Heller, Michael. “Chaos, Probability, and the Comprehensibility of the World.”

“The eternal mystery of the world is its comprehensibility.” This is, of course, Albert Einstein’s famous claim, and it serves as the point of departure for Michael Heller’s paper. According to Heller, this mystery is present in our prescientific cognition, but it reveals itself in full light only when one contemplates what Eugene Wigner called “the unreasonable effectiveness of mathematics in the natural sciences.” It is not a priori self-evident that the world should be “algorithmically compressible,” that is, that many of its phenomena should be captured by a few mathematical formulae.

There have been attempts to neutralize this wonder by reducing all regularities in the universe to the blind game of chance and probability. Heller briefly reviews two such attempts: the so-called chaotic gauge program and André Linde’s chaotic inflation in cosmology. If complete anarchy is the only law of nature (“laws from no laws”), then the fundamental rationality of the world is lost. The problem is important from a theological point of view. At the most fundamental level, God’s action in the world consists in giving the world its existence and giving it in such a way that everything that exists participates in its rationality, that is, is subject to the mathematically expressible laws of nature. If the ideology of the “pure game of chance and probability” turns out to be correct, then God’s action seems to be in jeopardy.

Heller responds by arguing that such attempts to neutralize the “mystery of comprehensibility” lead us even deeper into the problem. Probability calculus is as much a mathematical theory as any other, and even if chance and probability lie at the core of everything, the important philosophical and theological problem remains of why the world is probabilistically comprehensible. The probabilistic compressibility of the world is a special instance of its mathematical compressibility. Heller clarifies this point by reminding us that there are two kinds of elements (in the Greek sense of this word) in the universe - the cosmic elements, such as integrability, analyticity, calculability, predictability; and the chaotic elements, such as probability, randomness, unpredictability, and various stochastic properties. The chaotic elements are in fact as “mathematical” as the cosmic ones. If the cosmic elements provoke the question of why the world is mathematical, the same is true of the chaotic elements. In this view, cosmos and chaos are not antagonistic forces but rather two components of the same Logos immanent in the structure of the universe.

Email link | Printer-friendly | Feedback | Contributed by: CTNS/Vatican Observatory