Why Is the Universe So Amenable to Mathematical Description? At first glance, mathematics may seem something primary and fundamental. The astonishing elegance of its equations gives rise to a Platonic intuition: as though mathematical structures possessed an independent ideal existence and would exist even in the absence of the physical world. Yet another view is possible. Mathematics may be understood above all as a universal language for expressing the quantitative, structural, and logical relations of the real or possible world, rather than as an independent substance of which physical reality is composed. It is important to distinguish between what humans create and what they discover. We create the language of mathematics — its symbols, definitions, and formal systems — but by means of it we uncover relations and regularities that do not depend on our wishes. Historically, mathematics developed through the interaction of the intellect with the surrounding world: counting grew out of our ability to distinguish quantities, geometry from space and form, measurement from the comparison of magnitudes. Later, abstract thought allowed mathematics to reach far beyond immediate experience. Human cognitive capacities themselves were shaped in a world of stable patterns and regularities. The ability to distinguish quantity, form, distance, motion, causal connections, and recurring structures had adaptive value. It is therefore unsurprising that an intellect arising in such a world proved capable of discovering and formalizing many of its regularities. At the same time, the space of mathematically conceivable structures is considerably wider than what has been found in physical reality. Many mathematical constructions have no known physical application and perhaps never will. Moreover, the possibility of describing some world mathematically without contradiction does not yet mean that such a world is physically possible. One must distinguish between the mathematically conceivable, the physically possible, and the physically realized. It is especially interesting that certain mathematical structures were initially explored as pure abstractions and later found unexpected applications in physics. The historical connection of mathematics with practical experience is therefore not sufficient by itself to explain its effectiveness. Perhaps abstract thought explores a far wider space of structural relations, some of which are also found in physical reality. Seen in this light, the mathematical beauty of physical laws appears differently. Mathematics is astonishing not because the Universe obeys beautiful equations, but because the Universe those equations describe is itself astonishing. The elegance of the mathematics applicable to physics may reflect the depth and the intricacy of physical reality itself. But why is the Universe so amenable to mathematical description at all? Part of the answer may lie in the very possibility of a complex, self-organizing world. For stable structures, stars, chemistry, life, and ultimately intelligence to arise within it, such a world must be sufficiently ordered and governed by stable regularities. And the presence of such regularities makes their mathematical description possible. An observer-selection effect also comes into play here: we are able to pose this question precisely because we exist in a reality whose structure allows life and intelligence to emerge. In a world devoid of sufficient stability, observers capable of investigating it mathematically might simply never have arisen. Furthermore, our mathematics did not arise outside the Universe. Its language was developed by an intellect that itself arose within the Universe and whose cognitive capacities were formed through interaction with physical reality. The effectiveness of mathematics is therefore perhaps somewhat less mysterious than it seems: the intellect formalizes the structures of the very reality of which it is a part. Thus the enigma lies not so much in the existence of mathematics itself as in the question of why physical reality possesses precisely those regularities that permit complex self-organization — up to life, intelligence, and the capacity of intelligent beings to comprehend through mathematics the world that gave rise to them. On this understanding, mathematics is not a miracle governing matter from without, but an expression of the regularities of physical reality. Perhaps the Universe is so amenable to mathematical description in part because a complex, self-organizing world capable of giving rise to life and intelligence must possess stable regularities — and thereby contain within itself the possibility of its own mathematical description.

it is funny how life works in circles. When I was studying economics, I was thinking about a doctorate. Then I forgot about it completely. Now, while I'm working on the teaching materials for my new job, this old passion is starting to arise within once again.