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The Demon-Haunted World - Maxwell and the Nerds - Carl Sagan

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 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, 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 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 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 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 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.

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:

∇ * E = ρ/ε0
∇ * B = 0
∇ x E = -Ḃ
∇ x B = μ0j + μ0ε0Ė

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 quantity 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 and 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 space. The 'dot product' and the 'cross product' after the nablas are statements of two different kinds of spatial variation.

Ė and Ḃ represent the time variation, the rate of change of the electric and magnetic fields, J stands for the electrical current. The lower-case Greek letter ρ (rho) represents the density of electrical charges, while ε0 (pronounced 'epsilon zero') and μ (pronounced 'mu zero') are not variables, but properties of the substance E and B are measured in, and determined by experiment. In a vacuum, ε0 and μ are constants of nature.

Considering how many different quantities 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 space), 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 quantitatively.

Maxwell then asked himself a strange question: what would these equations look like in empty space, in a vacuum, in a place where there were no electrical charges and no electrical currents? We might very well anticipate 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 space is this:

∇ ⋅ E = 0
∇ ⋅ B = 0
∇ x E = -Ḃ
∇ x B = μ0ε0Ė

He set ρ 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, με0Ė feeble displacement current in insulators.

Why not? As you can see from the equations, Maxwell's intuition preserved the symmetry between the magnetic and electric fields. Even in a vacuum, in the total absence of electricity, or even matter, a changing magnetic field, he proposed, elicits an electric field and vice versa. The equations were to represent Nature, and Nature is, Maxwell believed, beautiful and elegant. (There was also another, more technical reason for preserving the displacement current in a vacuum, which we pass over here.) This essentially aesthetic judgement by a nerdish physicist, entirely unknown except to a few other academic scientists, has done more to shape our civilization than any ten recent presidents and prime ministers.

Briefly, the four Maxwell equations for a vacuum say (1) there are no electrical charges in a vacuum; (2) there are no magnetic monopoles in a vacuum; (3) a changing magnetic field generates an electrical field; and (4) vice versa.

When the equations were written down like this, Maxwell was readily able to show that E and B propagated through empty space as if they were waves. What's more, he could calculate the speed of the wave. It was just 1 divided by the square root of ε0 times μ. But ε0 and μ had been measured in the laboratory. When you plugged in the numbers you found that the electric and magnetic fields in a vacuum ought to propagate, astonishingly, at the same speed as had already been measured for light. The agreement was too close to be accidental. Suddenly, disconcertingly, electricity and magnetism were deeply implicated in the nature of light.

Since light now appeared to behave as waves and to derive from electric and magnetic fields, Maxwell called it electromagnetic. Those obscure experiments with batteries and wires had something to do with the brightness of the Sun, with how we see, with what light is. Ruminating on Maxwell's discovery many years later, Albert Einstein wrote, To few men in the world has such an experience been vouchsafed.'

Maxwell himself was baffled by the results. The vacuum seemed to act like a dielectric. He said that it can be 'electrically polarized'. Living in a mechanical age, Maxwell felt obliged to offer some kind of mechanical model for the propagation of an electromagnetic wave through a perfect vacuum. So he imagined space filled with a mysterious substance he called the aether, which supported and contained the time-varying electric and magnetic fields - something like a throbbing but invisible Jell-O permeating the Universe. The quivering of the aether was the reason that light travelled through it - just as water waves propagate through water and sound waves through air.

But it had to be very odd stuff, this ether, very thin, ghostly, almost incorporeal. The Sun and the Moon, the planets and the stars had to pass through it without being slowed down, without noticing. And yet it had to be stiff enough to support all these waves propagating at prodigious speed.

The word 'aether' is still, in a desultory fashion, in use - in English mainly in the adjective ethereal, residing in the aether. It has some of the same connotations as the more modern 'spacy' or 'spaced out'. When, in the early days of radio, they would say 'On the air', the aether is what they had in mind. (The Russian phrase is quite literally 'on the aether', v efir.) But of course radio readily travels through a vacuum, one of Maxwell's main results. It doesn't need air to propagate. The presence of air is, if anything, an impediment.

The whole idea of light and matter moving through the aether was to lead in another forty years to Einstein's Special Theory of Relativity, E = mc2, and a great deal else. Relativity, and experiments leading up to it, showed conclusively that there is no aether supporting the propagation of electromagnetic waves, as Einstein writes in the extract from his famous paper that I reproduced in Chapter 2. The wave goes by itself. The changing electric field generates a magnetic field; the changing magnetic field generates an electric field. They hold each other up, by their bootstraps.

Many physicists were deeply troubled by the demise of the 'luminiferous' ether. They had needed some mechanical model to make the whole notion of the propagation of light in a vacuum reasonable, plausible, understandable. But this is a crutch, a symptom of our difficulties in reconnoitring realms in which common sense no longer serves. The physicist Richard Feynman described it this way:

Today, we understand better that what counts are the equations themselves and not the model used to get them. We may only question whether the equations are true or false. This is answered by doing experiments, and untold numbers of experiments have confirmed Maxwell's equations. If we take away the scaffolding he used to build it, we find that Maxwell's beautiful edifice stands on its own.

But what are these time-varying electric and magnetic fields permeating all of space? What do Ė and Ḃ mean? We feel so much more comfortable with the idea of things touching and jiggling, pushing and pulling, rather than 'fields' magically moving objects at a distance, or mere mathematical abstractions. But, as Feynman pointed out, our sense that at least in everyday life we can rely on solid, sensible physical contact to explain, say, why the butter knife comes to you when you pick it up, is a misconception. What does it mean to have physical contact? What exactly is happening when you pick up a knife, or push a swing, or make a wave in a waterbed by pressing down on it periodically? When we investigate deeply, we find that there is no physical contact. Instead, the electrical charges on your hand are influencing the electrical charges on the knife or swing or waterbed, and vice versa. Despite everyday experience and common sense, even here, there is only the interaction of electric fields. Nothing is touching anything.

No physicist started out impatient with common-sense notions, eager to replace them with some mathematical abstraction that could be understood only by rarified theoretical physics. Instead, they began, as we all do, with comfortable, standard, common-sense notions. The trouble is that Nature does not comply. If we no longer insist on our notions of how Nature ought to behave, but instead stand before Nature with an open and receptive mind, we find that common sense often doesn't work. Why not? Because our notions, both hereditary and learned, of how Nature works were forged in the millions of years our ancestors were hunters and gatherers. In this case common sense is a faithless guide because no hunter-gatherer's life ever depended on understanding time-variable electric and magnetic fields. There were no evolutionary penalties for ignorance of Maxwell's equations. In our time it's different.

Maxwell's equations show that a rapidly varying electric field (making Ė large) ought to generate electromagnetic waves. In 1888 the German physicist Heinrich Hertz did the experiment and found that he had generated a new kind of radiation, radio waves. Seven years later, British scientists in Cambridge transmitted radio signals over a distance of a kilometre. By 1901, Guglielmo Marconi of Italy was using radio waves to communicate across the Atlantic Ocean.

The linking-up of the modern world economically, culturally and politically by broadcast towers, microwave relays and communication satellites traces directly back to Maxwell's judgement to include the displacement current in his vacuum equations. So does television, which imperfectly instructs and entertains us; radar, which may have been the decisive element in the Battle of Britain and in the Nazi defeat in World War Two (which I like to think of as 'Dafty', the boy who didn't fit in, reaching into the future and saving the descendants of his tormentors); the control and navigation of airplanes, ships and spacecraft; radio astronomy and the search for extraterrestrial intelligence; and significant aspects of the electrical power and microelectronics industries.

What's more, Faraday's and Maxwell's notion of fields has been enormously influential in understanding the atomic nucleus, quantum mechanics, and the fine structure of matter. His unification of electricity, magnetism and light into one coherent mathematical whole is the inspiration for subsequent attempts - some successful, some still in their rudimentary stages - to unify all aspects of the physical world, including gravity and nuclear forces, into one grand theory. Maxwell may fairly be said to have ushered in the age of modern physics.

Our current view of the silent world of Maxwell's varying electric and magnetic vectors is described by Richard Feynman in these words: Try to imagine what the electric and magnetic fields look like at present in the space of this lecture room. First of all, there is a steady magnetic field; it comes from the currents in the interior of the earth - that is, the earth's steady magnetic field. Then there are some irregular, nearly static electric fields produced perhaps by electric charges generated by friction as various people move about in their chairs and rub their coat sleeves against the chair arms. Then there are other magnetic fields produced by oscillating currents in the electrical wiring - fields which vary at a frequency of 60 cycles per second, in synchronism with the generator at Boulder Dam. But more interesting are the electric and magnetic fields varying at much higher frequencies. For instance, as light travels from window to floor and wall to wall, there are little wiggles of the electric and magnetic fields moving along at 186,000 miles per second. Then there are also infrared waves travelling from the warm foreheads to the cold blackboard. And we have forgotten the ultraviolet light, the X-rays, and the radiowaves travelling through the room.

Flying across the room are electromagnetic waves which carry music of a jazz band. There are waves modulated by a series of impulses representing pictures of events going on in other parts of the world, or of imaginary aspirins dissolving in imaginary stomachs. To demonstrate the reality of these waves it is only necessary to turn on electronic equipment that converts these waves into pictures and sounds.

If we go into further detail to analyze even the smallest wiggles, there are tiny electromagnetic waves that have come into the room from enormous distances. There are now tiny oscillations of the electric field, whose crests are separated by a distance of one foot, that have come from millions of miles away, transmitted to the earth from the Mariner [2] space craft which has just passed Venus. Its signals carry summaries of information it has picked up about the planets (information obtained from electromagnetic waves that travelled from the planet to the space craft).

There are very tiny wiggles of the electric and magnetic fields that are waves which originated billions of light years away - from galaxies in the remotest corners of the universe. That this is true has been found by 'filling the room with wires' - by building antennas as large as this room. Such radiowaves have been detected from places in space beyond the range of the greatest optical telescopes. Even they, the optical telescopes, are simply gatherers of electromagnetic waves. What we call the stars are only inferences, inferences drawn from the only physical reality we have yet gotten from them - from a careful study of the unendingly complex undulations of the electric and magnetic fields reaching us on earth.

There is, of course, more: the fields produced by lightning miles away, the fields of the charged cosmic ray particles as they zip through the room, and more, and more. What a complicated thing is the electric field in the space around you!

If Queen Victoria had ever called an urgent meeting of her counsellors, and ordered them to invent the equivalent of radio and television, it is unlikely that any of them would have imagined the path to lead through the experiments of Ampere, Biot, Oersted and Faraday, four equations of vector calculus, and the judgement to preserve the displacement current in a vacuum. They would, I think, have gotten nowhere. Meanwhile, on his own, driven only by curiosity, costing the government almost nothing, himself unaware that he was laying the ground for the Westminster Project, 'Dafty' was scribbling away. It's doubtful whether the self-effacing, unsociable Mr Maxwell would even have been thought of to perform such a study. If he had, probably the government would have been telling him what to think about and what not, impeding rather than inducing his great discovery.

Late in life, Maxwell did have one interview with Queen Victoria. He worried about it beforehand - essentially about his ability to communicate science to a non-expert - but the Queen was distracted and the interview was short. Like the four other greatest British scientists of recent history, Michael Faraday, Charles Darwin, P.A.M. Dirac and Francis Crick, Maxwell was never knighted (although Lyell, Kelvin, J.J. Thomson, Rutherford, Eddington and Hoyle in the next tier were). In Maxwell's case, there was not even the excuse that he might hold opinions at variance with the Church of England: he was an absolutely conventional Christian for his time, more devout than most. Maybe it was his nerdishness.

The communications media - the instruments of education and entertainment that James Clerk Maxwell made possible - have never, so far as I know, offered even a mini-series on the life and thought of their benefactor and founder. By contrast, think of how difficult it is to grow up in America without television teaching you about, say, the life and times of Davy Crockett or Billy the Kid or Al Capone.

Maxwell married young, but the bond seems to have been passionless as well as childless. His excitement was reserved for science. This founder of the modern age died in 1879 at the age of 47. While he is almost forgotten in popular culture, radar astronomers who map other worlds have remembered: the greatest mountain range on Venus, discovered by sending radio waves from Earth, bouncing them off Venus, and detecting the faint echoes, is named after him.

Less than a century after Maxwell's prediction of radio waves, the first quest was initiated for signals from possible civilizations on planets of other stars. Since then there have been a number of searches, some of which I referred to earlier, for the time-varying electric and magnetic fields crossing the vast interstellar distances from possible other intelligences - biologically very different from us - who had also benefited sometime in their histories from the insights of local counterparts of James Clerk Maxwell.

In October 1992, in the Mojave Desert, and in a Puerto Rican karst valley, we initiated by far the most promising, powerful and comprehensive search for extraterrestrial intelligence (SETI). For the first time NASA would organize and operate the programme. The entire sky would be examined over a ten-year period with unprecedented sensitivity and frequency range. If, on a planet of any of the 400 billion other stars that make up the Milky Way galaxy, anyone had been sending us a radio message, we might have had a pretty fair chance of hearing them.

Just one year later, Congress pulled the plug. SETI was not of pressing importance; its interest was limited; it was too expensive. But every civilization in human history has devoted some of its resources to investigating deep questions about the Universe, and it's hard to think of a deeper one than whether we are alone. Even if we never decrypted the message contents, the receipt of such a signal would transform our view of the Universe and ourselves. And if we could understand the message from an advanced technical civilization, the practical benefits might be unprecedented. Far from being narrowly based, the SETI programme, strongly supported by the scientific community, is also embedded in popular culture. The fascination with this enterprise is broad and enduring, and for very good reason. And far from being too expensive, the programme would have cost about one attack helicopter per year.

I wonder why those members of Congress concerned about price tags don't devote greater attention to the Department of Defense, which, with the Soviet Union gone and the Cold War over, still spends, when all costs are tallied, well over $300 billion a year. (And elsewhere in government there are many programmes that amount to welfare for the well-to-do.) Perhaps our descendants will look back on our time and marvel at us, possessed of the technology to detect other beings, but closing our ears because we insisted on spending the national wealth to protect us from an enemy that no longer exists.*

[* The SETI programme was briefly resurrected, using $7 million in private contributions, in 1995 under the appropriate name Project Phoenix.] David Goodstein, a physicist at Cal Tech, notes that science has been growing nearly exponentially for centuries and that it cannot continue such growth, because then everybody on the planet, would have to be a scientist, and then the growth would have to stop. He speculates that for this reason, and not because of any fundamental disaffection from science, the growth in funding of science has slowed measurably in the last few decades.

Nevertheless, I'm worried about how research funds are distributed. I'm worried that cancelling government funds for SETI is part of a trend. The government has been pressuring the National Science Foundation to move away from basic scientific research and to support technology, engineering, applications. Congress is suggesting doing away with the US Geological Survey, and slashing support for study of the Earth's fragile environment. NASA support for research and analysis of data already obtained is increasingly constrained. Many young scientists are not only unable to find grants to support their research; they are unable to find jobs.

Industrial research and development funded by American companies has slowed across the board in recent years. Government funding for research and development has declined in the same period. (Only military research and development increased in the decade of the 1980s.) In annual expenditures, Japan is now the world's leading investor in civilian research and development. In such fields as computers, telecommunications equipment, aerospace, machine tools, robotics, and scientific precision equipment, the US share of global exports has been declining, while the Japanese share has been increasing. In that same period the United States lost its lead to Japan in most semiconductor technologies. It experiences severe declines in market share in colour TVs, VCRs, phonographs, telephone sets and machine tools.

Basic research is where scientists are free to pursue their curiosity and interrogate Nature, not with any short-term practical end in view, but to seek knowledge for its own sake. Scientists of course have a vested interest in basic research. It's what they like to do, in many cases why they became scientists in the first place. But it is in society's interest to support such research. This is how the major discoveries that benefit humanity are largely made. Whether a few grand and ambitious scientific projects are a better investment than a larger number of small programmes is a worthwhile question.

We are rarely smart enough to set about on purpose making the discoveries that will drive our economy and safeguard our lives. Often, we lack the fundamental research. Instead, we pursue a broad range of investigations of Nature, and applications we never dreamed of emerge. Not always, of course. But often enough.

Giving money to someone like Maxwell might have seemed the most absurd encouragement of mere 'curiosity-driven' science, and an imprudent judgement for practical legislators. Why grant money now, so nerdish scientists talking incomprehensible gibberish can indulge their hobbies, when there are urgent unmet national needs? From this point of view it's easy to understand the contention that science is just another lobby, another pressure group anxious to keep the grant money rolling in so the scientists don't ever have to do a hard day's work or meet a payroll.

Maxwell wasn't thinking of radio, radar and television when he first scratched out the fundamental equations of electromagnet-ism; Newton wasn't dreaming of space flight or communications satellites when he first understood the motion of the Moon; Roentgen wasn't contemplating medical diagnosis when he investigated a penetrating radiation so mysterious he called it 'X-rays'; Curie wasn't thinking of cancer therapy when she painstakingly extracted minute amounts of radium from tons of pitchblende; Fleming wasn't planning on saving the lives of millions with antibiotics when he noticed a circle free of bacteria around a growth of mould; Watson and Crick weren't imagining the cure of genetic diseases when they puzzled over the X-ray diffractometry of DNA; Rowland and Molina weren't planning to implicate CFCs in ozone depletion when they began studying the role of halogens in stratospheric photochemistry.

Members of Congress and other political leaders have from time to time found it irresistible to poke fun at seemingly obscure scientific research proposals that the government is asked to fund. Even as bright a senator as William Proxmire, a Harvard graduate, was given to making episodic 'Golden Fleece' awards, many commemorating ostensibly useless scientific projects including SETI. I imagine the same spirit in previous governments - a Mr Fleming wishes to study bugs in smelly cheese; a Polish woman wishes to sift through tons of Central African ore to find minute quantities of a substance she says will glow in the dark; a Mr Kepler wants to hear the songs the planets sing.

These discoveries and a multitude of others that grace and characterize our time, to some of which our very lives are beholden, were made ultimately by scientists given the opportunity to explore what in their opinion, under the scrutiny of their peers, were basic questions in Nature. Industrial applications, in which Japan in the last two decades has done so well, are excellent. But applications of what? Fundamental research, research into the heart of Nature, is the means by which we acquire the new knowledge that gets applied.

Scientists have an obligation, especially when asking for big money, to explain with great clarity and honesty what they're after. The Superconducting Supercollider (SSC) would have been the preeminent instrument on the planet for probing the fine structure of matter and the nature of the early Universe. Its price tag was $10 to $15 billion. It was cancelled by Congress in 1993 after about $2 billion had been spent - a worst of both worlds outcome. But this debate was not, I think, mainly about declining interest in the support of science. Few in Congress understood what modem high energy accelerators are for. They are not for weapons. They have no practical applications. They are for something that is, worrisomely from the point of view of many, called 'the theory of everything'. Explanations that involve entities called quarks, charm, flavour, colour, etc. sound as if physicists are being cute. The whole thing has an aura, in the view of at least some Congresspeople I've talked to, of 'nerds gone wild' - which I suppose is an uncharitable way of describing curiosity-based science. No one asked to pay for this had the foggiest idea of what a Higgs boson is. I've read some of the material intended to justify the SSC. At the very end, some of it wasn't too bad, but there was nothing that really addressed what the project was about on a level accessible to bright but sceptical non-physicists. If physicists are asking for $10 or $15 billion to build a machine that has no practical value, at the very least they should make an extremely serious effort, with dazzling graphics, metaphors and capable use of the English language, to justify their proposal. More than financial mismanagement, budgetary constraints and political incompetence, I think this is the key to the failure of the SSC.

There is a growing free-market view of human knowledge, according to which basic research should compete without government support with all the other institutions and claimants in society. If they couldn't have relied on government support, and had to compete in the free-market economy of their day, it's unlikely that any of the scientists on my list would have been able to do their groundbreaking research. And the cost of basic research is substantially greater than it was in Maxwell's day -both theoretical and, especially, experimental.

But that aside, would free-market forces be adequate to support basic research? Only about ten per cent of meritorious research proposals in medicine are funded today. More money is spent on quack medicine than on all of medical research. What would it be like if government opted out of medical research?

A necessary aspect of basic research is that its applications lie in the future, sometimes decades or even centuries ahead. What's more, no one knows which aspects of basic research will have practical value and which will not. If scientists cannot make such predictions, is it likely that politicians or industrialists can? If free-market forces are focused only towards short-term profit - as they certainly mainly are in an America with steep declines in corporate research - is not this solution tantamount to abandoning basic research?

Cutting off fundamental, curiosity-driven science is like eating the seed corn. We may have a little more to eat next winter, but what will we plant so we and our children will have enough to get through the winters to come?

Of course there are many pressing problems facing our nation and our species. But reducing basic scientific research is not the way to solve them. Scientists do not constitute a voting bloc. They have no effective lobby. However, much of their work is in everybody's interest. Backing off from fundamental research constitutes a failure of nerve, of imagination and of that vision thing that we still don't seem to have a handle on. It might strike one of those hypothetical extraterrestrials that we were planning not to have a future.

Of course we need literacy, education, jobs, adequate medical care and defence, protection of the environment, security in our old age, a balanced budget, and a host of other matters. But we are a rich society. Can't we also nurture the Maxwells of our time? To take one symbolic example, is it really true that we can't afford one attack helicopter's worth of seed corn to listen to the stars?

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