Tony Smith
Meme Media
Melbourne, Australia
Registered: Oct 2003
Posts: 167 
Weak or strong Principle of Computational Equivalence?
I'm drawing here on the distinction between the weak and strong interpretations of the Anthropic Principle, the weak being inescapably true but still useful in clarifying thinking and the strong being as far as I can see wishful thinking.
In the case of Wolfram's central Principle of Computational Equivalence (PCE) I see a "weak" interpretation saying that results we find anywhere in the computational universe might also be found elsewhere, especially in the world we find ourselves in. The ultimate truth of the weak PCE has been demonstrated by extreme engineering built on top of a range of very simple computational programs (aka rules).
My reading of NKS sees Wolfram wavering both in practice and in principle between practical application of the weak PCE and a feeling that a stronger version ought to be true. In particular, the rule numbering system Wolfram extended from his original 256 2D CAs to much larger rule spaces carries with it an implication that all rules should be treated as equal, especially once the Class 1 and Class 2 rules have been discounted. It is instructive that the wider CA community seems to have become even more focused on its more naturalistic schemes for enumerating rules as it has expanded the rule space. (For example, my own current focus is on the Moore totalistic 2D rule "Generations 345/3/6" where the 345 indicates the number of neighbours for a cell to stay alive, the 3 the number for a dead cell to be born and the 6 says that their are six possible states: dead, alive and four other dying generations that each cell which dies must pass through before in can be born again. I can't imagine anybody ever identifying the significance of that rule if they were using Wolfram's numbering system.)
Yet in practice Wolfram often appears to have been a lot more insightful in his choice of targets for detailed exploration, showing a preference for simple starting points and a practical mix of comprehensive and random surveys. He even concedes that there may be substructure within Class 4 which any strong reading of the PCE implicitly makes unreachable.
At its extremes, Wolfram's rule numbering is almost reminiscent of the absurd "numbers" GÃ¶del invoked in corralling formalism. And I can only presume Wolfram's intellectual investment in Mathematica makes a strong reading of GÃ¶del extremely difficult, although it is something I would recommend to anybody who wants more substantial theory in the no longer escapable direction of Taleb's The Black Swan.
Another concern with a strong PCE is that it overburdens the notion of computing. Whatever is going on at levels below photon resolution limits, it is something which is an intrinsic dynamic of the fabric of the universe. Trying to think of it as a computer mostly just provides a short route to absurdity. As magical as they sometimes seem, computers are well understood to the point of only adding confusion when used as inappropriate metaphors.
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Tony Smith
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