I picked this up in Fulda Staat library, and am very pleasantly surprised by the fluent exposition.
I first came across finite automata over a decade ago when I read the New Turing Omnibus, back then recommended reading for the Cambridge computer science applicants. I got so interested at one point I considered switching subjects right away.
But the presentation in the New Turing Omnibus is a bit out dated, and also left quite a lot of gaps to be worked out by the students. The difficulty soon outweighed the excitement and finite automata and Turing machines lay forgotten.
In Turing’s Vision, the mix of historical background and simple illustrative puzzles is much more engaging.
Usually when reading popular maths, I am not too interested in any puzzles that take more than 10-15 minutes to solve. At the first reading, I just want to get the broad idea of what is going on: I am not invested enough to wrestle with the issues yet.
The author presents the puzzles particularly well in this text. Problems are very clearly explained and the walk-through are a joy to read. Even though some thinking is still required, the reader quickly gets what it is all about.
Even better, some difficulty results are summarised in an enticing way: I still don’t get why no finite automaton can determine whether a string contains an equal number of 0s and 1s, but I’ll be sure to be turning over in my mind!
I am also impressed by the author’s demonstration on how different ways of looking at the same result can be really useful. Apparently, even after reading Church’s paper on Lambda calculus. Gödel was not sure that it captures the essence of the idea of an algorithm (p.63). But he was after reading Turing’s paper on Turing machines, even though the two are shown to be equivalent (by Turing).
It is therefore no surprise that Turing is given so much credit for the Turing-Church thesis, even though his paper was published later.