Martin Gardner (1914–2010) was a science writer and novelist. He was the author of The New Ambidextrous Universe, Fractal Music, Hypercards and More, The Night is Large and Visitors from Oz.

The New New Math

Surveys have shown for many decades that the mathematical skills of American high school students lag far behind those of their counterparts in Japan, Korea, Singapore, and many European countries. In the United States whites do better than blacks, Hispanics, and Native Americans. Males outscore females. Students from high socioeconomic …

How He Lost It

Jim Bakker’s confessional I Was Wrong is a remarkable work in many respects, not least of which is the skill with which it is written. His earlier autobiography, Move That Mountain (1976), was a ghostwritten potboiler. I Was Wrong acknowledges the help of Ken Abraham, “who used his skills to …

A-Symmetry

When Blake wrote of the Tyger’s “fearful symmetry” he was using the noun as a synonym for beauty. Today the word usually means any kind of regular pattern. Geometers sharpen the definition by making symmetry the property of a figure that stays the same after a given operation is performed.

Beauty in Numbers

The front cover of Keith Devlin’s Penguin paperback is a dazzling computer image reproduced from a Springer Verlag book, The Beauty of Fractals. If it looks familiar it’s because you’ve seen it on the front cover of James Gleick’s recent best seller, Chaos, published by Viking. Two books with identical …

Seeing Stars

President Reagan, asked at his May 17 press conference if he believed in astrology, replied: “I’ve not tied my life to it, but I won’t answer the question the other way because I don’t know enough about it to say is there something to it or not.” In the unkind …

The Ultimate Turtle

“My goal is simple. It is complete understanding of the universe, why it is as it is and why it exists at all.” —Stephen Hawking, 1981 Stephen Hawking opens his new book with a marvelous old anecdote. A famous astronomer, after a lecture, was told by an elderly lady, …

Bumps on the Head

How can good science be distinguished from bad? Philosophers of science call this the “demarcation problem.” Like most problems about distinguishing parts of spectra, sharp definitions are impossible, but from hazy borders it doesn’t follow that distinctions between extremes are useless. Twilight doesn’t invalidate the contrast between day and night.

Count Up

“The world is colors and motion, feelings and thought…and what does math have to do with it? Not much, if “math” means being bored in high school, but in truth mathematics is the one universal science. Mathematics is the study of pure pattern, and everything in the cosmos is a …

Giving God a Hand

“It is too early, it seems to me, to send the firemen home. The fire is still burning on many a far-flung hill, and it may begin to roar again at any moment…. Heave an egg out of a Pullman window and you will hit a Fundamentalist almost anywhere in …

Isness Is Her Business

In the halcyon days of spiritualism, psychics whose vocal chords were seized by a spirit, or in whose presence the dead were able to speak without using a live mouth—often by talking through a floating trumpet—were called “direct-voice” mediums. In the United States the most gifted direct voicer was George …

Secrets of the Old One

“Newton, forgive me,” Einstein wrote in an autobiographical essay. “You found the only way which, in your age, was just about possible for a man of highest thought and creative power.” What was Einstein asking forgiveness for? That is the subject of this splendid book by Clifford Will, a physicist …

WAP, SAP, PAP, & FAP

It has been observed that cosmologists are often wrong but seldom uncertain, and the authors of this long, fascinating, exasperating book are no exceptions. They are John Barrow, astronomer at the University of Sussex, and Frank Tipler, Tulane University mathematical physicist. Physicist John Wheeler provides an enthusiastic foreword. No one …

Physics: The End of the Road?

O amazement of things—even the least particle! —Walt Whitman, “Song at Sunset” Theoretical physicists are in a state of high excitement these days, and for good reason. New discoveries in particle physics, combined with brilliant theoretical invention, suggest that they are on the verge of nothing less than …

Quiz Kids

In Brunswick, Germany, in 1780, a stonemason was calculating the wages due his workmen at the end of the week. Watching was his three-year-old son. “Father,” said the child, “the reckoning is wrong.” The boy gave a different total which, to everyone’s surprise, was correct. No one had taught the …

Is Mathematics for Real?

In precisely what sense do universals (such as blueness, goodness, cowness, squareness, and threeness) exist? For Plato they are transcendent things, independent of the universe. Aristotle agreed that they are outside human minds, but he pulled them down from Plato’s heaven to make them inseparable from the world. During the …