Book Reviews

Transcribed from the printed issue; not yet reviewed. Read it in the PDF of the issue, page 51

Books are welcomed for review on any topic likely to be of interest to the APL user, and should be sent to the Editor at the adress on the inside back cover.

LISP: A Gentle Introduction to Symbolic Computing¶

LISP: A Gentle Introduction to Symbolic Computing; Touretszy, Harper & Row 1984. £11.95 from Harper & Row, Tavistock Street, London WC2.

Question: what’s the difference between LISP and APL? Answer: they’re both over twenty years old, but LISP is getting more popular. It certainly shows that it takes more than a funny vocabulary to put people off a language. One hundred zillion Chinese can’t be wrong.

If you don’t know LISP already then you can certainly learn it with this book: the introduction is indeed gentle and sprinkled with wry humour. The first few chapters present LISP processing using a functional style that would work almost as it stands as a description of APL functions with arguments that return explicit results. Then we move off into the lisping world of CARs and CDRs (the legacy of bygone development days, Content Address Register and Content Decrement Register, as near to the “1 Take” and “1 Drop” of APL as makes no difference).

There’s a good bibliography and some real worked examples later on. Read it, and you’ll probably agree that APL could do it all with its eyes shut, and APL2 with no eyes at all. So where did we go wrong? I still blame our silly symbols. Even if technology is now no longer a penalty for implementing special character sets, it certainly used to be — and by now it’s too late.

Fuzzy Sets and Decision Analysis¶

Fuzzy Sets and Decision Analysis; Zimmermann, Zadeh & Gaines, North-Holland 1984. Available from Elsevier Science Publishers B.V., P.O. Box 1991, Amsterdam.

The interplay between techniques and applications in a discipline such as Operational Research is an interesting one. Students tend to start by imagining that the techniques are all that matters, often because of the difficulty of presenting real applications in an academic environment. Later, in the heady confrontation with “trouble up at t’mill” they may well over-react, praying that a blight may descent on the professors who made it all sound so neat, tidy and mathematically elegant. But in what I believe to be the final phase of this particular enlightenment, they tend to acknowledge the stimulus to creative thinking that comes from the exploitation of a genuine new technique, initially for its own sake.

In this context, fuzzy set theory ranks with catastrophe theory, the laser and the linear induction motor as having been described as a “solution looking for a problem”. However, patience is its own reward; the laser gets Reagan’s Star Wars as its prize; the rest — perhaps the best — is yet to come.

A brief reminder of what fuzzy sets are all about may be in order. Conventional mathematics allows us to make precise statements. For example: “John is over 180 cm tall”. Whether such a statement is true or false is a separate issue; the statement itself is intentionally exact. Fuzzy set theory relaxes this unnatural tyranny by introducing the concept of “degree of membership”, a real number varying over the interval 0 to 1. This allows us to recast this statement as “John belongs to the set of over 180 cm tall people with degree of membership 1”. More interesting things start happening once the degree of membership drops below 1.

Almost before the ink was dry on the definitive 1970 article on the subject by Zadeh (for that is he) and Bellman (inventor of dynamic programming, not to be confused with COBOL), the academic hounds were unleashed and promptly tore into the authors with the accusation that beneath the fuzzy emperor’s clothes were the unmistakable pyjamas of probability theory. This has made for a nice controversy ever since. However, with the coming of expert systems, genuine interest has reawakened in using fuzzy set techniques to design routines for user dialogue. These ought to allow people to respond adverbially rather than by interjection: it’s always more helpful to reply “Probably” to the computer’s question “How old are you?”.

Given this degree of topicality it is a pity to report that this collection of papers contains not one useful practical example of the application of the technique to a real problem. The nearest we get is an abstruse discussion of predicting television revenues using fuzzy sets by a pair of American researchers. Admittedly the book doesn’t try to be a do-it-yourself guide, but as a selection of papers one might reasonably have expected a balance between the academic and the practical. Since all that is left to comment on are the integral signs, I must declare myself incompetent. Nethertheless, I refuse to be intimidated by Zimmermann’s approach in one of his own papers: “Proof: The proof is almost trivial...”. There follow several paragraphs of algebraic formulation terminated by an academically witty exclamation mark (!).

Powers of Ten¶

Powers of Ten: About the Relative Size of Things in the Universe; P. & P. Morrison, Scientific American Books Inc. 1982.
Available from Freemans, Beaumont Street, Oxford.

This is one of the most delightful books I have ever seen, and “seen” is the operative term. The main feature of the book is a series of 42 photographs, each forming a square grid and related to its successor by an order of magnitude along each dimension. For example, the photograph of a square kilometre of Chicago viewed from the air is followed by a closeup of its centre, 100 metres on each side. The area of each successive photograph is therefore one-hundredth of its predecessor. This sounds unremarkable, almost pedestrian; but now extend the concept to a starting square with sides of 1 billion light years (10 to the 25 metres), expanded by 42 steps through to one of 0.1 fermis (10 to the minus 16 metres).

We gain many realisations from this wonderful book. Not the least is some sense of the recursive nature of the Universe. The photograph of stellar nebulae looks so like that of the electrons of the carbon atom. To speculate that our whole Universe is contained within some quark in another dimension of matter is a popular theme with science fiction writers, but if you look through this book you may even believe it. Worse still, you may wake up with the nightmare, as I did, that this recursion is closed: the quark that contains our Universe is the one that we plot in a bubble chamber.

As an aid to humility, notice also that the first photograph of a recognisable Earth occurs as 100 thousand kilometres away (10 to the 8 metres) while the smallest frame recognisable to the non-specialist is that of a human hand in Chicago, with area 10 by 10 centimetres (10 to the minus 1 metres). This range of 10 orders of magnitude out of the 42 depicted in this voyage is modest indeed; and for all of us save the astronauts, our lives are limited to a mere seven of these.

This is excellent science at work, and one suspects a labour of love by the Morrison duo. Philip Morrison teaches Physics and Astronomy at MIT and reviews books for Scientific American. Phylis Morrison teaches children and their teachers (sic) science and art in classroom and museum. I wonder what the Morrisons chat about after watching Dynasty. Well, maybe they’re the 0.00002% of Americans who don’t. This particular trip must make Denver Carrington look like a vicar’s tea party in Nether Wallop. So buy the book and I will buy it back from you myself if you’re underwhelmed.