The Faber Book of Science

by John Carey

  Over the past 20 years or so, this Newtonian vision has splintered and blurred. It is now widely recognised that the simplest rules or algorithms or mathematical equations, containing no random elements whatsoever, can generate behaviour which is as complicated as anything we can imagine.

  This mathematics which ‘is different’ is the mathematics of ‘deterministic chaos’. What it says is that a situation can be both deterministic and unpredictable; that is, unpredictable without being random (on the one hand) or (on the other hand) attributable to very complicated causes.

  ‘Simple’ as they may be in themselves, these chaos-generating equations have the property of being ‘nonlinear’. In a linear equation you can ‘guess ahead’. Imagine a road lined with telegraph poles in a perspective drawing. Given two or three poles, you can easily draw in the rest for yourself. But nature often draws itself differently, using nonlinear equations. Imagine a river running alongside the road. The water has flat bits and bumpy bits. But however many I draw in for you, there is no way for you to tell (with a real river) where the next flat bit or bumpy bit is going to be. This holds true on every scale. Look down from a balloon and you’ll see that parts of the bumpy bits look relatively flat. Put your face close to the water and you’ll see that the flat bits contain relatively bumpy bits. The maths is the same for each case, and equally unpredictable.

  In this sense, ‘nonlinear’ means two and two do not necessarily make four. Much of physics and other areas of science where so much progress has come, are linear (or at least decomposable into essentially linear bits). And so mathematical texts and courses have focused on linear problems. But increasingly it seems that most of what is interesting in the natural world, and especially in the biological world of living things, involves nonlinear mathematics. It was biologists – working on the ups and downs of animal population – who were among the first to see that not only can simple rules give rise to behaviour which looks very complicated, but the behaviour can be so sensitive to the starting conditions as to make long term prediction impossible (even when you know the rule).

  There is a flip side to the chaos coin. Previously, if we saw complicated, irregular or fluctuating behaviour – weather patterns, marginal rates of Treasury Bonds, colour patterns of animals or shapes of leaves – we assumed the underlying causes were complicated. Now we realize that extraordinarily complex behaviour can be generated by the simplest of rules. It seems likely to me that much complexity and apparent irregularity seen in nature, from the development and behaviour of individual creatures to the structure of ecosystems, derives from simple – but chaotic – rules. (But, of course, a lot of what we see around us is very complicated because it is intrinsically so!)

  I believe all this adds up to one of the real revolutions in the way we think about the world. Knowing the simple rule or equation that governs a system is not always sufficient to predict its behaviour. And, conversely, exceedingly complicated patterns or behaviour may derive not from exceedingly complex causes, but from the chaotic workings of some very simple algorithm. Ultimately, the mathematics of chaos offers new and deep insights into the structure of the world around us, and at the same time raises old questions about why abstract mathematics should be so unreasonably effective in describing this world.

  Sources: (for Caroline Series’s and Paul Davies’s pieces) The New Scientist Guide to Chaos, ed. Nina Hall, London, Penguin, 1991; Tom Stoppard, Arcadia, Faber and Faber, 1993; Robert May, Programme note to Arcadia, 1993.

  The Language of the Genes

  Steve Jones is Professor of Genetics at University College, London. His book The Language of the Genes, based on his 1991 BBC Reith Lectures, is a model of how wit, learning and clear-headedness can make a complex subject intelligible to a huge audience.

  The language of the genes has a simple alphabet, not with twenty-six letters, but just four. These are the four different DNA bases – adenine, guanine, cytosine and thymine (A, G, C and T for short). The bases are arranged in words of three letters such as CGA or TGG. Most of the words code for different amino acids, which themselves are joined together to make proteins, the building blocks of the body.

  Just how economical the language of inheritance is can be illustrated with a rather odd quotation from a book called Gadsby, written in 1939 by one Ernest Wright: ‘I am going to show you how a bunch of bright young folks did find a champion, a man with boys and girls of his own, a man of so dominating and happy individuality that youth was drawn to him as a fly to a sugar bowl.’ This sounds rather peculiar, as does the rest of the fifty-thousand word book, and it is. The quotation, and the whole book, does not contain the letter ‘e’. It is possible to write a meaningful sentence with twenty-five letters instead of twenty-six, but only just. Life manages with a mere four.

  Although the inherited vocabulary is simple its message is very long. Each cell in the body contains about six feet of DNA. A useless but amusing fact is that if all the DNA in all the cells in a single human being were stretched out it would reach to the moon and back eight thousand times. There is now a scheme, the Human Genome Project, to read the whole of its three thousand million letters and to publish what may be the most boring book ever written; the equivalent of a dozen or so copies of the Encyclopaedia Britannica. There is much disagreement about how to set about reading the message and even about whether it is worth doing at all. It probably is. The Admiralty sent the Beagle to South America with Darwin on board not because they were interested in evolution but because they knew that the first step to understanding (and, with luck, controlling) the world was to make a map of it. The same is true of the genes. To make this map will be expensive – about as much as a single Trident nuclear submarine. The task will be stupefyingly tedious for those who have to do the work, but, before the end of the century, someone will publish the inherited lexicon of a human being. To be more precise, there will be a map of a sort of Mr Average – the chart is, of course, of a male – as the information will come from short bits of DNA from dozens of different people …

  Human genetics was for most of its history more or less restricted to studying pedigrees which stood out because they contained an abnormality. This limited its ability to trace patterns of descent to those few families – like the Hapsburgs – who appeared to deviate from the perfect form. Biology has now shown that this perfect form does not exist. Instead there is a huge amount of inherited variation. Thousands of inherited characters – perfectly normal diversity, not diseases – distinguish each person. There is so much variety that everyone alive today is different, not only from everyone else, but from everyone who ever has lived or ever will live. The mass of diversity can be used to look at patterns of shared ancestry in any family, aristocratic or plebeian; healthy or ill. Because all modern genes are copies of those in earlier generations each can be used as a message from the past. They bring clues from the beginnings of humanity more than a hundred thousand years ago and from the origin of life three thousand million years before that …

  There have been claims that we may soon find the gene that makes us human. The ancestral message will then at last allow us to understand what we really are. The idea seems to me ridiculous.

  Just how ridiculous it is can be seen by looking at the search for another important gene, one which I inherited from my father, and he from his and so on back to a distant ancestor that lived long before the birth of our own species. This is the gene that makes me male. The maleness gene was tracked down recently and its message spelt out in the four DNA letters, A, G, C and T. It starts like this: GAT AGA GTG AAG CGA. There are 240 of these letters altogether and, between them, they contain the whole tedious biological story of being a man. This brief ancestral bulletin does nothing to tell that half of the population which is unfortunate enough not to have it what it is really like to be male rather than female. Being a man involves a lot more than a sequence of DNA bases; and the same is true for being a human.

  Source: Steve Jones, The Lang
uage of the Genes, London, HarperCollins, 1993.

  The Good Earth is Dying

  First published in Der Spiegel in 1971, Isaac Asimov’s warning fittingly concludes this book, since it takes a relentlessly scientific look at what is still humankind’s most pressing problem – humankind.

  How many people is the earth able to sustain?

  The question is incomplete as it stands. One must modify the question by asking further: At what level of technology? And modify it still further by asking: At what level of human dignity?

  As for technology, perhaps we can simply ask for the best. We can say that the more advanced technology is, the more people the earth can support, so let us not stint. After all, technology could give us the atomic bomb and put men on the moon and we should set no limits to it.

  Let us accept, then, the dream that technology is infinitely capable and proceed from there. How many people can the earth sustain assuming that technology can solve all reasonable problems?

  To begin with, it is estimated that there are twenty million million tons of living tissue on the earth, of which 10 percent, or two million million tons, is animal life. As a first approximation, this may be considered a maximum, since plant life cannot increase in mass without an increase in solar radiation or an increase in its own efficiency in handling sunlight. Animal life cannot increase in mass without an increase in the plant mass that serves as its ultimate food.

  The mass of humanity has been increasing throughout history; and it is still increasing, but is doing so at the expense of other forms of animal life. Every additional kilogram of humanity has meant, as a matter of absolute necessity, one less kilogram of nonhuman animal life. We might argue, then, that the earth can support, as a maximum, a mass of mankind equal to the present mass of all animal life. At that point, the number of human beings on the earth would be forty million million, or over eleven thousand times the present number. And no other species of animal life would then exist.

  What will this mean? The total surface of the earth is five hundred twenty million square kilometers, so that when human population reaches its ultimate number, the average density of population will be eighty thousand per square kilometer – twice the density of New York’s island of Manhattan. Imagine such a density everywhere if the earth’s population is spread out evenly – including over the polar regions, the deserts, and the oceans.

  Can we imagine, then, a huge, world-girdling complex of high-rise apartments (over both land and sea) for housing, for offices, for industry? The roof of this complex will be given over entirely to plant growth; either algae, which are completely edible, or higher plants that must be treated appropriately to make all parts edible.

  At frequent intervals, there will be conduits down which water and plant products will pour. The plant products will be filtered out, dried, treated, and prepared for food, while the water is returned to the tanks above. Other conduits, leading upward, will bring up the raw minerals needed for plant growth, consisting of (what else) human wastes and chopped-up human corpses. And at this point, of course, no further increase in human numbers is possible; so rigid population planning would then be necessary if it had not been before.

  But if this number can be supported in theory, does it represent a kind of life – and this is for each of you to ponder – consonant with human dignity?

  Can we buy space and time by transferring human beings to the moon? To Mars?

  Consider – How long, under present conditions, will it take us to reach the global high-rise? At present, the earth’s population is thirty-six hundred million and it is increasing at a rate that will double the figure in thirty-five years. Let us suppose that this rate of increase can be maintained. In that case, the ultimate population of forty million million will be reached in 465 years. The global high-rise will be in full splendor in AD 2436.

  In, that case, how many men do you think it will be possible to place, and support, on the moon, Mars, and elsewhere in the next 465 years? Be reasonable. Subtract your figure from forty million million and ask yourself if the contribution the other worlds can make is significant.

  Can we buy further time by going beyond the sun? Can we make use of hydrogen fusion power to irradiate plant life? Or can we make food in the laboratory, with artificial systems and synthetic catalysts, and declare ourselves independent of the plant world altogether?

  But that requires energy and here we come to another point. The sun pours down on the earth’s day-side, some fifteen thousand times as much energy per day as mankind now uses. The earth’s night-side must radiate exactly that much heat back into space if the earth’s average temperature is to be maintained. If mankind adds to the heat on earth by burning coal, that additional energy must also be radiated out to space; and to accomplish this the earth’s average temperature must rise slightly.

  At present, man’s addition to solar energy produces a terrestrial temperature-rise that is utterly insignificant; that addition, however, is doubling every twenty years. At this rate, in a hundred sixty-five years (by 2136) mankind’s contribution to the heat that the earth must radiate away will amount to one percent of the sun’s supply, and this will begin to produce unacceptable changes in the earth’s temperature.

  So, far from helping ourselves with further energy expenditures in the global high-rise world of ad 2436, we must accept a limitation of energy expenditure a full three centuries earlier, when man’s population is less than a five-hundredth of its ultimate. We might improve matters by increasing the efficiency with which energy is used; but the efficiency cannot rise above a hundred percent, and that does not represent an enormous increase over present levels.

  But, and this is a large ‘but,’ can we really depend on technology to make the necessary advances to bring us to energy-limits safely in a century and a half? By then the population, at the present level of increase, will be twenty times what it is today; and to bring man’s level of nourishment to a desirable point, we would need a fortyfold increase in the food supply. We would also have to ask technology not only to arrange the necessary hundred-fifty-fold increase in energy utilization in a century and a half but to arrange to take care of what will be, very likely, a hundred-fifty-fold increase in environmental pollution and in waste production of all kinds.

  How do things look at present?

  Far from making strides to keep up with the population increase, technology is falling visibly behind. How can the global high-rise be a reasonable future vision when present-day housing is steadily deteriorating even in the most advanced nations? How can we reach our limit of energy expenditure when New York City finds itself, each year with a growing deficit of power supply? Only yesterday, the third landing of men on the moon caused television viewing to go up, and a cutback in electrical voltage was immediately made necessary.

  The earth’s population will be at least six thousand million in the year 2000. Will the planet’s technology be able to support that population even at present-day, wholly unsatisfactory levels? Will human dignity be compatible with such a population (let alone with forty million million), when in our cities today human dignity is disappearing; when it is impossible to walk safely by night (and often by day) in the largest city of the world’s most technologically advanced nation.

  Let us not look into the future at all, then. Let us gaze firmly at the present. The United States is the richest nation on earth and every other nation would like to be at least as rich. But the United States can live as it does only because it consumes slightly more than half of all the energy produced on earth for human consumption – although it has only a sixteenth of the earth’s population.

  What, then, if some wizard were to wave his magic wand and produce an earth on which every part of the population everywhere were able to live at the scale and the standard of Americans? In that case, the rate of energy expenditure would increase instantly to eight times the present world level and, inevitably, the production of waste and pollution would increase sim
ilarly – this with no increase in population at all.

  And can present-day technology supply an eightfold increase in energy utilization (and that of other resources as well) and handle an eightfold increase in waste and pollution, when it is falling desperately short of supplying and handling present levels? Do you ask for time in which technology can arrange for such an eightfold increase? Very well, but in that time, population will increase, too, very likely more than eightfold.

  In short, then, to the revised question, How many people is the earth able to sustain at a desirable level of technology and dignity? there can be only a short and horrifying answer –

  Fewer than now exist!

  The earth cannot support its present population at the average level of the American standard of living. Perhaps, at the moment, it can only support five hundred million people at that standard. Nor can technology improve itself to better this mark, with the present population clamoring for what it cannot have and with that population growing at a terrible rate.

  What, then, will happen?

  If matters continue as they are now going, there will be a continuing decline in the well-being of the individual human being on earth. Calories per mouth will decrease; available living quarters will dwindle; attainable comfort will diminish. What is more, in the increasing desperation to reverse this, man may well make wild attempts to race the technology engine at all costs and will then further pollute the environment and decrease its ability to support mankind. With all this taking place, there will be a struggle of man against man, with each striving to grasp an adequate share of a shrinking life-potential. And there cannot help but be an intensification of the human-jungle characteristics of our centers of population.