**René Descartes** was a philosopher whose work, *La Géométrie*, proves Pythagorean mathematics. He posits, and this becomes the basis for scientific thought, that without proof, it’s all theory.

## *Le Monde, ou Traité de la Lumière*

Descartes first wrote Le Monde (The World or a treatise in light) while he was in the Netherlands, just as Galileo’s internment became headlines. He withheld it from publication concerned he would meet a similar fate.

Thus he remained in Holland, writing a treatise on science under the title *Discours de la méthode pour bien conduire sa raison et chercher la vérité dans les sciences*, and then three appendices to this work entitled, *La Dioptrique* (a book on Optics) , *Les Météores* (Meterology) and finally in 1637 *La Géométrie* (Geometrie).

### The proof of Geometry lies in algebra

Descartes showed in his La Geometrie, geometry was a valid branch of mathematics, making this proof via algebra and thus linking geometry and algebra. He then introduces two innovations. The first was denoting variables from letters at the end of the alphabet x+y=z and parameters from letters at the beginning of the alphabet (a,b,c) called originally the theory of invariants but now the Cartesian coordinate system.

Descartes’s second innovation was exponential notation — x^{2 }for squared; x^{3} for cubed, etc. Finally, his creation of Cartesian tables, a three-dimensional table of x, y, and zed coordinates, where three-dimensional data not only exists, but is shown on a plane, i.e. analytical geometry. This led, almost three hundred years later, to set theory and computer programming. Donald Knuth, the eminent computer scientist, and father of analytical algorithms use these concepts in his seminal The Art of Computer Programming.

### Nature is filled with vacuums

His Principia Philosophiae, published in 1644, was a far-fetched idea where he reduces the whole universe to a series of mechanistic mathematical equations. Descartes makes the universe run like a clock with a series of visible and invisible vortices at work where responsible for motion throughout the galaxy. He also negates Galileo’s theory of gravity because Descartes opined that “empty” space was possible.

That same year he wrote his Meditations. Then Descartes finally returned to France and met with Blaise Pascal who outraged about his beloved mentor’s assertion vacuums existed in nature and thus there was no gravity, and tried to convince Descartes of his error via several mathematical proofs. Descartes stubbornly (Mercury trine Saturn in the first both in earth) refused to agree.

#### Descartes Chart

## Descartes the Early Years.

Descartes was born on March 31, 1596 in La Haye in Touraine, which is about midway between Poitiers and Tours. The date above on the chart is the Gregorian equivalent. He was the second son and third child of Joachim Descartes (1563-1640) and Jeanne Brochard (1566-1597) and the family was living with her parents. A testament to the pride the French nation holds him, the house still stands.

*Bene vixit, bene qui latuit. He lived well who concealed well*.

Descartes’s motto from Ovid’s metamorphoses.

Joachim was the son of a medical doctor but turned to law, and was a counselor in the Parliament of Brittany at Rennes. Jeanne, whose family they lived with, was the daughter of military man René Brochard des Fontaines, and for whom they named the child The grandfather, absent for he was a gentleman soldier six months of the year, thus missing his name’s sake’s birth. Still, the elder Rene was at a garrison at Poitiers, fifty-one kilometers away and in contact with his family.

A year later, his mother died in childbirth and his father remarried, leaving his children with Jeanne with the grandparents. He and his new wife had four more, but the two sets remained in separate households.

This sets up an interesting duality in Rene’s life that follows him throughout. When he was born, his father there his grandfather, was absent. When the father leaves, the grandfather or uncle (both Rene) were there. Throughout his life, as one man appears, another recedes, showing us the effect of Mars in Gemini: no one ever competes with another and their effect is strong and complete throughout their time with Descartes.

### School Days at Le Fleche

Rene, being precocious, went to the school of La Fleche, founded by the Jesuits. By the time he graduated, the head schoolmaster wrote to the grandparents he was concerned about the boys’ skepticism and distrust of their authority. They sent him to Paris to help his father with his work.

While the working relationship between the two was poor (Mars opposite his Part of Fortune), it allowed him to re-establish a relationship with an associate from La Fleche, Father Marin Mersenne. (Sun Sextile Mars in the eleventh in Gemini — one fails, while the other succeeds). When Mersenne was sent to a provincial parish, Descartes returned to his studies, but after two years ,he got bored, and followed in his grandfather’s footsteps, and became a gentleman soldier for Maurice, Prince of Orange.

## Life in Holland

Attached to the foremost soldier of the day, Descartes, every lucky, met Isaac Beeckman who told Descartes of his theory of atomism, Galileo’s work in Italy, Paracelsus’s theory of Spontaneous Combustion in Germany. He also encouraged him further along mathematical lines. Descartes’ first work **Compendium musicae **is dedicated to and inspired by Beeckman’s theory of **consonance in music** as not determined by numerical ratios but by consonant and dissonant vibrations.

Through Beeckman, Descartes corresponded with Pierre Gassendi, also an atomist, and Constantijn Huygens (father of Christiaan the astronomer). He resumed his correspondence with Father Mersenne who encouraged the friendship.

## Vortex theory vs. Gravity

Now amongst fellow scientists who encouraged his work, Descartes studied and worked on his theory of parallel vortices controlling the universe, and started publishing books in rapid succession.

Ever distrustful, developed his own vortex theory and disagreed with gravity. His best student, Blaise Pascal, argued, using his own proofs, that nature abhorred a “vacuum.” No matter, Many years later, after when both he and Pascal had reposed, Isaac Newton spent a large part of his book, Principia, disproving the vortex theory. Newton using Descartes’s own dictum that only mathematics can prove anything right, uses as proof his newly created Calculus, a branch of mathematics considered an offshoot of Descartes own analytical geometry, to assert Galileo’s theory of gravity was a basic building block of the universe.

## How do you know you’re not in the Matrix?

His skepticism of reality becomes “I think, therefore I am” (best known in its Latin formulation, “Cogito, ergo sum,”) though it was originally penned in French as “Je pense, onc je suis”). In Meditations, Descartes creates the thorny problem of what makes existence and how can it be proved. He does detailing a three-dimensional philosophy composed of the mind, body, and thought and shows what is seen, or touched may not be real but a “dream” . He then negates the use of memory to prove existence, as it too is not trustworthy because perception colors it.

Rene Descartes

Both Thomas Hobbes and Pierre Gassendi objected and called it “nonsense.” Years later, when the Roman Catholic Church got wind of this, they did too and “indexed” him; Descartes greatest fear came true but thankfully, he was long dead.

Beeckman died. Mersenne died. Even his little daughter, the love of his life, died, and Descartes contemplated returning to France assured by the Jesuits he would not suffer the same fate as Galileo and be thrown in jail and indexed. As a lawyer of canon law, he knew the evils of jail and ways of the Church.

Then the daughter of Gustavus the Great, twenty-year-old Christina, asked him to come north to Stockholm. He agreed, of course, because he did not trust the Jesuits’ promises.

## Exalting in Practicality

Venus is at the midheaven exalted in Taurus and at the midheaven shows his desire to make things practical and organized. He does this with his Cartesian geometry and coordinate system. Typically Venus in Taurus is the mark of the artist, but that cannot be totally true as Descartes was in Holland during the era of the Dutch Masters epitomized in the greatest of them all, Rembrandt, and he never mentions them anywhere in his writings. Instead, his notes are filled with music, obviously Beeckman’s influence.

This leads to the conclusion that the Venus semi-sextile the Sun was particularly strong as the Sun is exalted in Aries. The two exaltations in aspect made him ignore all else but his own thoughts, as poor Pascal and others found.

Mercury rules his ascendant. It is found at the Midheaven with only one aspect a trine to Saturn, the harsh disciplinarian, who is partile his ascendant. Thus, Mercury and Saturn give form to his chart, while Venus and the Sun give it color and substance.

The Ascendant-Saturn-Mercury setup show how much his own pride (Saturn) would never have let him see the folly of his mistakes. When Descartes came to a conclusion, there were no second thoughts, but finality, for this is what absence of an aspect of Jupiter to Saturn create.

Neptune, which of course did not exist, but is found in its rulership in the twelfth house, showing his work with various royalty. He died on 11 February 1650 from pneumonia in Stockholm while helping the Swedish Queen Christina set up an academy of science. He was buried with honors in the Adolf Fredrik Church there.

The Moon is on the cusp of the second house, where it is exalted, but in Virgo, showing his strong analytical powers and ability to communicate standards. Also highlighted here is his desire to be of service to his fellow man and use those abilities for the greater good.

His planetary pattern is also interesting because while it has all the earmarks of a bundle, the most closed and introverted of all the patterns, the Moon breaks out and reaches for the second house creating a bucket with a Moon handle.

### The Scepticism of Action

Mars in Gemini in the eleventh house denotes the skepticism Descartes had in spades for other opinions. Sextile to his Sun he was confident his viewpoints were correct, if logic (Mercury conjunct the Sun at the midheaven) was followed in making them.

Yet on gravity on was wrong.

Perhaps we must agree with Descartes’s fellow Frenchmen, Francois-Marie Arout, about this brilliant and great man, the Father of Cartesian mathematics & modern philosophy, and admit, as hard as it is on the ego, no one is perfect.

*C’est le privilège du vrai génie, et surtout du génie qui ouvre une carrière, de faire impunément de grandes fautes.* — *It is the privilege of true genius, and above all a genius that opens up a new path, to commit great errors with impunity.*

Voltaire

### Footnotes:

- Bell, Eric Temple Ph.D. Men of Mathematics, New York: Simon & Schuster, 1937, 529 pp.
- This is an excellent review of 34 of the greatest mathematicians from ancient Greece to the end of the 19th century, complete with biographies and a discussion of their work. Highly recommended.