AS a boy, Clifford Pickover often visited his father鈥檚 study to look at the
books, especially The Volume Library, published in 1928. It was full of
strange facts, including how long it would take to reach each of the planets
in an aeroplane travelling at the heady speed of 100 miles per hour. Many
years later, he explains, he returned to the study and found a curious book
called The Lato篓o篓carfian Civilisation. It depicts an alien society
that developed in the distant past in a vast pocket of air deep within the ice
of Jupiter鈥檚 moon Ganymede. The Lato篓o篓carfians鈥� bodies are made from
aluminium gallium arsenide, with traces of silicon; they therefore think much
faster than we carbon-based beings do. All through the lunar nights and days
they increase their prestige by dreaming up chaotic mathematical patterns
produced by a simple but inexhaustible trigonometric formula.
Chaos in Wonderland is the story of that formula, as seen through
Lato篓o篓carfian sensory organs. It is also a courageous experiment in
imaginative mathematical exposition. Instead of setting out to teach the
reader about chaos, it offers up intriguing bits of the mathematics plus
Lato篓o篓carfian history, philosophy, psychology and cosmology.
We read of the pi slaves, doomed forever to the computation of successive
digits of Q; the death fungi with their internal labyrinths inhabited by
microscopic poodles; the fearsome Prohaptors with their fractal swords; and
the neon bats that trace space-filling curves in the sky. As we have come to
expect of any of Clifford Pickover鈥檚 books, this one is profusely illustrated
with intricate and astonishing graphics, ranging from Dore麓 engravings
to pictures created by the Lato篓o篓carfians themselves. The overall
effect is one of uninhibited fun, but real mathematics lurks beneath the
frolics.
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Any writing as radical as this will have its flaws. Occasionally the author
will trip and fall on his face; some things will work for some readers but not
others. I thought the idea of compiling a list of the 100 strangest
mathematical titles published marvellous, but was disappointed when I read
it.
Chaos in Wonderland is a book in the same tradition as Edwin Abbott鈥檚
Flatland or Kee Dewdney鈥檚 The Planiverse, a member of the tiny genre of
鈥渕athematics fiction鈥� in which the reader is placed in a world that normally
exists only in mathematicians鈥� imaginations. This style of exposition does not
appeal to those who believe that to be serious about science you have be
solemn, but it has the potential to attract a new audience into mathematics.
Those who are solemnly serious ought to appreciate the value of such an
attempt, even if it leaves them cold. It is a book that will, I suspect,
appeal more to the imaginative and uncritical young than to their elders.
But anyone who is young at heart and adept at the suspension of disbelief
that is necessary for the enjoyment of any science fiction or fantasy story
will find considerable amusement and enlightenment in this book. They may even
join the Lato篓o篓carfians, Granvilles and Milnors in their dreams of
new mathematics.