David Deutsch. The Fabric of Reality.

David Deutsch is not Max Tegmark. His book, though full of metaphysical hoey now embellishing any treatise of well-known quantum physicist, does not lose connection with physical facts. But his "multiverse" exercises are poorly compiled.

For instance, he suggests that a quantum computer can perform computations unfeasible to the Turing machine (currently an unproven fact, by the mathematicians) because in alternative universes, other signs can occupy the same physical place on paper and interact with each other. This has nothing to do with paradigmatic quantum mechanics. Paradigmatic quantum mechanics in this instance, simply states that sign is described by the wave function (or density matrix), which contains maximum information we can obtain about a letter sign.

Similarly, he perverts message of mathematical intuitionism. Not being an intuitionist and not understanding enough mathematics to judge one way or the other, I must mention that intuitionism does not claim that natural numbers are finite.

All it claims (contrary to p. 232 of Deutsch's) that there is algorithm allowing to add 1 to any natural number (e.g. 9+1=10) and this algorithm is what we mean by the "natural numbers." Equally, the real number Pi means that we have an algorithm (countable filter by the parlance of the set theory), which allows to compute arbitrary decimal of Pi. Yes, for the Pi+horse such algorithm may not exists and this expression is thus not a real number.