Foucault's Pendulum

In 1851, Leon Foucault built a large pendulum and observed its behaviour : besides the expected back-and-forth motion, the pendulum's swinging plane underwent a very slow rotation, achieving a 360° turn in about 31 hours. He was, as he later put it, "seeing the earth spinning round".

You may understand this more easily if you place the pendulum on the North Pole instead of some Parisian cave. Imagine the Earth, with the pendulum on the top of it. The Earth spins around its axis, but why would the pendulum follow it ? It keeps swinging in the same plane, regardless of the outside world's orientation. Thus, for an observer located at some spot on the planet's surface (and therefore following its spinning motion), the pendulum actually seems to rotate with a 24 hours period.

Rotation also occurs on other locations, but with a longer period, and it becomes perfectly still on the Equator. The period is 28 hours in Saint-Petersburg (Russia), 37 hours in New York (United States), 119 hours in Phnom Penh (Cambodia) and 6329 hours in Quito (Equator).

To find the rotation of the plane of oscillation of Foucault's pendulum we consider a pendulum consisting of a massless string of length l with a mass at the end. Describe the position of the mass by a triple of Cartesian coordinates (x, y, z), where (0, 0, 0) is the equilibrium position of the pendulum, (1, 0, 0) and (0, 1, 0) are two orthogonal horizontal vectors and (0, 0, 1) is directed upwards.

As always when dealing with pendulums we assume that the maximum deflection is small. In this case it means that we ignore the z-component altogether, and that we approximate the restoring force of the pendulum by F = -k²(x, y), where k² = g/l.

Normally we would be satisfied with this, but the whole point of the Foucault pendulum is to observe its behaviour over a longer time. We therefore also have to take into account the Coriolis effect. This produces a pseudo force C = 2w(sin L)(y', -x'), where L is the latitude of the pendulum and w is the angular velocity of Earth.

Now we release the pendulum from rest at (0, y₀), and consider its motion during a half period, ie the time it takes it to get to roughly y = -y₀.

Since the Corilois effect is relatively small, x will remain small during the half period, and hence the influence of the Coriolis effect on y is second order small. Therefore we can approximate the equation for y to y'' = -k²y, which as usual has the solution y = y₀*cos kt. The period is T = 2π/k.

In finding the expression for x we must take the Coriolis effect into account. The equation of motion is

x'' = -k²x + 2w(sin L)y' = -k²x - 2wky₀(sin L)(sin kt)

which has solution x = wy₀(sin L)(t*cos kt - k^-1sin kt).

Hence at t = T/2 the mass is at rest and (x, y) = (-wy₀(sin L)T/2, -y₀). The plane of oscillation of the pendulum has turned by an angle given by sin da = x/y. Since x/y is small this implies da = x/y, and thus da/dt = (x/y)/(T/2) = w*sin L. In 24 hours the angle turned by the plane is 2π*sin L, and the time taken to turn through 2π radians is 1/sin L.

Foucault's Pendulum
by Umberto Eco, translated by William Weaver.
Harcourt, Brace, Jovanovich, 1983.

"Gentlemen, I will now show you this text. Forgive me for using a photocopy. It's not distrust. I don't want to subject the original to further wear."
"But Ingolf's copy wasn't the original," I said."The parchment was the original."
"Causabon, when originals no longer exist, the last copy is the original."

Reading Foucault's Pendulum is like going down a rabbit hole, only instead of White Rabbits and the Queen of Hearts, you get Templars and Rosicrucians and Alchemists (oh my!). It is a kaleidoscope of the twentieth century, a physical book with multiple texts between its covers, intermixed and commenting on each other at each turn. It is the internet, hyptertextuality before we knew it existed. It is a fantasy, an adventure story, a war memoir, a historical novel, and an exploration of semiotics. It is a mindfuck.

There are 120 chapters, divided into ten sections, named after the Sephiroth, the ten spheres on the tree of life which eminate from ain sopf. There are illustrations of medieval magical amuletes. And there is the promise of a great secret to be revealed.

That said, the rest of this w/u will spoil more than milk in the sun.

---

First, why is it called Foucault's Pendulum? We have a double meaning here: the book opens with our protagonist--the often-left-unnamed Causabon, a still-fairly-young intellectual who works for a vanity publishing company--hiding in the Paris museum which houses the pendulum of the title. As stated in the above w/us, this pendulum demonstrates the rotation of the earth. It is also the axis upon which the universe exists, the single point in space--the place which is not a place, the location without length, width, depth--from which all originates. The point from which that pendulum hangs is the omphalos of the universe, is the kingdom of God, is the marriage of heaven and hell.

The other Foucault is Michel Foucault, the 20th century French philosopher:

Much of {Michel} Foucault's early work centers around the history of science -- not science's discoveries, per se, but rather the history of the prejudices and metaphysical beliefs which lurk behind science. As time went on, Foucault became increasingly interested in organisational technologies and what he called "technologies of power" and "technology of the self" -- the ways in which we use ideas and arguments to centralise and decentralise systems of power.

from Cletus the Foetus' w/u

This Foucault's theories apply then to the rest of the book and its texts--namely, the power of the word to make manifest, even when that which the word describes does not actually exist. And it is through machines--the computer Abulafia, Garamond Press--that these ideas take on life. It is in a museum dedicated to machines that Causabon hides, having witnessed the ritual murder of his friend and co-conspirator Belbo, owner of Abulafia, by the very cult who believed in Causabon and Belbo's hoax.

Confused? Right. Well, we begin to untangle that the main text is the story of Casaubon, a young Italian intellectual who was a half-hearted revolutionary in 1968, and student of medieval history and philosophy. His interest in the Knights Templar--as well as his revolutionary activities--lead him to fall in with Belbo, a failed poet who works for Garamond Press, a vanity publishing company. Casaubon joins the company, where he meets Diotallevi, who is obsessed with the kabbalah, to the point that he believes he is actually Jewish instead of an Italian Catholic.

Meanwhile, mysterious characters like Colonel Ardenti, SS collaborator & veteran of the French Foreign Legion, come to have their books published. In Ardenti's case, he claims to know of a secret plot to take over the world using telluric energies. Of course, in the "real" world, the Nazis did have a belief in telluric currents, energies, a hollow earth, and other such ideas, all of which come out in connection with Ardenti. Who of course disappears.

All the while, the three intellectuals play with Belpo's computer, nicknamed "Abulafia," which we learn later was the name of Belbo's unrequited love, as well as an early Qabalist. They take the bizare theories surrounding them--Templars, Rosicrucians, the Holy Grail, Nazis--and feed them into a computer, telling Abulafia to connect sentences randomly. Quickly, they come up with a theory about the bloodline of Jesus, symbolized by the Grail and hidden by the Templars/Freemasons. Casaubon--IIRC--is quick to point out that this little game neatly summed up the book Holy Blood, Holy Grail, which was a best seller at the time (ca. 1983).

An offshoot, Mantius Press, specializing in books on the occult, is set up by their boss. As a game, the three indicate to the occultists that they have a secret manuscript--which is in part true, as they have the Ardenti manuscript. One man in particular--who claims to be the Comte de Saint-Germain--seeks out this manuscript, which claims to hold the secrets of the Templars. They are taken to strange rituals, cult meetings. Even us druids show up at one point.

Casaubon wisely maintains a certain detatchment to all this. He goes off to Brazil, falls in love, is exposed to a Santoria-like religion, and yet--there is Saint-Germain. Looking for his secret.

Belbo, meanwhile, becomes obsessed with the Plan, their hoax--that the Templars never dissolved, but would meet every 111 years. They became Rosicrucians, Freemasons, at war with each other. Each group had one word in the sentence that held the secret, and at each meeting--at Mont Segur, at London, at Jerusalem--a new word would be introduced until the day that the sentence would be complete. But they were interrupted, one word was lost, the order of the sentence was lost. Some of its secret was built into the landscape at Rennes le Chateau. Some was built into the museum where Foucault's Pendulum is housed. But our three protagonists had discovered the secret, and THEY want it.

Who are THEY? THEY are the occultists. In this book, there is a REAL secret society--THEM--and there is the secret society which contained those secrets. The Templars. The Rosicrucians. Only these people--we've called them the Illuminati, we've called them Enlightened Masters, we've called them Templars--don't actually exist in the manner THEY believe them to. The real society is a poor mirror of the imaginary society; the real society is an attempt to embody that imaginary society, which has always existed in the minds of men since the beginnings of civilization, the secret rulers, the angels, the gods, the magi. The real society reads texts, performs rituals they don't understand.

And what are they after? The power of the universe. It is found in currents that run through the earth, and it is through knowing the secret words the Templars discovered at the ruins of the Temple in Jerusalem. Belbo--the failed writer, who once swore to only be an observer of life and not a participant--gets caught up in this, adding more and more to this Plan. Even the works of William Shakespeare are part of the Plan, written secretly by an imprisoned Francis Bacon, which we learn in a fragment of a historical novel by Belbo.

In truth, our three didn't create the plan. Fragments of it have existed since at least the fifteenth century, when the historical Templars were disbanded and Jacques de Molay was burned at the stake for heresey. Or more, it has existed since the fear of Christians, gnostics, Jews, witches, lead to holocausts found all through history.

And it is history which obsesses Belbo. As a child, he lived through World War II in a section of Italy--left unnamed--where rebels against Mussolini hid. Those same rebels who also fought the Nazis, who, of course, are now connected to the occultists, forty or so years later. Interspersed through the text of Casaubon's narrative are excerpts of Belbo's reminiscences of his childhood during wartime, and the secrets of daily life--that the real power worth seeking isn't found in earth currents, but in daily life, in just struggling to survive, to grow up, to fall in love.

It isn't only Belbo's memories we see, though. Casaubon's own history--but only that of his college years and beyond, his days in Brazil, his days with Belbo--are repeated to us. Belbo focuses on the child, Casaubon the man.

BUT--we find that THEY know about Belbo's text, the Plan in Abulafia, and yet don't believe that it is all a hoax. THEY must have a secret which doesn't exist, but which they believe exists because they need it to exist. The lies we create are the most appealing parts of our existence, for they construct meaning out of chaos. And it is this constructed meaning--these signs and symbols, these structuralist fantasies--that lead Belbo to his death.

"You mocked the creators of illusion, and now...you write using the alibi of a machine, telling yourself you are a spectator because you read yourself on the screen as if the words belonged to another, but you have fallen into the trap: you, too, are trying to leave footprints on the sands of time. You have dared to change the text of the romance of the world, and the romance of the world has taken you instead into its coils and involved you in its plot, a plot not of your making."--Belbo's files on Abulafia

Casaubon learns that THEY have come for Belbo, to learn the secret words. He has no secret, of course, only his memories of a childhood wondering at the mysteries of real life. Casaubon finds that THEY will meet at the Conservatoire des Artes et Metiers in Paris, where they will learn the secret words and unleash the telluric currents, which are particularly strong in Paris' sewer system.

Of course, there are no words. And so Belbo is hung, the cord of Foucault's Pendulum wrapped around his neck and let go--time stops as the creator of the Plan is hung from the center of the universe.

Casaubon runs to Belbo's hometown, the unnamed place, and waits to be found and killed by THEM. But here he discovers that the real mystery of the universe is home with his wife and child. And we're left with his realization, and his hope that he might make it home, his doubt that he ever will.

---

This is not an easy read. It jumps between texts, narrators, time and place. It is almost Tralfamadorian. It talks about conspiracies that some people may not be familiar with, and people who are more footnotes than headlines in history. But if you can get through it, it's worth it.