Short works

Books : reviews

Clifford A. Pickover.
Computers, Pattern, Chaos and Beauty.
Alan Sutton. 1990

rating : 3.5 : worth reading

Pickover writes in the spirit of Hofstadter’s Gödel, Escher, Bach and Mandelbrot’s The Fractal Geometry of Nature. With a combination of text and stunning computer-generated images, Pickover reveals an entirely new way of seeing. It is in the field of advanced computer graphics that he finds themes from high-level mathematics and chaos theory to philosophy, art and aesthetics, all interweaving in a unique and beautiful synthesis of science and art.

Clifford A. Pickover.
Computers and the Imagination.
Alan Sutton. 1991

rating : 5 : waste of time
review : 11 June 1998

Recent books by James Gleick, Martin Gardner, and Benoit Mandelbrot have made the topics of Chaos theory and fractals an integral part of the terrain for the computer literate. They have shown the revolutionizing role of the visualization of complex mathematical data. Computers and the Imagination pushes the adventure one step further.

Pickover, a renowned science writer whose work has been featured in such diverse publications as Artforum, OMNI, Scientific American, and Computers in Physics, examines the manifold ways in which visualization transforms how we both perceive and understand the world around us. Computers and the Imagination includes a range of topics from the how-to construction of artificial spider webs to pain-inducing pattens to computer-generated poetry. Along the way, Pickover paradoxically uses the computer—a machine—to gain new insights into the very origins of human creativity.

This book is an unfortunate mishmash of underdeveloped ideas. Each ‘chapter’, a reprint from a column, is a mere three or four pages long, barely space to describe the theme, sketch some simple developments, then list a few references.

The themes range broadly: fractals and chaos, number theory, computer developments, with observations ranging from deep puzzles to trivial surface patterns (for example, I fail to have any deep interest in properties of numbers that hold only in base 10).

Some topics can be done justice in this limited space – I liked the use of Moiré patterns to detect loose screws, for example. But most of the topics would benefit from more background, and deeper exploration.

A disappointing sequel.

Clifford A. Pickover.
Keys to Infinity.
John Wiley. 1995

Clifford A. Pickover.
Surfing Through Hyperspace: understanding higher universes in six easy lessons.
OUP. 1999

Clifford A. Pickover.
The Math Book: from Pythagoras to the 57th dimension, 250 milestones in the history of mathematics.
Sterling. 2009

When did humans tie their first knots?
Why was the first woman mathematician murdered?
Is it possible to turn a sphere inside out?

These are just a few of the thought-provoking questions answered in this beautifully illustrated book. Author Clifford Pickover reveals the magic and mystery behind some of the most significant milestones as well as the oddest objects and ideas humanity has ever contemplated, beginning in 150 million B.C. and ending with the latest cutting-edge breakthroughs.

Mathematics has permeated every field of scientific endeavor. It can be used to explain the colors of the sunset or the architecture of our brains, and help us explore subatomic quantum realities and imagine faraway galaxies.

Notable formulas and mathematical concepts are accompanied by fascinating facts about mathematicians’ lives and real-world, practical applications of theorems. Journey with Pickover as he traces 250 achievements like ancient ant “odometers,” the first abacus, the discovery of computer-generated fractals, and the quest for new dimensions. Here also are remarkable thinkers from Pythagoras and Euclid to modern-day math icon Martin Gardner and cosmologist Max Tegmark.

Chronologically organized, each entry is short enough to digest in a few minutes and is presented along with a striking full-color image.

“For me,” writes Pickover, “mathematics cultivates a perpetual state of wonder about the nature of mind, the limits of thoughts, and our place in this vast cosmos.”