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

emulate.

---------

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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