Our Mathematical Universe: My Quest for the Ultimate Nature of Reality by Max Tegmark
My rating: 3 of 5 stars

The Mind of God

It starts with Plato, this idea that the universe is a mathematical expression, populated by objects which are (often imperfect) copies of abstract ‘forms’ (the most perfect of which are numbers), which in turn interact according to strict rules of geometry and aesthetic necessity.* More importantly it was Plato who suggested that things are not what they seem. What we are able to perceive are distorted manifestations of eternal truths which are permanently beyond our grasp, leaving open, therefore, the meaning of what we glibly call reality. In a sense he was the first post-modernist in pointing out that reality isn’t even verifiable much less obvious through our observation and experience.**

Hence the general preference of ‘hard’ scientists, like physicists, for Aristotle rather than Plato. Aristotelians like to rely on their senses; they crave observational data, facts. They look down on Platonists, including mathematicians, just as Freudians look down on Jungians, and for the same reason. They simply can’t abide the idea that eternal laws could generate facts - whether those laws are of the Collective Unconscious or the Eternal Forms. For science, facts precede laws both logically and ontologically. Facts are real. Laws are inferred regularities, evolving theories. As such they can only be considered as expedient hypotheses.

So the conflict of fact and law has been fought for two and a half millennia with no victory for either side in sight. Tegmark‘s book is a chronicle of a recent skirmish in which the Platonic standard is held high. Tegmark is a bit coy but he puts forth the historical Platonist party line clearly as: “a crazy-sounding belief of mine that our physical world not only is described by mathematics, but that it is mathematics, making us self-aware parts of a giant mathematical object... our physical world not only is described by mathematics, but that it is mathematics: a mathematical structure, to be precise.”

This particular battle is part of a much larger war, in a sense a cosmic war, called metaphysics. Metaphysics is the discipline of thinking about ‘what’s really there.’ The main difficulty in the metaphysical war from an intellectual point of view is the same as in any other war, namely that the cause one is fighting for justifies its own arguments. Each side has an implicit criterion of validity which, quelle surprise, produces precisely the results to show success by that criterion and failure by the opposing view. All wars in metaphysics are, therefore, ‘just’ - for both sides.

To oversimplify, but not by much, mathematicians really appreciate patterns. They search for them constantly and revel in the thought that they are already there waiting to be discovered. While scientists are also attuned to patterns, however, they know that scientific progress is most often generated not by taking patterns at face value but by concentrating on the apparent exceptions to patterns which are the source of new theoretical patterns. The standards of evidence in the two disciplines are very different.

So for the scientist, the weirdness of quantum physics and black holes is a spur to create a new theory, to confront a resistant universe with observational challenges. For the mathematician the challenge is to coax out the already existing pattern within the structure of his mathematical representations and techniques. One man’s Mede is another man’s Persian, to coin a phrase. Each considers the other to be somewhat Gnostic in their reliance on esoteric knowledge and their distinctive forms of mistrust of the universe - the scientific hesitation about generalization, and the mathematical disdain for the particular.

It makes no sense trying to reconcile the two views because, as an observant philosopher might point out, each already contains a presumption about what reality is and these presumptions are validated by there very use not by their results, which are fundamentally incomparable. This incomparability is not rational; it is aesthetic, that is, pre-rational. The aesthetic is the foundation upon which each constructs his own edifice of Reason.

The bottom line then is that while Our Mathematical Universe is an entertaining as well as informative read, its real value is probably to confirm the views already held by the Platonist choir. It is only likely to irritate the Aristotelians who already think that mathematics has ruined real science by its entirely abstract reasoning. To the latter, Tegmark will not seem merely “crazy-sounding” but crazy tout court.

*It turns out that Plato was more correct than even he could have thought according to the latest science: https://www.sciencefocus.com/news/sci...

**For a rather wonderful tale of the Platonic view of mathematics, see: https://www.goodreads.com/review/show...

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