An event with an astronomically slim chance of happening (probability very, very close to zero) will, in all likelihood, never happen - at least in the meaningful lifetime of this universe. It is extremely important, however, to note that this conclusion only applies to events happening in the future. If we look at events that have already happened, we find all manner of seeming exceptions. Individuals do win large lotteries. A large pile of sand heaped upon a table has an arrangement of grains so improbable that we would never expect it to happen again despite billions of years of trials. Is this a contradiction in our understanding of probability? Should we arrest the lottery winner on the assumption that fraud is more likely that an honest win?
A little reflection, of course, tells us that somebody is going to win the lottery; a pile of sand is going to assume some arrangement on that table, however improbable. Attempting to calculate such probabilities AFTER THE FACT is like firing an arrow at a distant wall and painting the target around that arrow. Thus, that arrow appears to have defied the odds by "hitting" the very center of the target. In effect, we are accepting all outcomes. Any arrangement of that sand pile will count as a hit. Any spot where the arrow strikes the wall will become the center of our target. On what grounds, then, might we suspect that mere chance is not enough - after the fact?
The trick is to mentally roll back the clock and see if the present result is in some way marked or set apart from all the other alternatives. If Joe won the lottery, and we roll back the clock to before the winning ticket was announced, would we have any means of picking Joe out from the crowd? Would the present configuration of that sand pile on the table stand out in some way from all the other possible arrangements? If the answer is no, then any attempt to calculate their odds is a meaningless exercise akin to painting a target around the arrow. However "unlikely" they may be, we have no grounds for suspecting that anything other than ordinary chance is involved.
If we rolled back the clock and found Joe writing huge checks just before he won the lottery, despite a limited bank account, despite being a rational, intelligent person, then an investigation would certainly be warranted. In that sense Joe has been "marked" in that he naturally stands out in the crowd before the event occurred, and the inspector would be wondering how Joe expected to win such an improbable event. The number of people writing such checks, who also participated in the lottery, would be virtually zip compared to the number of total ticket holders. We would not expect such a person to win by fair means. Inside knowledge is strongly implied.
Sue, on the other hand, is the mayor of a small town. Only a few mayors hold tickets to the lottery. However, Sue is not similarly "marked" in that being a mayor bears no meaningful connection to the lottery. We have no reason to single Sue out, a priori. On the other hand, if Sue were an official involved in the lottery, we would rightly be very suspicious if she won the grand prize. Such an obvious connection to the lottery would clearly "mark" her. The probability of someone in that position rigging the results is much greater than the probability of winning the grand prize. On the other, other hand, if we lived in a society where everyone was scrupulously honest, then Sue, as a lottery official, would not be marked.
If we randomly rolled a ten-sided die 100 times and found that the numbers generated corresponded to the first hundred digits of pi, what should we conclude? In a sense, the number pi is marked before the event happened in that pi is a famous number in mathematics. However, there are many other remarkable numbers too, including simple numbers like 1.0000... and 2.50000... that would certainly catch our attention. It is the "catching of our attention" that counts here and not just the odds of getting pi to the first hundred digits. For most of us, those numbers that would catch our attention, if expressed to 100 digits, are but a tiny drop in the bucket compared to all possible outcomes. Thus, we would rightly feel that a genuinely rare event has happened, leading us to suspect that someone was playing a slick trick on us.
Any string of 100 digits, of course, is equally improbable. However, we have no means of identifying, a priori, the vast bulk of them. They are not "marked" as discussed above. Consequently, upon getting such a "random" result, we would rightly conclude that nothing remarkable has happened. Yet, that same roll of the dice, yielding 100 digits meaningful to some alien race, would be counted as a remarkable event in their eyes. To the extent that a target can be identified before the arrow is shot, to that extent a meaningful after-the-fact probability can be calculated.
Creationists, who wish to calculate the odds of starting with hydrogen gas and winding up with humans, have fallen headlong into the above pit. If we rolled back the clock, humans would not exist - and we would (as detached, logical observers) have no reason to even consider such animals. The only thing that is meaningfully "marked" is ANY form of intelligent life, ANYWHERE, ANY TIME, that is capable of reflecting on this issue. Nobody has the means, at present, to even recognize all the forms that intelligent life may take -- let alone calculate the odds of such happening anywhere in this universe or, possibly, in an infinity of other universes, at any time. Therefore, any attempt to calculate such odds is plain silly and reflects a basic ignorance of probability theory.
The same problem holds for those "impossible" odds that creationists come up with when they calculate the probability of some protein (and thus life) forming all by itself. Aside from making other grievous errors, such as neglecting to factor in the various, possible intermediate steps of an evolving product, they fall into the above pit. If we roll back the clock, once again, is the arrangement of that particular protein "marked" as a requirement for the evolution of life? Might countless, alternative forms of life arise that don't even use that protein or anything like it? And of those that do, will their earliest forms require anything like the efficiency of that protein? We know for a fact that quite a few changes can occur in most proteins (outside of the critical sites) without significantly affecting their function. Indeed, entirely different proteins often do similar jobs at various levels of efficiency.
What is actually "marked" is ANY natural means for life arising, ANY direction that evolution might take towards "higher" life, at ANY time, and ANYWHERE in this universe or, possibly, others -- not just the particular path life took on earth. Consequently, those who would deny the natural origin and evolution of life on earth on the basis of such calculations HAVE NOT EVEN BEGUN to consider the appropriate data. We presently have no way of even knowing the scope of the problem, let alone having the data and knowledge for anything like a rigorous calculation. The one, telling fact that we do have is that life seems to have originated as soon as conditions permitted. If life were a truly rare event, it would be unlikely to appear at the earliest possible moment on Earth. (Any time within a one or two billion-year interval would work just as well in terms of the odds.) The fact that life appears so quickly right after the primordial, meteoritic bombardment (prior to which life could not survive), thus being "marked" in that respect, suggests that the odds of it arising naturally are quite good - at least for conditions that prevailed when the earth was young. Invoking a direct, supernatural origin of life in an attempt to deny this conclusion does not explain the timing of life's appearance on earth. The theistic evolutionist might well conclude that God wound up the clock and let things take their own course.
Therefore, we have good reasons to reject those dazzling calculations expounded upon by so many anti-evolutionists. All those strings of zeros of improbability they come up with, filling the universe as it were, become rather silly when we realize that those guys are not even playing the right game - let alone being in the right ball park!
Dave E. Matson,