The key difference between modern and ancient science is not that one is based on experience and experiment and the other is not (as Galileo polemically presents it), but that modern science is mathematical. Numbers are not found in things, nor are things numbers. What is mathematical has to be brought to nature, but for nature to be brought under mathematics it already has to be understood in a certain way. Mathematics provides the certainty (what Descartes thinks of as self-evident truths), but we must already think of nature as something that one could be certain about in the first place.

To think of nature as something certain is to think of it as homogenous. It is because Descartes already conceives of nature as extension (the corpuscular theory of matter) that it is mathematical. It is not because it is mathematical that he thinks of it as extension. Descartes claims that this idea has its validity in the idea of God. Heidegger would argue that this theory of nature is a projection, however useful it might be, of the scientist himself. This does not mean that what science describes is not real, as though its objects were ghosts, but that science never relates to nature empty handed. It only encounters reality within certain limitations.

¶ 7:39 AM