What Isn't Complexity?

TL;DR

This paper explores the nature of complexity, proposing that it arises from structural and functional hierarchies linked by properties like fitness or meaning, and can be measured by the human brain.

Contribution

It introduces a phenomenological framework for understanding complexity through hierarchical structures and their associated properties, emphasizing the role of the brain as a measuring device.

Findings

Complex systems exhibit structural/functional hierarchies.

Complexity is linked to properties like fitness and meaning.

The human brain can measure complexity.

Abstract

The question What is Complexity? has occupied a great deal of time and paper over the last 20 or so years. There are a myriad different perspectives and definitions but still no consensus. In this paper I take a phenomenological approach, identifying several factors that discriminate well between systems that would be consensually agreed to be simple versus others that would be consensually agreed to be complex - biological systems and human languages. I argue that a crucial component is that of structural building block hierarchies that, in the case of complex systems, correspond also to a functional hierarchy. I argue that complexity is an emergent property of this structural/functional hierarchy, induced by a property - fitness in the case of biological systems and meaning in the case of languages - that links the elements of this hierarchy across multiple scales. Additionally, I argue that non-complex systems "are" while complex systems "do" so that the latter, in distinction to physical systems, must be described not only in a space of states but also in a space of update rules (strategies) which we do not know how to specify. Further, the existence of structural/functional building block hierarchies allows for the functional specialisation of structural modules as amply observed in nature. Finally, we argue that there is at least one measuring apparatus capable of measuring complexity as characterised in the paper - the human brain itself.