  The concept of "logical depth" introduced by Charles H. Bennett (1988) seems
to capture, at least partially, the notion of organized complexity, so central
in big history. More precisely, the increase in organized complexity refers
here to the wealth, variety and intricacy of structures, and should not be
confused with the increase of random complexity, formalized by Kolmogorov
(1965). If Bennett is right in proposing to assimilate organized complexity
with "computational content", then the fundamental cause of the increase of
complexity in the universe is the existence of computing mechanisms with
memory, and able to cumulatively create and preserve computational contents. In
this view, the universe computes, remembers its calculations, and reuses them
to conduct further computations. Evolutionary mechanisms are such forms of
cumulative computation with memory and we owe them the organized complexity of
life. Language, writing, culture, science and technology can also be analyzed
as computation mechanisms generating, preserving and accelerating the increase
in organized complexity. The main unifying theme for big history is the energy
rate density, a metric based on thermodynamics. However useful, this metric
does not provide much insight into the role that information and computation
play in our universe. The concept of "logical depth" provides a new lens to
examine the increase of organized complexity. We argue in this paper that
organized complexity is a valid and useful way to make sense of big history.
Additionally, logical depth has a rigorous formal definition in theoretical
computer science that hints at a broader research program to quantify
complexity in the universe.
  Keywords: organized complexity, Kolmogorov complexity, logical depth, big
history, cosmic evolution, evolution, complexity, complexification,
computation, artificial life, philosophy of information
