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  clickbait: 'Sample spaces are often large, so it is hard to do probabilistic computations using a raw distribution over the sample space.',
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  text: '[summary: Sample spaces enumerate everything that could possibly happen, so that we can reason consistently under uncertainty. But this enumeration usually enumerates too many things, making it difficult to do computations using the raw sample space.]\n\nWhen we are reasoning about an uncertain world using [1bv probability theory], we have a [3t4 sample space] of possible ways the world could be, and we assign\nprobabilities to outcomes in the sample space with a [3tb probability distribution]. Unfortunately, often the sample space (which is supposed to contain every possible way the world might turn out) is very large and possibly infinite.\n\nFor example, if we are thinking about a box with some particles in it, our sample space is the enormous set of all possible arrangements of the particles. \nTo reason usefully about the box, we'd have to do computations using a gigantic table specifying a separate number for every single distinct arrangement of particles. \nTwo arrangements that are pretty much the same, as far as we care, take up just as much of our computational resources as two importantly different arrangements.\nSo, even though we could in principle reason consistently under uncertainty just using a probability distribution over a sample space, we cannot do so easily,\nbecause we are trying to keep track of too much. \n\n[todo: examples]',
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