This line of thought is indicated in the first section of the first chapter of an earlier book of Thom:

Reality presents itself to us in the form of phenomena, of forms, whose presence we detect through their qualitative discontinuities: "objects" quite often undergo only slow transformations and it is only because of their relative stability that we can situate ourselves amidst their multiplicity and diversity.

 By what process does the mind come to postulate the permanence of a single being behind the infinite variety of its aspects ?  This problem of the recognition of forms raises very difficult questions for physiology and philosophy.  Provisionally, we shall leave aside these difficult problems.  But we shall nonetheless affirm this first principle: every science is the study of a phenomenology.

Now, what is a "phenomenon" ?  Etymologically, a phenomenon is what is seen, what appears, and every appearance is manifested in a certain space.  In most cases, this space is simply that Euclidean space-time in which the normal morphology of everyday reality unfolds.  One will note that this morphology is not itself an object of science; why is this ?  Because we possess mental mechanisms linked to "common sense", to logic, to ordinary language, which generally allow us to act efficaciously in our environment.  The gardener who sows carrot seeds in order to harvest carrots does not for all that hold himself up as a scientist, even though he is implicitly doing Biology.  If Biology and the "human sciences" have up to now been so little mathematized, this is because our immediate intuitive understanding of biological, psychological or social facts suffices for the needs of ordinary life.  Science is born at the moment when errors, setbacks and disagreeable surprises prompt us to look more closely at reality.  Mechanics was perhaps the first of the sciences, because it was dealing with delicately balanced situations with an uncertain outcome (for instance, to hit one's prey with a projectile), in which a more fine-grained representation of the real, i.e. that which is given by numbers, becomes necessary.