Abstract

All science is founded on the assumption that the physical universe is ordered. Our aim is to challenge this hypothesis using arguments from the algorithmic information theory. 1 Introduction Algorithmic information theory opens new vistas that extend far beyond the traditional boundaries of mathematics and computer science. How can we describe the seemingly random processes in nature and reconcile them with the supposed order? How much can a given piece of information be compressed? These are matters of fundamental scientific importance that will be discussed below, mainly from an informal or semi-formal point of view. The descriptional complexity of a sequence of bits, finite or infinite, is the length of the shortest sequence of bits defining the originally given sequence. A given sequence being random means, roughly, that its descriptional complexity equals its length. In other words the simplest way to define the sequence is to write it down. This seems to be the case for the seq...

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