## 4 Complete ToEs (CToEs)
In Sections 4 and 8 I will show that simpler theories more likely lead to correct predictions, and therefore [PERSON]'s razor is suitable for finding ToEs. **Complexity of a ToE. ** In order to apply [PERSON]'s razor in a non-heuristic way, we need to quantify simplicity or complexity. Roughly, the complexity of a theory can be defined as the number of symbols one needs to write the theory down. More precisely, write down a program for the state evolution together with the initial conditions, and define the complexity of the theory as the size in bits of the file that contains the program. This quantification is known as algorithmic information or Kolmogorov complexity [6] and is consistent with our intuition, since an elegant theory will have a shorter program than an inelegant one, and extra parameters need extra space to code, resulting in longer programs [4,5]. From now on I identify theories with programs and write \(\mathrm{Length}(q)\) for the length=complexity of program=theory \(q\). **Standard model versus string theory. ** To keep the discussion simple, let us pretend that standard model (SM) + gravity (G) and string theory (S) both qualify as ToEs. SM+Gravity is a mixture of a few relatively elegant theories, but contains about 20 parameters that need to be specified. String theory is truly elegant, but ensuring that it reduces to the standard model needs sophisticated extra assumptions (e.g., the right compactification). SM+G can be written down in one line, plus we have to give 20+ constants, so lets say one page. The meaning (the axioms) of all symbols and operators require another page. Then we need the basics, natural, real, complex numbers, sets (ZFC), _etc._, which is another page. That makes 3 pages for a complete description in first-order logic. There are a lot of subtleties though: (a) The axioms are likely mathematically inconsistent, (b) it's not immediately clear how the axioms lead to a program simulating our universe, (c) the theory does not predict the outcome of random events, and (d) some other problems. So to transform the description into a C program simulating our universe, needs a couple of pages more, but I would estimate around 10 pages overall suffices, which is about 20,000 symbols=bytes. Of course this program will be (i) a very inefficient simulation and (ii) a very naive coding of SM+G. I conjecture that the _shortest_ program for SM+G on a universal Turing machine is much shorter, maybe even only one tenth of this. The numbers are only a quick rule-of-thumb guess. If we start from string theory (S), we need about the same length. S is _much_ more elegant, but we need to code the compactification to describe our universe, which effectively amounts to the same. Note that everything else in the world (all other physics, chemistry, _etc._) is emergent. It would require a major effort to quantify which theory is the simpler one in the sense defined above, but I think it would be worth the effort. It is a quantitative objective way to decide between theories that are (so far) predictively indistinguishable. **CToE selection principle. ** It is trivial to write down a program for an All-a-Carte multiverse (A). It is also not too hard to write a program for the universal multiverse (U), see Section 6. Lengthwise (A) easily wins over (U), and (U) easily wins over (P) and (S), but as discussed (A) and (U) have serious defects. On the other hand, these theories can only be used for predictions after extra specifications: Roughly, for (A) this amounts to tabling the whole universe, (U) requires defining a ToE in the conventional sense,(P) needs 20 or so parameters and (S) a compactification scheme. Hence localization-wise (P) and (S) easily win over (U), and (U) easily wins over (A). Given this trade-off, it now nearly suggests itself that we should include the description length of the observer location in our ToE evaluation measure.