Descartes: A Biography

c CUNYB/Clarke     December, :

 Descartes: A Biography

crucial features of that correspondence, apart from his obvious disdain for

Roberval, was Descartes’ recognition that his mathematical calculations

had to coincide with experimental observations and that any solution to

the queries that he received relied essentially on observations. ‘My rea-

soning does not agree with the observations that you were kind enough to

send me, and I acknowledge honestly that I cannot yet see why not.’

The renewed controversy with Roberval was mediated, as before, by

Mersenne, who forwarded Roberval’s criticisms and Descartes’ replies.

Descartes had the impression that, when they met in Paris in,Rober-

val had offered to explain why he thought Descartes had not fully solved the

Pappus problem. This was evidently something to which he did not wish

to return two years later. Out of politeness, however, he offered to review

Roberval’sAristarchusand to explain his principal reservations about it if

Roberval, for his part, would promise to write his residual doubts about the

Geometry.The subsequent discussion of Roberval’s mathematics was

confused by the fact that they were discussing two distinct problems –

the oscillations of asymmetrical pendulums, and the relative merits of

Descartes’Geometryand Roberval’sAristarchus– and by a background

disagreement about the significance of experiments intended to resolve

the former issue.

Descartes consistently claimed that the anomalies observed in the oscil-

lations of different pendulums was due entirely to variations in the obstruc-

tion caused by the air, and that this factor was so complicated that it could

be known only from experiments.

That is why I shall say nothing more here about it except that the great difference

between (a) the oscillations of very obtuse triangles or those that are suspended by their

bases and (b) the calculation that I did for all triangles in general, results only from the

cause that I have called the obstruction of the air which...is much greater in the case

of obtuse triangles than in others. Now I believe that one can quantify this obstruction

only by experience....All I claim to do is to try to make sense of what someone else

has experienced; but I think the most appropriate way to examine experiences is to

choose those that depend on fewer distinct causes and of which one can more easily

discover the true cause.

This caveat appears almost as a refrain in later letters on the same topic.

‘I have said that the quantity of this obstruction can be determined only

byexperience.’‘I distinguish between what moves a body and what

impedes it, and between what can be determined by reasoning and what

can be determined only by experience.’