Mathematics

Science is, in other words, a system of relations. It is only in relations that we should attempt to find objectivity; it would be futile to search for it in the things themselves instead of in their relations to one another…’ (Poincare)

Mathematics is the language used by science to describe the physical world. And science can sometimes achieve extraordinary degrees of accuracy on its measurements and predictions. Does this mean that Nature is written in a mathematical language?

No. There are several reasons for which mathematics has been so successful in describing Nature. First, it is an objective and universal language (i.e. it is independent from culture, age, gender, etc) and Nature is an objective and universal order. It is also precise and unambiguous. But most crucially, mathematics is based on constructions of spatial relations (algebras): and that is exactly what Nature is about. The difference is that, while mathematics is based on abstract spatial relations, Nature is about spatial relations on a physical Space. Nature is an order on the behaviour of a unitary physical Space. Physics then, owes its success to mathematics, because mathematics is a powerful tool to model physical Space.

The success of mathematics to describe Nature, is yet another piece of evidence about the spatial nature of the universe. It is because Nature has a spatial nature that mathematics has been so successful.

But the success of mathematics to describe Nature, doesn’t mean that Nature has a mathematical nature. Mathematics is objective and universal, only among man. Mathematics seems to be objective, for it seems to be independent from place and time. Once an algebra is defined, it is culturally independent and it doesn’t change with time. But this objectivity is only in appearance. From a human point of view, it is humanly objective. But from an objective point of view, mathematics is in the end a mental construction that is humanly subjective. It is a subjective mental space. Physical Space on the other hand is objective, universal and independent from our thought.

In physics there is a multiplicity if spaces describing Nature: Newtonian mechanics, Maxwell’s electro-magnetism, General relativity, Quantum Field theory, etc. And there is also a multiplicity of tools to describe these spaces: Euclidean geometry, Riemannian geometry, vectors, tensors, imaginary numbers, fields, Hilbert spaces, etc.
Physics is progressing towards the gradual unification of these spaces (see unification theories). And the successful unification of spaces into ever more universal theories, is yet another piece of evidence about the unicity of physical space.
We might interpret Nature through different mental spaces, but physical space is one and everywhere the same. And our understanding of Nature progresses, with the gradual understanding of the unity of things.

Mathematical truths – Mathematical truths seem to be absolute, for they seem to be universal and invariable. But this is only in appearance, mathematical truths are in the end subjective and relative (see also the subjectivity & relativity of truth).


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