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John D. Moore
Author of Confusing Love with Obsession

The book makes me wonder: Is God omniscient in all universes? I've read the four books in this Neoreality set (they can be read in any order) and recommend this book. Does anyone know what molecule is depicted on the cover by Neuron's shoulder?

Most of the books in Pickover's Neoreality series have a bit of fun strangeness tossed in, and Egg Drop Soup is no exception. For example, I like the cryptic puzzle in the Enochian language that David finds in the library. I've read the four books in the Neoreality set (they can be read in any order) and really liked this one.

1. The Yellow-brick Road
2. An Experiment with Kansas
8. The Problem of the Bones
16. Omega Sphere
28. Legions' Number
29. The Problem of the Tombs
35. Prime-poor Equations
36. Number Satellite
43. Ramanujan Congruences and the Quest for Transcendence
49. The Jellyfish of Europa
99. A Connection Between Pi and e
103. The Scarecrow Formula
107. The Omega Crystal
108. Attack of the Undulating Undecamorphs

I've already spent hours reading and rereading the book, and showing it to friends, and I know I'll spend many hours more!

It is a rough rule of thumb that the power of the mainframe appears on the desktop in 10 years, so if you see pictures like those in this book and want to recreate them on your desktop computer, then today you stand a chance. When Alan Norton wrote Julia sets in the Quaternions in the late 1980s you'd have needed what was then a highly advanced system at the IBM Watson Research Center. His article, reproduced in this book, goes into some depth on how his programs were designed. Nevertheless a reader would probably still need to spend several days designing software that would enable him to fly through these objects on his Pentium with 3D graphic acceleration. If there is already a program on the Internet that offers such a flythrough, I have not found it. So if you want a project, then you could buy this book and gain some fame by writing it in Visual Basic or whatever.

There are some shorter projects too, with software listings. As an exercise, I scanned in the listing for J. C. Sprott's Automatic Generation of Strange Attractors (1993). I had it scanned in and working in less than a quarter of an hour. A few minor changes were needed as BASIC is not, of course, an exact language and it varies from version to version. It would in fact have converted into a very nice little "screensaver" had I spent more time - but of course in 1993 "screensavers" were not so popular. It is a tribute to the quality of paper and reproduction that the scanning was so fast and successful. There are many other listings in the book and I am sure that they could be got working with equal ease.

There are also lots of articles without listings and these would make projects for those wishing to learn graphics programming that would be shorter than the ambitions quaternion flythough mentioned before.

Computer Art

The articles range from the deadly serious "frontiers of mathematics" type to deliberate attempts to use chaos theory to produce objects of artistic merit. Computer art has not yet hit the artistic word in any big way. One can still go around an art gallery and see the results of some photographic artist having spent five years using wet chemical methods to produce something that a PC could have done in five minutes. Art PhDs may still admire this outdated enterprise and stand in awe when they see the result in the art gallery. But the future must lie in the sum total of modern computer methods and some form of artistic talent, coupled of course with good sales technique and social standing in the art world. I would advise any up and coming student of modern art to buy this book (or persuade his college library to buy it) and study the sections on computer art - that is where the future of the next generation of artists lie. Desktop computer systems have moved beyond being toys and can produce real work. Not being computer literate, even for an art student, is as big a disadvantage as not being able to read and write was to an earlier generation. In fact it is a bigger barrier - a painter could get by without being able to read and write, but not if he couldn't wield the tools of his trade, however talented his ideas. Computers will be one of the main tools of art in the coming years.

To produce the computer art results in a paper dated 1994, Dr Pickover used a contraption made of a mainframe and much "advanced" graphics equipment.

Today, with the advances in desktop graphics, these patterns could be generated on any modern machine using ideas expressed in articles such as Automatic Parallel generation of Aeolian Fractals on the IBM Power Visualization System.

There are countless beautiful colour plates in this book - if it were less costly I could recommend it for these people just to browse the pictures.

I expect that we shall see more books like this. Hopefully in the future they will also contain CDs where applications for the IBM PC have been made available for people to load in and run straight away. Using the Internet and getting one volunteer for each article it should be possible to use "human parallel processing" not to make it too arduous a task for any one individual. Each volunteer could be rewarded by a copy of the completed book and CD.

Ideally a company like Microsoft could also donate a license to a version of Visual Basic so that the book could contain a Visual Basic development application and source codes that readers could modify. It need not be the latest Visual Basic - an older version is capable of a lot of graphics work, and who knows, the project could help produce a new generation of Visual Basic programmers.

It has been suggested that the style of Dr Pickover's books was doomed to a slow death once programming languages were no longer bundled with new computers. Without buying a development package such as Visual Basic, no one would write Basic as a casual activity. Bundling Visual Basic (or something similar) with a disk at the back of these books may be one solution. Bulk printings of CDs cost about 10 pence each, so the costs are in the development only.

In Conclusion

If you fit into any of the categories of people who would benefit from this book, then you will not be disappointed by it.

For additional enjoyment the Further Exploring section offers additional background including references to books and web sites and also some challenges to readers - a few of which even include a cash prize. And, best of all Wonders of Numbers is written in plain English and accompanied by splendid graphics, lively anecdotes, and a generous supply of epigraphs. A fun way to while away a weekend.

But if you aren't a fan, if you've tasted and returned to the kitchen previous titles by Mr. Pickover, you might still enjoy this fascinating buffet.

And those are 5 hard-earned stars in my rating! I was well past starting to think that the best parts of Pickover's books were the always-intriguing titles. I had started a number of these in the past, but usually ended up skimming or setting them aside. None that I have read would have earned more than 3 stars. Until now!

"Wonders of Numbers" is, somehow, different. It still has some of his quirky lists ("The Unabomber's 10 Most Mathematical Technical Papers", "A Ranking of the 5 Strangest Mathematicians Who Ever Lived"). It still has the intriguing titles - each of 125 "chapters" carries one, ranging from "The Pipes of Papua" to "Anchovy Marriage Test". The pieces still seem to jump all over the place. Most of these things didn't grab me in past Pickover titles. Here, they all fit together and work nicely.

Oddly enough, I think the appeal of this volume might be its eclecticism. Pickover is not trying to create a whole story as he has in some earlier books ("Time: A Traveler's Guide", "Surfing through Hyperspace"). The unifying center of this book is, simply, mathematics and the myriad ways it exposes its wonders to us. I'm guessing that the reason I haven't put this one down is my own fascination with mathematics itself. The broader the scope the better - and none takes a wider view than Clifford Pickover. The book has something for everyone - but it will also draw you in to other pieces you thought you weren't interested in. Martin Gardner meets Conway & Guy ! A nice combo.

Overall it is an excellent overview of Black Holes, and a joy to read!

The story is entertaining & has many didactic features. Pickover also inserts some humor so as to make the book enjoyable as opposed to a dense treatise of rather complex mathematical concepts. Also, at the end of each chapter is a section called "The science behind the science fiction." It is a detailed account of what we presently know (or think we know) about the notions which were presented in the narrative.

And, the concepts are many. We learn of various weird things that happen in & near a black hole, such as time slowing, the "shrinking" of one's perspective due to the singularity & the mind-numbing gravitational power which is projected by black holes.....a gravity field so immense that the escape velocity exceeds light speed. We learn how black holes were predicted by Einstein's theory of Relativity as well as how the many principles of quantum mechanics come into the picture when one is attempting to understand the nature of singularities.

Much of this book is speculation, but it is educated speculation. The conjectures on what happens inside of a singularity, as well as the possiblity of wormholes which lead to other universes & dimensions is exciting & based on our best available current knowledge of the cosmos. As an added bonus, there is a chapter in the back of the book in which many of the world's leading cosmologists answer questions posed by the author on various topics about & related to black holes. There are also computer animation pictures of some of the more dazzling geometrical effects that are generated by black holes. For anyone who is planning to visit a black hole anytime soon, this book is a must.

Strange Brains and Genius is by far the best book I have read that catalogues numerous examples of the fine line between genius and frailty in a wide range of colorful and influential people. Nikola Tesla had a horror of women's pearl earrings. Oliver Heaviside, the father of modern electric-circuit design, painted his nails cherry pink. Renowned scholar Samuel Johnson had so many tics and quirks that some mistook him for an idiot. Jeremy Bentham, the British philosopher who promoted the idea, "the greatest good for the greatest number of people", fell in love with rats. He also advised rich people to plant embalmed corpses of their ancestors upright along highways. There apparently is a link between extreme genius and madness in certain individuals. Pickover also goes further and discusses the role of the brain in religious and alien abduction experiences.

Pickover points out that in repressive times, strange geniuses have been persecuted, but in more enlightened eras these nonconformists have had the freedom to make great contributions to science and society. Are their minds like our own, or are they so different that these geniuses should be viewed as entirely different beings? What do geniuses have in common, and how can we foster their continued emergence? Is their a link between their obsessions and their creativity?

This book is organized into three parts. In Part I, Pickover discusses several geniuses with obsessive-compulsive (and Asperger's) tendencies. Many of the individuals might have Asperger's syndrome (characterized by an impairment in social interaction and development of restricted and repetitive patterns of behavior, interests, and activities). Part II is smorgasbord of short subjects ranging from IQ to the influence of the brain's structure on behavior. Part III discusses how individuals were selected for this book and describes the effect of other disorders such as bipolar disorder and temporal-lobe epilepsy on creativity, religion, and even the alien abduction experience.

Buy this amazing book and go beyond "A Beautiful Mind"

I came across a wonderful Publisher's Weekly weview of Strange Brains and Genius. Here is a brief excerpt:
"Filled with I200 years of eccentric geniuses, this delightful collection of profiles assemble an eclectic and fascinating sampling of scientists (as well as some artists and writers) with a far-ranging assortment of phobias, compulsions, odd belief systems and extraordinarily weird habits. Chief among the scientists is Nikola Tesla, father of alternating current and countless other electrical devices, who could be seen on New York City streets covered in pigeons, was obsessed with the number three, and repulsed by jewelry, particularly pearls. Then there is Oliver Heaviside, a Victorian mathematician and electrical researcher who painted his nails bright pink, signed his correspondence "W.O.R.M.", and cruelly kept the woman charged with his care a virtual prisoner in her own house, later driving her into catatonia. Also explored are the lives of Samuel Johnson, van Gough, and legendary mathematician Paul Erdos, among others. Pickover, a high-tech inventor and researcher at IBM and a prolific author (TIME -- A TRAVELER'S GUIDE, reviewed Apr 20) shows genuine fondness for his subjects and an appreciation of their accomplishments, which he explains clearly and succinctly. More than simply cataloging unusual traits, Pickover also speculates on causes and diagnoses, such as obsessive-compulsive disorder and temporal lobe epilepsy. This is a lively and immensely enjoyable scientific history. Photos throughout." - Publisher's Weekly, May 25, 1998