Figure 7.6 illustrates that the debate over how classical mechanics emerges from quantum mechanics is just a small piece of a larger puzzle. Indeed, the debate over the interpretation of quantum mechanics - and the broader issue of parallel universes - is in a sense the tip of an iceberg. For there is a still deeper question that arguably goes as far back as Plato and Aristotle. This concerns the status of mathematics and how it relates to physical reality.

Aristotelian paradigm The internal perspective is physically real, while the external perspective and all its mathematical language is merely a useful approximation.

Platonic paradigm The external perspective (the mathematical structure) is physically real, while the internal perspective and all the human language we use to describe it is merely a useful approximation for describing our subjective perceptions.

What is more basic - the internal or external perspective, human language or mathematical language? Your answer will determine how you feel about parallel universes. Our feeling that the Level III multiverse is 'weird' merely reflects the extreme difference between the internal and external perspectives. We may break the symmetry by calling the latter weird, because we were all indoctrinated with the Aristotelian paradigm as children, long before we even heard of mathematics. If this is true, there can never be a 'Theory of Everything' (TOE), since one is ultimately just explaining certain verbal statements by other verbal statements. This is known as the infinite regress problem [29].

Fig. 7.6. Theories can be crudely organized into a family tree where each might, at least in principle, be derivable from more fundamental ones above it. For example, classical mechanics can be obtained from special relativity in the approximation that the speed of light c is infinite. Most of the arrows are less well understood. All these theories have two components: mathematical equations and words that explain how they are connected to what we observe. At each level in the hierarchy of theories, new words (e.g., protons, atoms, cells, organisms, cultures) are introduced because they are convenient, capturing the essence of what is going on without recourse to the more fundamental theory above it. It is important to remember, however, that it is humans who introduce these concepts and the words for them; in principle, everything could have been derived from the fundamental theory at the top of the tree, although such an extreme reductionist approach would be useless in practice. Crudely speaking, the ratio of equations to words decreases as we move down the tree, dropping to near zero for highly applied fields, such as medicine and sociology. In contrast, theories near the top are highly mathematical, and physicists are still struggling to understand the concepts, if any, in terms which we can understand. The Holy Grail of physics is to find a 'Theory of Everything' from which all else can be derived. If such a theory exists at all, it should replace the big question mark at the top of the theory tree. However, something is missing here, since we lack a consistent theory unifying gravity with quantum mechanics.

On the other hand, if you prefer the Platonic paradigm, you should find multiverses natural. In this case, all of physics is ultimately a mathematics problem, since an infinitely intelligent mathematician - given the fundamental equations of the cosmos - could in principle compute the internal perspective, i.e. what self-aware observers the universe would contain, what they would perceive, and what language they would invent to describe their perceptions to one another. In other words, there is a TOE at the top of the tree in Fig. 7.6, whose axioms are purely mathematical.

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