Historical Note on René Descartes

Historical Note on René Descartes

René Descartes(1596 – 1650) was a mathematician and philosopher (and other things) who made two gigantic contributions to the accumulated knowledge of the world. The one he is best known for is his phrase:

Cogito, ergo sum

which translates as

I think, therefore I am.

With this phrase, he challenged the ascendancy of Greek philosophy which had dominated the western mind for almost 2,000 years.

Greek philosophy split on the question of whether or not to trust the information given to you by your senses. Half of them believed you could, that when you tripped over a rock, you could believe a rock existed to trip you. The other half believed you couldn’t, using experiments such as the following to prove their point:

Suppose you have three bowls of water in front of you – one full of hot water, one full of ice-cold water, and one full of lukewarm water. Place one hand in the bowl of hot water and the other hand in the bowl of ice-cold water. After a few minutes, move both hands to the bowl of lukewarm water. Your hand from the ice-cold bowl will tell you the bowl of lukewarm water is hot, while your hand from the hot bowl will tell you the lukewarm water is cold. Since it obviously cannot be hot and cold at the same time, you can’ trust your senses.

Those that believed you couldn’t trust your senses pointed out that it was not possible to prove that anyone’s entire existence was anything more than the random daydream of another person. This bothers some people, because it cannot be shown to be wrong.

Descartes decided to start over, discarding everything that was subject to doubt. As a result, he discarded everything except the fact that there existed something (himself) that doubted. He reasoned that if he had the ability to doubt his own existence, then he must exist. Therefore, his famous phrase.

The full phrase is:

I think, therefore I am. If I think not, then I am not

and this indirectly led to the end of his life. He was riding on a train and the server came to him and asked whether he wanted to go to the first serving of dinner. Lost in meditation, Descartes absent-mindedly responded “I think not,” and vanished.

It was actually a good thing that this happened, because of the rituals that surrounded burials at that time. It seems that a funeral carriage would carry the body from the person’s house to the church, and after the funeral service the pall bearers would carry the coffin from the church to the graveyard, with the funeral carriage following along behind. In this case, that would have meant (are you ready for this?):

putting Descartes before the hearse

which we have all been taught is a bad thing to do.

By the way, none of this stuff about his death is true. The truth is even more bizarre. He died, basically of overwork, while at the court of Queen Christina of Sweden. His fame was such that he was widely believed to be a saint. As his body was taken back to France for burial, people who collected relicts of saints took pieces of his body, to the point where there was very little of him left to bury. They must have been very disappointed when the Roman Catholic Church failed to canonize him.

The following, however, is true. After completing his education, Descartes served for a while in the armies of Holland and Bavaria. At some point, he managed to get in trouble and was ordered (as a punishment) to stand guard in an empty room. For a normal person, this would have been incredibly boring, but not for a mathematician. Descartes was simply daydreaming about geometry (at the time, a rather abstract study of shapes) when he got distracted by a fly that was buzzing about the room. He suddenly realized that the location of the fly could be precisely determined by using the lines coming from a corner of the room (where the floor met the walls and the walls met each other). If you treat those lines as the axes of a graph, then any point in the room has three coordinates, one measured on the vertical axis, one measured on the axis of the left-hand wall and the floor, and one measured on the axis of the right-hand wall and the floor.

This seems obvious to us, but he was the first to create this link between geometry and algebra, which makes him responsible for all of analytic geometry and most engineering. As a result, the proper name for a graph is a Cartesian Coordinate System, named for René Descartes.