deletions | additions       diff --git a/untitled.tex b/untitled.tex  index e48ba03..8bbfdc0 100644  --- a/untitled.tex  +++ b/untitled.tex 
...
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.  Besides the "finite description for a non-zero fraction of the observable universe" property, we can look at some of the properties of our universe like homogeneity, isotropy or having the same forces acting through the entire universe. It is harder to give a mathematical proof that these are zero-probability ones, but if we think that given a set of universes having any of these properties, sharing the same (mathematical space) and having at least two distinct elements, one can slice and recombine them in infinite ways, it is likely that these properties are also zero-probability ones. An example of such a combined possible universe is the one with infinite planets on a line mentioned above. In other words, the cosmological principle is (very) likely to be a zero-probability property.  [TODO: Start rewriting from here.]  [TODO: Give examples in which our main assumptions about the universe, i.e. homogeneity and isotropy, are broken. Are these finite properties, or zero-probability ones? They are not finite, but considering that we can combine any at most countable set of homogenous and isotropic universes with compatible times into another universe, then it's likely that they are zero-probability ones. We need intelligent beings to be able to live through these changes, but even then it looks like we can combine a lot of universes into one, suggesting that these properties are zero-probability for many reasonable probability distributions. TODO: Give examples on how to combine. Say in a clear way what do I mean by combining a lot of universes into one, making it obvious why the probability should be zero. We experience gravity differently at various times and places - tides, variation from one place to another on Earth, on the Moon, when falling, although the law that describes gravitation does not change. We could imagine an universe where the actual law changes.]  When talking about a mathematical description of the universe as one sees it, it is obvious that the description may depend both on time and place of the observers (assuming that the universe has a concept of place that is close enough to ours). The laws of the universe as observed at a given time and place can be quite different from the laws that one can observe at another time and/or place. If these differences are unpredictable, then an intelligent being will never be able to find a full mathematical description of the universe, even if we assume that it could live through all these changes (as time passes, and/or as it moves through the space). Note that these beings must be able to live through the changes, otherwise the universe does not count for our problem. From the above, we have two options. Either our universe is created and then we might be able to make predictions for a non-trivial part of the universe we can observe (assuming that we have enough details about the state of the universe), or the universe is not created and then, although we can make predictions for a small part of the universe, we can't make predictions outside of it, no matter how much information about the state of the universe we would have; also, this small part would be an insignificant fraction of what we could observe.  We seem to be able to make predictions for mostly everything that we can observe, even if we may not be able to make many predictions for very distant things. We also have no sign that the laws of the universe would be significantly different outside of Earth, so it seems that the limiting factor is that we don't know the state of the universe. Then the second option is probably false and the first one is probably true.