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Ooooo this topic has been intellectually tingling me for two weeks now - ontologies, knowledge, how we construct the line between abstract (mathematical objects

• chriswarbo 11y ago
  One thing to keep in mind with ideas like the Mathematical Universe Hypothesis is their predictive power. Once a "theory of everything" describes what could have been as well as what is, you end up needing another theory to distinguish between the two [1]. For example, Champernowne's constant contains every number in its decimal expansion, and hence contains a complete description of our universe, all of the true laws of Physics and the outcome of every random quantum effect. However, it's not a very satisfactory "theory of everything", since it makes no predictions. (Note that I could have used pi instead, but its not yet known whether pi is a "normal" number [3]). This is the same idea as the Library of Babel [4]. On the other hand, if you start distinguishing between possible worlds in some way, then you can do real science. For example, the Boltzmann Brain idea describes ordered systems (like our Universe) emerging from disordered systems (like clouds of gas) by pure chance [5]. Such a statistical argument is useful, since we can reason about probability distributions over possible Universes. In this case, small pockets of order are vastly more likely to arise spontaneously than large ones (since we can consider a large pocket to be a contiguous collection of smaller pockets), hence we obtain predictions for all kinds of experiments: namely that we'll probably see a cloud of gas, rather than any ordered structure. Since we tend to see ordered structure, we can prove the hypothesis wrong experimentally. A related idea, which is also relevant for this article, is that the Universe could be generated by a random computer program [7]. If we apply the same reasoning as with Boltzmann Brains, we would expect short programs to be vastly more likely than long programs. Since the length of a program determines how "random" its result is (in the Kolmogorov sense [8]), short programs would produce more ordered structure than long programs, hence this hypothesis make the opposite prediction to the Boltzmann Brain: i.e. that when we observe new places, we will tend to see the same kind of order as we have already observed elsewhere. So far, these predictions seem to hold ;) [1] http://arxiv.org/abs/0912.5434 http://arxiv.org/abs/0912.5434 [2] https://en.wikipedia.org/wiki/Champernowne_constant https://en.wikipedia.org/wiki/Champernowne_constant [3] https://en.wikipedia.org/wiki/Normal_number https://en.wikipedia.org/wiki/Normal_number [4] https://en.wikipedia.org/wiki/The_Library_of_Babel https://en.wikipedia.org/wiki/The_Library_of_Babel [5] https://en.wikipedia.org/wiki/Boltzmann_brain https://en.wikipedia.org/wiki/Boltzmann_brain [6] http://www.preposterousuniverse.com/blog/2008/12/29/richard-feynman-on-boltzmann-brains/ http://www.preposterousuniverse.com/blog/2008/12/29/richard-... [7] http://arxiv.org/abs/quant-ph/0011122 http://arxiv.org/abs/quant-ph/0011122 [8] https://en.wikipedia.org/wiki/Kolmogorov_complexity https://en.wikipedia.org/wiki/Kolmogorov_complexity