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We can then say that for virtually all models, only properties with non-zero probability are true. This means that, if the probability of our world being created is non-zero, the only rational choices are that either our world is created or only non-zero probability properties are true.  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), alphabet,  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 axiomatize yet  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: Find the right term for "has a finite description" thing. Is it property? Is it proposition? How are these terms used in philosophy?]  \section{Approximations}  For each of the universes containing intelligent beings, let us take a fixed set of measuring units covering everything that those beings would measure. As an example, when measuring distance in our space we could use meters, lights seconds or various other measuring units. The measuring unit is not important as long as we pick something.  Then \definitie{predicting things with a precision $\epsilon$} 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?]  Also, 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: 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 $\epsilon$;  \item restrict Restrict  ourselves to universes in which we can measure things with real numbers; numbers.  \item ignore Fix $\delta \gt 0$ and say that we care about measuring  things which happen rarely, even if are larger than $\delta$ [TODO: replace epsilon with delta where needed]. This means that  we can measure have three sizes $a$, $b$ and $c$ with $a=b$ and $b=c$ but $a\not\=c$. This should be fine as long as we're aware that equality here actually means  thatthey happened using  the $\epsilon$ precision. [TODO: this difference  is included in the fraction $f$ below] smaller than $\delta$.  \item Fix a time length $s$ and ignore things which happen rarely.  \end{itemize}  This is a bit hand-wavy, but we We  could use any reasonable definition of "measuring" and "happen rarely". Then we could say that the important things are the ones which we can measure with a precision greater are larger  than $\epsilon$ $\delta$  and which do not happen rarely. Let us also fix an arbitrary time length $t\ge 0$, an acceptable error $\delta $\epsilon  \ge 0$ and a probability $q\ge 0$ for our predictions [TODO: did I define this?]  and let us denote by $f$ with $0 < f \le 1$ a the  fraction of the world where we can make predictions using the given time length $t$, the acceptable error $\delta$, having a probability $p$ that the prediction is correct. Then, if the world is not created, we have a countable number of finite observable [TODO: is observable the right term?] descriptions out of a $\reale$ total number of descriptions. Then,  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?] 
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[TODO: I should think about what happens when replacing $p$ with a distribution probability.]  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. Similarly, if we take the rules for how the universe works as we perceive them, most likely there is a zero chance that they would apply through the entire universe and a very low chance that they would apply outside of earth / our solar system.  [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.] [TODO: Do I need this paragraph? Where is the best place to put it?  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. 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.