It seemed to me that Pierres d’ailleurs, a shop housed in a semi-basement on St. Denis street just south of Mont-Royal Avenue, had been around forever. It offered everything from crystals to semi-precious stones; crystal skulls to pendulums—all sorts of new-age paraphernalia imaginable.

Grand Troll
The big troll

Whenever I passed the shop. I was invariably drawn to its display window, filled with merchandise of infinite shapes and colors. However, on more than one occasion I was struck and caught unawares by an enormous troll that stood guard next to the shop’s door. It looked to be made from materials retrieved from nature, including wood, rope fibers, nuts, seeds and cones. Inside the shop, dozens of smaller trolls could be discovered taking refuge on shelves along the wall.

Everything about Pierres d’ailleurs, gave off a Disneyland-like atmosphere that seemed to belong to another time, to another continent of thought.

From Potions to Pharmacology; from Astrology to Statistics

Pierres d`ailleurs
Pierres d`ailleurs on St-Denis east, north of Marie-Anne

Historically, wizards and sorcerers could cast spells and curses from afar; astrologers and fortune-tellers could predict one’s future. Alchemists and apothecaries concocted potions against multiple ailments, including love. Such activities presumed a natural sympathy between the logic of will and hidden mechanisms existing within the universe.

However, magic and other such practices did not survive the scrutiny of the experimental sciences. During the sixteenth century, specifically in Europe, the science of mathematics began to evolve as a powerful tool for predicting and discovering what was happening around us. Mathematics made it possible to predict a lunar eclipse; a torrential downpour; the fall of an empire; the success of an advertising campaign, as well as the effectiveness of a remedy or the source of an epidemic. Math became the new magic of our times.

Marketing a New Science

Up until the late eighteenth century, astronomers were aware of only six planets. They were also aware of their irregular motions in relation to that of the stars, the sun and the moon. Then around 1780 against the backdrop of rising social and political uneasiness in France, a British astronomer named William Herschel, discovered a new planet.

L’attribut alt de cette image est vide, son nom de fichier est sortilèges-1.jpg.
Store Charme et Sortilège, on de Grand-Pré east, south of St-Joseph

He had been testing one of the new telescope prototypes that he planned to market when he noticed a small iridescent twinkling appearing as a circle of light through the lens. He had stumbled upon a new planet. The planet would become known as Uranus, following the tradition of naming planets after the Roman gods. According to Roman mythology, Uranus was the father of Saturn and grandfather of Jupiter—the names of the two planets that preceded Uranus. Until Herschel’s discovery, Uranus was thought to be a star, since most astronomical observations were made by the unaided human eye. Herschel couldn’t have wished for a better marketing angle for his telescopes with his new discovery.

After Herschel’s discovery, astronomers tried calculating Uranus’ theoretical trajectory using Isaac Newton’s Law of Universal Gravitation with little success. The 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 sidereal backdrop. The influence of that unknown planet was too slight to cause any perceptible effect upon the other gods (planets) in the solar family—a new and enigmatic astronomical mystery was born.

What could be influencing Uranus? It was speculated that another planet which had already been christened Neptune, after one of Jupiter’s brothers, was to blame. But where could this damn planet be hiding? Among the millions of stars displaying themselves in front of the astronomer’s lens, one was a pretender. But which one?

One would assume that if we took the time to patiently scrutinize every cubic inch of the sky with a telescope, we’d eventually locate Neptune. Unfortunately, that is not the case. This would be to forget the astronomical number of stars in the sky. For example, if someone were to operate the same telescope to scan every nook and cranny of a sizable city like New York City; seeking a murderer who had already been identified through a photograph—they’d be capable of finding such a person faster than our astronomer looking for his planet.

A Sherlockian Mystery

Half a century had passed since Uranus’s official discovery by Herschel (1780) with no signs of unravelling its mysterious vagaries or discovering Neptune’s position. In France, a young and rising French astronomer and mathematician named, Urbain Le Verrier (1811-1877) is hoping to secure a prestigious teaching and research position in Paris, in the heart of the developing Latin Quarter. However, there’s a catch. The job is his, only if he places first in a national math competition occurring at the time. Unfortunately, he finishes second. So, he goes on to accept a position with the Paris Observatory, which turns out to be a blessing in disguise. Le Verrier’s field of specialty is celestial mechanics, a branch of astronomy which examines the motion of objects in space by applying physics and ephemeris data―the trajectory of naturally occurring astronomical objects.


Ironically, Le Verrier, whose name means the glassmaker had no use for telescopes. By all accounts, he never looked through one during his lifetime. It was the art of mathematics, specifically celestial mechanics, that Le Verrier believed would inevitably predict and reveal Neptune’s hidden position.

So, Le Verrier, the superior sleuth that he was, embarked on his search for the unknown—the phenomenon regarding the mathematical variables of Uranus’ mysterious vagaries. He reduced the number of possible suspects with the help of Sherlock Holmes-style field observations.

Elementary, my dear Watson

The planets orbit along the same plane and share the same elliptical foci. So, in searching for Neptune’s location, we are talking about exploring a surface, not a volume. Moreover, each planet is moving farther away from the one before it, the same way harmonics play out with the strings on a guitar.

Conclusion: Neptune is within the breadth of the zodiacal band, in a quadrilateral located behind Uranus, with a smaller mass and an approximate distance, and on an elliptical trajectory aligned with that of the other planets. In our comparison of trying to locate a murderer in the city, let’s say that we’ve narrowed the search for the murderer to Queens or Manhattan.

Le Verrier realized the error made by earlier astronomers in predicting Uranus’ position. It was due to Newton’s law of attraction, that is, Uranus’s mass in relation to that of Neptune’s. The gravitational force depends directly on the mass of the planet and decreases to the square of its distance between the two planets. As a result, Le Verrier correctly deduced that Neptune must be lurking somewhere nearby.

Le Verrier enlisted the help of a German astronomer by the name Johann Gottfried Galle to find out if his deductions were correct. Galle had access to the latest high-tech telescope located at the Berlin Observatory. This would prove to be a profitable initiative, since an astronomer and mathematician based in England by the name of John Couch Adams was also scrutinizing the skies for the mysterious plane; unknowingly basing his own research on the same deductive model that Le Verrier had developed.

Le Verrier had asked Galle to search the delineated perimeter with the specific goal of tracking down a luminous circle. Galle beat Adams by one day. Just before midnight on the 23-24, 1846, Neptune was spotted by Galle. It was detected less than one degree from where Le Verrier had predicted it would be.

Two days later Galle wrote Le Verrier with the news, stating that: « the planet whose position you indicated really exists. »

Pure magic! And as Galle further described Le Verrier approach to his discovery « with the point of his pen. » Le Verrier through reasoning and mathematics had discovered the position of a planet beyond our limited field of vision. He could have been blind and still calculated Neptune’s location. Needless to say, one would still require a telescope (the magic glass eye) to confirm the reality of Le Verrier’s deduction.

I don’t know if a troll can protect your garden or if a dream catcher can save you from nightmares. If they continue to use them, just be aware that they can’t be reasoned with.


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