Without studying it in detail, I’m skeptical of the importance its claim. David says he has found class 1 and 3 systems that produce gliders. Perhaps David is poor at classifying systems. The existence of gliders strongly implies a system is class 2 or 4.
But perhaps he really has found class 1 and 3 systems in which a glider can exist. Is that important? Well, since the classification is statistical, being “class 1” really means “behavior is more class-1-like than any other class”. So particular structures can still exist in a class 1 or class 3 CA that exhibit a particular behavior. They’re just less-common.
I think Wolfram’s classifications are very well-defined as these things go (you can probably state them mathematically in terms of Lyapunov exponents, or number of attractors for finite worlds, or number of state transitions over time in Monte Carlo simulations, for instance). The problem is that the classification is statistical, so you can’t say “this is class 1 and therefore behavior X is impossible”.
The more important point, popping back up to the grandparent of this comment, is that I’m not convinced that the distribution of possible CAs resembles the distribution of possible physics.
Without studying it in detail, I’m skeptical of the importance its claim. David says he has found class 1 and 3 systems that produce gliders. Perhaps David is poor at classifying systems. The existence of gliders strongly implies a system is class 2 or 4.
But perhaps he really has found class 1 and 3 systems in which a glider can exist. Is that important? Well, since the classification is statistical, being “class 1” really means “behavior is more class-1-like than any other class”. So particular structures can still exist in a class 1 or class 3 CA that exhibit a particular behavior. They’re just less-common.
It’s the second paragraph that’s right here, I believe.
I generally agree with Epstein’s comments. Except that in his classification scheme, I tend to regard the “Contraction impossible.” case as pretty similar to the “Expansion impossible” case.
I think a major point of interest of Wolfram’s classification is that is suggested that universal automata were in class 4. If that is more false than true, the classification scheme loses much of its interest.
Without studying it in detail, I’m skeptical of the importance its claim. David says he has found class 1 and 3 systems that produce gliders. Perhaps David is poor at classifying systems. The existence of gliders strongly implies a system is class 2 or 4.
But perhaps he really has found class 1 and 3 systems in which a glider can exist. Is that important? Well, since the classification is statistical, being “class 1” really means “behavior is more class-1-like than any other class”. So particular structures can still exist in a class 1 or class 3 CA that exhibit a particular behavior. They’re just less-common.
I think Wolfram’s classifications are very well-defined as these things go (you can probably state them mathematically in terms of Lyapunov exponents, or number of attractors for finite worlds, or number of state transitions over time in Monte Carlo simulations, for instance). The problem is that the classification is statistical, so you can’t say “this is class 1 and therefore behavior X is impossible”.
The more important point, popping back up to the grandparent of this comment, is that I’m not convinced that the distribution of possible CAs resembles the distribution of possible physics.
It’s the second paragraph that’s right here, I believe.
I generally agree with Epstein’s comments. Except that in his classification scheme, I tend to regard the “Contraction impossible.” case as pretty similar to the “Expansion impossible” case.
I think a major point of interest of Wolfram’s classification is that is suggested that universal automata were in class 4. If that is more false than true, the classification scheme loses much of its interest.