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From: Hal Finney <hal.domain.name.hidden>

Date: Sun, 24 Nov 2002 16:17:26 -0800

I think there are a couple of things about Wolfram's book which aren't

well understood.

Most importantly, he is not specifically commited to cellular automata.

He does focus on them, especially 1-dimensional, 2-state CAs, as a

particularly simple model of computation, which also has the property

that a relatively high percentage of randomly chosen programs produce

apparent complexity. But he explores a number of other computational

systems, including higher dimensional and higher state CAs; mobile CAs;

Turing machines; substitution systems; sequential substitution systems;

tag systems; cyclic tag systems; register machines; symbolic systems;

arithmetic; recursive sequences; iterated maps; continuous (non-quantized)

CAs; partial differential equations; network systems; multiway systems;

constraint satisfaction systems; and higher dimension versions of many

of these.

The lesson he draws is that generally, the same kinds of patterns

are seen in virtually all of these ways of expressing computation.

You see simple, constant outputs; simple repetition; chaotic patterns;

and occasionally, the mysterious "structure" on the edge of chaos, which

often shows tantalizing particle-like phenomena and other interesting

analogs to real-world phenomena.

Where he does fall back on CAs, I don't think his point is so much

that the phenomena are based precisely on CAs, but that random, simple

algorithms when implemented in CAs often produce very similar patterns to

what we see in the real world. And that this is probably not coincidence.

It suggests that these kinds of patterns could be considered attractors

in pattern space. They are easier to produce than other patterns that

might seem superficially similar. Their algorithm complexity is lower.

And this insight might inform our efforts to understand the true nature

of the phenomena which create these patterns.

Where Wolfram turns to physics, his speciality, he explicitly departs

the CA model as he tries to sketch a possible mathematical basis for

the universe that is consistent with the paradoxical phenomena of QM and

relativity. He uses network systems, hypothetical sub-quantum "nodes"

which are connected to one another and whose connections might change

under simple rules. This is not completely original; I think Wheeler

and others pursued ideas similar to this back in the 70s. Wolfram takes

it a little farther in showing how you could get some relativity-style

phenomena, but it's a very bare beginning effort.

My main point is that characterizing Wolfram as saying that the universe

is a CA, or biological patterns or fluid turbulence or any other phenomena

are caused by CAs, is not correct. He is not saying these phenomena are

caused by CAs, he is saying that extremely simple CA programs produce

similar phenomena, suggesting that such phenomena emerge spontaneously

from computational systems.

As for the universe, I think his point is that the grand, mathematical

elegance of string theory and similar methods is the wrong approach.

These beautiful mathematical models are too rigid and brittle to describe

a universe like ours. The universe is more likely to be built out of

a messy, random and simple little program that just happens to create

patterns that have the properties necessary for life to evolve.

In the context of our list, this can be thought of as a philosophical

bias towards Schmidhuber and away from Tegmark. In Tegmark's model,

string theory is relatively near the origin of the tree of mathematical

structure; it is simple. If it produced enough particles and interactions

of the right kinds to allow for life, it would be an excellent candidate

for the place where we live. But in Schmidhuber's model, it's just as

likely that some random hodgepodge of a program a few thousand bits in

length will "just happen" to produce a very robust, dynamic and varied

universe with all kinds of structure at different size scales. Such a

universe is an inherently friendly home for life as there are so many

possible niches for it to grow.

Of course, at this point we are in no position to decide between these

two philosophies. Wolfram's book is ultimatly a call to our intuition,

an appeal for equal time to be given to Schmidhuber-ish approaches

based on random programs, as for the traditional Tegmarkian mathematical

modelling which is done in physics. I think there is something to be

said for this shift in perspective, and I hope that at least a small

minority of researchers will attempt to move Wolfram's program forward.

Hal Finney

Received on Sun Nov 24 2002 - 19:18:29 PST

Date: Sun, 24 Nov 2002 16:17:26 -0800

I think there are a couple of things about Wolfram's book which aren't

well understood.

Most importantly, he is not specifically commited to cellular automata.

He does focus on them, especially 1-dimensional, 2-state CAs, as a

particularly simple model of computation, which also has the property

that a relatively high percentage of randomly chosen programs produce

apparent complexity. But he explores a number of other computational

systems, including higher dimensional and higher state CAs; mobile CAs;

Turing machines; substitution systems; sequential substitution systems;

tag systems; cyclic tag systems; register machines; symbolic systems;

arithmetic; recursive sequences; iterated maps; continuous (non-quantized)

CAs; partial differential equations; network systems; multiway systems;

constraint satisfaction systems; and higher dimension versions of many

of these.

The lesson he draws is that generally, the same kinds of patterns

are seen in virtually all of these ways of expressing computation.

You see simple, constant outputs; simple repetition; chaotic patterns;

and occasionally, the mysterious "structure" on the edge of chaos, which

often shows tantalizing particle-like phenomena and other interesting

analogs to real-world phenomena.

Where he does fall back on CAs, I don't think his point is so much

that the phenomena are based precisely on CAs, but that random, simple

algorithms when implemented in CAs often produce very similar patterns to

what we see in the real world. And that this is probably not coincidence.

It suggests that these kinds of patterns could be considered attractors

in pattern space. They are easier to produce than other patterns that

might seem superficially similar. Their algorithm complexity is lower.

And this insight might inform our efforts to understand the true nature

of the phenomena which create these patterns.

Where Wolfram turns to physics, his speciality, he explicitly departs

the CA model as he tries to sketch a possible mathematical basis for

the universe that is consistent with the paradoxical phenomena of QM and

relativity. He uses network systems, hypothetical sub-quantum "nodes"

which are connected to one another and whose connections might change

under simple rules. This is not completely original; I think Wheeler

and others pursued ideas similar to this back in the 70s. Wolfram takes

it a little farther in showing how you could get some relativity-style

phenomena, but it's a very bare beginning effort.

My main point is that characterizing Wolfram as saying that the universe

is a CA, or biological patterns or fluid turbulence or any other phenomena

are caused by CAs, is not correct. He is not saying these phenomena are

caused by CAs, he is saying that extremely simple CA programs produce

similar phenomena, suggesting that such phenomena emerge spontaneously

from computational systems.

As for the universe, I think his point is that the grand, mathematical

elegance of string theory and similar methods is the wrong approach.

These beautiful mathematical models are too rigid and brittle to describe

a universe like ours. The universe is more likely to be built out of

a messy, random and simple little program that just happens to create

patterns that have the properties necessary for life to evolve.

In the context of our list, this can be thought of as a philosophical

bias towards Schmidhuber and away from Tegmark. In Tegmark's model,

string theory is relatively near the origin of the tree of mathematical

structure; it is simple. If it produced enough particles and interactions

of the right kinds to allow for life, it would be an excellent candidate

for the place where we live. But in Schmidhuber's model, it's just as

likely that some random hodgepodge of a program a few thousand bits in

length will "just happen" to produce a very robust, dynamic and varied

universe with all kinds of structure at different size scales. Such a

universe is an inherently friendly home for life as there are so many

possible niches for it to grow.

Of course, at this point we are in no position to decide between these

two philosophies. Wolfram's book is ultimatly a call to our intuition,

an appeal for equal time to be given to Schmidhuber-ish approaches

based on random programs, as for the traditional Tegmarkian mathematical

modelling which is done in physics. I think there is something to be

said for this shift in perspective, and I hope that at least a small

minority of researchers will attempt to move Wolfram's program forward.

Hal Finney

Received on Sun Nov 24 2002 - 19:18:29 PST

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