What is this “complexity” of which you speak?

Melanie Mitchell

Melanie Mitchell (Photo credit: hukuzatuna)

Complexity: A Guided Tour

This excellent work of popular science is very cheap and I have to confess that was part of the attraction – I could see from a quick scan that it covered a lot of subjects I was interested in and I could still feel I was using my leisure/pleasure time in pursuit of science if I read it (one day I will be back to reading novels, I promise).

In fact it turned out to be a very good companion volume to Godel, Escher, Bach: not a surprise when you discover its author, Melanie Mitchell, had her PhD supervised by Doug Hofstadter.

The book built on the knowledge I gained from GEB – especially in (computational) biology and genetics (the explanation of a genetic algorithm here is streets ahead of that in The New Turing Omnibus – and that’s a very good book) and a number of other fields – including the ideas of A New Kind of Science – which I am now determined to have another look at.

The book’s principal weakness, one that Mitchell discusses at some length, though never quite satisfactorily, is the very idea of “complexity” – are these areas really the core of a science (of emergent properties?) or are they interesting areas which are analogically related but where the links might not be that much greater? At the end of the book I can certainly see the links between the subjects discussed but, as with GEB, one is left puzzling over whether this is really as profound as the author thinks. Maybe it is, maybe it isn’t.

Anyway, it’s a very good (and cheap!) book.


Eternal is the right word

Godel, Escher, Bach: An Eternal Golden Braid (20th anniversary edition with a new preface by the author)

This diagram shows the syntactic divisions wit...

This diagram shows the syntactic divisions within a formal system. Strings of symbols may be broadly divided into nonsense and well-formed formulas. The set of well-formed formulas is divided into theorems and non-theorems. (Photo credit: Wikipedia)

The other day I remarked to a friend that the best thing about reading Crime and Punishment and Moby-Dick was that you could then show off to other friends that you had read them. In neither case is that the full story, both novels throw up images that will live with you for life, but it is not, to me at least, an unfair summary.

Godel, Escher, Bach: An Eternal Golden Braid feels quite a bit like that. It is a book that has always been present in my life much like the works of “the canon” must be for arts students and graduates – in the physics labs at Finchley Catholic High School three decades ago, on the shelves of science students at Edinburgh, popping up in discussions on artificial intelligence, computability and how to be a nerd now and forever. And finally, finally, finally, I have trudged through the 745 pages of text, musical scores and good and bad (very bad in some cases) drawings to finish it.

It is certainly not without insight, in some cases what feels like quite profound insight. You have to wade a long way in to get to Doug Hofstadter‘s explicit comparison between formal mathematical systems and molecular biology but when you get there it is worth the effort if, like me, you were taught biology before the genetic revolution really got going. I had thought I understood why people talked about biological computation before – Fibonacci series and plant growth and so on – but Hofstadter was the first to make me see that the connection between number theory and computation and biology is really a very deep one.

But the book is also full of – and pardon me for being vulgar – crap. Drivel about Zen Buddism, the drawings of Escher (who cares? Not me anyway) and quite repetitive meanders round Hofstadter’s concept of tangled hierarchies (I got it the first time Doug). The mathematical explanations in the book (generally of  Gödel’s incompleteness theorems) suffer, too, I feel, from Hofstadter’s unwillingness to delve deeper into the maths. There are too many words in the way.

In general the book also suffers because it appears to have been poorly edited the first time around for length and could do with a comprehensive edit now to take advantage of the advances in computer typesetting technology since its first publication – there is no reason why the reader should be sent scuttling back several hundred pages looking for references – these could be made specific.

So those are the downsides, what are the positives beyond being able to say you have read it?

I have already mentioned the passages on molecular biology, but there are others too, such as his discussions on Bach (though like much here they are long-winded) and on Alan Turing. Though the book convinced me that Hofstadter was insufficiently robust in his defence of the materialist/reductionist view – the book left me more certain than ever that Turing’s view that what ‘imitates’ intelligence is, in fact, intelligence is the correct one. There is nothing magical inside our heads (and by magical I am twisting Arthur C. Clarke – any technology insufficiently incomprehensible is indistinguishable from magic).

Perhaps most of all the book makes me want to re-read Charles Petzold‘s masterpiece, The Annotated Turing: A Guided Tour Through Alan Turing’s Historic Paper on Computability and the Turing Machine.