The Blind Watchmaker (28 page)

So, what do we mean by a miracle? A miracle is something that happens, but which is exceedingly surprising. If a marble statue of the Virgin Mary suddenly waved its hand at us we should treat it as a miracle, because all our experience and knowledge tells us that marble doesn’t behave like that. I have just uttered the words ‘May I be struck by lightning this minute’. If lightning did strike me in the same minute, it would be treated as a miracle. But actually neither of these two occurrences would be classified by science as utterly impossible. They would simply be judged very improbable, the waving statue much more improbable than the lightning. Lightning does strike people. Any one of us might be struck by lightning, but the probability is pretty low in any one minute (although the
Guinness Book of Records
has a charming picture of a Virginian man, nicknamed the human lightning conductor, recovering in hospital from his seventh lightning strike, with an expression of apprehensive bewilderment on his face). The only thing miraculous about my hypothetical story is the
coincidence
between my being struck by lightning and my verbal invocation of the disaster.

Coincidence means multiplied improbability. The probability of my being struck by lightning in any one minute of my life is perhaps 1 in 10 million as a conservative estimate. The probability of my inviting a lightning strike in any particular minute is also very low. I have just done it for the only time in the 23,400,000 minutes of my life so far, and I doubt if I’ll do it again, so call these odds one in 25 million. To calculate the joint probability of the coincidence occurring in any one minute we multiply the two separate probabilities. For my rough calculation this comes to about one in 250 trillion. If a coincidence of this magnitude happened to me, I should call it a miracle and would watch my language in future. But although the odds against the coincidence are extremely high, we can still calculate them. They are not literally zero.

In the case of the marble statue, molecules in solid marble are continuously jostling against one another in random directions. The jostlings of the different molecules cancel one another out, so the whole hand of the statue stays still. But if, by sheer coincidence, all the molecules just happened to move in the same direction at the same moment, the hand would move. If they then all reversed direction at the same moment the hand would move back. In this way it is
possible
for a marble statue to wave at us. It could happen. The odds against such a coincidence are unimaginably great but they are not incalculably great. A physicist colleague has kindly calculated them for me. The number is so large that the entire age of the universe so far is too short a time to write out all the noughts! It is theoretically possible for a cow to jump over the moon with something like the same improbability. The conclusion to this part of the argument is that we can
calculate
our way into regions of miraculous improbability far greater than we can
imagine
as plausible.

Let’s look at this matter of what we think is plausible. What we can imagine as plausible is a narrow band in the middle of a much broader spectrum of what is actually possible. Sometimes it is narrower than what is actually there. There is a good analogy with light. Our eyes are built to cope with a narrow band of electromagnetic frequencies (the ones we call light), somewhere in the middle of the spectrum from long radio waves at one end to short X-rays at the other. We can’t see the rays outside the narrow light band, but we can do calculations about them, and we can build instruments to detect them. In the same way, we know that the scales of size and time extend in both directions far outside the realm of what we can visualize. Our minds can’t cope with the large distances that astronomy deals in or with the small distances that atomic physics deals in, but we can represent those distances in mathematical symbols. Our minds can’t imagine a time span as short as a picosecond, but we can do calculations about picoseconds, and we can build computers that can complete calculations within picoseconds. Our minds can’t imagine a timespan as long as a million years, let alone the thousands of millions of years that geologists routinely compute.

Just as our eyes can see only that narrow band of electromagnetic frequencies that natural selection equipped our ancestors to see, so our brains are built to cope with narrow bands of sizes and times. Presumably there was no need for our ancestors to cope with sizes and times outside the narrow range of everyday practicality, so our brains never evolved the capacity to imagine them. It is probably significant that our own body size of a few feet is roughly in the middle of the range of sizes we can imagine. And our own lifetime of a few decades is roughly in the middle of the range of times we can imagine.

We can say the same kind of thing about improbabilities and miracles. Picture a graduated scale of improbabilities, analogous to the scale of sizes from atoms to galaxies, or to the scale of times from picoseconds to aeons. On the scale we mark off various landmark points. At the far lefthand end of the scale are events which are all but certain, such as the probability that the sun will rise tomorrow the subject of G.H.Hardy’s halfpenny bet. Near this lefthand end of the scale are things that are only slightly improbable, such as shaking a double six in a single throw of a pair of dice. The odds of this happening are 1 in 36.1 expect we’ve all done it quite often. Moving towards the right-hand end of the spectrum, another landmark point is the probability of a perfect deal in bridge, where each of the four players receives a complete suit of cards. The odds against this happening are 2,235,197,406,895,366,368,301,559,999 to 1. Let us call this one dealion, the unit of improbability. If something with an improbability of one dealion was predicted and then happened, we should diagnose a miracle unless, which is more probable, we suspected fraud. But it
could
happen with a fair deal, and it is far far far more probable than the marble statue’s waving at us. Nevertheless, even this latter event, as we have seen, has its rightful place along the spectrum of events that could happen. It is measurable, albeit in units far larger than gigadealions. Between the double-six dice throw, and the perfect deal at bridge, is a range of more or less improbable events that do sometimes happen, including any one individual’s being struck by lightning, winning a big prize on the football pools, scoring a hole-in-one at golf, and so on. Somewhere in this range, too, are those coincidences that give us an eerie spine-tingling feeling, like dreaming of a particular person for the first time in decades, then waking up to find that they died in the night. These eerie coincidences are very impressive when they happen to us or to one of our friends, but their improbability is measured in only picodealions.

Having constructed our mathematical scale of improbabilities, with its benchmark or landmark points marked on it, let us now turn a spotlight on that subrange of the scale with which we, in our ordinary thought and conversation, can cope. The width of the spotlight’s beam is analogous to the narrow range of electromagnetic frequencies that our eyes can see, or to the narrow range of sizes or times, close to our own size and longevity, that we can imagine. On the spectrum of improbabilities, the spotlight turns out to illuminate only the narrow range from the lefthand end (certainty) up to minor miracles, like a hole-in-one or a dream that comes true. There is a vast range of mathematically calculable improbabilities way outside the range of the spotlight.

Our brains have been built by natural selection to assess probability and risk, just as our eyes have been built to assess electromagnetic wavelength. We are equipped to make mental calculations of risk and odds, within the range of improbabilities that would be useful in human life. This means risks of the order of, say, being gored by a buffalo if we shoot an arrow at it, being struck by lightning if we shelter under a lone tree in a thunderstorm, or drowning if we try to swim across a river. These acceptable risks are commensurate with our lifetimes of a few decades. If we were biologically capable of living for a million years, and wanted to do so, we should assess risks quite differently. We should make a habit of not crossing roads, for instance, for if you crossed a road every day for half a million years you would undoubtedly be run over.

Evolution has equipped our brains with a subjective consciousness of risk and improbability suitable for creatures with a lifetime of less than one century. Our ancestors have always needed to take decisions involving risks and probabilities, and natural selection has therefore equipped our brains to assess probabilities against a background of the short lifetime that we can, in any case, expect. If on some planet there are beings with a lifetime of a million centuries, their spotlight of comprehensible risk will extend that much farther towards the right-hand end of the continuum. They will expect to be dealt a perfect bridge hand from time to time, and will scarcely trouble to write home about it when it happens. But even they will blench if a marble statue waves at them, for you would have to live dealions of years longer than even they do to see a miracle of this magnitude.

What has all this to do with theories of the origin of life? Well, we began this argument by agreeing that Cairns-Smith’s theory, and the primevalsoup theory, sound a bit far-fetched and improbable to us. We naturally feel inclined to reject these theories for that reason. But ‘we’, remember, are beings whose brains are equipped with a spotlight of comprehensible risk that is a pencil-thin beam illuminating the far lefthand end of the mathematical continuum of calculable risks. Our subjective judgement of what seems like a good bet is irrelevant to what is actually a good bet. The subjective judgement of an alien with a lifetime of a million centuries will be quite different. He will judge as quite plausible an event, such as the origin of the first replicating molecule as postulated by some chemist’s theory, which we, kitted up by evolution to move in a world of a few decades’ duration, would judge to be an astounding miracle. How can we decide whose point of view is the right one, ours or the long-lived alien’s?

There is a simple answer to this question. The long-lived alien’s point of view is the right one for looking at the plausibility of a theory like Cairns-Smith’s or the primevalsoup theory. This is because those two theories postulate a particular event - the spontaneous arising of a selfreplicating entity - as occurring only once in about a billion years, once per aeon. One and a half aeons is about the time that elapsed between the origin of the Earth and the first bacteria-like fossils. For our decade-conscious brains, an event that happens only once per aeon is so rare as to seem a major miracle. For the long-lived alien, it will seem less of a miracle than a golf hole-in-one seems to us - and most of us probably know somebody who knows somebody who has scored a hole-in-one. In judging theories of the origin of life, the long-lived alien’s subjective timescale is the relevant one, because it is approximately the timescale involved in the origin of life. Our own subjective judgement about the plausibility of a theory of the origin of life is likely to be wrong by a factor of a hundred million.

In fact our subjective judgement is probably wrong by an even greater margin. Not only are our brains equipped by nature to assess risks of things in a short time; they are also equipped to assess risks of things happening to us personally, or to a narrow circle of people that we know. This is because our brains didn’t evolve under conditions dominated by mass media. Mass reporting means that, if an improbable thing happens to anybody, anywhere in the world, we shall read about it in our newspapers or in the
Guinness Book of Records
. If an orator, anywhere in the world, publicly challenged the lightning to strike him if he lied, and it promptly did so, we should read about it and be duly impressed. But there are several billion people in the world to whom such a coincidence
could
happen, so the apparent coincidence is actually not as great as it seems. Our brains are probably equipped by nature to assess the risks of things happening to ourselves, or to a few hundred people in the small circle of villages within drumrange that our tribal ancestors could expect to hear news about. When we read in a newspaper about an amazing coincidence happening to somebody in Valparaiso or Virginia, we are more impressed by it than we should be. More impressed by a factor of perhaps a hundred million, if that is the ratio between the world population surveyed by our newspapers, and the tribal population about whom our evolved brains ‘expect’ to hear news.

This ‘population calculation’ is also relevant to our judgement of the plausibility of theories of the origin of life. Not because of the population of people on Earth, but because of the population of planets in the universe, the population of planets where life
could
have originated. This is just the argument we met earlier in this chapter, so there is no need to dwell on it here. Go back to our mental picture of a graduated scale of improbable events with its benchmark coincidences of bridge hands and dice throws. On this graduated scale of dealions and microdealions, mark the following three new points. Probability of life arising on a planet (in, say, a billion years), if we assume that life arises at a rate of about once per solar system. Probability of life arising on a planet if life arises at a rate of about once per galaxy. Probability of life on a randomly selected planet if life arose only once in the universe. Label these three points respectively the Solar System Number, the Galaxy Number and the Universe Number. Remember that there are about 10,000 million galaxies. We don’t know how many solar systems there are in each galaxy because we can only see stars, not planets, but we earlier used an estimate that there may be 100 billion billion planets in the universe.

When we assess the improbability of an event postulated by, for instance the Cairns-Smith theory, we should assess it, not against what we subjectively think of as probable or improbable, but against numbers like these three numbers, the Solar System Number, the Galaxy Number and the Universe Number. Which of these three numbers is the most appropriate depends upon which of the following three statements we think is nearest the truth: