René Descartes (1596 – 1650) was an outstanding physicist, mathematician and philosopher. In physics, he laid the ground work for Isaac Newton’s (1642 – 1727) laws of motion by pioneering work on the concept of inertia. In mathematics, he developed the foundations of analytic geometry, as illustrated by the term Cartesian coordinates. However, it is in his role as a philosopher that he is best remembered. Rather ironic, as his breakthrough method was a failure.
Descartes’s goal in philosophy was to develop a sound basis for all knowledge based on ideas that were so obvious they could not be doubted. His touch stone was that anything he perceived clearly and distinctly as being true was true. The archetypical example of this was the famous I think therefore I am. Unfortunately, little else is as obvious as that famous quote and even it can be––and has been––doubted.
Euclidean geometry provides the illusionary ideal to which Descartes and other philosophers have strived. You start with a few self-evident truths and derive a superstructure built on them. Unfortunately even Euclidean geometry fails that test. The infamous parallel postulate has been questioned since ancient times as being a bit suspicious and even other Euclidean postulates have been questioned; extending a straight line depends on the space being continuous, unbounded and infinite.
So how are we to take Euclid’s postulates and axioms? Perhaps we should follow the idea of Sir Karl Popper (1902 – 1994) and consider them to be bold hypotheses. This casts a different light on Euclid and his work; perhaps he was the first outstanding scientist. If we take his basic assumptions as empirical rather than sure and certain knowledge, all we lose is the illusion of certainty. Euclidean geometry then becomes an empirically testable model for the geometry of space time. The theorems, derived from the basic assumption, are prediction that can be checked against observations satisfying Popper’s demarcation criteria for science. Do the angles in a triangle add up to two right angles or not? If not, then one of the assumptions is false, probably the parallel line postulate.
Back to Descartes, he criticized Galileo Galilei (1564 – 1642) for having built without having considered the first causes of nature, he has merely sought reasons for particular effects; and thus he has built without a foundation. In the end, that lack of a foundation turned out to be less of a hindrance than Descartes’ faulty one. To a large extent, sciences’ lack of a foundation, such as Descartes wished to provide, has not proved a significant obstacle to its advance.
Like Euclid, Sir Isaac Newton had his basic assumptions—the three laws of motion and the law of universal gravity—but he did not believe that they were self-evident; he believed that he had inferred them by the process of scientific induction. Unfortunately, scientific induction was as flawed as a foundation as the self-evident nature of the Euclidean postulates. Connecting the dots between a falling apple and the motion of the moon was an act of creative genius, a bold hypothesis, and not some algorithmic derivation from observation.
It is worth noting that, at the time, Newton’s explanation had a strong competitor in Descartes theory that planetary motion was due to vortices, large circulating bands of particles that keep the planets in place. Descartes’s theory had the advantage that it lacked the occult action at a distance that is fundamental to Newton’s law of universal gravitation. In spite of that, today, Descartes vortices are as unknown as is his claim that the pineal gland is the seat of the soul; so much for what he perceived clearly and distinctly as being true.
Galileo’s approach of solving problems one at time and not trying to solve all problems at once has paid big dividends. It has allowed science to advance one step at a time while Descartes’s approach has faded away as failed attempt followed failed attempt. We still do not have a grand theory of everything built on an unshakable foundation and probably never will. Rather we have models of widespread utility. Even if they are built on a shaky foundation, surely that is enough.
Peter Higgs (b. 1929) follows in the tradition of Galileo. He has not, despite his Noble prize, succeeded, where Descartes failed, in producing a foundation for all knowledge; but through creativity, he has proposed a bold hypothesis whose implications have been empirically confirmed. Descartes would probably claim that he has merely sought reasons for a particular effect: mass. The answer to the ultimate question about life, the universe and everything still remains unanswered, much to Descartes’ chagrin but as scientists we are satisfied to solve one problem at a time then move on to the next one.
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