Virgil Șerbănuță edited untitled.tex  about 8 years ago

Commit id: f70ee0a82095f0bda7e73db558f0c0994dd94bbb

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Not being able to model the entire universe precisely is not that bad if we can at least have an approximation of most of the universe. Let us see how much we can approximate.  Let us say that \definitie{predicting things with a relative error $\epsilon$} means that when predicting that something is of size $l$, then the actual size is in the range $(l(1-\epsilon), l(1+\epsilon))$. One could give a similar definition by using a statistical distribution that depends on the size $l$ and the precision relative error  $\epsilon$ instead of just using an interval. Given a time length $s$, we say that something \definitie{happens rarely} if in any given unit volume of space the time between two occurrences of that something is at least $s$. One could give similar definitions based on the probability of an intelligent being observing that something. 

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.  [TODO: Fix ``quotes".]  [TODO: Make sure I'm using quotes correctly and consistently.]  [TODO: Fix spaces between math mode and punctuation.]  [TODO: Fix the usage of I and we.] 

[TODO: Think a bit more about the fact that even statistically we can't model more than $0$].  [TODO: How can we observe the universe without having uniforme laws?]  [TODO: define "mathematical prediction" or something like that and use it here, since I have two meanings of prediction - I think this is done/not needed, I added a footnote in the only place where I use the normal meaning of prediction. I have to check. Maybe I should be more explicit about this.]  [TODO: I should use precision and accuracy as defined in Things to check at  the standard way e.g. here: https://en.wikipedia.org/wiki/Accuracy_and_precision] end: my macro is used for \ghilimele{quotes}.]