A simple, practical definition of a Complex System:
A complex system is a distributed system with many interrelated (possibly networked) parts,
governed by no centralized control,
emergent behavior—'More is Different'.
A few optional extras:
Explicit nonlinear relationships.
Being open or driven, opaque boundaries.
Modular, multiscale structure.
And: Complex is a very good word—Latin: with + fold/weave (com + plex).
A Complex Systems Manifesto:
Systems are ubiquitous and systems matter.
From roughly 1700 to 2000, we enjoyed
the Golden Age of Reductionism,
where we discovered the fundamental components
of systems across many scales: atoms, sub-atomic particles, and DNA.
Atoms weren't universally accepted until
Understanding and creating systems (including new 'atoms'
and possible networked interactions) becomes the greater part of science and engineering.
systems with quantitatively different micro details
exhibit qualitatively similar macro behavior, bringing
scientists together from different fields.
We nevertheless fully understand the limits to universality,
and that distinct classes of systems obey different rules,
even if we can model the economy with
fluid flow in pipes.
Computing and technological advances make the Sciences of Complexity possible,
and the universality of tools and techniques further brings fields together:
We can measure and record enormous amounts of data,
and as research areas transition from data scarce to data rich,
we can more soundly build our theories (and throw away most of those developed in a data vacuums).
We can simulate, model, and create complex systems
in extraordinary detail.
Computing greatly empowers the modeling of systems
which needed only pencil, paper, and large brains to first understand
(e.g., ones that obey partial differential equations such as fluids).
Inevitably, Science's focus had to move to understanding, managing, and creating complex systems.
Grab a shovel. There's a lot of work to do.