Marcus du Sautoy 2015. What We Cannot Know. Explorations at the edge of knowledge. London: 4th Estate, ebook.

Marcus du Sautoy is a mathematician and Charles Simonyi Professor of the Public Understanding of Science at Oxford, a chair previously held by Richard Dawkins.

Terrific cover. Very nearly enough to make me buy the printed edition instead.

This book covers much of the same material found in other recent mathematics and physics books that aim to introduce general readers to the Big Questions. However the flavour is interesting, emphasising what is not known (and, according to the author, cannot be known). Writing about what is known is easier and much more common.

This book covers much of the same material found in other recent mathematics and physics books that aim to introduce general readers to the Big Questions. However the flavour is interesting, emphasising what is not known (and, according to the author, cannot be known). Writing about what is known is easier and much more common. This material is arranged in 7 sections or “Edges”, being Edges in the sense that these are the edges of what can be known in 7 different fields.

Edge 1 is about statistics, Chaos theory and chance events.

Edge 2 is about fundamental particles and whether matter is infinitely divisible.

Edge 3 is about quantum theory, Waves vs particles, Schrödinger and quantum entanglement. And perhaps what is reality. Thus Einstein

I don’t demand that theory corresponds to reality … All I’m concerned with is that the theory should predict the results of measurement

Edge 4 is about the universe and is it infinite? And about symmetry. This was the part of the book that was most compelling: an explanation of how the mathematics of symmetry provided an understanding of how the quantity ‘strangeness’ and the pairing and classification of fundamental particles. How thrilling to discover that mathematics reflects reality at this very small scale. Surely the universe really is fundamentally mathematical (sensu Max Tegmark)?

Edge 5 is about time. Is it infinite?

Edge 6 Consciousness. Will consciousness and our brains ever be understood or modelled or recreated as Artifial Intelligence?

Edge 7 is about mathematical limits, specifically Gödel’s theorem (there are true statements that we can never prove to be true so long as we stay within the system). And also Cantor on infinite sets. I can’t remember anyone else but du Sautoy converting this theorem to the statement that seems all too obvious: is it ever possible to understand a system of which we are part? Of course this also applies to investigating consciousness. If the universe is really a mathematical object then (it seems to me) this is the crucial edge of knowledge and all the others are special case derivations.

I don’t think there is much here that is original and a fair bit is covered better by other authors (Edge 6 on consciousness, for example) but I always get something reinforced or explained successfully for the first time by hearing a new author tackle a subject. The devices used by the author to introduce his material (dice, cello playing, optical illusions) didn’t do much for me. Nevertheless a rewarding read and it would be a mistake to skip through this because one thought one knew this stuff already.

There is a great review publishied in Physics Education (2017) 52: 7-9 by Peter Campbell.