The sources of degradation may differ from world to world, or desert to desert, or epoch to epoch. But if you know what they are you can determine a great deal from how crisp or blurred the crater is. If insect or other animal tracks are superposed on the hoofprints, this also argues against their freshness. The subsurface moisture content of the soil and the rate at which it dries out after being exposed by a hoof determine how crumbly the crater walls are. All these matters are closely studied by the IKung.

The galloping herd hates the hot Sun. The animals will use whatever shade they can find. They will alter course to take brief advantage of the shade from a stand of trees. But where the shadow is is depends on the time of day, because the Sun is moving across the sky. In the morning, as the Sun is rising in the east, shadows are cast west of the trees. Later in the afternoon, as the Sun is setting toward the west, shadows are cast to the east. From the swerve of the tracks, it's possible to tell how long ago the animals pa.s.sed. This calculation will be different in different seasons of the year. So the hunters must carry in their heads a kind of astronomical calendar predicting the apparent solar motion. depends on the time of day, because the Sun is moving across the sky. In the morning, as the Sun is rising in the east, shadows are cast west of the trees. Later in the afternoon, as the Sun is setting toward the west, shadows are cast to the east. From the swerve of the tracks, it's possible to tell how long ago the animals pa.s.sed. This calculation will be different in different seasons of the year. So the hunters must carry in their heads a kind of astronomical calendar predicting the apparent solar motion.

To me, all of these formidable forensic tracking skills are science in action.

Not only are hunter-gatherers expert in the tracks of other animals; they also know human tracks very well. Every member of the band is recognizable by his or her footprints; they are as familiar as their faces. Laurens van der Post recounts, [M]any miles from home and separated from the rest, Nxou and I, on the track of a wounded buck, suddenly found another set of prints and spoor joining our own. He gave a deep grunt of satisfaction and said it was Bauxhau's footmarks made not many minutes before. He declared Bauxhau was running fast and that we would soon see him and the animal. We topped the dune in front of us and there was Bauxhau, already skinning the animal.

Or Richard Lee, also among the IKung San, relates how when briefly examining some tracks a hunter commented, 'Oh, look, Tunu is here with his brother-in-law. But where is his son?'

Is this really science? Does every tracker in the course of his training sit on his haunches for hours, following the slow degradation of an eland hoofprint? When the anthropologist asks this question, the answer given is that hunters have always used such methods. They observed their fathers and other accomplished hunters during their apprenticeships. They learned by imitation. The general principles were pa.s.sed down from generation to generation. The local variations - wind speed, soil moisture - are updated as needed in each generation, or seasonally, or day-by-day.

But modern scientists do just the same. Every time we try to judge the age of a crater on the Moon or Mercury or Triton by its degree of erosion, we do not perform the calculation from scratch. We dust off a certain scientific paper and read the tried-and-true numbers that have been set down perhaps as much as a generation earlier. Physicists do not derive Maxwell's equations or quantum mechanics from scratch. They try to understand the principles and the mathematics, they observe its utility, they note how Nature follows these rules, and they take these sciences to heart, making them their own.

Yet someone had to figure out all these tracking protocols for the first time, perhaps some palaeolithic genius, or more likely a succession of geniuses in widely separated times and places. There is no hint in the IKung tracking protocols of magical methods -examining the stars the night before or the entrails of an animal, or casting dice, or interpreting dreams, or conjuring demons, or any of the myriad other spurious claims to knowledge that humans have intermittently entertained. Here there's a specific, well-defined question: which way did the prey go and what are its characteristics? You need a precise answer that magic and divination simply do not provide, or at least not often enough to stave off starvation. Instead hunter-gatherers - who are not very superst.i.tious in their everyday life, except during trance dances around the fire and under the influence of mild euphoriants - are practical, workaday, motivated, social, and often very cheerful. They employ skills winnowed from past successes and failures.

Scientific thinking has almost certainly been with us from the beginning. You can even see it in chimpanzees when tracking on patrol of the frontiers of their territory, or when preparing a reed to insert into the termite mound to extract a modest but much-needed source of protein. The development of tracking skills delivers a powerful evolutionary selective advantage. Those groups unable to figure it out get less protein and leave fewer offspring. Those with a scientific bent, those able patiently to observe, those with a penchant for figuring out acquire more food, especially more protein, and live in more varied habitats; they and their hereditary lines prosper. The same is true, for instance, of Polynesian seafaring skills. A scientific bent brings tangible rewards.

The other princ.i.p.al food-garnering activity of pre-agrarian societies is foraging. To forage, you must know the properties of many plants, and you must certainly be able to distinguish one from another. Botanists and anthropologists have repeatedly found that all over the world hunter-gatherer peoples have distinguished the various plant species with the precision of western taxonomists. They have mentally mapped their territory with the finesse of cartographers. Again, all this is a precondition for survival.

So the claim that, just as children are not developmentally ready for certain concepts in mathematics or logic, so 'primitive' peoples are not intellectually able to grasp science and technology, is nonsense. This vestige of colonialism and racism is belied by the everyday activities of people living with no fixed abode and almost no possessions, the few remaining hunter-gatherers - the custodians of our deep past.

Of Cromer's criteria for 'objective thinking', we can certainly find in hunter-gatherer peoples vigorous and substantive debate, direct partic.i.p.atory democracy, wide-ranging travel, no priests, and the persistence of these factors not for 1,000 but for 300,000 years or more. By his criteria hunter-gatherers ought ought to have science. I think they do. Or did. to have science. I think they do. Or did.

What Ionia and ancient Greece provided is not so much inventions or technology or engineering, but the idea of systematic inquiry, the notion that laws of Nature, rather than capricious G.o.ds, govern the world. Water, air, earth and fire all had their turn as candidate 'explanations' of the nature and origin of the world. Each such explanation - identified with a different pre-Socratic philosopher - was deeply flawed in its details. But the mode of explanation, an alternative to divine intervention, was productive and new. Likewise, in the history of ancient Greece, we can see nearly mode of explanation, an alternative to divine intervention, was productive and new. Likewise, in the history of ancient Greece, we can see nearly all all significant events driven by the caprice of the G.o.ds in Homer, only a few events in Herodotus, and essentially none at all in Thucydides. In a few hundred years, history pa.s.sed from G.o.d-driven to human-driven. significant events driven by the caprice of the G.o.ds in Homer, only a few events in Herodotus, and essentially none at all in Thucydides. In a few hundred years, history pa.s.sed from G.o.d-driven to human-driven.

Something akin to laws of Nature were once glimpsed in a determinedly polytheistic society, in which some scholars toyed with a form of atheism. This approach of the pre-Socratics was, beginning in about the fourth century BC, quenched by Plato, Aristotle and then Christian theologians. If the skein of historical causality had been different - if the brilliant guesses of the atomists on the nature of matter, the plurality of worlds, the vastness of s.p.a.ce and time had been treasured and built upon, if the innovative technology of Archimedes had been taught and emulated, if the notion of invariable laws of Nature that humans must seek out and understand had been widely propagated - I wonder what kind of world we would live in now.

I don't think science is hard to teach because humans aren't ready for it, or because it arose only through a fluke, or because, by and large, we don't have the brainpower to grapple with it. Instead, the enormous zest for science that I see in first-graders and the lesson from the remnant hunter-gatherers both speak eloquently: a proclivity for science is embedded deeply within us, in all times, places and cultures. It has been the means for our survival. It is our birthright. When, through indifference, inattention, incompetence, or fear of scepticism, we discourage children from science, we are disenfranchising them, taking from them the tools needed to manage their future.

19.

No Such Thing as a Dumb Question

So we keep asking, over and over, Until a handful of earth Stops our mouths- But is that an answer?

Heinrich Heine, 'Lazarus' (1854)

In East Africa, in the records of the rocks dating back to about two million years ago, you can find a sequence of worked tools that our ancestors designed and executed. Their lives depended on making and using these tools. This was, of course, Early Stone Age technology. Over time, specially fashioned stones were used for stabbing, chipping, flaking, cutting, carving. Although there are many ways of making stone tools, what is remarkable is that in a given site for enormous periods of time the tools were made in the same way - which means that there must have been educational inst.i.tutions hundreds of thousands of years ago, even if it was mainly an apprenticeship system. While it's easy to exaggerate the similarities, it's also easy to imagine the equivalent of professors and students in loincloths, laboratory courses, examinations, failing grades, graduation ceremonies and postgraduate education.

When the training is unchanged for immense periods of time, traditions are pa.s.sed on intact to the next generation. But when what needs to be learned changes quickly, especially in the course of a single generation, it becomes much harder to know what to teach and how to teach it. Then, students complain about relevance; respect for their elders diminishes. Teachers despair at how educational standards have deteriorated, and how lackadaisical students have become. In a world in transition, students and teachers both need to teach themselves one essential skill -learning how to learn.

Except for children (who don't know enough not to ask the important questions), few of us spend much time wondering why Nature is the way it is; where the Cosmos came from, or whether it was always here; if time will one day flow backward, and effects precede causes; or whether there are ultimate limits to what humans can know. There are even children, and I have met some of them, who want to know what a black hole looks like; what is the smallest piece of matter; why we remember the past and not the future; and why there is is a Universe. a Universe.

Every now and then, I'm lucky enough to teach a kindergarten or first-grade cla.s.s. Many of these children are natural-born scientists - although heavy on the wonder side and light on scepticism. They're curious, intellectually vigorous. Provocative and insightful questions bubble out of them. They exhibit enormous enthusiasm. I'm asked follow-up questions. They've never heard of the notion of a 'dumb question'.

But when I talk to high school seniors, I find something different. They memorize 'facts'. By and large, though, the joy of discovery, the life behind those facts, has gone out of them. They've lost much of the wonder, and gained very little scepticism. They're worried about asking 'dumb' questions; they're willing to accept inadequate answers; they don't pose follow-up questions; the room is awash with sidelong glances to judge, second-by-second, the approval of their peers. They come to cla.s.s with their questions written out on pieces of paper, which they surrept.i.tiously examine, waiting their turn and oblivious of whatever discussion their peers are at this moment engaged in.

Something has happened between first and twelfth grade, and it's not just p.u.b.erty. I'd guess that it's partly peer pressure not not to excel (except in sports); partly that the society teaches short-term gratification; partly the impression that science or mathematics won't buy you a sports car; partly that so little is expected of students; and partly that there are few rewards or role models for intelligent discussion of science and technology - or even for learning for its own sake. Those few who remain interested are vilified as 'nerds' or 'geeks' or 'grinds'. to excel (except in sports); partly that the society teaches short-term gratification; partly the impression that science or mathematics won't buy you a sports car; partly that so little is expected of students; and partly that there are few rewards or role models for intelligent discussion of science and technology - or even for learning for its own sake. Those few who remain interested are vilified as 'nerds' or 'geeks' or 'grinds'.

But there's something else: I find many adults are put off when young children pose scientific questions. Why is the Moon round? the children ask. Why is gra.s.s green? What is a dream? How deep can you dig a hole? When is the world's birthday? Why do we have toes? Too many teachers and parents answer with irritation or ridicule, or quickly move on to something else: 'What did you expect the Moon to be, square?' Children soon recognize that somehow this kind of question annoys the grown-ups. A few more experiences like it, and another child has been lost to science. Why adults should pretend to omniscience before 6-year-olds, I can't for the life of me understand. What's wrong with admitting that we don't know something? Is our self-esteem so fragile?

What's more, many of these questions go to deep issues in science, a few of which are not yet fully resolved. Why the Moon is round has to do with the fact that gravity is a central force pulling towards the middle of any world, and with how strong rocks are. Gra.s.s is green because of the pigment chlorophyll, of course - we've all had that drummed into us by high schools - but why do plants have chlorophyll? It seems foolish, since the Sun puts out its peak energy in the yellow and green part of the spectrum. Why should plants all over the world reject sunlight in its most abundant wavelengths? Maybe it's a frozen accident from the ancient history of life on Earth. But there's something we still don't understand about why gra.s.s is green.

There are many better responses than making the child feel that asking deep questions const.i.tutes a social blunder. If we have an idea of the answer, we can try to explain. Even an incomplete attempt const.i.tutes a rea.s.surance and encouragement. If we have no idea of the answer, we can go to the encyclopedia. If we don't have an encyclopedia, we can take the child to the library. Or we might say: 'I don't know the answer. Maybe no one knows. Maybe when you grow up, you'll be the first person to find out.'

There are naive questions, tedious questions, ill-phrased questions, questions put after inadequate self-criticism. But every question is a cry to understand the world.* There is no such thing as a dumb question.

[* I'm excluding the fusillade of 'whys' that two-year-olds sometimes pelt their parents with - perhaps in an effort to control adult behaviour.]

Bright, curious children are a national and world resource. They need to be cared for, cherished, and encouraged. But mere encouragement isn't enough. We must also give them the essential tools to think with.

'It's Official', reads one newspaper headline: 'We Stink in Science'. In tests of average 17-year-olds in many world regions, the US ranked dead last in algebra. On identical tests, the US kids averaged 43% and their j.a.panese counterparts 78%. In my book, 78% is pretty good - it corresponds to a C+, or maybe even a B-; 43% is an F. In a chemistry test, students in only two of 13 nations did worse than the US. Britain, Singapore and Hong Kong were so high they were almost off-scale, and 25% of Canadian 18-year-olds knew just as much chemistry as a select 1% of American high school seniors (in their second chemistry course, and most of them in 'advanced' placement programmes). The best of 20 fifth-grade cla.s.srooms in Minneapolis was outpaced by every one of 20 cla.s.srooms in Sendai, j.a.pan, and 19 out of 20 in Taipei, Taiwan. South Korean students were far ahead of American students in all aspects of mathematics and science, and 13-year-olds in British Columbia (in western Canada) outpaced their US counterparts across the board (in some areas they did better than the Koreans). Of the US kids, 22% say they dislike school; only 8% of the Koreans do. Yet two-thirds of the Americans, but only a quarter of the Koreans, say they are 'good at mathematics'.

Such dismal trends for average students in the United States are occasionally offset by the performance of outstanding students. In 1994, American students at the International Mathematical Olympiad in Hong Kong achieved an unprecedented perfect score, defeating 360 other students from 68 nations in algebra, geometry and number theory. One of them, 17-year-old Jeremy Bern, commented 'Maths problems are logic puzzles. There's no routine - it's all very creative and artistic.' But here I'm concerned not with producing a new generation of first-rate scientists and mathematicians, but a scientifically literate public.

Sixty-three per cent of American adults are unaware that the last dinosaur died before the first human arose; 75 per cent do not know that antibiotics kill bacteria but not viruses; 57 per cent do not know that 'electrons are smaller than atoms'. Polls show that something like half of American adults do not know that the Earth goes around the Sun and takes a year to do it. I can find in my undergraduate cla.s.ses at Cornell University bright students who do not know that the stars rise and set at night, or even that the Sun is a star.

Because of science fiction, the educational system, NASA, and the role that science plays in society, Americans have much more exposure to the Copernican insight than does the average human. A 1993 poll by the China a.s.sociation of Science and Technology shows that, as in America, no more than half the people in China know that the Earth revolves around the Sun once a year. It may very well be, then, that more than four and a half centuries after Copernicus, most people on Earth still think, in their heart of hearts, that our planet sits immobile at the centre of the Universe, and that we are profoundly 'special'.

These are typical questions in 'scientific literacy'. The results are appalling. But what do they measure? The memorization of authoritative p.r.o.nouncements. What they should should be asking is be asking is how we know - how we know - that antibiotics discriminate between microbes, that electrons are 'smaller' than atoms, that the Sun is a star which the Earth orbits once a year. Such questions are a much truer measure of public understanding of science, and the results of such tests would doubtless be more disheartening still. that antibiotics discriminate between microbes, that electrons are 'smaller' than atoms, that the Sun is a star which the Earth orbits once a year. Such questions are a much truer measure of public understanding of science, and the results of such tests would doubtless be more disheartening still.

If you accept the literal truth of every word of the Bible, then the Earth must be flat. The same is true for the Qu'ran. p.r.o.nouncing the Earth round then means you're an atheist. In 1993, the supreme religious authority of Saudi Arabia, Sheik Abdel-Aziz Ibn Baaz, issued an edict, or fatwa, declaring that the world is flat. Anyone of the round persuasion does not believe in G.o.d and should be punished. Among many ironies, the lucid evidence that the Earth is a sphere, acc.u.mulated by the second-century Graeco-Egyptian astronomer Claudius Ptolemaeus, was transmitted to the west by astronomers who were Muslim and Arab. In the ninth century, they named Ptolemy's book in which the sphericity of the Earth is demonstrated, the Almagest, Almagest, 'The Greatest'. 'The Greatest'.

I meet many people offended by evolution, who pa.s.sionately prefer to be the personal handicraft of G.o.d than to arise by blind physical and chemical forces over aeons from slime. They also tend to be less than a.s.siduous in exposing themselves to the evidence. Evidence has little to do with it: what they wish to be true, they believe is is true. Only nine per cent of Americans accept the central finding of modern biology that human beings (and all the other species) have slowly evolved by natural processes from a succession of more ancient beings with no divine intervention needed along the way. (When asked merely if they accept evolution, 45 per cent of Americans say yes. The figure is 70 per cent in China.) When the movie true. Only nine per cent of Americans accept the central finding of modern biology that human beings (and all the other species) have slowly evolved by natural processes from a succession of more ancient beings with no divine intervention needed along the way. (When asked merely if they accept evolution, 45 per cent of Americans say yes. The figure is 70 per cent in China.) When the movie Jura.s.sic Park Jura.s.sic Park was shown in Israel, it was condemned by some Orthodox rabbis because it accepted evolution and because it taught that dinosaurs lived a hundred million years ago, when, as is plainly stated at every Rosh Hashanah and every Jewish wedding ceremony, the Universe is less than 6,000 years old. The clearest evidence of our evolution can be found in our genes. But evolution is still being fought, ironically by those whose own DNA proclaims it - in the schools, in the courts, in textbook publishing houses, and on the question of just how much pain we can inflict on other animals without crossing some ethical threshold. was shown in Israel, it was condemned by some Orthodox rabbis because it accepted evolution and because it taught that dinosaurs lived a hundred million years ago, when, as is plainly stated at every Rosh Hashanah and every Jewish wedding ceremony, the Universe is less than 6,000 years old. The clearest evidence of our evolution can be found in our genes. But evolution is still being fought, ironically by those whose own DNA proclaims it - in the schools, in the courts, in textbook publishing houses, and on the question of just how much pain we can inflict on other animals without crossing some ethical threshold.

During the Great Depression in America, teachers enjoyed job security, good salaries, respectability. Teaching was an admired profession, partly because learning was widely recognized as the road out of poverty. Little of that is true today. And so science (and other) teaching is too often incompetently or uninspiringly done, its pract.i.tioners, astonishingly, having little or no training in their subjects, impatient with the method and in a hurry to get to the findings of science - and sometimes themselves unable to distinguish science from pseudoscience. Those who do have the training often get higher-paying jobs elsewhere.

Children need hands-on experience with the experimental method rather than just reading about science in a book. We can be told about oxidation of wax as the explanation of the candle flame. But we have a much more vivid sense of what's going on if we witness the candle burning briefly in a bell jar until the carbon dioxide produced by the burning surrounds the wick, blocks access to oxygen, and the flame flickers and dies. We can be taught about mitochondria in cells, how they mediate the oxidation of food like the flame burning the wax, but it's another thing altogether to see them under the microscope. We may be told that oxygen is necessary for the life of some organisms and not others. But we begin really to understand when we test the proposition in a bell jar fully depleted of oxygen. What does oxygen do for us? Why do we die without it? Where does the oxygen in the air come from? How secure is the supply?

Experiment and the scientific method can be taught in many matters other than science. Daniel Kunitz is a friend of mine from college. He's spent his life as an innovative junior and senior high school social sciences teacher. Want the students to understand the Const.i.tution of the United States? You could have them read it, Article by Article, and then discuss it in cla.s.s but, sadly, this will put most of them to sleep. Or you could try the Kunitz method: you forbid the students to read the Const.i.tution. Instead, you a.s.sign them, two for each state, to attend a Const.i.tutional Convention. You brief each of the thirteen teams in detail on the particular interests of their state and region. The South Carolina delegation, say, would be told of the primacy of cotton, the necessity and morality of the slave trade, the danger posed by the industrial north, and so on. The thirteen delegations a.s.semble, and with a little faculty guidance, but mainly on their own, over some weeks write a const.i.tution. Then Then they read the real Const.i.tution. The students have reserved war-making powers to the President. The delegates of 1787 a.s.signed them to Congress. Why? The students have freed the slaves. The original Const.i.tutional Convention did not. Why? This takes more preparation by the teachers and more work by the students, but the experience is unforgettable. It's hard not to think that the nations of the Earth would be in better shape if every citizen went through a comparable experience. they read the real Const.i.tution. The students have reserved war-making powers to the President. The delegates of 1787 a.s.signed them to Congress. Why? The students have freed the slaves. The original Const.i.tutional Convention did not. Why? This takes more preparation by the teachers and more work by the students, but the experience is unforgettable. It's hard not to think that the nations of the Earth would be in better shape if every citizen went through a comparable experience.

We need more money for teachers' training and salaries, and for laboratories. But all across America, school-bond issues are regularly voted down. No one suggests that property taxes be used to provide for the military budget, or for agriculture subsidies, or for cleaning up toxic wastes. Why just education? Why not support it from general taxes on the local and state levels? What about a special education tax for those industries with special needs for technically trained workers?

American schoolchildren don't do enough schoolwork. There are 180 days in the standard school year in the United States, as compared with 220 in South Korea, about 230 in Germany, and 243 in j.a.pan. Children in some of these countries go to school on Sat.u.r.day. The average American high school student spends 3.5 hours a week on homework. The total time devoted to studies, in and out of the cla.s.sroom, is about 20 hours a week. j.a.panese fifth-graders fifth-graders average 33 hours a week. j.a.pan, with half the population of the United States, produces twice as many scientists and engineers with advanced degrees every year. average 33 hours a week. j.a.pan, with half the population of the United States, produces twice as many scientists and engineers with advanced degrees every year.

During four years of high school, American students spend less than 1,500 hours on such subjects as mathematics, science and history. j.a.panese, French and German students spend more than twice as much time. A 1994 report commissioned by the US Department of Education notes: The traditional school day must now fit in a whole set of requirements for what has been called the 'new work of the schools' - education about personal safety, consumer affairs, AIDS, conservation and energy, family life and driver's training.

So, because of the deficiencies of society and the inadequacies of education in the home, only about three hours a day are spent in high school on the core academic subjects.

There's a widely held perception that science is 'too hard' for ordinary people. We can see this reflected in the statistic that only around 10 per cent of American high school students ever opt for a course in physics. What makes science suddenly 'too hard'? Why isn't it too hard for the citizens of all those other countries that are outperforming the United States? What has happened to the American genius for science, technical innovation and hard work? Americans once took enormous pride in their inventors, who pioneered the telegraph, telephone, electric light, phonograph, automobile and airplane. Except for computers, all that seems a thing of the past. Where did all that 'Yankee ingenuity' go?

Most American children aren't stupid. Part of the reason they don't study hard is that they receive few tangible benefits when they do. Competency (that is, actually knowing the stuff) in verbal skills, mathematics, science and history these days doesn't increase earnings for average young men in their first eight years out of high school, many of whom take service rather than industrial jobs.

In the productive sectors of the economy, though, the story is often different. There are furniture factories, for example, in danger of going out of business - not because there are no customers, but because so few entry-level workers can do simple arithmetic. A major electronics company reports that 80 per cent of its job applicants can't pa.s.s a fifth-grade a fifth-grade mathematics test. The United States already is losing some $40 billion a year (mainly in lost productivity and the cost of remedial education) because workers, to too great a degree, can't read, write, count or think. mathematics test. The United States already is losing some $40 billion a year (mainly in lost productivity and the cost of remedial education) because workers, to too great a degree, can't read, write, count or think.

In a survey by the US National Science Board of 139 high technology companies in the United States, the chief causes of the research and development decline attributable to national policy were (1) lack of a long-term strategy for dealing with the problem; (2) too little attention paid to the training of future scientists and engineers; (3) too much investment in 'defence', and not enough in civilian research and development; and (4) too little attention paid to pre-college education. Ignorance feeds on ignorance. Science phobia is contagious.

Those in America with the most favourable view of science tend to be young, well-to-do, college-educated white males. But three-quarters of new American workers in the next decade will be women, nonwhites and immigrants. Failing to rouse their enthusiasm, to say nothing of discriminating against them, isn't only unjust, it's also stupid and self-defeating. It deprives the economy of desperately needed skilled workers.

African-American and Hispanic students are doing significantly better in standardized science tests now than in the late 1960s, but they're the only ones who are. The average maths gap between white and black US high school graduates is still huge - two to three grade levels; but the gap between white US high school graduates and those in, say, j.a.pan, Canada, Great Britain or Finland is more than twice as large (with the US students behind). If you're poorly motivated and poorly educated, you won't know much - no mystery there. Suburban African-Americans with college-educated parents do just as well in college as suburban whites with college-educated parents. According to some statistics, enrolling a poor child in a Head Start programme doubles his or her chances to be employed later in life; one who completes an Upward Bound programme is four times as likely to get a college education. If we're serious, we know what to do.

What about college and university? There are obvious steps to take: improved status based on teaching success, and promotions of teachers based on the performance of their students in standardized, double-blind tests; salaries for teachers that approach what they could get in industry; more scholarships, fellowships and laboratory equipment; imaginative, inspiring curricula and textbooks in which the leading faculty members play a major role; laboratory courses required of everyone to graduate; and special attention paid to those traditionally steered away from science. We should also encourage the best academic scientists to spend more time on public education - textbooks, lectures, newspaper and magazine articles, TV appearances. And a mandatory freshman or soph.o.m.ore (first- or second-year) course in sceptical thinking and the methods of science might be worth trying.

The mystic William Blake stared at the Sun and saw angels there, while others, more worldly, 'perceived only an object of about the size and colour of a golden guinea'. Did Blake really see angels in the Sun, or was it some perceptual or cognitive error? I know of no photograph of the Sun that shows anything of the sort. Did Blake see what the camera and the telescope cannot? Or does the explanation lie much more inside Blake's head than outside? And is not the truth of the Sun's nature as revealed by modern science far more wonderful: no mere angels or gold coin, but an enormous sphere into which a million Earths could be packed, in the core of which the hidden nuclei of atoms are being jammed together, hydrogen transfigured into helium, the energy latent in hydrogen for billions of years released, the Earth and other planets warmed and lit thereby, and the same process repeated four hundred billion times elsewhere in the Milky Way galaxy?

The blueprints, detailed instructions, and job orders for building you from scratch would fill about 1,000 encyclopedia volumes if written out in English. Yet every cell in your body has a set of these encyclopedias. A quasar is so far away that the light we see from it began its intergalactic voyage before the Earth was formed. Every person on Earth is descended from the same not-quite-human ancestors in East Africa a few million years ago, making us all cousins.

Whenever I think about any of these discoveries, I feel a tingle of exhilaration. My heart races. I can't help it. Science is an astonishment and a delight. Every time a s.p.a.cecraft flies by a new world, I find myself amazed. Planetary scientists ask themselves: 'Oh, is that that the way it is? Why didn't we think of that?' But nature is the way it is? Why didn't we think of that?' But nature is always always more subtle, more intricate, more elegant than what we are able to imagine. Given our manifest human limitations, what is surprising is that we have been able to penetrate so far into the secrets of Nature. more subtle, more intricate, more elegant than what we are able to imagine. Given our manifest human limitations, what is surprising is that we have been able to penetrate so far into the secrets of Nature.

Nearly every scientist has experienced, in a moment of discovery or sudden understanding, a reverential astonishment. Science - pure science, science not for any practical application but for its own sake - is a deeply emotional matter for those who practise it, as well as for those nonscientists who every now and then dip in to see what's been discovered lately.

And, as in a detective story, it's a joy to frame key questions, to work through alternative explanations, and maybe even to advance the process of scientific discovery. Consider these examples, some very simple, some not, chosen more or less at random: * Could there be an undiscovered integer between 6 and 7?

* Could there be an undiscovered chemical element between atomic number 6 (which is carbon) and atomic number 7 (which is nitrogen)?

* Yes, the new preservative causes cancer in rats. But what if you have to give a person, who weighs much more than a rat, a pound a day of the stuff to induce cancer? In that case, maybe the new preservative isn't all that dangerous. Might the benefit of having food preserved for long periods outweigh the small additional risk of cancer? Who decides? What data do they need to make a prudent decision?

* In a 3.8 billion-year-old rock, you find a ratio of carbon isotopes typical of living things today, and different from inorganic sediments. Do you deduce abundant life on Earth 3.8 billion years ago? Or could the chemical remains of more modern organisms have infiltrated into the rock? Or is there a way for isotopes to separate in the rock apart from biological processes?

* Sensitive measurements of electrical currents in the human brain show that when certain memories or mental processes occur, particular regions of the brain go into action. Can our thoughts, memories and pa.s.sions all be generated by particular circuitry of the brain neurons? Might it ever be possible to simulate such circuitry in a robot? Would it ever be feasible to insert new circuits or alter old ones in the brain in such a way as to change opinions, memories, emotions, logical deductions? Is such tampering wildly dangerous?

* Your theory of the origin of the solar system predicts many flat discs of gas and dust all over the Milky Way galaxy. You look through the telescope and you find flat discs everywhere. You happily conclude that your theory is confirmed. But it turns out the discs you sighted were spiral galaxies far beyond the Milky Way, and much too big to be nascent solar systems. Should you abandon your theory? Or should you look for a different kind of disc? Or is this just an expression of your unwillingness to abandon a discredited hypothesis?

* A growing cancer sends out an all-points bulletin to the cells lining adjacent blood vessels: 'We need blood,' the message says. The endothelial cells obligingly build blood vessel bridges to supply the cancer cells with blood. How does this come about? Can the message be intercepted or cancelled?

* You mix violet, blue, green, yellow, orange and red paints and make a murky brown. Then you mix light of the same colours and you get white. What's going on?

* In the genes of humans and many other animals there are long, repet.i.tive sequences of hereditary information (called 'nonsense'). Some of these sequences cause genetic diseases. Could it be that segments of the DNA are rogue nucleic acids, reproducing on their own, in business for themselves, disdaining the well-being of the organism they inhabit?

* Many animals behave strangely just before an earthquake. What do they know that seismologists don't?

* The ancient Aztec and the ancient Greek words for 'G.o.d' are nearly the same. Is this evidence of some contact or commonality between the two civilizations, or should we expect occasional such coincidences between two wholly unrelated languages merely by chance? Or could, as Plato thought in the Cratylus, Cratylus, certain words be built into us from birth? certain words be built into us from birth?

* The Second Law of Thermodynamics states that in the Universe as a whole, disorder increases as time goes on. (Of course, locally worlds and life and intelligence can emerge, at the cost of a decrease in order elsewhere in the Universe.) But if we live in a Universe in which the present Big Bang expansion will slow, stop, and be replaced by a contraction, might the Second Law then be reversed? Can effects precede causes?

* The human body uses concentrated hydrochloric acid in the stomach to dissolve food and aid digestion. Why doesn't the hydrochloric acid dissolve the stomach?

* The oldest stars seem to be, at the time I'm writing, older than the Universe. Like the claim that an acquaintance has children older than she is, you don't have to know very much to recognize that someone has made a mistake. Who?

* The technology now exists to move individual atoms around, so long and complex messages can be written on an ultra-microscopic scale. It is also possible to make machines the size of molecules. Rudimentary examples of both these 'nano-technologies' are now well demonstrated. Where does this take us in another few decades?

* In several different laboratories, complex molecules have been found that under suitable conditions make copies of themselves in the test tube. Some of these molecules are, like DNA and RNA, built out of nucleotides; others are not. Some use enzymes to hasten the pace of the chemistry; others do not. Sometimes there is a mistake in copying; from that point forward the mistake is copied in successive generations of molecules. Thus there get to be slightly different species of self-replicating molecules, some of which reproduce faster or more efficiently than others. These preferentially thrive. As time goes on, the molecules in the test tube become more and more efficient. We are beginning to witness the evolution of molecules. How much insight does this provide about the origin of life?

* Why is ordinary ice white, but pure glacial ice blue?

* Life has been found miles below the surface of the Earth. How deep does it go?

* The Dogon people in the Republic of Mali are said by a French anthropologist to have a legend that the star Sirius has an extremely dense companion star. Sirius in fact does have such a companion, although it requires fairly sophisticated astronomy to detect it. So (1) did the Dogon people descend from a forgotten civilization that had large optical telescopes and theoretical astrophysics? Or, (2) were they instructed by extraterrestrials? Or, (3) did the Dogon hear about the white dwarf companion of Sirius from a visiting European? Or, (4) was the French anthropologist mistaken and the Dogon in fact never had such a legend?

Why should it be hard for scientists to get science across? Some scientists, including some very good ones, tell me they'd love to popularize, but feel they lack talent in this area. Knowing and explaining, they say, are not the same thing. What's the secret?

There's only one, I think: don't talk to the general audience as you would to your scientific colleagues. There are terms that convey your meaning instantly and accurately to fellow experts. You may pa.r.s.e these phrases every day in your professional work. But they do no more than mystify an audience of non-specialists. Use the simplest possible language. Above all, remember how it vas before you yourself grasped whatever it is you're explaining. Remember the misunderstandings that you almost fell into, and note them explicitly. Keep firmly in mind that there was a time when you didn't understand any of this either. Recapitulate the first steps that led you from ignorance to knowledge. Never forget that native intelligence is widely distributed in our species. Indeed, it is the secret of our success.

The effort involved is slight, the benefits great. Among the potential pitfalls are oversimplification, the need to be sparing with qualifications (and quantifications), inadequate credit given to the many scientists involved, and insufficient distinctions drawn between helpful a.n.a.logy and reality. Doubtless, compromises must be made.

The more you make such presentations, the clearer it is which approaches work and which do not. There is a natural selection of metaphors, images, a.n.a.logies, anecdotes. After a while you find that you can get almost anywhere you want to go, walking on consumer-tested stepping-stones. You can then fine-tune your presentations for the needs of a given audience.

Like some editors and television producers, some scientists believe the public is too ignorant or too stupid to understand science, that the enterprise of popularization is fundamentally a lost cause, or even that it's tantamount to fraternization, if not outright cohabitation, with the enemy. Among the many criticisms that could be made of this judgement - along with its insufferable arrogance and its neglect of a host of examples of highly successful science popularizations - is that it is self-confirming. And also, for the scientists involved, self-defeating.

Large-scale government support for science is fairly new, dating back only to World War Two - although patronage of a few scientists by the rich and powerful is much older. With the end of the Cold War, the national defence trump card that provided support for all sorts of fundamental science became virtually unplayable. Only partly for this reason, most scientists, I think, are now comfortable with the idea of popularizing science. (Since nearly all support for science comes from the public coffers, it would be an odd flirtation with suicide for scientists to oppose competent popularization.) What the public understands and appreciates, it is more likely to support. I don't mean writing articles for Scientific American, Scientific American, say, that are read by science enthusiasts and scientists in other fields. I'm not just talking about teaching introductory courses for undergraduates. I'm talking about efforts to communicate the substance and approach of science in newspapers, magazines, on radio and television, in lectures for the general public, and in elementary, middle and high school textbooks. say, that are read by science enthusiasts and scientists in other fields. I'm not just talking about teaching introductory courses for undergraduates. I'm talking about efforts to communicate the substance and approach of science in newspapers, magazines, on radio and television, in lectures for the general public, and in elementary, middle and high school textbooks.

Of course there are judgement calls to be made in popularizing. It's important neither to mystify nor to patronize. In attempting to prod public interest, scientists have on occasion gone too far - for example, in drawing unjustified religious conclusions. Astronomer George Smoot described his discovery of small irregularities in the ratio radiation left over from the Big Bang as 'seeing G.o.d face-to-face'. Physics n.o.bel laureate Leon Lederman described the Higgs boson, a hypothetical building block of matter, as 'the G.o.d particle', and so t.i.tled a book. (In my opinion, they're all G.o.d particles.) If the Higgs boson doesn't exist, is the G.o.d hypothesis disproved? Physicist Frank Tipler proposes that computers in the remote future will prove the existence of G.o.d and work our bodily resurrection.

Periodicals and television can strike sparks as they give us a glimpse of science, and this is very important. But - apart from apprenticeship or well-structured cla.s.ses and seminars - the best way to popularize science is through textbooks, popular books, CD-ROMs and laser discs. You can mull things over, go at your own pace, revisit the hard parts, compare texts, dig deep. It has to be done right, though, and in the schools especially it generally isn't. There, as the philosopher John Pa.s.smore comments, science is often presented as a matter of learning principles and applying them by routine procedures. It is learned from textbooks, not by reading the works of great scientists or even the day-to-day contributions to the scientific literature ... The beginning scientist, unlike the beginning humanist, does not have an immediate contact with genius. Indeed... school courses can attract quite the wrong sort of person into science -unimaginative boys and girls who like like routine. routine.

I hold that popularization of science is successful if, at first, it does no more than spark the sense of wonder. To do that, it is sufficient to provide a glimpse of the findings of science without thoroughly explaining how those findings were achieved. It is easier to portray the destination than the journey. But, where possible, popularizers should try to chronicle some of the mistakes, false starts, dead ends and apparently hopeless confusion along the way. At least every now and then, we should provide the evidence and let the reader draw his or her own conclusion. This converts obedient a.s.similation of new knowledge into personal discovery. When you make the finding yourself - even if you're the last person on Earth to see the light - you never forget it.

As a youngster, I was inspired by the popular science books and articles of George Gamow, James Jeans, Arthur Edding-ton, J.B.S. Haldane, Julian Huxley, Rachel Carson and Arthur C. Clarke - all of them trained in, and most of them leading pract.i.tioners of science. The popularity of well-written, well-explained, deeply imaginative books on science that touch our hearts as well as our minds seems greater in the last twenty years than ever before, and the number and disciplinary diversity of scientists writing these books is likewise unprecedented. Among the best contemporary scientist-popularizers, I think of Stephen Jay Gould, E.O. Wilson, Lewis Thomas and Richard Dawkins in biology; Steven Weinberg, Alan Lightman and Kip Thorne in physics; Roald Hoffmann in chemistry; and the early works of Fred Hoyle in astronomy. Isaac Asimov wrote capably on everything. (And while requiring calculus, the most consistently exciting, provocative and inspiring science popularization of the last few decades seems to me to be Volume I of Richard Feynman's Introductory Lectures on Physics.) Introductory Lectures on Physics.) Nevertheless, current efforts are clearly nowhere near commensurate with the public good. And, of course, if we can't read, we can't benefit from such works, no matter how inspiring they are. Nevertheless, current efforts are clearly nowhere near commensurate with the public good. And, of course, if we can't read, we can't benefit from such works, no matter how inspiring they are.