mistreating a doll resembling their victim. Astrologers, fortune-tellers and clairvoyants predicted the future. Alchemists, sorcerers and apothecaries concocted potions to cure various diseases and ailments and sometimes even to cast spells, to make someone ill or to poison him. Such activities presumed of a natural relationship between the « logics of willpower » and the universe’s hidden mechanisms.

Magic and other such practices failed to survive the scrutiny of experimental science. However, a powerful predictive and discovery tool had been developing in the course of the last seven centuries, mainly through books and teaching institutions. This magical tool allowed us to foretell moon eclipses and torrential rains, the fall of empires and the success of an advertising campaign, the effectiveness of a remedy or the source of an epidemic and I could go on. I’m talking here about mathematics: the art of building stable relationships between the human ability to calculate on the one hand and, on the other hand, between the mechanical regularities that we assume capable of governing our lives.

An Instant Advertising Campaign

There were five planets which astronomers could always observe with the naked eye: their irregular movement contrasted with the stars and luminaries’, such as the sun and moon, regular movement. Around 1780, at a time when, in Paris, the population was getting restless, a British astronomer called William Herschel, was scrutinizing the skies with one of the telescopes that he assembled and sold. He thus discovered a star which « in fact » was really a planet. In front of his lens, the small iridescent twinkling appeared as a circle of light. Herschel couldn’t possibly have conceived a better advertisement for his telescopes! The new planet was to be called « Uranus », as Saturn’s father, himself father of Jupiter, the two planets preceding it.

Astronomers tried to calculate Uranus’ theoretical trajectory using Isaac Newton’s equation of gravitational attraction, but the new planet would not conform to the equation’s formula. So, rather than questioning Newton’s theory, they assumed that Uranus’ vagaries must have been due to the influence of another planet, located somewhere in the sideral backdrop. The influence of that unknown planet was too slight to have any perceptible effect upon the other gods in the family. And, after all, if Hershel had been able to find a planet, nothing prevented him from discovering others.

A new astronomic enigma was just born: where could that damn planet, disguised as a star and already baptized Neptune (one of Jupiter’s brothers), possibly be hiding? Among the millions of stars displaying themselves in front of the astronomer’s lens, one was only pretending to be so, but which one? If you’ve been moving about the center of a major city in the last year, you most probably ran across a murderer. But which one of all the people you passed by could be the one?

Now, if you were to scrutinize every single light in the sky with a telescope, shouldn’t that be enough to find Neptune? In theory, yes. But, practically speaking, you’d have to forget the « astronomical » amount of stars the sky is sheltering. As a comparison, just imagine that someone, using the same telescope and a photo as a reference, would search every nook and cranny of a city set in time – let’s say New York City – trying to find one individual (our murderer for instance). He would most probably find him faster than our astronomer searching for his planet.

An Armchair Explorer

Uranus has been discovered and its sidetrackings officialized for half a century now. France has taken a generation to recover from Napoleon’s mischiefs and an auspicious future promises to deliver the dreams of Urbain LeVerrier, a bright and ambitious young mathematician. A Teaching and Research Chair is available in Paris, as long as he succeeds at finishing the national examination first.

Urbain came in second. The genius who beat him will one day become enthroned in the pantheon of math wizards and, in the meantime, will of course choose the coveted Chair. Being offered another choice on the second draw, LeVerrier opted for a Chair in Astronomy in Paris. In spite of his prophetic surname, the young mathematician has about as much interest in telescopes than a Master chef has in dishwashers; we are not really speaking about a vocation here.

In his office, once his lectures ready, LeVerrier seeks some astronomical enigma that could challenge his talents as a theorician. That’s how he comes across the « Neptune File » and its suspicions about the existence of the planet. The mathematician dives into the case, reducing the phenomenon to the « variables » involved. A super sleuth at researching « unknowns », LeVerrier will narrow down the number of possible suspects, examining the planet’s « ways of life » through field observations, Sherlock Holmes’ style.

The planets’ orbits are all lined up in the same plane. So, we are speaking here of a surface to explore rather than a volume. And incidentally, each planet moves further away from the planet preceding it, somewhat in the same way as harmonics are distributed on the chord of a guitar. Furthermore, Neptune should also share with its sisters the foci of the ellipse it traces. Finally Le Verrier’s fragile hypothesis is that the masses of the two planets following Jupiter should decrease, while they increased as they moved further away from the Sun. Conclusion: Neptune is located within the zodiacal band, in a quadrangle located behind Uranus; its mass is smaller, its distance approximate and its is aligned along the same elliptical path as its sisters.

Elementary, my Dear Watson

If the error in predicting the position of Uranus was caused by Neptune’s presence, Newton’s Law should provide a way to locate the mysterious planet. If the gravitational attraction force of the planet, calculated in regard to its deviance from the predictions should be equal to the product of the estimated masses of Uranus and Neptune, divided by the squared estimated distance between the two planets, the culprit should be found within the delineated quadrangle, subject to the margin of error involved in field observations.

Having sketched out the « unknown’s » composite picture, LeVerrier hired a certain Galle whom he assigned to a new mega-telescope built in Berlin. This would reveal itself a profitable initiative as, in England, an astronomer called Adams is also scrutinizing the skies, unknowingly basing his search on the same « deductive model ». LeVerrier asks the German to examine the delineated perimeter with the specific goal of tracking down a luminous circle. Having chosen as a livelihood to handle the telescope, Galle beat Adams by one day at the finish line. The German’s telegram makes it clear that he has definitely been able to observe the planet discovered by the French mathematician.

Pure magic! Reasoning from the basis of an « abstract, quantified model » (a model scaled-down for the mind), a man sitting with his calculations succeeded in discover the position of a planet located beyond our field of vision. Vision had been useless in unraveling this enigma. Had LeVerrier been blind and calculating by touch, he would have come up with the same visual directions. Of course, the lens (the magic eye) came in useful to confirm the “reality” of his deductions. History maintains that LeVerrier never saw Neptune through a telescope.

Mathematics might have made a planet appear as if by magic, but field observation data also played a major part in this. Pluto will not be observed until 1939, as it was approaching Neptune. Pluto’s body orbits most of the time outside of the zodiacal band, which it meets only occasionally and, for this reason, its status as a planet was withdrawn.

I don’t know whether or not a troll might protect your garden or whether a dream catcher might ward off nightmares, but if that kind of belief persists, it must be for a reason, even if it is beyond reason itself.

 

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