**8. Is the Universe Lawless?**

In this section we add another argument—to many others [12,34–40]—in favour of the hypothesis in the title.

There are uncountable infinite binary sequences, each of which could be a (the) "true" simplest model of our universe. Among these candidates, we have the set of Martin-Löf random sequences, which will fit with the hypothesis: this set is very large, because as we have already mentioned, the probability that an infinite binary sequence is not Martin-Löf random is (constructively) zero. However, the complement of this set—which has then probability zero—is not only infinite, but also uncountable and therefore cannot be lightly discarded.

The so-called physical/universal/natural "laws" deal with the infinity, on one hand; but can be verified only on finitely many cases. What about the situation when a "true model" is not a Martin-Löf random sequence, possibly a highly improbable computable one?

In order to be able to attempt to confirm the "laws" in this model we have to surf the initial bits of the infinite sequence. How many bits can be surfed? A possible bound from below is the number of atoms in the universe which is believed to be less than Numberatoms = 1082. What is then the probability that an infinite sequence, thought as a model of our universe, starts with an *α*-random string of length Numberatoms? In this set there are infinitely many Martin-Löf random sequences and a sequence is Martin-Löf random with probability one, see Section 6, but also infinitely many computable sequences. The analysis in Section 4 shows that this probability will be larger than

$$1 - 2^{-\alpha \cdot 10^{82}} + 2^{-10^{82}}$$

because this is the probability that an infinite binary sequence starts with an *α*-random string of length Numberatoms. With this probability—which is infinitesimally close to one—*every choice for our model of our universe* starts with an *α*-random string; consequently, all patterns and correlations which can be verified in this model are spurious!

Let us hasten to note that spurious does not mean wrong, not genuine, useless. On the contrary, correlations can be, and many times are, interesting, useful and give us insight about the working of the universe; they are, however, local and not universal.
