Godel, Escher, Bach: An Eternal Golden Braid" by Douglas Hofstadter

I first read started reading this book shortly after its publication in the early 1980s. I gave up. I started it again in the 2000s. I gave up. In 2016 I started and finished it.

Was it worth it?

In 20 chapters Hofstadter attempts to teach the elements of Typographical Theory and therefore to (a) explain Godel's Incompleteness Theorem (b) lay down some rules for developing Artificial Intelligence. Along the way he tries to explore the concept of Strange Loops, recursive propositions that are self referential and paradoxical, such as "This statement is false". In order to help the general reader get anywhere near these difficult ideas he uses the art of Escher, which is full of self-reference and paradox, and the structure of a musical fugue such as those developed by Bach. He also intersperses every heavyweight chapter with a diversion, such as a dialogue between Achilles and a Tortoise (also involving a Crab, an Anteater and the Author) or the Jabberwocky in three languages.

Well I really enjoyed the diversions, which gave me some basic understanding of Hofstadter's arguments, and I enjoyed a lot of the more heavyweight stuff, although I skipped quite a lot too and there were bits that I frankly didn't understand.

A lot of the music stuff was really interesting and I learned about fugues, hemiolas, canons, organ points, strettos and fermatas. 

He made a lot of interesting points such as that "Intelligence loves patterns and baulks at randomness. For most people, the randomness in Cage's music requires much explanation ... whereas with much of Bach, words are superfluous.In that sense Bach's music is more self-contained than Cage's music." (p 175)

A brilliant attempt to make a really hard subject accessible which nearly worked for me and no doubt has enlightened many cleverer than myself.

August 2016; 680 pages



This review was written by the author of Bally and Bro, Motherdarling  and The Kids of God

"Chaotic fishponds and mirror universes" by Richard Elwes

This is a whistlestop tour through some of the more interesting uses of mathematics. As usual with such things, it left me wanting more depth. You could not ask for more breadth! From economics to correcting errors in digital communication, from astrophysics to topology, from electoral systems to significance to social networks to double-crossing spies, this book has an extraordinary range. Mostly it is well written so that I understood the maths although Elwes has an infuriating tendency to use different (often undeclared) bases for his logarithms. Sometimes he offers results without backing them up sufficiently (at least for my taste). But I am not a general reader and I think that, for the general reader, this book will provide a brilliant introduction to the ubiquity of maths.

Breathless. June 2015; 363 pages

"Fuzzy thinking" by Bart Kosko

This book starts from the premise that things are rarely black and white; often they are shades of grey. Fifty? Therefore the logic that we use should reflect this. We have a logic based on bi-valence: true or false, yes or no, one or zero. Instead, Kosko proposes a multivalent logic in which truth could hold any value between zero and one. He insists that this is not a probabilistic view: he points out that a car parked 70% in one space and 30% in another does not have a 70% chance of being all in one space.

These are important ideas and this is an important book. What lets it down somewhat is the anger that Kosko feels for mathematicians and scientists and indeed anyone who disagrees with him and the insults he hurls at them. He treats maths and science as if they are not only wrong but, worse, run by incompetent charlatans who are well aware of the frauds they are perpetrating on the public. He is also rather too full of himself; he is an immodest messiah. He proposes a number of applications of fuzzy logic that he himself has developed; since this is an introduction to the subject they are not detailed and I would have appreciated a little more explanation here but then I am not a general reader (indeed, I was considering these issues in 1986 when working at Brunel University in Artificial Intelligence but at that time I did not know enough to be able to move forward past the problems). Unfortunately, many of his applications seem to involve digital computers which seem to give the last laugh to the world of bi-valence.

Despite these weaknesses, this book has many really critical ideas which I cannot do justice to in a review meant for a general reader. I shall be studying Fuzzy Thinking more carefully in a second reading. It was certainly an entertaining read and very well written and I am looking forward to understanding more of this field.

March 2015; 285 pages

"Alan Turing: the Enigma" by Andrew Hodges

This is a very thorough, indeed exhaustive, biography of Alan Turing and his ideas. It is the book that has been filmed as the Imitation Game

Turing (most people apart from 'Alan' and his closest associates are referred to either by their surnames or by their initials and surnames like a cricket card) was not a particularly distinguished school boy who had a particular love for Maths but took two goes to get a scholarship to Cambridge. He seemed to go from zero to infinity as an undergraduate and before his doctorate published his ground breaking work on the Universal Turing Machine. Then he was recruited to code breaking and solved the secrets of the naval Enigma machine so saving Britain's convoyed food supplies (and many thousands of sailors) during the Battle of the Atlantic. But after the war he failed to have much of an impact on the birth of the primitive computers despite working at the NPL (where he met my father) on the ACE and at Manchester University. He wrote a truly ground-breaking paper on morphology but this was mostly unrecognised at the time. Then he was arrested and convicted of homosexuality and forced to undergo hormone therapy as an alternative to prison. Some time after that ended he died from cyanide poisoning.

This is a difficult biography to write. Turning's work was in the hardest bits of mathematics and logic and I found the explanations hard to understand. (And I think I might have a small edge of a general reader, having taught Physics for 33 years.) There is much that is mysterious. His wartime work was under conditions of the strictest secrecy but so was his sex life (being criminal at that time) and so was his death (was it suicide? if so, why? - he left no note - or was it an an accident? or was he, as the conspiracy theorists suggest, murdered by the security services who in the height of the Cold War were frightened that this gay man might spill wartime secrets?). Hodges has done well to tell us as much as he has.

But there was an awful lot of speculation. Hodges tends to assume that Turing's scientific ideas mostly come from a text book he had as a child; there are many quotes from it. Other major influences are a book by Eddington and Back to Methuselah by George Bernard Shaw. There is a lot of talk about Red Queens and White Queens and chess problems and Alice Through the Looking Glass. But there seems little evidence for most of this.

I think this book would have benefited from a severe pruning. Although the book leaps over the last year of his life and dismisses non-suicide theories of his death, it then spends 50 pages discussing the invidious position of homosexuals in Cold War Britain. There is an awful lot of detail on the early days of computing in Britain. It could have been shorter and tighter and this would have been better.

And it really isn't for the general reader.

January 2015; 656 pages

More scientific biographies, reviewed in this blog, may be found by clicking here.

This review was written by the author of Motherdarling  and The Kids of God