From sudoku to DNA in six steps

What do encryption, the double helix and sudoku have in common? They are all bound together by the newish science of biocomputing in rather surprising ways, as Martyn Amos masterfully shows in this compendious volume. Amos is a born communicator, that rare breed among scientists who write fluently in an understandable and approachable way about difficult concepts. Amos is not Bill Bryson, nor does he pretend to be; but unlike Bryson he is a practitioner in the area he writes about, and his enthusiasm for it is as evident as it is infectious.

I was initially sceptical about what seemed to be exaggerated claims for biocomputing, but I must admit I was won over as I read Genesis Machines . DNA will never replace silicon for number crunching, for reasons Amos explains, but the class of problems that DNA systems may be able to solve in the future could be much more interesting and wide ranging than the merely computational.

Len Adleman of the University of Southern California, the "A" of the RSA algorithm, provides the encryption link - he was one of the first people to realise the power of biocomputing by solving a simple Hamiltonian path problem of connecting four cities using a clever encoding of it on to strands of DNA. The extraordinary solution involves the powerful laboratory techniques of gel electrophoresis and the polymerase chain reaction. It is hard to imagine many mathematicians being motivated enough to learn these techniques and patient enough to carry out the incredibly laborious experiments necessary to implement the simple algorithm described. It turns out that Adleman also worked for years on Fermat's last theorem but failed to prove it - he is human, too, it seems.

The popular sudoku puzzle is given as an example of NP-hard problems, along with the computer games Tetris and Minesweeper. But this is not to the exclusion of the classic satisfiability problem for which biocomputing solutions are described in detail, both for a trivial example involving who should be invited to the embassy ball, which could be done by hand, and for a much more complicated one, which certainly could not.

The book's first few chapters are devoted to a historical perspective of computation, with useful sections on the Ishango Bone and Charles Babbage's difference engine - though the possibly more interesting work on the Antikythera mechanism is not mentioned. Alan Turing and John von Neumann get the obligatory and justified outing, with some interesting human details picked out. Amos offers insights into von Neumann's extraordinary precocity, though not George P"lya's characterisation of him as being the only student he had ever feared.

At times, the huge cast of characters involved is reminiscent of a Cecil B. de Mille epic, and one sometimes gets confused who exactly Smith, Shapiro (there are three) and Alan are in the text. The cinematic allusion is appropriate as Amos is obviously a film buff - many of his references and analogies are to movies, and none the worse for that. In explaining graph theory, for example, Amos entertainingly invokes the Six Degrees of Kevin Bacon number party game - a film version of the Erd"+s number beloved of some mathematicians as a measure of prestige. The Kevin Bacon number for an actor is defined as the number of jumps via film collaboration that an actor must make in order to be connected to Bacon. Audrey Hepburn's number, we are told, is two.

The book has an unusual structure that involves many digressions explaining the development of the techniques mentioned, but for the most part adds to the interest and the thread of the story is maintained. There is what virtually amounts to a roll call of Nobel prizewinners when each of the techniques is explained. Andrew Fire and Craig Mello's prize for medicine this year on RNA interference would, I expect, have merited a mention if Amos had not already gone to press.

What is particularly interesting is the insight this account gives of the author's personal involvement. When he was a student at Coventry Polytechnic, his life was changed by his choice of final-year project. He also describes late-night problem-solving sessions and notes found at midnight wedged under his door by his supervisor. He describes walking in the grounds of the Institute of Advanced Studies at Princeton University with his supervisor while at a conference - who but a real enthusiast would bother?

There are a few infelicities that jar. I was surprised, for example, to read that Vannevar Bush invented hypertext - this is normally attributed to Ted Nelson and Douglas Engelbart. Wang tiles are mentioned, but not Penrose tiles - and Amos is perhaps too trusting of Erik Winfree's account of their development, but if you can't trust a MacArthur fellow, who can you trust?

The book's editing could have been more thorough - some typos remain and, for example, Amos mentions the Riemann hypothesis but does not say what it is. A few things are repeated, some possibly out of necessity, but others superfluously.

It is a shame that there are not more illustrations. A well-known Escher picture is described rather than reproduced, allegedly because of cost - but one cannot imagine that this excuse could ever have been given in Douglas Hofstadter's classic, Gödel, Escher, Bach . Amos does, however, mention that the image is available on the web, as are many of the references in the hypertext version of the notes in the book on the companion website.

As an interdisciplinary work, this book will have a varied readership. It will be of interest to molecular biologists and bioinformaticians and also to computer science students with a taste for biology. To a specialist, the explanations in one field or another sometimes seem oversimplified, but there are many references to more serious treatments that one can follow up, and it is unlikely that many of the readers of this book will be expert in all the interesting avenues it pursues.

Tony Valsamidis is senior lecturer in information systems, Greenwich University.