SpaceweaverWed, Dec 26, 2007 To Wildcat: The question whether quantity in terms of speed can be turned into quality in terms of understanding or intelligence, is a hard and very interesting question. In view of Wolfram's work I would not overstate if I will call it the 21st century alchemical question: Can we produce the modern philosopher's stone that will turn computational speed into the gold of intelligence? Or, should we demystify the concept of intelligence and realize it is just speed, nothing but speed... I am not entirely set about this very question. I lean with caution towards the principle of computational equivalence that essentially demystifies intelligence. However admittedly it is very difficult to accept that there is nothing over and above, and intrinsically different from computational speed, that we mean when we think about intelligence.
As to your other remark, I think that the answer is negative, that is, if Wolfram's hypothesis is valid. I would point here the weakness of the principle: Wolfram presents the principle of computational equivalence as a scientific hypothesis and not as a mathematical theory. As such, there is no possible mathematical proof to it. But also as a scientific theory it is problematic because it offers no clear method of how it can be refuted. So, fact is that it cannot rise much above the status of a very strong intuition. Yet, assuming it is correct, the physical limits of our universe, will not allow to compute the universe fast enough because (this is a huge simplification of course) the universe is the fastest computation of itself. In other words, the principle of computational equivalence states that if we imagine the universe as a series of numbers, this series has no shortcut formula, so we cannot predict its unfoldment but only to simulate it, and any simulation of it is slower than its natural unfoldment.
To Wildcat: The question whether quantity in terms of speed can be turned into quality in terms of understanding or intelligence, is a hard and very interesting question. In view of Wolfram's work I would not overstate if I will call it the 21st century alchemical question: Can we produce the modern philosopher's stone that will turn computational speed into the gold of intelligence? Or, should we demystify the concept of intelligence and realize it is just speed, nothing but speed... I am not entirely set about this very question. I lean with caution towards the principle of computational equivalence that essentially demystifies intelligence. However admittedly it is very difficult to accept that there is nothing over and above, and intrinsically different from computational speed, that we mean when we think about intelligence.
As to your other remark, I think that the answer is negative, that is, if Wolfram's hypothesis is valid. I would point here the weakness of the principle: Wolfram presents the principle of computational equivalence as a scientific hypothesis and not as a mathematical theory. As such, there is no possible mathematical proof to it. But also as a scientific theory it is problematic because it offers no clear method of how it can be refuted. So, fact is that it cannot rise much above the status of a very strong intuition. Yet, assuming it is correct, the physical limits of our universe, will not allow to compute the universe fast enough because (this is a huge simplification of course) the universe is the fastest computation of itself. In other words, the principle of computational equivalence states that if we imagine the universe as a series of numbers, this series has no shortcut formula, so we cannot predict its unfoldment but only to simulate it, and any simulation of it is slower than its natural unfoldment.