by John Carey
But to what extent can we really know the universe around us? Sometimes this question is posed by people who hope the answer will be in the negative, who are fearful of a universe in which everything might one day be known. And sometimes we hear pronouncements from scientists who confidently state that everything worth knowing will soon be known – or even is already known – and who paint pictures of a Dionysian or Polynesian age in which the zest for intellectual discovery has withered, to be replaced by a kind of subdued languor, the lotus eaters drinking fermented coconut milk or some other mild hallucinogen. In addition to maligning both the Polynesians, who were intrepid explorers (and whose brief respite in paradise is now sadly ending), as well as the inducements to intellectual discovery provided by some hallucinogens, this contention turns out to be trivially mistaken.
Let us approach a much more modest question: not whether we can know the universe or the Milky Way Galaxy or a star or a world. Can we know, ultimately and in detail, a grain of salt? Consider one microgram of table salt, a speck just barely large enough for someone with keen eyesight to make out without a microscope. In that grain of salt there are about 1016 sodium and chlorine atoms. This is a 1 followed by 16 zeros, 10 million billion atoms. If we wish to know a grain of salt, we must know at least the three-dimensional positions of each of these atoms. (In fact, there is much more to be known – for example, the nature of the forces between the atoms – but we are making only a modest calculation.) Now, is this number more or less than the number of things which the brain can know?
How much can the brain know? There are perhaps 1011 neurons in the brain, the circuit elements and switches that are responsible in their electrical and chemical activity for the functioning of our minds. A typical brain neuron has perhaps a thousand little wires, called dendrites, which connect it with its fellows. If, as seems likely, every bit of information in the brain corresponds to one of these connections, the total number of things knowable by the brain is no more than 1014, one hundred trillion. But this number is only one percent of the number of atoms in our speck of salt.
So in this sense the universe is intractable, astonishingly immune to any human attempt at full knowledge. We cannot on this level understand a grain of salt, much less the universe.
But let us look a little more deeply at our microgram of salt. Salt happens to be a crystal in which, except for defects in the structure of the crystal lattice, the position of every sodium and chlorine atom is predetermined. If we could shrink ourselves into this crystalline world, we would see rank upon rank of atoms in an ordered array, a regularly alternating structure – sodium, chlorine, sodium, chlorine, specifying the sheet of atoms we are standing on and all the sheets above us and below us. An absolutely pure crystal of salt could have the position of every atom specified by something like 10 bits of information.* This would not strain the information-carrying capacity of the brain.
If the universe had natural laws that governed its behavior to the same degree of regularity that determines a crystal of salt, then, of course, the universe would be knowable. Even if there were many such laws, each of considerable complexity, human beings might have the capability to understand them all. Even if such knowledge exceeded the information-carrying capacity of the brain, we might store the additional information outside our bodies – in books, for example, or in computer memories – and still, in some sense, know the universe.
Human beings are, understandably, highly motivated to find regularities, natural laws. The search for rules, the only possible way to understand such a vast and complex universe, is called science. The universe forces those who live in it to understand it. Those creatures who find everyday experience a muddled jumble of events with no predictability, no regularity, are in grave peril. The universe belongs to those who, at least to some degree, have figured it out.
It is an astonishing fact that there are laws of nature, rules that summarize conveniently – not just qualitatively but quantitatively – how the world works. We might imagine a universe in which there are no such laws, in which the 1080 elementary particles that make up a universe like our own behave with utter and uncompromising abandon. To understand such a universe we would need a brain at least as massive as the universe. It seems unlikely that such a universe could have life and intelligence, because beings and brains require some degree of internal stability and order. But even if in a much more random universe there were such beings with an intelligence much greater than our own, there could not be much knowledge, passion or joy.
Fortunately for us, we live in a universe that has at least important parts that are knowable. Our common-sense experience and our evolutionary history have prepared us to understand something of the workaday world. When we go into other realms, however, common sense and ordinary intuition turn out to be highly unreliable guides. It is stunning that as we go close to the speed of light our mass increases indefinitely, we shrink toward zero thickness in the direction of motion, and time for us comes as near to stopping as we would like. Many people think that this is silly, and every week or two I get a letter from someone who complains to me about it. But it is a virtually certain consequence not just of experiment but also of Albert Einstein’s brilliant analysis of space and time called the Special Theory of Relativity. It does not matter that these effects seem unreasonable to us. We are not in the habit of traveling close to the speed of light. The testimony of our common sense is suspect at high velocities.
Or consider an isolated molecule composed of two atoms shaped something like a dumbbell – a molecule of salt, it might be. Such a molecule rotates about an axis through the line connecting the two atoms. But in the world of quantum mechanics, the realm of the very small, not all orientations of our dumbbell molecule are possible. It might be that the molecule could be oriented in a horizontal position, say, or in a vertical position, but not at many angles in between. Some rotational positions are forbidden. Forbidden by what? By the laws of nature. The universe is built in such a way as to limit, or quantize, rotation. We do not experience this directly in everyday life; we would find it startling as well as awkward in sitting-up exercises, to find arms outstretched from the sides or pointed up to the skies permitted but many intermediate positions forbidden. We do not live in the world of the small, on the scale of 10–13 centimeters, in the realm where there are twelve zeros between the decimal place and the one. Our common-sense intuitions do not count. What does count is experiment – in this case observations from the far infrared spectra of molecules. They show molecular rotation to be quantized.
The idea that the world places restrictions on what humans might do is frustrating. Why shouldn’t we be able to have intermediate rotational positions? Why can’t we travel faster than the speed of light? But so far as we can tell, this is the way the universe is constructed. Such prohibitions not only press us toward a little humility; they also make the world more knowable. Every restriction corresponds to a law of nature, a regularization of the universe. The more restrictions there are on what matter and energy can do, the more knowledge human beings can attain. Whether in some sense the universe is ultimately knowable depends not only on how many natural laws there are that encompass widely divergent phenomena, but also on whether we have the openness and the intellectual capacity to understand such laws. Our formulations of the regularities of nature are surely dependent on how the brain is built, but also, and to a significant degree, on how the universe is built.
For myself, I like a universe that includes much that is unknown and, at the same time, much that is knowable. A universe in which everything is known would be static and dull, as boring as the heaven of some weak-minded theologians. A universe that is unknowable is no fit place for a thinking being. The ideal universe for us is one very much like the universe we inhabit. And I would guess that this is not really much of a coincidence.
Source: Carl Sagan, Broca’s Brain: The Romance of Science, London, Hodder & Stoughton, 1979.
*Chlorine i
s a deadly poison gas employed on European battlefields in World War 1. Sodium is a corrosive metal which burns upon contact with water. Together they make a placid and unpoisonous material, table salt. Why each of these substances has the properties it does is a subject called chemistry, which requires more than 10 bits of information to understand.
Brain Size
Trained as a zoologist at Oxford, Anthony Smith has ballooned over East African herds, discovered the world’s first blind loach (Noemacheilus smithi) and explored wildernesses from the Arctic to the Antarctic. His book The Body (1968) sold 400,000 hardback in the US alone, and was translated into twelve languages. This is from the follow-up, The Mind (1984).
The human brain consists of ten to fifteen thousand million nerve cells. (The anatomy books are always more precise, each opting for fourteen or eleven or fifteen billion as if its choice is the true and unassailable figure.) If that kind of number is bewildering, being three times as many as there are human brains alive on this planet, the number of synapses (nerve cell connections) is a thousand times more so, there being about one hundred million million of them, or more than the total number of humans who have ever lived since we acquired this fantastic brain in full measure those thousand centuries ago. Coupled with the nerve cells, supporting and nourishing them, are the glial cells whose number is on a par with the nerve cells that they sustain. By way of comparison, appreciating that such figures can put normal minds in turmoil, the clever little honey bee has about seven thousand nerve cells.
The whole human brain weighs some three pounds in the male and about 10 per cent less in females (or 1,400 grams as against 1,250 grams). This disproportion can seem unfair to women but their brains are relatively bigger, being 2½ per cent of total body weight as against 2 per cent for men. The three pound weight makes our brain among the lightest of our organs, being very much less than muscle (42 per cent of the total weight for males, 36 per cent for females), much less than the combined total for the 206 bones of the human skeleton, less than the twenty-plus square feet of skin, less than the twenty-eight feet of intestine, less than the eleven pounds or so of blood, and just less than the four pounds of liver. However, it weighs more than the heart (which is one pound), the kidneys (a mere five ounces each), the spleen (six ounces), the pancreas (three ounces), and the lungs (two and a half pounds). A foetus, with its relatively huge head plus brain and its small everything else, is arguably a more accurate representation of Homo sapiens, but that big head wanes proportionately as the child grows wiser. There is undoubted paradox about our most remarkable property, all three pounds of it.
There is also conflict over its abilities. On the one hand, and for many a normal day, a particular brain may exhibit precious little intelligence. Its owner may eat what has been set before him, walk to a bus stop, reach work, perform the same repetitive task, return home, eat again and sleep. An animal could do the same. On the other hand there is the musician Hans von Bülow travelling by train from Hamburg to Berlin, reading Stanford’s Irish Symphony, previously unknown to him, and then conducting it that evening without a score. Some musicians prefer reading a piece of music to hearing the work, claiming that the experience is without the blemishes of an actual performance. Wolfgang Mozart confided that a whole new composition would suddenly arise in his mind. At convenient moments he would translate this entire fabric of rhythm, melody, harmony, counterpoint and tone into the written symbols of a score. For those who have trouble with a telephone number or with a name to fit a face, it is even problematical contemplating the gap between us and them, the normal and the genius. Someone once asked A. C. Aitken, professor at Edinburgh University, to make 4 divided by 47 into a decimal. After four seconds he started and gave another digit every three-quarters of a second: ‘point 08510638297872340425531914’. He stopped (after twenty-four seconds), discussed the problem for one minute, and then restarted: ‘191489’ – five-second pause – ‘361702127659574468. Now that’s the repeating point. It starts again with 085. So if that’s forty-six places, I’m right.’ To many of us such a man is from another planet, particularly in his final comment.
The bizarre fact is that the brains of von Bülow, Mozart and Aitken were inherited from a long line of hunter-gatherers. Why on earth, or even how on earth, did a brain system evolve that could remember symphonies or perform advanced mental arithmetic when its palaeolithic requirements were assuredly less demanding? And why, as the second major conundrum, did the process stop at least 100,000 years ago? Only since then, via population increase, larger and more settled communities, division of labour and a subjugation of nature, has the brain of man begun to realize its potential. Yet it is a prehistoric brain, there being no detectable difference (so far as can be judged from fossils) between then and now, theirs and ours, extremely primitive and very modern man.
The solar system is vast, incomprehensible to most of us, and staggering in its distances, and to mention it in the same breath as our three pounds of brain is apparently to relate like with unlike, a thing colossal with a thing minute. But the bracketing together is fairer than might be imagined. The dimensions that astronomers talk about, and seem to understand, have their parallel in the numbers that neuroanatomists relate, almost in passing, as if these too are understood. Already mentioned are the fifteen billion nerve cells, which is also the numeric total (more or less) of stars in our galaxy. Also mentioned are the synapses, a thousandfold greater, and therefore as plentiful as the stars of a thousand galaxies. Astronomers do use such figures, being more aware than most of the thousands of millions of light years existing between us and the furthest parts of the known universe; but there must be a limit even to their comprehension.
The human brain, I suspect, can confound them, not in its neurons but in the range of its possibilities. Nerve cells are the basic units, but their synapses create a framework for interconnections, for a variety of ways in which one nerve cell may be linked with another, and for that other to be connected with others yet again. The figure of possible connections within our modern brain is as good as infinite. It is certainly larger than the number of atoms presumed to exist in the entire universe and no one, I warrant, can begin to grapple with that thought. Somehow or other a bipedal, fairly hairless, hunting, scavenging ape did acquire this incredible possession and then handed it on to us. Why it did no one knows, or can even surmise. ‘I haven’t the foggiest notion,’ replied Richard Leakey, anthropologist and skilful finder of early hominids, when asked why or how such a swelling of brain power could have occurred among early, primitive, and scattered tribes of men.
Growth
The speed of that swelling was considerable. From about five hundred cubic centimetres – and therefore comparable in size with gorilla brains – it leaped to the human size of fourteen hundred cubic centimetres in about three million years. Assuming the brain cells of earliest man to be as compressed as in a modern brain this means that some nine billion cells were added during those years, or approximately one hundred and fifty thousand per generation. That seems like a big increase for every single leap from parent to offspring, particularly when it is remembered that many invertebrates, all quite astute, have far less than that number, but in size it is not very large. In the brain there are about ten million cells in every cubic centimetre, and therefore that generation gap of one hundred and fifty thousand occupies a sixtieth of one cubic centimetre or just fifteen cubic millimetres. Such an increment is modest if viewed simply as bulk, and many another animal has increased its body size by much more than that per generation, the weight increase being only 0.015 grams or one two-thousandth of an ounce.
If elephants had only achieved their seven-ton weight from their, say, one-ton ancestors at this increment of 0.015 grams a generation it would have taken about four hundred million generations, or roughly eight thousand million years. However, it is tempting to regard brain-tissue weight-gain as more problematical in evolution than elephant weight-gain. The brain-gain seems more so becaus
e brains are of more significance – at least from our sapiens point of view – than mere bulk, a thicker skin or larger trunk. It is easier to be impressed with a tripling of nerve cells in three million years.
The brain growth seems less remarkable if thought of solely in terms of cell division. To achieve 15,000 million nerve cells it is necessary to have just 33 doublings of the parent cell. To achieve half that number only 32 doublings are necessary. In this light the difference between primitive and modern man seems less marked – scarcely more than one extra doubling in three million years. As the adult complement of brain cells is made during the first three months of pregnancy the 33 divisions therefore take place at an average rate of about one every three days. Bacteria double their number every twenty minutes or so, and the foetal brain increase is therefore not particularly rapid. In fact it is equivalent to all sorts of other increases going on in the embryonic human at the same time: liver growth, skin growth and so on. Brain growth just seems more remarkable, particularly when it is brought down to the level of brain cells. To possess 15,000 million neurons at the end of three months’ gestational activity means growing them at the rate of 2,000 a second. Knowing that many small animals lead quite complex lives with that number of nerve cells, it is arguable that we should be far more intelligent than is actually the case; but it is obviously wrong to compare insect ability, however complex and admirable, with human capability. We are not equivalent to seven million insects. We just happen to have as many brain cells as they possess.