When we represent a group of connections by a closed and coherent set of concepts, axioms, definitions and laws which in turn is represented by a mathematical scheme, we have in fact isolated and idealized this group of connections with the purpose of clarification.
But even if complete clarity has been achieved in this way, it is not known how accurately the set of concepts describes reality.
Physics and Philosophy
“These idealizations may be called a part of the human language that has been formed from the interplay between the world and ourselves, a human response to the challenge of nature. In this respect they may be compared to the different styles of art, say of architecture or music.
A style of art can also be defined by a set of formal rules which are applied to the material of this special art. These rules can perhaps not be represented in a strict sense by a set of mathematical concepts and equations, but their fundamental elements are very closely related to the essential elements of mathematics.
Equality and inequality, repetition and symmetry, certain group structures play the fundamental role both in art and in mathematics. Usually the work of several generations is needed to develop that formal system which later is called the style of the art, from its simple beginning to the wealth of elaborate forms which characterize its completion.
… the question of how far the formal rules of the style represent that reality of life which is meant by the art, cannot be decided from the formal rules. Art is always an idealization; the ideal is different from reality — at least from the reality of the shadows, as Plato would have put it — but idealization is necessary for understanding.
This comparison between the different sets of concepts in natural science with different styles of art may seem very far from the truth to those who consider the different styles of art as rather arbitrary products of the human mind. They would argue that in natural science these different sets of concepts represent objective reality, have been taught to us by nature, are therefore by no means arbitrary, and are a necessary consequence of our gradually increasing experimental knowledge of nature. About these points most scientists would agree; but are the different styles of art an arbitrary product of the human mind?
Here again we must not be misled by the Cartesian partition. The style arises out of the interplay between the world and ourselves, or more specifically between the spirit of the time and the artist. The spirit of a time [(Zeitgeist)] is probably a fact as objective as any fact in natural science, and this spirit brings out certain features of the world which are even independent of time, and are in this sense eternal. The artist tries by his work to make these features understandable, and in this attempt he is led to the forms of the style in which he works.
Therefore, the two processes, that of science and that of art, are not very different. Both science and art form in the course of the centuries a human language by which we can speak about the more remote parts of reality …”
Thanks for understanding, Heisenberg.