this is for holding javascript data
Virgil Șerbănuță edited untitled.tex
over 8 years ago
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Now, let us return to the issue of observable models being finite or infinite. With an finite alphabet (and even with an infinite but countable one), only a countable set of models have a finite observable description. Then the "has a finite description" proposition is a zero-probability one, so either our universe is created, or at any point in time there will be an infinite number of things that we didn't manage to model about our universe but we think that they are important. [TODO: It's probably better to say that there will be an important part of our universe that we can observe but can't model. Also, since we chosed the precision and prediction error in an arbitrary way, this part that can't be modelled is visible at any "zoom" level.]
[TODO: Say that we are using any reasonable definition for measuring things with a given precision at the beginning.]
Let us now do the following:
\begin{itemize}
\item fix $\epsilon \gt 0$ and say that we care about measuring things with a precision $\epsilon$;