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      "text": "2 Depending on whether the universe is open or closed. These are the same alternatives that T.S. Elliot presented - either a bang or a whimper. 3 This may seem self serving, but its a good time to point out that I used to be a cosmologist myself!",
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      "text": "there are many simple problems which would require more computing than a 1993, or even a 2033, level supercomputer could do between now and the recollapse or heat death of our the universe2. Computer scientists classify problems of this sort as \"NP hard\"",
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      "text": "This is a fundamental lesson for us. It is extraordinarily difficult for people to really grasp the power of exponential growth. No experience in our every day life prepares us for it.",
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      "text": "The key issue behind this point is that computing is on a very fast exponential growth curve. Anything which isn't exponential in growth, or which is exponential but with a slower growth rate, will quickly and inexorably be overwhelmed.",
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      "text": "Here is the simplest example of why NP hard problems are hard. Consider trying to enumerate all possible combinations or orderings of N unique objects (characters or whatever). The number of combinations is N factorial, usually written as N!.",
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      "text": "Many open problems in computing - including some classified as \"artificial intelligence\" fall into a grey area - they are likely to be NP hard in principle, but there may efficient approximations which allow us to get arbitrarily good results.",
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      "text": "Road Kill on the Information Highway",
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