among the ancients. What was original in him was the use of coordinates, i.e., the determination
of the position of a point in a plane by its distance from two fixed lines. He did not himself
discover all the power of this method, but he did enough to make further progress easy. This was
by no means his sole contribution to mathematics, but it was his most important.
The book in which he set forth most of his scientific theories was Principia Philosophiae,
published in 1644. There were however some other books of importance: Essais philosophiques
( 1637) deals with optics as well as geometry, and one of his books is called De la formation du
foetus. He welcomed Harvey's discovery of the circulation of the blood, and was always hoping
(though in vain) to make some discovery of importance in medicine. He regarded the bodies of
men and animals as machines; animals he regarded as automata, governed entirely by the laws of
physics, and devoid of feeling or consciousness. Men are different: they have a soul, which resides
in the pineal gland. There the soul comes in contact with the "vital spirits," and through this
contact there is interaction between soul and body. The total quantity of motion in the universe is
constant, and therefore the soul cannot affect it; but it can alter the direction of motion of the
animal spirits, and hence, indirectly, of other parts of the body.
This part of his theory was abandoned by his school--first by his Dutch disciple Geulincx, and
later by Malebranche and Spinoza. The physicists discovered the conservation of momentum,
according to which the total quantity of motion in the world in any given direction is constant.
This showed that the sort of action of mind on matter that Descartes imagined is impossible.
Assuming--as was very generally assumed in the Cartesian school--that all physical action is of
the nature of impact, dynamical laws suffice to determine the motions of matter, and there is no
room for any influence of mind. But this raises a difficulty. My arm moves when I will that it shall
move, but my will is a mental phenomenon and the motion of my arm a physical phenomenon.
Why then, if mind and matter cannot interact, does my body behave as if my mind controlled it?
To this Geulincx invented an answer, known as the theory of the "two clocks." Suppose you have
two clocks which both keep perfect time: whenever one points to the hour, the other will strike, so
that if you saw one and heard the other, you would think the one caused the other to strike. So it