The basic superstition underlying modern science, operative particularly since Descartes, is the idea that reality can be accurately and completely described mathematically.
While the monotony of consistent evidence that every mathematical projection proves to be merely approximate the moment more accurate measuring apparatus is devised should be sufficient to demonstrate that the idea is flawed, the very basis of the idea when thought through is absurd.
Looked at from a non-Cartesian perspective, without the theological assumptions that underpin his absolute faith in mathematics, the notion that something invented largely as a game about 2700 years ago says anything fundamental about reality would be odd in itself. When you also consider that with the exception of geometers, mathematicians have repeatedly insisted that mathematics has no empirical or ontological implications, i.e. it says nothing about reality, the belief that it somehow must seems even odder. Even the exception of geometers was decisively disproved in the 19th century when geometries with any arbitrary number of dimensions were found to be as usable an approximation of reality as Euclidean geometry, in fact the most accurate geometrical approximations are most often found using a six dimensional geometry rather than a three dimensional Euclidean geometry.
Finally, the recasting of mathematics itself from an axiomatic foundation, that is, based on simple notions that while unprovable are self evident, to being founded on the ZFS formulation of set theory, something not in any way self evidently the case as far as reality goes, should have been the final nail in the coffin for the superstition.
Yet it continues to persist as the common belief of the majority of scientific researchers, popularizers and teachers. Reality is judged somehow wanting as an approximation of mathematical ‘perfection’, rather than mathematics being judged an imperfect and radically incomplete approximation of reality.
The reason this assumption retains such a hold is twofold:
- It corresponds to the basic mythos of western society, the substantialization of number as measure itself as somehow ‘real’.
- So many of science’s basic assumptions depend on it that even scientists who became aware of the issue, such as Bohr and Heisenberg, have been reluctant to make their conclusions clear, since those conclusions invalidate fundamental tenets of modern science such as the truth-claim of the repeatable experiment.
Avoiding admitting the falsity of such claims, though, doesn’t change the fact that they are inherently false. There is, however, a further belief that serves to prop up the notion that even if it’s completely irrational, somehow the superstition must be correct: the belief that the functioning of modern technology proves conclusively the correctness of modern science’s basic assumptions.
This last belief is at the heart of the notion of technology as “applied science”. Yet the reality is that technologists rarely use scientific results unless it happens to be a convenient shortcut, and almost never use scientific method. Further, it is not science that ‘discovers’ things, but technology itself. Something has to already be ‘uncovered’, revealed in some way in order to become an object for science. Science itself, in thus coming after the a priori revealing, which in modern times is for the most part via technology, merely attempts to account-for what has been revealed.
As a simple example, Galileo didn’t invent the telescope to test his theories about the orbits of Jupiter’s moons; rather the existence of the telescope revealed data concerning both that and what the moons were in the first place, and gave strong hints as to how they behaved. Only after having determined that and what Jupiter’s moons were could Galileo use those hints to come up with a hypothesis to account-for how they must behave in order to generate the appearances he observed via the telescope. It took significantly better technology, not available until the late 17th century, for Jesuit scholars to demonstrate that his hypothesis in fact correctly accounted for the apparent behaviour.