'Mathematica': peephole into the fun and wit of mathematics
Charles Babbage, the English mathematician, once wrote to poet Alfred Lord Tennyson: ''In your otherwise beautiful poem ('The Vision of Sin'), there is a verse which reads:
'Every moment dies a man,
Every moment one is born.'
''It must be manifest that, were this true, the population of the world would be at a standstill. In truth the rate of birth is slightly in excess of that of death. I would suggest for the next edition of your poem you have it read:
'Every moment dies a man,
Every moment 1 1/16th is born.'
''Strictly speaking,'' the hair-splitter added, ''this is not correct. The actual figure is a decimal so long that I cannot get it in the line, but I believe that 1 1/16th will be sufficiently accurate for poetry. . . .''
It's ''Mathematica: A World of Numbers and Beyond,'' a much-acclaimed exhibit by the celebrated designers known as the Office of Charles and Ray Eames, that provides such peepholes into the wit, powers, and inner workings of the mathematical mind.
A whole generation of Americans in the West and Midwest has grown up enjoying this popular, pace-setting exhibit about the world's great mathematicians and the fun, joy, and power they found in their work.
The exhibit, sponsored by the International Business Machines Corporation, has been seen by millions at the California Museum of Science and Industry in Los Angeles, where the original opened in 1963 and is still going strong, and at Chicago's Museum of Science and Industry, which until 1980 had an exact duplicate.
Now it's Boston's turn for a run of at least five years. The ''Mathematica'' that Chicago enjoyed for so long, and reluctantly released, made its East Coast debut a year ago last November at the Museum of Science here. Children and adults in New England are learning that mathematics, far from being dull, boring , and intimidating, can be a friendly and exciting subject.
Math, exciting? Yes, the fun and noise begin only a few steps inside the sliding metal gate of the exhibit at the ''Probability'' display. Every 10 minutes, 30,000 balls drop one by one inside a tall, thin glass sandwich, dancing at random down through row upon row of horizontal pegs. Piling up in the bottom half of the sandwich, they invariably form the ''normal distribution curve'' that looks like the high point of a roller coaster.
This is the Eames's way of proving the probability theory of the French mathematician Blaise Pascal. Probability deals with questions that we answer with such everyday words as ''possibly,'' ''sometimes,'' ''maybe,'' and ''I hope so.'' In just such ways mathematics sneaks unnoticed into our lives. Today, Pascal's theory is important in insurance, traffic control, thermodynamics, astrophysics, genetics, etc.
Towering above other displays is a ''prove-it-yourself'' model of a favorite geometrical curiosity: the serpentine Moebius band, which has only one side and one edge. Pushing a button, the visitor sets in motion a red arrow that looks like a little red train. It travels on a black track over the whole surface of the big white plastic Moebius band, returning, amazingly, to the spot where it began.
Delightful stories have been written about painters being hired to paint one side of a Moebius band and scrape the paint off the other side. ''But if you peeled off a coat of paint and opened it out, the exhibit explains, ''the paint would not be a Moebius band.''
Fun? Yes. Silly? Not really. This clever geometrical joke has its practical side. A twist is often put in conveyor belts and moving sidewalks so that the whole surface wears out simultaneously.
''Minimal surfaces.'' Now there is a stodgy-sounding subject. Or is it? The Belgian physicist Joseph Plateau set scientists scratching their heads with this conundrum: ''Is there a surface of minimal area spanning any given closed curve?'' For over 100 years mathematicians struggled to solve this problem.
An empirical answer was finally found in soap bubbles. And ''Mathematica'' proves it before your eyes: Metal wires in the shapes of two cubes, one closed, the other with one side open, are suspended inside a glass display case. Push a button and the two forms descend into a soapy bath. Then up they come, covered with soap bubbles. And, would you believe it? For a few fleeting seconds the bubbles are not only beautiful and intricate, but they also span the surfaces of the cubes with what is obviously the smallest area possible.
This mathematical principle, too, has practical application. It's the presto-findo solution, for instance, to the shortest possible road to connect several towns.
These and other displays illustrating mathematical principles express the very special gift that the late and celebrated Charles Eames had with which to communicate complex ideas dramatically, yet so simply that even a young child could enjoy and grasp something of their truth.
But for the sheer volume of scholarly research that went into it, ''Mathematica's'' History Wall is, for the mature viewer who enjoys reading, perhaps the one display that packs the greatest punch. No fewer than 2,500 books were studied in the making of it.
The Eameses managed to telescope the highlights of modern mathematical development from the 11th century to the late 1950s in one sweeping 50-foot-long timeline that covers the exhibit's longest wall.
You may know that Omar Khayyam was a great Persian poet. But did you know he was also a mathematician and scientist? His book on algebra is the largest of the 14 scientific volumes ascribed to him. And his reformed calendar, the timeline says, ''was as accurate as ours.''
By the time Genghis Khan showed up (1162), Arabs had perfected the astrolabe, one of the earliest analog computers. For the traveling Muslim, the pocket astrolabe used for locating Mecca was necessary equipment.
More than 200 years before Columbus discovered America, a 1280 version of the Hereford Mappa Mundi pictures a spherical world. ''Among the learned clergy,'' says the History Wall, ''there is no doubt that the world is round.''
Everything about the ''Mathematica'' package exhibit is special. Even the color and weave of the taupe carpeting were specially designed for best effect. And instead of just putting up conventional stands to display all his interesting information, Mr. Eames designed showcases like fine furniture, providing footrests and a lovely piece of smooth wood on which the visitor may rest his hand.
''Each part is thought out,'' says I. Bernard Cohen, a history of science professor at Harvard University and a consultant on ''Mathematica.'' ''That is the thing that makes designers look upon [Eames's] work as being so classic. He had a skill for conveying ideas. He always thought of the high point of art as communication.''
He was also liked and well respected by scientists and mathematicians. ''Most of the time,'' says Professor Cohen, ''they tend to look upon people who try to convey their message as low-level popularizers or vulgarizers. Charles wasn't of that kind. His efforts were appreciated by that community, not only for the sincerity of his approach to the subject, but because of the great success he had in conveying high standards and high qualities of thought. Among designers he stands out as the man that everybody admired and emulated.''
It was Lewis Carroll, who knew something about the fun of imagination, who wrote: ''It may be doubted whether in all the range of science there is any field so fascinating to the explorer - so rich in hidden treasures - so fruitful in delightful surprises - as that of pure mathematics.''