Wolfram is fascinated by the generation of complexity and randomness from simple
rules, and sees this as a fundamental and unexpected observation.

(As a long-time programmer, I'm puzzled by his surprise at this. My bugs often have
a complex and seemingly random nature, even in programs thought to be trivially simple. ;-)

But seriously, we were taught in 3rd or 4th year comp sci. that if your computing
system can do IFs, LOOPs, and SUBROUTINE CALLS (or equivalent), it can compute
anything that can be computed (anything that can be computed using a finite number of
computing steps operating on finite data, that is). It is a universal computer.

It is not really surprising at all to a programmer that some simple
combinations of IFs LOOPs and SUBROUTINE calls can start to generate assymetric
output, which when fed back in as input data can lead to non-linear systems and
complexity, and even randomness, in a hurry.

Wolfram criticizes current scientific theories, almost all based on simple mathematical
equations, as being able to model only the simple and regular aspects of systems.
These aspects, he seems to imply, might in many cases not be the most interesting
aspects of the systems. We are only describing those aspects, and those particular
systems, he says, because simple regularities are all that our pathetically limited
mathematical equation toolbox allow us to describe. And there is so much
more interesting complexity to the world, which cellular automata can better
But what if, in general, irregular complexity is boring, and it is only really
fundamental simplicities, and emerged simplicities, that are interesting?
What if mathematical-equation-based science was right all along?

Alright. Overly simple arrangements might be a little dull (limited in
capacity for interesting properties or behaviours) too.

What if there is a kind of "interesting" range of complexity of system.
A system characterised by simplicities and order sufficient to ensure some regular
structures (identifiable system components, hierarchical organization of components)
and regular behaviours, but with enough constrained complexities of
interaction between components to make the system capable of a range
of non-trivial behaviour and interaction with other systems or components.

Is this a kind of system that is only of interest to us with our particular
human interests? Or is there anything more fundamentally important about
systems with particular levels or arrangements or mixes of order and complexity?

Are there, for example, any general rules about the mix of simplicity, order,
and complexity (arrangements of entropy) that can produce higher-level
emerged systems which may have properties of being identifiable,
sustainable or recurring, instrumental in even higher level systems etc.

This is way out there stuff vaguely sketched. I know.

In any case, I tend to agree with Kurzweil's criticism of Wolfram that Wolfram
doesn't focus enough the issue of how we find rules that produce the emergence of
higher-level order (simplicities, but with enough "mobility" to be interesting).
Wolfram, he says, focusses purely on the generation of
arbitrary complexity, and that's only part of the picture.

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