Ever since National Basketball a.s.sociation games became a television staple, it's seemed to me that it could be used to teach science and mathematics. To appreciate a free-throw average of 0.926, you must know something about converting fractions into decimals. A lay-up is Newton's first law of motion in action. Every shot represents the launching of a basketball on a parabolic arc, a curve determined by the same gravitational physics that specifies the flight of a ballistic missile, or the Earth orbiting the Sun, or a s.p.a.cecraft on its rendezvous with some distant world. The centre of ma.s.s of the player's body during a slam dunk is briefly in orbit about the centre of the Earth.

To get the ball in the basket, you must loft it at exactly the right speed; a one per cent error and gravity will make you look bad. Three-point shooters, whether they know it or not, compensate for aerodynamic drag. Each successive bounce of a dropped basketball is nearer to the ground because of the Second Law of Thermodynamics. Daryl Dawkins or Shaquille O'Neal shattering a backboard is an opportunity for teaching - among some other things - the propagation of shock waves. A spin shot off the gla.s.s from under the backboard goes in because of the conservation of angular momentum. It's an infraction of the rules to touch the basketball in 'the cylinder' above the basket; we're now talking about a key mathematical idea: generating n-dimensional objects by moving (n - l)-dimensional objects.

In the cla.s.sroom, in newspapers and on television, why aren't we using sports to teach science?

When I was growing up, my father would bring home a daily paper and consume (often with great gusto) the baseball box scores. There they were, to me dry as dust, with obscure abbreviations (W, SS, K, W-L, AB, RBI), but they spoke to him. Newspapers everywhere printed them. I figured maybe they weren't too hard for me. Eventually I too got caught up in the world of baseball statistics. (I know it helped me in learning decimals, and I still cringe a little when I hear, usually at the very beginning of the baseball season, that someone's 'batting a thousand'. But 1.000 is not 1,000.. The lucky player is batting one.) Or take a look at the financial pages. Any introductory material? Explanatory footnotes? Definitions of abbreviations? Almost none. It's sink or swim. Look at those acres of statistics! Yet people voluntarily read the stuff. It's not beyond their ability. It's only a matter of motivation. Why can't we do the same with maths, science and technology?

In every sport the players seem to perform in streaks. In basketball it's called the hot hand. You can do no wrong. I remember a play-off game in which Michael Jordan, not ordinarily a superb long-range shooter, was effortlessly making so many consecutive three-point baskets from all over the floor that he shrugged his shoulders in amazement at himself. In contrast, there are times when you're cold, when nothing goes in. When a player is in the groove he seems to be tapping into some mysterious power, and when ice-cold he's under some kind of jinx or spell. But this is magical, not scientific thinking.

Streakiness, far from being remarkable, is expected, even for random events. What would would be amazing would be no streaks. If I flip a penny ten times in a row, I might get this sequence of heads and tails: H H H T H T H H H H. Eight heads out of ten, and four in a row! Was I exercising some psychokinetic control over my penny? Was I in a heads groove? It looks much too regular to be due to chance. be amazing would be no streaks. If I flip a penny ten times in a row, I might get this sequence of heads and tails: H H H T H T H H H H. Eight heads out of ten, and four in a row! Was I exercising some psychokinetic control over my penny? Was I in a heads groove? It looks much too regular to be due to chance.

But then I remember that I was flipping before and after I got this run of heads, that it's embedded in a much longer and less interesting sequence: H T H T T H H H T H T H H H H T H T T H T H T T. If I'm permitted to pay attention to some results and ignore others, I'll always be able to 'prove' there's something exceptional about my streak. This is one of the fallacies in the baloney detection kit, the enumeration of favourable circ.u.mstances. We remember the hits and forget the misses. If your ordinary field goal shooting percentage is 50 per cent and you can't improve your statistics by an effort of will, you're exactly as likely to have a hot hand in basketball as I am in coin-flipping. As often as I get eight out of ten heads, you'll get eight out of ten baskets. Basketball can teach something about probability and statistics, as well as critical thinking.

An investigation by my colleague Tom Gilovich, professor of psychology at Cornell, shows persuasively that our ordinary understanding of the basketball streak is a misperception. Gilovich studied whether shots made by NBA players tend to cl.u.s.ter more than you'd expect by chance. After making one or two or three baskets, players were no more likely to succeed than after a missed basket. This was true for the great and the near-great, not only for field goals but for free throws - where there's no hand in your face. (Of course some attenuation of shooting streaks can be attributed to increased attention by the defence to the player with the 'hot hand'.) In baseball, there's the related but contrary myth that someone batting below his average is 'due' to make a hit. This is no more true than that a few heads in a row makes the chance of flipping tails next time anything other than 50 per cent. If there are streaks beyond what you'd expect statistically, they're hard to find.

But somehow this doesn't satisfy. It doesn't feel true. Ask the players, or the coaches, or the fans. We seek meaning, even in random numbers. We're significance junkies. When the celebrated coach Red Auerbach heard of Gilovich's study, his response was: 'Who is this guy? So he makes a study. I couldn't care less.' And you know exactly how he feels. But if basketball streaks don't show up more often than sequences of heads or tails, there's nothing magical about them. Does this reduce players to mere marionettes, manipulated by the laws of chance? Certainly not. Their average shooting percentages are a true reflection of their personal skills. This is only about the frequency and duration of streaks.

Of course, it's much more fun to think that the G.o.ds have touched the player who's on a streak and scorned the one with a cold hand. So what? What's the harm of a little mystification? It sure beats boring statistical a.n.a.lyses. In basketball, in sports, no harm. But as a habitual way of thinking, it gets us into trouble in some of the other games we like to play.

'Scientist, yes; mad, no' giggles the mad scientist on 'Gilligan's Island' as he adjusts the electronic device that permits him to control the minds of others for his own nefarious purpose.

'I'm sorry, Dr Nerdnik, the people of Earth will not appreciate being shrunk to three inches high, even if it will will save room and energy...' The cartoon superhero is patiently explaining an ethical dilemma to the typical scientist portrayed on Sat.u.r.day-morning children's television. save room and energy...' The cartoon superhero is patiently explaining an ethical dilemma to the typical scientist portrayed on Sat.u.r.day-morning children's television.

Many of these so-called scientists - judging from the programmes I've seen (and plausible inference about ones I haven't, such as the Mad Scientist's 'Toon Club) - Mad Scientist's 'Toon Club) - are moral cripples driven by a l.u.s.t for power or endowed with a spectacular insensitivity to the feelings of others. The message conveyed to the moppet audience is that science is dangerous and scientists worse than weird: they're crazed. are moral cripples driven by a l.u.s.t for power or endowed with a spectacular insensitivity to the feelings of others. The message conveyed to the moppet audience is that science is dangerous and scientists worse than weird: they're crazed.

The applications of science, of course, can can be dangerous, and, as I've tried to stress, virtually every major technological advance in the history of the human species - back to the invention of stone tools and the domestication of fire - has been ethically ambiguous. These advances can be used by ignorant or evil people for dangerous purposes or by wise and good people for the benefit of the human species. But only one side of the ambiguity ever seems to be presented in these offerings to our children. be dangerous, and, as I've tried to stress, virtually every major technological advance in the history of the human species - back to the invention of stone tools and the domestication of fire - has been ethically ambiguous. These advances can be used by ignorant or evil people for dangerous purposes or by wise and good people for the benefit of the human species. But only one side of the ambiguity ever seems to be presented in these offerings to our children.

Where in these programmes are the joys of science? The delights in discovering how the universe is put together? The exhilaration in knowing a deep thing well? What about the crucial contributions that science and technology have made to human welfare, or the billions of lives saved or made possible by medical and agricultural technology? (In fairness, though, I should mention that the Professor in 'Gilligan's Island' often used his knowledge of science to solve practical problems for the castaways.) We live in a complex age where many of the problems we face can, whatever their origins, only have solutions that involve a deep understanding of science and technology. Modern society desperately needs the finest minds available to devise solutions to these problems. I do not think that many gifted youngsters will be encouraged towards a career in science or engineering by watching Sat.u.r.day-morning television - or much of the rest of the available American video menu.

Over the years, a profusion of credulous, uncritical TV series and 'specials' - on ESP, channelling, the Bermuda Triangle, UFOs, ancient astronauts, Big Foot, and the like - have been sp.a.w.ned. The style-setting series 'In Search of...' begins with a disclaimer disavowing any responsibility to present a balanced view of the subject. You can see a thirst for wonder here untempered by even rudimentary scientific scepticism. Pretty much whatever anyone says on camera is true. The idea that there might be alternative explanations to be decided among by the weight of evidence never surfaces. The same is true of 'Sightings' and 'Unsolved Mysteries' - in which, as the very t.i.tle suggests, prosaic solutions are unwelcome - and innumerable other clones.

'In Search of...' frequently takes an intrinsically interesting subject and systematically distorts the evidence. If there is a mundane scientific explanation and one which requires the most extravagant paranormal or psychic explanation, you can be sure which will be highlighted. An almost random example: an author is presented who argues that a major planet lies beyond Pluto. His evidence is cylinder seals from ancient Sumer, carved long before the invention of the telescope. His views are increasingly accepted by professional astronomers, he says. Not a word is mentioned of the failure of astronomers - studying the motions of Neptune, Pluto and the four s.p.a.cecraft beyond - to find a trace of the alleged planet.

The graphics are indiscriminate. When an offscreen narrator is talking about dinosaurs, we see a woolly mammoth. The narrator describes a hovercraft; the screen shows a shuttle liftoff. We hear about lakes and flood plains, but are shown mountains. It doesn't matter. The visuals are as indifferent to the facts as is the voice-over.

A series called 'The X Files', which pays lip-service to sceptical examination of the paranormal, is skewed heavily towards the reality of alien abductions, strange powers and government complicity in covering up just about everything interesting. Almost never does the paranormal claim turn out to be a hoax or a psychological aberration or a misunderstanding of the natural world. Much closer to reality, as well as a much greater public service, would be an adult series ('s...o...b.. Doo' does it for children) in which paranormal claims are systematically investigated and every case is found to be explicable in prosaic terms. The dramatic tension would be in uncovering how misapprehension and hoax could generate apparently genuine paranormal phenomena. Perhaps one of the investigators would always be disappointed, hoping that next next time an unambiguously paranormal case will survive sceptical scrutiny. time an unambiguously paranormal case will survive sceptical scrutiny.

Other shortcomings are evident in television science fiction programming. 'Star Trek', for example, despite its charm and strong international and interspecies perspective, often ignores the most elementary scientific facts. The idea that Mr Spock could be a cross between a human being and a life form independently evolved on the planet Vulcan is genetically far less probable than a successful cross of a man and an artichoke. The idea does, however, provide a precedent in popular culture for the extraterrestrial/human hybrids that later became so central a component of the alien abduction story. There must be dozens of alien species on the various 'Star Trek' TV series and movies. Almost all we spend any time with are minor variants of humans. This is driven by economic necessity, costing only an actor and a latex mask, but it flies in the face of the stochastic nature of the evolutionary process. If there are aliens, almost all of them I think will look devastatingly less human than Klingons and Romulans (and be at widely different levels of technology). 'Star Trek' doesn't come to grips with evolution.

In many TV programmes and films, even the casual science -the throwaway lines that are not essential to a plot already innocent of science - is done incompetently. It costs very little to hire a graduate student to read the script for scientific accuracy. But, so far as I can tell, this is almost never done. As a result we have such howlers as 'pa.r.s.ec' mentioned as a unit of speed instead of distance in the - in many other ways exemplary - film Star Wars. Star Wars. If such things were done with a modic.u.m of care, they might even improve the plot; certainly, they might help convey a little science to a ma.s.s audience. If such things were done with a modic.u.m of care, they might even improve the plot; certainly, they might help convey a little science to a ma.s.s audience.

There's a great deal of pseudoscience for the gullible on TV, a fair amount of medicine and technology, but hardly any science, especially on the big commercial networks, whose executives tend to think that science programming means ratings declines and lost profits, and nothing else matters. There are network employees with the t.i.tle 'Science Correspondent', and an occasional news feature said to be devoted to science. But we almost never hear any science from them, just medicine and technology. In all the networks, I doubt if there's a single employee whose job it is to read each week's issue of Nature Nature or or Science Science to see if anything newsworthy has been discovered. When the n.o.bel Prizes in science are announced each fall, there's a superb news 'hook' for science: a chance to explain what the prizes were given for. But, almost always, all we hear is something like '... may one day lead to a cure for cancer. Today in Belgrade...' to see if anything newsworthy has been discovered. When the n.o.bel Prizes in science are announced each fall, there's a superb news 'hook' for science: a chance to explain what the prizes were given for. But, almost always, all we hear is something like '... may one day lead to a cure for cancer. Today in Belgrade...'

How much science is there on the radio or television talk shows, or on those dreary Sunday morning programmes in which middle-aged white people sit around agreeing with each other? When is the last time you heard an intelligent comment on science by a President of the United States? Why in all America is there no TV drama that has as its hero someone devoted to figuring out how the Universe works? When a highly publicized murder trial has everyone casually mentioning DNA testing, where are the prime-time network specials devoted to nucleic acids and heredity? I can't even recall seeing an accurate and comprehensible description on television of how television television works. works.

By far the most effective means of raising interest in science is television. But this enormously powerful medium is doing close to nothing to convey the joys and methods of science, while its 'mad scientist' engine continues to huff and puff away.

In American polls in the early 1990s, two-thirds of all adults had no idea what the 'information superhighway' was; 42 per cent didn't know where j.a.pan is; and 38 per cent were ignorant of the term 'holocaust'. But the proportion was in the high 90s who had heard of the Menendez, Bobbit and O.J. Simpson criminal cases; 99 per cent had heard that the singer Michael Jackson had allegedly s.e.xually molested a boy. The United States may be the best-entertained nation on Earth, but a steep price is being paid.

Surveys in Canada and the United States in the same period show that television viewers wish there were more science programming. In North America, often there's a good science programme in the 'Nova' series of the Public Broadcasting System, and occasionally on the Discovery or Learning Channels, or the Canadian Broadcasting Company. Bill Nye's 'The Science Guy' programmes for young children on PBS are fast-paced, feature arresting graphics, range over many realms of science, and sometimes even illuminate the process of discovery. But the depth of public interest in science engrossingly and accurately presented - to say nothing of the immense good that would result from better public understanding of science - is not yet reflected in network programming.

How could we put more science on television? Here are some possibilities: * The wonders and methods of science routinely presented on news and talk programmes. There's real human drama in the process of discovery.

* A series called 'Solved Mysteries', in which tremulous speculations have rational resolutions, including puzzling cases in forensic medicine and epidemiology.

* 'Ring My Bells Again' - a series in which we relive the media and the public falling hook, line and sinker for a coordinated government lie. The first two episodes might be the Bay of Tonkin 'incident' and the systematic irradiation of unsuspecting and unprotected American civilians and military personnel in the alleged requirements of 'national defence' following 1945.

* A separate series on fundamental misunderstandings and mistakes made by famous scientists, national leaders and religious figures.

* Regular exposes of pernicious pseudoscience, and audience-partic.i.p.ation 'how-to' programmes: how to bend spoons, read minds, appear to foretell the future, perform psychic surgery, do cold reads, and press the TV viewers' personal b.u.t.tons. How we're bamboozled: learn by doing.

* A state-of-the-art computer graphics facility to prepare in advance scientific visuals for a wide range of news contingencies.

* A set of inexpensive televised debates, each perhaps an hour long, with a computer graphics budget for each side provided by the producers, rigorous standards of evidence required by the moderator, and the widest range of topics broached. They could address issues where the scientific evidence is overwhelming, as on the matter of the shape of the Earth; controversial matters where the answer is less clear, such as the survival of one's personality after death, or abortion, or animal rights, or genetic engineering; or any of the presumptive pseudosciences mentioned in this book.

There is a pressing national need for more public knowledge of science. Television cannot provide it all by itself. But if we want to make short-term improvements in the understanding of science, television is the place to start.

23.

Maxwell and The Nerds

Why should we subsidize intellectual curiosity?

Ronald Reagan, campaign speech, 1980

There is nothing which can better deserve our patronage than the promotion of science and literature. Knowledge is in every country the surest basis of public happiness.

George Washington, address to Congress, 8 January 1790

Stereotypes abound. Ethnic groups are stereotyped, the citizens of other nations and religions are stereotyped, the genders and s.e.xual preferences are stereotyped, people born in various times of the year are stereotyped (Sun-sign astrology), and occupations are stereotyped. The most generous interpretation ascribes it to a kind of intellectual laziness: instead of judging people on their individual merits and deficits, we concentrate on one or two bits of information about them, and then place them in a small number of previously constructed pigeonholes.

This saves the trouble of thinking, at the price in many cases of committing a profound injustice. It also shields the stereotyper from contact with the enormous variety of people, the multiplicity of ways of being human. Even if stereotyping were valid on average, it is bound to fail in many individual cases: human variation runs to bell-type curves. There's an average value of any quality, and smaller numbers of people running off in both extremes.

Some stereotyping is the result of not controlling the variables, of forgetting what other factors might be in play. For example, it used to be that there were almost no women in science. Many male scientists were vehement: this proved that women lacked the ability to do science. Temperamentally, it didn't fit them, it was too difficult, it required a kind of intelligence that women don't have, they're too emotional to be objective, can you think of any great women theoretical physicists?... and so on. Since then the barriers have come tumbling down. Today women populate most of the subdisciplines of science. In my own fields of astronomy and planetary studies, women have recently burst upon the scene, making discovery after discovery, and providing a desperately needed breath of fresh air.

So what data were they missing, all those famous male scientists of the 1950s and 1960s and earlier who had p.r.o.nounced so authoritatively on the intellectual deficiencies of women? Plainly, society was preventing women from entering science, and then criticizing them for it, confusing cause and effect: You want to be an astronomer, young woman? Sorry.

Why can't you? Because you're unsuited.

How do we know you're unsuited? Because women have never been astronomers.

Put so baldly, the case sounds absurd. But the contrivances of bias can be subtle. The despised group is rejected by spurious arguments, sometimes done with such confidence and contempt that many of us, including some of the victims themselves, fail to recognize it as self-serving sleight of hand.

Casual observers of meetings of sceptics, and those who glance at the list of CSICOP Fellows, have noted a great preponderance of men. Others claim disproportionate numbers of women among believers in astrology (horoscopes in most 'women's' but few 'men's' magazines), crystals, ESP and the like. Some commentators suggest that there is something peculiarly male about scepticism. It's hard-driving, compet.i.tive, confrontational, tough-minded - whereas women, they say, are more accepting, consensus-building, and uninterested in challenging conventional wisdom. But in my experience women scientists have just as finely honed sceptical senses as their male counterparts; that's just part of being a scientist. This criticism, if that's what it is, is presented to the world in the usual ragged disguise: if you discourage women from being sceptical and don't train them in scepticism, then sure enough you may find that many women aren't sceptical. Open the doors and let them in, and they're as sceptical as anybody else.

One of the stereotyped occupations is science. Scientists are nerds, socially inept, working on incomprehensible subjects that no normal person would find in any way interesting - even if he were willing to invest the time required, which, again, no sensible person would. 'Get a life,' you might want to tell them.

I asked for a fleshed-out contemporary characterization of science-nerds from an expert on eleven-year-olds of my acquaintance. I should stress that she is merely reporting, not necessarily endorsing, the conventional prejudices: Nerds wear their belts just under their rib cages. Their short-sleeve shirts are equipped with pocket protectors in which is displayed a formidable array of multicoloured pens and pencils. A programmable calculator is carried in a special belt holster. They all wear thick gla.s.ses with broken nose-pieces that have been repaired with Band-Aids. They are bereft of social skills, and oblivious or indifferent to the lack. When they laugh, what comes out is a snort. They jabber at each other in an incomprehensible language. They'll jump at the opportunity to work for extra credit in all cla.s.ses except gym. They look down on normal people, who in turn laugh at them. Most nerds have names like Norman. (The Norman Conquest involved a horde of high-belted, pocket-protected, calculator-carrying nerds with broken gla.s.ses invading England.) There are more boy nerds than girl nerds, but there are plenty of both. Nerds don't date. If you're a nerd you can't be cool. Also vice versa.

This of course is a stereotype. There are scientists who dress elegantly, who are devastatingly cool, who many people long to date, who do not carry concealed calculators to social events. Some you'd never guess were scientists if you invited them to your home.

But other scientists do match the stereotype, more or less. They're pretty socially inept. There may be, proportionately, many more nerds among scientists than among backhoe operators or fashion designers or traffic wardens. Perhaps scientists are more nerdish than bartenders or surgeons or short-order cooks. Why should this be? Maybe people untalented in getting along with others find a refuge in impersonal pursuits, particularly mathematics and the physical sciences. Maybe the serious study of difficult subjects requires so much time and dedication that very little is left over for learning more than the barest social niceties. Maybe it's a combination of both.

Like the mad-scientist image to which it's closely related, the nerd-scientist stereotype is pervasive in our society. What's wrong with a little good-natured fun at the expense of scientists? If, for whatever reason, people dislike the stereotypical scientist, they are less likely to support science. Why subsidize geeks to pursue their absurd and incomprehensible little projects? Well, we know the answer to that: science is supported because it provides spectacular benefits at all levels in society, as I have argued earlier in this book. So those who find nerds distasteful, but at the same time crave the products of science, face a kind of dilemma. A tempting resolution is to direct the activities of the scientists. Don't give them money to go off in weird directions; instead tell them what we need - this invention, or that process. Subsidize not the curiosity of the nerds, but what will benefit society. It seems simple enough.

The trouble is that ordering someone to go out and make a specific invention, even if price is no object, hardly guarantees that it gets done. There may be an underpinning of knowledge that's unavailable, without which no one will ever build the contrivance you have in mind. And the history of science shows that often you can't go after the underpinnings in a directed way, either. They may emerge out of the idle musings of some lonely young person off in the boondocks. They're ignored or rejected even by other scientists, sometimes until a new generation of scientists comes along. Urging major practical inventions while discouraging curiosity-driven research would be spectacularly counterproductive.

Suppose you are, by the Grace of G.o.d, Victoria, Queen of the United Kingdom of Great Britain and Ireland, and Defender of the Faith in the most prosperous and triumphant age of the British Empire. Your dominions stretch across the planet. Maps of the world are abundantly splashed with British pink. You preside over the world's leading technological power. The steam engine is perfected in Great Britain, largely by Scottish engineers, who provide technical expertise on the railways and steamships that bind up the Empire.

Suppose in the year 1860 you have a visionary idea, so daring it would have been rejected by Jules Verne's publisher. You want a machine that will carry your voice, as well as moving pictures of the glory of the Empire, into every home in the kingdom. What's more, the sounds and pictures must come not through conduits or wires, but somehow out of the air, so people at work and in the field can receive instantaneous inspirational offerings designed to insure loyalty and the work ethic. The Word of G.o.d could also be conveyed by the same contrivance. Other socially desirable applications would doubtless be found.

So with the Prime Minister's support, you convene the Cabinet, the Imperial General Staff, and the leading scientists and engineers of the Empire. You will allocate a million pounds, you tell them - big money in 1860. If they need more, just ask. You don't care how they do it; just get it done. Oh, yes, it's to be called the Westminster Project.

Probably there would be some useful inventions emerging out of such an endeavour - 'spin-off. There always are when you spend huge amounts of money on technology. But the Westminster Project would almost certainly fail. Why? Because the underlying science hadn't been done. By 1860 the telegraph was in existence. You could imagine at great expense telegraphy sets in every home, with people ditting and dahing messages out in Morse code. But that's not what the Queen asked for. She had radio and television in mind but they were far out of reach.

In the real world, the physics necessary to invent radio and television would come from a direction that no one could have predicted.

James Clerk Maxwell was born in Edinburgh, Scotland, in 1831. At age two he found that he could use a tin plate to bounce an image of the Sun off the furniture and make it dance against the walls. As his parents came running he cried out, 'It's the Sun! I got it with the tin plate!' In his boyhood, he was fascinated by bugs, grubs, rocks, flowers, lenses, machines. 'It was humiliating,' later recalled his Aunt Jane, 'to be asked so many questions one couldn't answer by a child like that.'

Naturally, by the time he got to school he was called 'Dafty' -not quite right in the head. He was an exceptionally handsome young man, but he dressed carelessly, for comfort rather than style, and his Scottish provincialisms in speech and conduct were a cause for derision, especially by the time he reached college. And he had peculiar interests.

Maxwell was a nerd. He fared little better with his teachers than with his fellow students. Here's a poignant couplet he wrote at the time: Ye years roll on, and haste the expected time When flogging boys shall be accounted crime. When flogging boys shall be accounted crime.

Many years later, in 1872, in his inaugural lecture as professor of experimental physics at Cambridge University, he alluded to the nerdish stereotype:

It is not so long ago since any man who devoted himself to geometry, or to any science requiring continued application, was looked upon as necessarily a misanthrope, who must have abandoned all human interests, and betaken himself to abstractions so far removed from all the world of life and action that he has become insensible alike to the attractions of pleasure and to the claims of duty.

I suspect that 'not so long ago' was Maxwell's way of recalling the experiences of his youth. He then went on to say,

In the present day, men of science are not looked upon with the same awe or with the same suspicion. They are supposed to be in league with the material spirit of the age, and to form a kind of advanced Radical party among men of learning.

We no longer live in a time of untrammelled optimism about the benefits of science and technology. We understand that there is a downside. Circ.u.mstances today are much closer to what Maxwell remembered from his childhood.

He made enormous contributions to astronomy and physics -from the conclusive demonstration that the rings of Saturn are composed of small particles, to the elastic properties of solids, to the disciplines now called the kinetic theory of gases and statistical mechanics. It was he who first showed that an enormous number of tiny molecules, moving on their own and incessantly colliding with each other and bouncing elastically, leads not to confusion, but to precise statistical laws. The properties of such a gas can be predicted and understood. (The bell-shaped curve that describes the speeds of molecules in a gas is now called the Maxwell-Boltzmann distribution.) He invented a mythical being, now 'Maxwell's demon', whose actions generated a paradox that took modern information theory and quantum mechanics to resolve.

The nature of light had been a mystery since antiquity. There were acrimonious learned debates on whether it was a particle or a wave. Popular definitions ran to the style, 'Light is darkness - lit up'. Maxwell's greatest contribution was his discovery that electricity and magnetism, of all things, join together to become light. The now conventional understanding of the electromagnetic spectrum - running in wavelength from gamma rays to X-rays to ultraviolet light to visible light to infrared light to radio waves - is due to Maxwell. So is radio, television and radar.

But Maxwell wasn't after any of this. He was interested in how electricity makes magnetism and vice versa. I want to describe what Maxwell did, but his historic accomplishment is highly mathematical. In a few pages, I can at best give you only a flavour. If you do not fully understand what I'm about to say, please bear with me. There's no way we can get a feeling for what Maxwell did without looking at a little mathematics.

Mesmer, the inventor of 'mesmerism', believed he had discovered a magnetic fluid, 'almost the same thing as the electric fluid', that permeated all things. On this matter as well, he was mistaken. We now know that there is no special magnetic fluid, and that all magnetism - including the power that resides in a bar or horseshoe magnet - is due to moving electricity. The Danish physicist Hans Christian Oersted had performed a little experiment in which electricity was made to flow down a wire and induce a nearby compa.s.s needle to waver and tremble. The wire and the compa.s.s were not in physical contact. The great English physicist Michael Faraday had done the complementary experiment: he made a magnetic force turn on and off and thereby generated a current of electricity in a nearby wire. Time-varying electricity had somehow reached out and generated magnetism, and time-varying magnetism had somehow reached out and generated electricity. This was called 'induction' and was deeply mysterious, close to magic.

Faraday proposed that the magnet had an invisible 'field' of force that extended into surrounding s.p.a.ce, stronger close to the magnet, weaker farther away. You could track the form of the field by placing tiny iron filings on a piece of paper and waving a magnet underneath. Likewise, your hair after a good combing on a low-humidity day generates an electric field which invisibly extends out from your head, and which can even make small pieces of paper move by themselves.

The electricity in a wire, we now know, is caused by submicroscopic electrical particles, called electrons, which respond to an electric field and move. The wires are made of materials like copper which have lots of free electrons -electrons not bound within atoms, but able to move. Unlike copper, though, most materials, say, wood, are not good conductors; they are instead insulators or 'dielectrics'. In them, comparatively few electrons are available to move in response to the impressed electric or magnetic field. Not much of a current is produced. Of course there's some movement or 'displacement' of electrons, and the bigger the electric field, the more displacement occurs.

Maxwell devised a way of writing what was known about electricity and magnetism in his time, a method of summarizing precisely all those experiments with wires and currents and magnets. Here they are, the four Maxwell equations for the behaviour of electricity and magnetism in matter: * E E = a/ = a/ * B B = = 0 0 x E E = - = - x B B = u = uJ + u + u

It takes a few years of university-level physics to understand these equations. They are written using a branch of mathematics called vector calculus. A vector, written in bold-face type, is any quant.i.ty with both a magnitude and a direction. Sixty miles an hour isn't a vector, but sixty miles an hour due north on Highway 1 is. E E and and B B represent the electric and magnetic fields. The triangle, called a nabla (because of its resemblance to a certain ancient Middle Eastern harp), expresses how the electric or magnetic fields vary in three-dimensional s.p.a.ce. The 'dot product' and the 'cross product' after the nablas are statements of two different kinds of spatial variation. represent the electric and magnetic fields. The triangle, called a nabla (because of its resemblance to a certain ancient Middle Eastern harp), expresses how the electric or magnetic fields vary in three-dimensional s.p.a.ce. The 'dot product' and the 'cross product' after the nablas are statements of two different kinds of spatial variation.

and represent the time variation, the rate of change of the electric and magnetic fields, J J stands for the electrical current. The lower-case Greek letter a (rho) represents the density of electrical charges, while stands for the electrical current. The lower-case Greek letter a (rho) represents the density of electrical charges, while 0 (p.r.o.nounced 'epsilon zero') and u (p.r.o.nounced 'epsilon zero') and u (p.r.o.nounced 'mu zero') are not variables, but properties of the substance (p.r.o.nounced 'mu zero') are not variables, but properties of the substance E E and and B B are measured in, and determined by experiment. In a vacuum, are measured in, and determined by experiment. In a vacuum, and u and u are constants of nature. are constants of nature.

Considering how many different quant.i.ties are being brought together in these equations, it's striking how simple they are. They could have gone on for pages, but they don't.

The first of the four Maxwell equations tells how an electric field due to electrical charges (electrons, for example) varies with distance (it gets weaker the farther away we go). But the greater the charge density (the more electrons, say, in a given s.p.a.ce), the stronger the field.

The second equation tells us that there's no comparable statement in magnetism, because Mesmer's magnetic 'charges' (or magnetic 'monopoles') do not exist: saw a magnet in half and you won't be holding an isolated 'north' pole and an isolated 'south' pole; each piece now has its own 'north' and 'south' pole.

The third equation tells us how a changing magnetic field induces an electric field.

The fourth describes the converse - how a changing electric field (or an electrical current) induces a magnetic field.

The four equations are essentially distillations of generations of laboratory experiments, mainly by French and British scientists. What I've described here vaguely and qualitatively, the equations describe exactly and quant.i.tatively.

Maxwell then asked himself a strange question: what would these equations look like in empty s.p.a.ce, in a vacuum, in a place where there were no electrical charges and no electrical currents? We might very well antic.i.p.ate no electric and no magnetic fields in a vacuum. Instead, he suggested that the right form of the Maxwell equations for the behaviour of electricity and magnetism in empty s.p.a.ce is this: