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What are those limits? One of the big ideas out of Wolfram's book A New Kind of Science is that, once a rather small threshold is reached, a system made of simp

What are those limits? One of the big ideas out of Wolfram's book A New Kind of Science is that, once a rather small threshold is reached, a system made of simple rules becomes universal. And since by definition any universal system can emulate any other universal system, there cannot be a thing computable by one universal system that is not computable by another. (One of the implications of this idea he suggests is that the weather, which he argues is a universal system made of simple rules, is able to do no less sophisticated computations than the human brain.) He develops this argument more than I have time to do here: http://www.wolframscience.com/nksonline/page-822-text http://www.wolframscience.com/nksonline/page-822-text (note that this is near the end of the main section of the book and rests on ideas established earlier). Wolfram himself seems pretty bullish on the idea of making computers that think sometime in the future in the section I linked to, in a talk he gave at HAL's birthday party called Hal Isn't Here back in '97, and much more recently in some comments on the movie Her.

algorias 13y ago
This is not an original idea by any means; it's called the Church-Turing thesis, and has been around for 50+ years. As for your question "what are those limits?": In a nutshell, no computer program can ever fully answer questions about the properties of other computer programs. Unlike what GP is implying, that is a hard limit we can never ever get rid of. So if weather is universal, we will never be able to fully understand it!
- nswanberg 13y ago
  Certainly Wolfram didn't invent the notion of a universal system, nor claim to, nor was that intended to be implied above, as bad as my writing might be. Indeed, on page 1125 of NKS he discusses Church's and Turing's contributions. What Wolfram repeatedly points out throughout his book is that the threshold for such universality is much lower than one might suspect given the complications involved in, say, a Turing machine. And because that threshold is so low, there exists the possibility that much of the natural world that is not obviously simple is exhibiting universal computation.

algorias 13y ago

This is not an original idea by any means; it's called the Church-Turing thesis, and has been around for 50+ years. As for your question "what are those limits?": In a nutshell, no computer program can ever fully answer questions about the properties of other computer programs. Unlike what GP is implying, that is a hard limit we can never ever get rid of. So if weather is universal, we will never be able to fully understand it!

nswanberg 13y ago
Certainly Wolfram didn't invent the notion of a universal system, nor claim to, nor was that intended to be implied above, as bad as my writing might be. Indeed, on page 1125 of NKS he discusses Church's and Turing's contributions. What Wolfram repeatedly points out throughout his book is that the threshold for such universality is much lower than one might suspect given the complications involved in, say, a Turing machine. And because that threshold is so low, there exists the possibility that much of the natural world that is not obviously simple is exhibiting universal computation.