# ‘What We Cannot Know’ by Marcus du Sautoy

### ‘Fine Romp Through Science’

**Score: 4/5**

Marcus du Sautoy was over in Belfast for our Science Festival and SWMBO and I got to see him give his talk based on this book. It was thoroughly engaging so of course she bought me the book!

The book covers far, far more than he could mention in his talk - he only really talked about 3 of the ‘edges’ out of the 7 in the book. What he did cover was interesting though.

On the other hand, I did say to SWMBO we could gauge how deep a talk it would be by noting when he mentioned Gödel’s Incompleteness Theorem. Gödel’s proof that there are true things in mathematics (or really any formal axiomatic system) that you cannot prove are true is an obvious candidate to cover when talking about the limits of knowledge.

Or so I thought, anyway.

Sadly, Gödel didn’t crop up until the questions at the end. Ah well.

It does get talked about in the book though. The book covers so many topics that Gödel’s incompleteness theorems aren’t covered in any great depth, but they are there and covered well. (And as a side note, this reminds me how remarkable Gödel, Escher, Bach was when I read it decades ago. I have an urge to read it again, but not at £19 for the paperback! I may hunt down a secondhand copy...)

I’m a programmer though (no kidding!) so one thing I’m really disappointed that didn’t get a mention in the book is the Halting Problem.

What is the Halting Problem I hear you cry?

The problem is to determine, given a program and an input to the program, whether the program will eventually halt when run with that input. In this abstract framework, there are no resource limitations on the amount of memory or time required for the program's execution; it can take arbitrarily long, and use arbitrarily as much storage space, before halting. The question is simply whether the given program will ever halt on a particular input.

And in 1936, Turing proved that sometimes you just couldn’t know:

Turing proved no algorithm exists that always correctly decides whether, for a given arbitrary program and input, the program halts when run with that input. The essence of Turing's proof is that any such algorithm can be made to contradict itself and therefore cannot be correct.

This well-known thing-you-cannot-know seemed like such an obvious candidate for a book on Things We Cannot Know that I’m genuinely surprised it doesn't make the cut. Turing gets 4 mentions in the index, but they’re all about the Turing Test rather than this.

That quibble aside, the tour of current science in the book does cover topics like chaos, quantum mechanics, relativity, time, consciousness. And my copy of the book is signed by the man himself. No, you can’t have it.

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