Stereotypes abound. Ethnic groups are stereotyped, the citizens of other nations and religions are stereotyped, the genders and sexual 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 pronounced 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, competitive, confrontational, toughminded - 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 glasses 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 classes 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 glasses 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. 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 reaming 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 God, 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 God 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 endeavor - '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 'Daffy' - 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."

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. Circumstances 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 compass needle to waver and tremble. The wire and the compass 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 space, 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:

V•B = 0

Vx E = - dB/dt

He set r equal to zero, indicating that there are no electrical charges. He also set j equal to zero, indicating that there are no electrical currents. But he didn't discard the last term in the fourth equation, m₀ e₀ dE/dt, the feeble displacement current in insulators.

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