Descartes' Secret Notebook

(Conspiracy Nation, 01/02/06) -- Johann Kepler visualized a universe founded upon geometrical solids. The image at left depicts planetary orbits having ratios tied to such platonic solids as the cube and the tetrahedron. This medieval idea of a geometrical foundation for the universe was modified by Albert Einstein's use of non-Euclidian geometries. However Einstein's paradigm, which fits this solar system, may be inferior to the medieval system when it comes to describing the wider universe. This concept of a mathematical foundation for the universe is explored in a fascinating book by Amir D. Aczel, Descartes' Secret Notebook (ISBN: 0-7679-2033-3). Enlivening the theme is a journey through the secret life of French philosopher and mathematician Rene Descartes. "I advance masked," was Descartes motto. The mask was necessary at the time due to church hostility to science. The mathematician needed to veil many of his discoveries, especially when they tended to support the heliocentric model.

After Descartes death on February 11, 1650, his secret papers including an encrypted notebook found their way into the safekeeping of Claude Clerselier in Paris. Avid student of Descartes, Gottfried Wilhelm Leibniz, learned of these secret documents and begged Clerselier for permission to study them. This was briefly allowed. The secret notebook, entitled De solidorum elementis, contained apparent gibberish: astrological signs and a series of numbers: 4 6 8 12 20 & 4 8 6 20 12.

Leibniz, credited along with Isaac Newton with inventing calculus, was no slouch when it came to puzzles. He quickly understood the hidden meaning.

De solidorum elementis began with these words: "Offered, once again, to the erudite scholars of the entire world, and especially to G.F.R.C." Leibniz had no difficulty understanding that G.F.R.C. meant Germania Fraternitas Roseae Crucis, the Brotherhood of the Rosy Cross, otherwise known as the Rosicrucians.

In 1095 A.D., Pope Urban II had climbed atop a scaffold in Clermont, France. His exhortation was vehement: Jerusalem must be saved! The crowd went wild. "Deus vult, Deus vult!" they shouted. Pope Urban II urged the Crusaders to wear a conspicuous cross, a red, a bloody cross, on their outer garments.

A side-effect of the Crusades was an inter-cultural exchange. In Europe, it had been the "Dark Ages"; the lamp of learning had gone out. However in the Middle East, the Arabs had not stalled in scientific pursuits. As far back as 825 A.D., in Baghdad, had been published the mathematical text, Al-Jabr wa-al-Muqabalah, from which the word "Algebra" is derived. Some of the Crusaders, wearing the red, the bloody cross (Rosy Cross), returned to Europe enlightened by mathematical concepts.

To circumvent the closed-mindedness of church and universities, a secret society of renegade scholars, "The Invisibles," was formed. Among their distinguished membership was Descartes, who "advanced masked."

Descartes' books are marked by a struggle against the prevailing "false beliefs." In his Meditations he starts by discarding everything he a priori "knows." "What do I really know?" is his question. His heretofore "knowledge" had been formed and automatically accepted during his unquestioning youth. Descartes seems to exhort us that everything you "know" is wrong.

On November 11, 1620, the French mathematician wrote in his journal, "I begin to conceive the foundation of an admirable discovery." Through vicissitudes he labored on. Descartes frequently changed residences and hid his address from friends so as not to be disturbed. His fame as a philosopher and mathematician increased. Queen Christina of Sweden invited him to her court, to serve as royal tutor.

Reluctantly, Descartes journeyed to "the land of ice and bears." Sweden was a Protestant country and Descartes was Catholic, so many Swedes were hostile to him. One secret enemy, a physician named Weulles, secretly poisoned Descartes, under the cover of medicine. The great mathematician was buried in Sweden, but his head was severed from his body. Later, his remains were exhumed and moved to Paris, where they lie in separate locations: his body in a crypt and his skull on display in a tawdry museum.

Gottfried Liebniz, in a flash of insight, understood the message of the secret notebook: F+V-E=2. This was a universal formula deduced from the cryptic series of numbers, 4 6 8 12 20 & 4 8 6 20 12. Aczel, in Descartes' Secret Notebook, explains.

There are five platonic solids: the tetrahedron, cube, octahedron, dodecahedron, and icosahedron. These five platonic solids equate with the five medieval elements: earth (cube), water (icosahedron), air (octahedron), fire (tetrahedron), and aether (dodecahedron). The platonic solids are unified through the formula F+V-E=2. Here is how:

The number of faces of the platonic solids are, respectively, 4 (tetrahedron), 6 (cube), 8 (octahedron), 12 (dodecahedron), and 20 (icosahedron). This matches Descartes' first string of seemingly random numbers.

The number of vertices (corners) of the platonic solids are, respectively, 4 (tetrahedron), 8 (cube), 6 (octahedron), 20 (dodecahedron), and 12 (icosahedron). This matches Descartes' second string of seemingly random numbers.

The number of edges of the platonic solids are 6 (tetrahedron), 12 (cube), 12 (octahedron), 30 (dodecahedron), and 30 (icosahedron), realized Leibniz.

What is universal here is, the sum of the faces and the vertices, minus the edges, is always equal to two. This applies not only to the platonic solids. Hence the universal formula, F+V-E=2.

Descartes secret formula, decoded by Leibniz, is a topological invariant; it is, writes Aczel, "a property of space itself."

Albert Einstein modernized the approach with non-Euclidian geometries used to describe the universe. Yet the latest research indicates Descartes may have got it right after all. True, the planetary orbits do not mimic the structure of the platonic solids. But the wider universe may duplicate ancient geometry. The Geometry of the Universe now appears to be analogous to, e.g., an enormous dodecahedron folded in upon itself. A spaceship traveling outward inside the dodecahedron goes through a face, then immediately goes back in through the opposite face of the dodecahedron. Here would be a paradox: a universe which is closed, yet has no boundaries.

-------
Conspiracy Nation
http://www.shout.net/~bigred/cn.html