  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.
