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
selfevident 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 socalled 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.
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