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Abstract:

From the birth of galaxies to the self-organizing dynamics of our planet to the ongoing expansion of the universe, the more we discover about the evolution of the cosmos, the more acutely we realize the enormity of what remains to be known. Just this year astrophysicists at the University of Nottingham confirmed that there are at least two trillion galaxies in the cosmos, 10 times more than had been previously thought. What guidance or wisdom can the study of cosmology and astrophysics offer us in our search for meaning and purpose? In conversation with Steve Paulson, executive producer and host of To the Best of Our Knowledge, theoretical physicists Paul Davies and Ard Louis, and astrophysicist Lucianne Walkowicz share their perceptions based on years of gazing upward and beyond our own intimate planet.

Abstract:

Many systems in nature can be described using discrete input–output maps. Without knowing details about a map, there may seem to be no a priori reason to expect that a randomly chosen input would be more likely to generate one output over another. Here, by extending fundamental results from algorithmic information theory, we show instead that for many real-world maps, the a priori probability P(x) that randomly sampled inputs generate a particular output x decays exponentially with the approximate Kolmogorov complexity K˜(x) of that output. These input–output maps are biased towards simplicity. We derive an upper bound P(x) ≲ 2−aK˜(x)−b, which is tight for most inputs. The constants a and b, as well as many properties of P(x), can be predicted with minimal knowledge of the map. We explore this strong bias towards simple outputs in systems ranging from the folding of RNA secondary structures to systems of coupled ordinary differential equations to a stochastic financial trading model.