Registered: Jun 2004
You mentioned a principle of simplicity in your blog. Really, why do we
believe that, other things being equal, simple theory is better than complex
one? Why scientists are always looking for elegant theories, not for ugly ones?
For, objectively, there's no difference. For computer, the equation with 25
parameters is not better or worse than with 2.
In general, when we are talking about simplicity, we are using HUMAN language.
Simple means: easy to understand. When Wolfram says: simple programs lead to
complex behaviour, this translates to (apparently, contrary to his intentions):
programs that are easy to understand lead to behaviour that is hard to
understand. But wait: if nature has no intelligent designer (or: designers)
behind it, why does it care about our ability to understand it. Remove human
being from the picture - and there's no difference between "simple" and
"complex", these notions don't have "objective meaning". True, he could use the
term "short" instead of "simple", but what would he use instead of "complex"? [
BTW, formula "short program can lead to complex behaviour" would be in
contradiction with Kolmogorov's definition of complexity, but this fact doesn't
matter much in the context of this discussion - let's forget about it for now]
Be it "simple", or "short", why would it matter in objective world having no
intelligent observer? Why there's so much excitement about rule 110? What
difference would it make if the minimal universal rule had 1000 digits in it
instead of 3? And only one out of 10 million rules would be universal? From
computers's viewpoint, this difference wouldn't make any difference.
The point is that all science, including math, has some background belief behind
it - belief that the "rules" of this world are simple and beautiful, AS IF (!)
they were constructed by intelligent being. Wolfram, as a mathematician, shares
this view, no matter if he is aware of it or not. In this context, rule 110
really matters: it's BEAUTIFUL, there's no other value in it, but this is the
absolutely the most important value mathematical result can have. Somehow, I
suspect that Wolfram didn't fully realize what he really discovered; or, maybe,
he realized, became overly excited, and in this excitement, produced a number of
statements that reduce this sense of beauty to absolute ugliness of universe
driven by cellular automation. (Critics overlooked this beauty, too. What's
the difference between rule with 5 neighbours and 3 colors, and 2 neighbours and
2 colors? There's a difference, I would say. Infinitely big difference in
So, what's wrong if people make this background belief more explicit? It's
USEFUL. It leads to things like Newtonian laws, relativity, Euler's identity,
etc,... - and, among other things, modest rule 110, which is not that bad
either. On what grounds should anyone administratively prohibit this idea?
What an irony: official science is engaged in a struggle with the fundamental
idea of science: the belief in beauty.
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