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An attempt to reason about why our world is the way it is.  A Christian believes that the world is created. However, this belief is not shared by everyone, so it's worth thinking about what this means. If the world is created, then it's likely to be the way it is because its Creator\footnote{Not everybody that believes that the world is created thinks that God created it. Still, I hope that they would agree that naming the creator of this world as "the Creator" is reasonable.} wanted it to have certain properties so in order to understand why our world works the way it does, one would need to understand the intent of its Creator. While it is worth thinking about it, I will not try to pursue this path here.  Let us consider the other case. If the world was not created, then there may be other worlds\footnote{We don't have any proof for the existence of other worlds, but one could expect them to exist for the same reason that ours exists. If ours has no reason at all for existing, which is likely if it is not created, then it's likely that other worlds would also not need any reason for existing and would simply be. However, for this paper it does not matter if there are other worlds or not.}. Even if there aren't other worlds, ours could have been different. We will denote by \textbf{possible worlds} these other worlds that either are or could have been.  \section{Possible worlds}  How would a possible world look like? It could have exactly the same fundamental laws as ours, but with the matter organized differently. It could have similar laws, but with different universal constants. It could have different fundamental particles (or whatever the basic building blocks of our universe are, assuming that there are any). Or it could be completely different, i.e. different in all possible ways.  It could be that our logic and reasoning are universal instruments, but it could also be that some of these possible worlds could be beyond what our reasoning can grasp and others could have properties for which our logic is flawed. Aknowledging that, let us see if we can say anything about the possible worlds that we could understand and could model in some way. In the following, the \textbf{possible worlds} term will denote only the possible worlds which we could model (at least theoretically).  This notion of "model" is not precise enough. Let us restrict the "possible worlds" term even more to the possible worlds that we could model mathematically, even if that may leave out some worlds. We will also do the reverse and say that any non-contradictory set of axioms models some possible worlds.  If there isn't any designer for our world then we have no way of prefering one over the other, except that there is one of them in which we live. It seems that reasoning about all the possible worlds could be very hard, but maybe we could do something easier, maybe we could reason about the mathematical axioms that model the worlds.  Let us consider the set of axioms that define a monoid. All groups are models for this set of axioms, but intuitively a group is something more interesting than a monoid and we should include extra axioms for defining it. On the other hand, we could include all possible axioms for each model (e.g. for each monoid), uniquely identifying it, but again, intuitively this is not a useful way of modeling. For a given world, a much better set of axioms would be one that would allow us to make all possible predictions for that world. We will call this the "too-specific/too-general" problem.  The term prediction is not a clear one. To make it more clear, let us restrict again the "possible worlds" term to denote all possible worlds that/which? have a concept of time (which is something reasonably well ordered), that/which have a concept of the state of the world at a given time, for which describing the state of the world at all possible times is equivalent to describing the world, and for which given the state of the world up to a given time $t$ one could find the state of the world at a future time $s > t$. Making predictions would mean finding the state at a future time.  This ignores some important issues like the fact that it's reasonable to have a concept of time without having a well defined concept of "the state of the world at a given time". However, one could rephrase the definition above in a suitable fashion for many concepts of time, e.g. for worlds where "point" is a concept and we can know which pairs (point, time) are before a given (point, time) pair, prediction could mean predicting the state of the world at a given point from the state of the world at previous points in time.  If we define "prediction" in some useful way, as suggested above, and restrict the "possible worlds" term to the ones where we can make predictions, then it makes sense to use only systems of axioms that allow predictions. This solves the "too-general" part of the "too-specific/too-general" problem since such a system would describe its possible worlds in a way that does not leave out important things. Still, there is nothing that prevents such a system from going into too much details.   Given a specific formalism for specifying axioms, for each possible world, we could only consider the smallest set of axioms that allow predictions, smallest being defined as "having the smallest length when written on paper". This is not a well defined notion for a few reasons. First, there could be multiple systems with "the smallest length" (one obvious case is given by reordering the axioms). In such a case, we could define an order for the symbols that we are using in our formalism and we could pick the system with the smallest length and that is the smallest in the lexicographic order. Second, there could be systems of axioms of infinite length. For this, we will only consider systems which, when "written on an infinite paper", use a countable set of symbol places on that paper and we will say that all the infinite length systems have the same length, but all of them have a length greater than any finite length. We will ignore systems which need an uncountable set of symbol places.  Now let us see if we actually need infinite length systems. We can have infinite systems of axioms, and there is no good reason to reject such systems and to ignore their possible worlds, so we will take them into account. It is less clear that we can't replace these infinite systems with finite ones. Indeed, let us use any binary encoding allowing us to represent these systems as binary strings, i.e. as binary functions over the set of natural numbers, i.e. $f:\naturale\longrightarrow \multime{0, 1}$. Then it seems likely that we can define a finite system of axioms that will allow prediction for a universe that also contains an encoding of an axiom system. While, strictly speaking, this would be a different system than the one we had at the beginning, it is also similar enough to it so one may be tempted to use only finite systems of axioms.  On the other hand, using only finite systems of axioms in this way seems to be some sort of cheating. In order to get a more "honest" system of axioms, we could work with very specific systems of axioms, e.g. we could only talk about worlds which have $\reale^4$ as their space and time, whose objects are things similar to the wave functions used by quantum mechanics and so on.  We could also completely avoid this problem by talking only about worlds which could contain intelligent beings and talking about how the intelligent beings would model their world. This approach may also be a more interesting one, since we may never have a complete and correct model for our world, but we can build better and better models.  As a parathesis, note that until now we restricted the "possible world" concept several times. The argument below works with any concept of "possible world" that is "large" enough, has a few basic properties (e.g. one can make predictions and it can contain intelligent beings) and at the same time it is plausible that our world is such a "possible world".  First of all, let us assume that those intelligent beings are continuously trying to find better models for their world and, at any given time, they are trying to use the most simple model which is reasonable at that time (the model could, of course, change as they find out more things about their world) and that they are reasonably efficient at this, i.e. they don't need to find the most simple model, but they aren't very far from it, for a reasonable definition of "very far" (e.g. for each length $n$ of the most simple model there is a maximum length $Max_n$ such that the actual model is not longer than $Max_n$).  Then we would have two possible cases.   First, those intelligent beings could, at some point in time, find a model which is the best possible model that they could find for their world. They could stop because they found the perfect model for their world or because the model is so precise that it seems to predict everything that happens in their world and they can't find anything which is not part of their model. We could also relax these conditions by not requiring them to find the best model, but to find one that is good enough for all practical purposes. As an example, for an universe based on real numbers, knowing the axioms precisely with the exception of some constants and measuring all constants with a billion digits precision might (or might not) be good enough. Only caring about things which occur frequently enough could also be good enough.  Second, if those intelligent beings could study their universe forever, they would improve their models in some essential way forever.  For the given intelligent beigns we would say in the first case that their universe has a finite observable model and in the second case it has an infinite observable model. Of course, a possible universe could have multiple types of intelligent beings and some would find a finite observable model and others would find an infinite observable model.  If we can have infinite descriptions, then it is likely that the set of descriptions would have the same cardinality as the set of real numbers $\reale$. Indeed, one can find an infinite set of disjoint sets of axioms that are different enough from which one can select any infinite subset and join the subset to form another set of axioms which is predictive, has at least a model and can't be defined in a finite way [TODO: example or a better explanation. And a demonstration if needed].  These observable models 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 mathematical proposition $P$ we could try to see what is the chance that it's true in a random observable model. If we can agree on what "true" means, we could ask the same thing about any natural language proposition.  In order to compute the probability of a proposition $P$ we would need a statistical distribution for the set of observable models. Unfortunately, we have no good way of chosing among the many possible distributions. Still, there is a class of distributions which stands out as being reasonable. 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 observable model description is zero.  [TODO: use a consistent term for observable model/definition]  While this is designed such that we can't directly say 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 a proposition that is true for only one universe model has a zero probability (i.e. it is false virtually everywhere). Even more, any property which is true for a countable number of universes has a zero probability. This means that any property with a non-zero probability is for sure true in an uncountable number of universes. Of course, there may be properties which are true for an uncountable number of descriptions and still have a zero probability.  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 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.  Let us now fix $\epsilon \gt 0$ say that we care about measuring things with a precision $\epsilon$, that we are working only with universes in which we can measure things with real numbers and that we don't care about things which happen rarely, even if we can measure that they happened using the $\epsilon$ precision. 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.  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 deeply about this, it's tricky.]  When predicting weather we also can't make long-term precise predictions, and this happens because weather is chaotic??, that is, a small difference in the start state can create large differences over time. However, in an infinite observable model we wouldn't be able to make long term predictions because we don't actually know how the world works, not because we don't know its state precisely enough.  \section{Introduction}  A Christian believes that God created the Universe, but there are many people that think that there is no Creator, implying that the Universe is not created. I think it's worth thinking about what that means and I will try to make a prediction from the fact that there is no Creator. 
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A \textbf{universe description} $D$ is a set of noncontradictory mathematical axioms that describe the "laws of the universe". I will call each of the mathematical models in which these axioms are true a possible universe for the description $D$ and $D$ is a description for each of this possible universes. Note that a universe will have many possible descriptions and a description may describe multiple universes.  DE PUS MAI INCOLO  Given a universe that has a concept of time, the laws of the universe allow that, given the state of the universe at a time $t$, one can predict the state at any later time.  One could argue that a mathematical definition of the laws of a possible universe is too limiting and that there may be possible universes without this kind of description. That could be, and we could replace "mathematical axioms" with "natural language sentences" without changing much of what follows, except for making the argument somehow more complicated. Still, even "natural language sentences" could be too limiting, but the argument below only needs that our universe has a mathematical description of its laws.  A description $D$ \textbf{implies} a statement $S$ if $S$ is $S$ is a property of all universes $U$ for which $D$ is a description. In this case I will also say that $S$ is \textbf{true for} $D$. 
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\begin{definitie}  Two entity types are connected if their objects may interact.  Două tipuri de entități sunt \textbf{conectate} dacă interacționează între ele.  % Este rezonabil să cer ca oricare două tipuri de entități să fie conectate (direct sau indirect), vezi mai jos o afirmație care spune că probabilitatea de a nu fi conectate este zero.  \end{definitie}  \begin{definitie}  Două descrieri sunt \textbf{echivalente} dacă există Two descriptions are \textbf{equivalent} if there is an isomophism between their universe sets [TODO: De spus ce e  un izomorfism bijectiv între universurile uneia și universurile celeilalte. universe set pentru o descriere, de spus ce e un izomorfism].  \end{definitie}  \begin{afirmatie}  Dacă If  $M$ este mulțimea descrierilor de universuri, atunci is the set of universe descriptions then  $M$ poate fi pusă în bijecție cu mulțimea numerelor reale has the same cardinality as  $\reale$. \end{afirmatie}  \begin{argument}  Fie Let  $A$ mulțimea posibilelor propoziții despre un univers. be the set of all sentences.  $A$ este numărabilă. is countable.  $M$ este inclusă în mulțimea submulțimilor lui $A$, deci $M$ are cel mult același is included in the power set of $A$ so the  cardinal cu of $M$ is at most  $\reale$. Deoarece avem o mulțime numărabilă de propoziții There is a countable set of sentences  $P = \{a=a, b=b, \dots\}$, pe care le putem adăuga și scoate din orice mulțime din \dots\}$ which can be added and removed to any description in  $M$ fără a schimba descrierea, atunci cardinalul lui without actually changing it, so the cardinal of  $M$ este mai mare decât cel al mulțimii submulțimilor lui is at least the cardinal of the power set of  $P$, care are același which has the same  cardinal cu as  $\reale$. \end{argument}  Această afirmație nu ne spune însă foarte mult, pentru că, așa cum se vede din demonstrație, avem un număr infinit de descrieri echivalente pentru fiecare univers. Următoarea propoziție spune însă ceva mai consistent: However, this ??? does not tell us much because, as it's obvious from its proof, any set of universes that has a description has an uncountably infinite number of equivalent descriptions. However, the next ??? tells us something more interesting.  \begin{afirmatie}  Dacă Let  $L$ este mulțimea claselor de echivalență a descrierilor de universuri, atunci be the set of equivalence classes of universe descriptions. Then  $L$ este în bijecție cu has the same cardinal as  $\reale$. \end{afirmatie}  \begin{argument}  În acest argument, dacă $E_1, E_2, E_3, E_4$ sunt niște tipuri de entități, nu neapărat distincte, iar $I_{1,2}, I_{3,4}$ sunt regulile de interacțiune între $E_1, E_2$ respectiv $E_3, E_4$, atunci spunem că $I_{1,2}$ și $I_{3,4}$ sunt \textbf{neechivalente} dacă descrierea formată din $E_1, E_2, I_{1,2}$ nu este echivalentă cu descrierea formată din $E_3, E_4, I_{3,4}$. Putem cere ceva mai puternic decât neechivalența, spre exemplu $I_{1,2}$ și $I_{3,4}$ ar putea fi bazate pe polinoame de grade diferite.