Descartes' Secret Notebook (3)

Aczel, Amir D. Descartes' Secret Notebook: A True Tale of Mathematics, Mysticism, and the Quest to Understand the Universe. New York: Broadway Books, 2005. xiv, 273 pp.

Now we come to Chapter 20: Leibniz's Quest for Descartes' Secret. Leibniz was attracted to aspects of Descartes' philosophy but was seriously repelled by it as well. Leibniz was critical of Descartes' principle of doubt, suggesting that degrees of doubt rather than absolute doubt be admitted in specific cases (209).

Some of Leibniz's major interests are outlined. I note a mutual interest with Descartes in Ramón Llull's ars combinatoria (210). After three years in Paris, facing the prospect of being recalled to Hanover, Leibniz urgently pursued his aim of inspecting everything that Descartes ever wrote. On June 1, 1676 he succeeded in gaining permission to view Descartes' hidden manuscripts. Scanning the Preambles, Leibniz, a Rosicrucian, recognized an oblique reference to the Rosicrucians (213). The secret notebook, De solidorum elementis, contained obscure formulas and figures. The geometrical figures were depictions of the five Platonic solids, and a connection to mysticism was evident. Leibniz began to copy the records, recognized what was going on, and added a marginal note (219).

Descartes' notebook disappeared, and Leibniz's papers on this subject remained undetected for two centuries. Several subsequent viewers of these documents failed to crack the code. Finally, in 1987, Peter Costabel published his analysis of Leibniz's copy of Descartes' manuscript (220). Leibniz had discovered that Descartes discovered a formula that generalizes the structural characteristics of the Platonic solids (221).

Chapter 21: Leibniz Breaks Descartes' Code and Solves the Mystery. Kepler had postulated a connection between the five Platonic solids and the spacing of the six known planets. Descartes found a formula for all polyhedra, but because others would connect this with Kepler and Copernicus, and so kept it to himself (225-229). Descartes' formula F + V - E = 2 inaugurates the field of topology. Euler discovered this formula, which was named after him.

Other misfortunes befell Descartes' legacy in the 17th century, when his works were proscribed by the Catholic Church and teaching of Cartesian philosophy banned in France. It wasn't until 1824 that his works were reprinted. Adrien Baillet came close to crediting Descartes' discoveries in his biography, but not being a mathematician, did not understand Leibniz's explanation and omitted publishing the information (230). Leibniz remained obsessed and ambivalent concerning Descartes, praising him while alleging limitations. Leibniz kept in contact with Cartesian scholars (231). Leibniz was at work developing the calculus. Concerned about the priority dispute with Newton, Leibniz would not have wanted to acknowledge an influence from Descartes (234-235).

Aczel adds an epilogue to this story. Descartes is seen as the great forerunner of contemporary astrophysics, heavily dependent on geometry linked to algebraic methods. The Platonic solids are n longer relevant, but . . . but satellite data obtained in 2001 supports the notion that the geometry of the universe as a whole fits the geometry of some of the Platonic solids (238-239). One new model posits the universe as an octahedron folded onto itself. The icosahedron and dodecahedron have also served as models.

It's a somewhat peculiar final tribute to Descartes, and Descartes' whole life story is a somewhat roundabout way of getting to discussing the mysterious notebook, but the story is nonetheless interesting, and, aside from the tribute to the mathematical and scientific geniuses of the early modern world, it reveals even more the peculiarities and complexities of the Enlightenment and the scientific revolution.

Descartes' Secret Notebook (2)

Aczel, Amir D. Descartes' Secret Notebook: A True Tale of Mathematics, Mysticism, and the Quest to Understand the Universe. New York: Broadway Books, 2005. xiv, 273 pp.

Chapter 12 finds Descartes moving to Holland in 1628, meeting and eventually breaking with his friend Isaac Beeckman over claims about what Beeckman taught Descartes.

Descartes worked on his book Le Monde from 1629-1633. Descartes was a Copernican, but cancelled publication in November 1633 upon learning of Galileo's ordeal under the Inquisition. Descartes' situation was probably much safer, but he continued to steer clear of publication, fearing reprisals. Details follow.

Chapter 13 recounts Descartes' secret affair or marriage with a servant woman, Hélène Jans, which produced a daughter Francine. Descartes was devastated when Francine died in 1640 (p. 147).

Chapter 14 is devoted to Descartes' epoch-making 1637 work Discourse on the Method. Descartes' invention of analytical geometry was a revolutionary discovery. Chapter 15 details Descartes' solution to the ancient Greek mystery of doubling a cube—the Delian problem.

Chapter 16 concerns Descartes' friendship with Princess Elizabeth of Bohemia, hungry for knowledge of metaphysics, physics, and mathematics.

In Chapter 17 we find Descartes embroiled in confrontation with academics in Utrecht, chief among them Gisbert Voetius, who in opposing Cartesianism levelled the dangerous accusation of atheism. Cartesian philosophy was banned from the university. Ultimately, there was a vicious lawsuit which Descartes lost, and he had to issue a letter of apology to avoid imprisonment.

In Chapter 18 we approach the final chapter of Descartes' life, in which he is induced to come to Stockholm by Queen Christina. She lavished honors on him while others in the court were hostile. Tutoring the queen also cramped Descartes' lifestyle. Worse, as we see in Chapter 19, the Swedish climate did him in. He resisted until almost the end the quack cure of bleeding the patient, and then gave in, and then died. His last words were: "Ah, my dear Schluter, this is the time I must leave." (p. 197)

The fate of Descartes' remains is summarized here, but you can also read the whole story in Russell Shorto's Descartes’ Bones. Now we return to the story of what became of Descartes' locked box (202).This box contained copies of various correspondence and responses to critics, but also secret manuscripts—Preambles, Olympica, Democritica, Experimenta, Parnassus—and a notebook containing cryptic mathematical and other symbols. In the final installment, we shall review Leibniz's inspection of Descartes' notebook and the ultimate deciphering of the mysterious text.

Conspiracy thinking – my name in lights

Note this blog post:

Conspiracy Thinking – Turning Points
Oct. 2, 2011

The blogger reviews some key books on social paranoia, links it to American individualism, and recommends Chip Berlet's Political Research Associates, G. William Domhoff's power structure research, and my The Paranoia Papers: Theory of the (Un)Natural History of Social Paranoia: Selected Bibliography.