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[TODO: Maybe say that "predict" means "predict given enough time and other resources" or something similar.]  Let us assume that if those intelligent beings could study their universe forever, they would try to improve their models in some essential way forever. Since they have an infinite time, they could use strategies like generating possible theories in order, checking if they seem to make sense and testing their predictions against their world, so let us assume that if there is a possible improvement to their current theory, they will find it at some point. Note that in this case the fraction of the world that can be modelled [TODO: Define separately] (if that notion makes sense) is increasing, but is limited, so it converges at some value. Also, the prediction error [TODO: define separately] is decreasing and is limited, so it converges. If the fraction converges at 1 $1$  and the prediction error converges at 0, $0$,  then we are in the first case, because we reach a point when the fraction is so close to 1 $1$  and the error is so close to 0 $0$  that one would find them "good enough". If the fraction or the error converge[S?] converges  to different values then we are in the second case. There is also a third case when there is no reasonable way to define the fraction of the world that can be modelled, except when the fraction is $0$. As an example, imagine a world with an infinite number of earth-like planets that lie on one line and with humans living on the first one. The planets would be close enough and would have enough resources like food and fuel so that humans would have no issues travelling between them. Light would have to come to them in a different way than in our world and something else, not gravitation would keep them in place. The laws of this hypothetical world, as observed by humans, would be both close enough to the laws in our world so that humans can live on any of the planets, but also different in an easily observable way. Let us say that, starting at 10 $10$  meters above ground, gravity would be described with a different function on each planet. On some planets it would follow the inverse of a planet-specific polynomial function of the distance, on others it would follow the inverse of an exponential function, on others it would behave in some way if the distance to the center of the planet in meters is even and in another way if the distance is odd, and so on. [TODO: I had this comment: Will use infinite descr. instead of ... obser.] 
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For the given intelligent beings we would say in the first case that their universe has a finite observable description and in the second and third case that it has an infinite observable description. Of course, a possible universe $U$ could have multiple types of intelligent beings, each type perceiving the universe in a different way. Because of this difference in perception, for some types $U$ may have a finite observable description while for others it may have an infinite observable description.  If we can have infinite descriptions, then the set of optimal systems of axioms would have the same cardinality as the set of real numbers $\reale$. Indeed, for the planets-on-a-line example above, we could select any subset of planets and get an universe with an optimal set of axioms that is distinct from any other subset. The set of all subsets of $\naturale$ has the same cardinality as $\reale$, so the set of optimal systems of axioms would have at least this cardinality. On the other hand, each system of axioms is written using an at most countable set of symbols, so there can't be more than $\reale$ systems of axioms. [TODO: Add a footnote or a chapter at the end with more mathematical justification for this. Maybe add there the half-proof given here.]  These observable descriptions of possible worlds are general enough and different enough that it's hard to say something about them, except that they make sense in a mathematical way. Still, given any property $P$ we could try to see what is the chance that it's true in the set of observable descriptions.  In order to compute the probability of a property $P$ we would need a statistical distribution for the set of observable models. Unfortunately, we descriptions. We  have no good way of choosing among the many possible distributions. Still, distributions, but we can still find interesting things without much choosing. Let us note that  there is a class of distributions which stands out as being reasonable. As reasonable for this purpose: as  long as we don't see any reason to prefere a specific description over all the others, our only choice is to use continuous distributions, that is, distributions for which the probability of any given observablemodel  description is zero. [TODO: use While this is designed such that we can't directly say anything about  a consistent term for specific observable description, we can say things about what has a real chance of being true in a random  observable model/definition] description. First, let us note that a property that is true for only one description has a zero probability (i.e. it is false virtually everywhere). Even more, any property which is true for a countable number of descriptions has a zero probability. This means that any property with a non-zero probability is for sure true for an uncountable number of descriptions. Of course, there may be properties which are true for an uncountable number of descriptions and still have a zero probability.  While this Now, it could happen that for any description there  is designed such a zero-probability property which is true for that description, making it likely  that we can't directly say find  anything about a specific observable model, we can say things about what has a real chance of being true in a random observable model. First, let us note that interesting this way. Fortunately, this is not true. Indeed,  a proposition that property  is true for only one universe model written using a finite alphabet and  has a zero probability (i.e. it is false virtually everywhere). Even more, any property which finite length, so there  is true for at most  a countable number of universes has a zero probability. This means that any property with a non-zero such properties. Let $Y$ be this set. Then $P(Y)$, the  probability is of the set of observable models  for sure true which at least one proposition  in an uncountable number $Y$ is true, is the sum  of universes. Of course, there may be properties which are true for an uncountable number the probabilities  of descriptions and still have a zero probability. all elements in $Y$, so $P(Y) = 0$.  Now one may ask if these properties with zero probability tell us anything interesting. If, say, for any description there is a zero-probability property which is true for that description then it's likely that we can't find anything interesting this way. Fortunately, this is not true. Indeed, a property is over a finite alphabet and has a finite length, so there is at most a countable number of such properties. Let Y be this set. Then the probability of the set of observable models for which at least one proposition in Y is true also has a zero probability. [TODO: Explain in more detail]. We can then say that for virtually all models, only propositions 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), 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.]  Let us now do the following:  \begin{ennumerate}   \item  fix $\epsilon \gt 0$ and  say that we care about measuring things with a precision $\epsilon$, that we are working only with $\epsilon$;  \item restrict ourselves to  universes in which we can measure things with real numbers and that we don't care about numbers;  \item ignore  things which happen rarely, even if we can measure that they happened using the $\epsilon$ precision. [TODO: this is included in the fraction $f$ below]  \end{ennumerate}  This is a bit hand-wavy, but 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 than $\epsilon$ and which do not happen rarely. Let us also fix an arbitrary time length $t>0$, an acceptable error $\delta \ge 0$ for our predictions and let us denote by $f$ with $0 < f \le 1$ a fraction of the world where we can make predictions using the given time $t$ and the acceptable error $\delta$.  Then, if the world is not created, then using any continuous distribution the probability of having a finite description with which we can do this is $0$, which means (with probability 1) that $f=0$. This happens even if we don't care about predicting things precisely (i.e. making $\delta$ larger) or if we restricts ourselves to small time scales (making $t$ smaller). We can only make prediction for a tiny part of the universe, so tiny that it's practically nothing ($f=0$).  [TODO: Start rewriting from here.]  Then, again, our choice is between the world being created and us missing an infinite part of our observable model description which models things that we deem important. If we miss an important infinite part of our observable model description then I argue that we could not make any long term prediction or speak about the relatively distant past because, by definition, the important parts that we are missing would change the outcome of our predictions too much. Therefore saying that our world is (say) 100 years old would have roughly the same chance of being true as saying that is n billion years old [TODO: Think about this, it's tricky. If there are intelligent beings in a world then their intelligence is likely to be useful. Then it means that at least a part of the world must be understandable and predictions can be made with a finite model of the world. But then the model they would build is infinite. This means that they can find a model that allows some sort of predictions for a fraction $f$ of their world and they can increase this fraction by research. They will never have $f=1$, but if we denote the theory they have at a time $t$ by $T_t$ and the fraction of the world that they can predict by $f_t$ then $f_t$ converges to $1$ when $t$ converges to infinity. But then for any fraction of the world $f<1$, no matter how close to $1$, there is a finite time at which there is a theory that can predict a fraction $f$ of the universe. ].