A Pythagorean Universe

What is physics? What would a good definition for it be, if possible at all? This question takes the author on a search for the most important in the history of physics starting in antiquity. Following that, he discovers a certain synthesis of philosophical and religious ideas that gave physics a new wind in Modernity, which he calls Pythagorean Faith. Recognizing the very specific character of the known laws of nature, namely, a particular minimax of their complexity, leads to a new formulation of the physico-theological argument, the Pythagorean argument for the intelligent design of the universe. In conclusion, the author comes to a new definition of physics.

When Galileo professed that the book of nature is written in the language of mathematics, his claim was not at all that the natural processes are conducive to quantitative analysis, that there are relationships and correlations between measured parameters. In his time, as in ours, that would have been a banality, while the thought of Galileo was revolutionary. It was much more than counting or measuring: farmers have been counting sheep and measuring their property since prehistory. It was of an entirely different order than even the Ptolemean model, which, though a magnificent example of the ancient art of curve-fitting, had not progressed the understanding of nature beyond the confirmation of the fact that some regularities exist in the trajectories of the planets. In reality, Galileo was establishing a programme of searching out the postulates of nature, its mathematical principles, hidden behind complex theorems of phenomena.

To see in mathematics nothing but a collection of all possible, value-neutral, formal systems is no better than to view the art of sculpture as a collection of all possible articles made of stone, or defining man, according to the old anecdote, as a two-legged creature without feathers.

Our universe is special not only because it is populated by living and conscious beings but also because it is theoretizable by means of elegant mathematical forms, both rather simple in presentation and extremely rich in consequences. To allow life and consciousness, the mathematical structure of laws has to be complex enough so as to be able to generate rich families of material structures. On the other hand, the laws have to be simple enough to be discoverable by the appearing conscious beings. To satisfy both conditions, the laws must be just right. The laws of nature are not only fine-tuned with respect to the anthropic principle but also selected with respect to their discoverability. In other words, the structural axioms of the Universe include what can be called the Discoverability Principle: its laws are purposefully chosen for the universe to be cosmically observed. Such a special universe deserves a proper term, and we do not see a better choice than to call it Cosmos or to qualify it as Pythagorean, in honor of the first prophet of theoretical cognition, who coined such important words as cosmos, philosophy and theory.