Virgil Șerbănuță edited untitled.tex  over 8 years ago

Commit id: 2f4419e44ef2cc630d02cffa6d7ce2380eeee9b0

deletions | additions      

       

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 $\epsilon$ instead of just using an interval.[TODO: Do I need this definition?] [TODO: I should use precision and accuracy as defined in the standard way e.g. here: https://en.wikipedia.org/wiki/Accuracy_and_precision]  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. 

[TODO: Use can't, won't, isn't and can not, will not, is not consistently.]  [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 the standard way e.g. here: https://en.wikipedia.org/wiki/Accuracy_and_precision]