Virgil Șerbănuță edited untitled.tex  over 8 years ago

Commit id: 52ada981c08de5a6d034f929905dc188fc6ef908

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Then, if the world is not created, for any continuous distribution, the probability of having a finite description with which we can make predictions for a time length of $t$, with an error $\delta$, with a probability $p$ and for a fraction of the world $f$, is $0$. To have a non-zero probability either $t = 0$ (which means that we are not making any prediction), $\delta = \infty$ (which means that our predictions have no connection to the reality), $p=0$ (which means that our predictions always fail) or $f=0$. We can discard the first option since then we would have no predictions. We can also discard the second and the third since such a description would not be useful in any way. The only remaining option is that $f=0$; as argued above, a description with $f=0$ can actually make sense. Therefore, with probability $1$, we have $f=0$ and the world has an infinite model.  [TODO: Should I replace $f=0$ with "the minimal fraction absolutely needed", because having a space-time is a property of the entire universe, so f may not be zero? On the other hand, it does not allow any prediction. Should I add a footnote?]  There is a distinction that we should make. When predicting (say) weather we can't make long-term precise predictions, and this happens because weather is chaotic, that is, a small difference in the start state can create large differences over time. This could happen even if the universe is deterministic and we know the laws of the universe perfectly, as long as we don't know the full current state of the universe. However, as argued above, with probability $1$, our hypothetical intelligent beings would not be able to make predictions for a significant part of the universe because they would have no idea about how their universe works, not because they don't know its state precisely enough.  [TODO: I should think about what happens when replacing $p$ with a distribution probability.]