Algorithmic Complexity as the Most Appropriate Metric to Estimate the Randomness of Objects

The act of explaining what our eyes see has always been a human need. The act of trying to understand reality, for which some have called science, common sense, etc., is nothing more than classifying randomness. That is, when one discovers the mechanism of operation of a phenomenon, what we have done is finding that this phenomenon is not random, that it has a cause and we have found it. To do this, the phenomenon is abstracted to a chain of symbols and we call that "the object."

However, measuring randomness is a challenge, there are several metrics used in the scientific community such as Shannon entropy (in the field of Information Theory), compression methods, etc.; but the one that has proven to be the best metric is the one used in Algorithmic Complexity (AC), and in particular the methodology used by Professor Hector Zenil that is used in this work. The idea is that to evaluate the content of an object -which can be identified with a generating algorithm and a causal mechanism, CA provides us with a precise criterion to decide whether an object is random or not. And as in science, we can find a shorter description than the phenomenon itself.

In this work, the estimation of the randomness of several objects is compared, such as the Thue-Morse sequence, structured binary chains and some representations of physical phenomena, where the effectiveness of AC against other metrics to classify the randomness of an object is demonstrated. This work also offers a new paradigm to the scientific community by presenting the underlying formalism for using the tools that Dr. Zenil provides, and applying the CA methodology to any area of science that requires measuring randomness.