My Goodreads Review
rating: 4 of 5 stars
A lost gem among the wonderful flood of books merging biology, mathematics, and computers following Norbert Weiner’s “Cybernetics” in the 1960s. The only reason I discovered it is because the author is a professor at my university.
I suspect that the very reason I gave this book 4 stars will be the reason that many will give it 2 or avoid it all together – its heavy on mathematical notation. Assuming you’ve got some set theory and a hearty constitution for exploring forests of equations, this is a stellar little handbook covering automata, neural nets, perceptrons, communication theory, and error-correction – the heart of the early attempts at mathematical models of the brain. Computational neuroscience has moved into many other areas today but this is still a great place to start if you’re interested in the subject matter.
The clincher for me (and the fourth star above) was Arbib’s clear and concise presentation of recursive logics and Godel’s Incompleteness Theorem. Perhaps other books have filled this role since, but I’ve never found such an accessible presentation of it. I was literally trembling page-by-page as I entered the world of recursively enumerable sets and arithmetical logics somewhere over the airspace of Dallas, TX, emerging in a daze of sheer amazement at the airport.
I credit this book with making me comfortable with a great deal set theory and functional notation that has recently come in handy tackling modern algebra and the works of Rene Thom.
My biggest criticism is that this book does not convey the excitement of the author at all. The book reads exactly like a textbook. Profound and interesting conclusions are followed with sentences like, “The reader may be interested in learning more among the literature [see ref. 1 and 2:].” Also, while I appreciated the mathematical rigor, I believe well-placed analogy and colloquialisms would have served this book well. I suppose the style was a product of both the era and the author’s country of origin (Australia). In any case, this book still christened one of the more memorable plane rides I’ve ever had.
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