Probability and Meaning

Probability and Meaning

One of the things that well-meaning apologists for the Christian Faith do from time to time, is argue that the odds against the universe having the laws that it has, especially in the combination of these laws, is astronomically unlikely. This is a fact that everyone who is aware of the issues will grant. However, the conclusion that is often drawn from this is that such an incredible statistic should drive us to conclude that the Christian doctrine of creation (and who knows but all other traditional doctrines of Christian faith) is true.

The chief problem with this, as atheists are quick to point out, is that the argument trades on a conviction that "Incredibly Unlikely" => (that's "implies") "Designed by an Intelligent Source (or at least profoundly significant in some way)." In spite of the best efforts of such apologists, such an implication is simply not valid. Not valid, that is, as stated. There is an additional dimension that is taken for granted by the apologists that needs to be made explicit and, until it is, it will not hold any water at all.

Michael Polanyi, a Hungarian Physician/Chemist/Philosopher of Science, wrote his monumental work, "Personal Knowledge" based on the Gifford Lectures of 1951-52 on a wide range of topics, ultimately arguing that the goal of absolute objectivity (or, perhaps more accurately, "objectivism") that some claim for science is unattainable and should never have been viewed as the goal in the first place. It should be noted that Polanyi did not set out to undermine science in any way, but rather to help put it back on its proper foundations, where it functions quite authoritatively. In fact, he was trying to provide a more accurate account of how science actually works (which, as a scientist, he found was not the same as the way many scientists believed it to work) and promote more complete honesty among scientists. It should also be noted, for the sake of total disclosure, that Polanyi was himself a Christian, though his Christian faith does not enter into his writings on science and his views on evolution would not be agreeable to many particularly conservative Christians.

In the third chapter, on Order (and following a chapter on Probability), Polanyi suggests three scenarios. The first is that, at a particular village, when one enters by rail, there is a statement on the railway embankment in pebbles that reads "Welcome to Wales by British Railways." It is clear that those stones were placed by an intelligent human being who designed their location with some care. If someone were to challenge this view, how might we defend it? We would take the number of all the different ways that those pebbles could be arranged to make the phrase, and divide it by the total number of ways the pebbles could be arranged on the embankment (an incomprehensibly higher number) and say something along the lines of, "See? It is so improbable that it would have happened by accident; it must have been planned."

The problem arises if we imagine that, long after the person responsible for the phrase dies, the pebbles may find themselves scattered around the embankment in a haphazard manner. But what if someone were to argue that the evidence was just as strong that they are in this position by intelligent design than it was earlier. If we do the math, we find that the odds of the pebbles falling to this exact location is just as astronomical as before. Using a purely statistical approach, the evidence is identical on both sides.

Another example is that we would find it coincidental, interesting and incredibly unlikely (in the sense of "surprising") that someone was the 500,000 visitor to an exhibition, whereas we would not if they were the 573,522nd visitor, even though, if we do the math, the odds against being the latter are higher than against being the former.

The third example is to take twenty flips of a (fair) coin. Let us say they are all heads. What are the odds of this happening? Two to the twentieth power, or 1,048,576 to one. Sounds significant. But if we think about it, it turns out that every unique sequence of twenty throws of a coin are equally improbable. We now have over a million results that are, statistically, equally unlikely. Why single out one of them (or two if we also consider twenty tails in a row to be significant) to be particularly striking?

The point that Polanyi is getting at is that probability is not the only factor at work in this kind of reasoning. The striking thing about the first example is not that it is unlikely that the pebbles would be arranged at random, but that they were arranged at random and it resulted in an English phrase that made complete sense in that particular location where it wouldn't in nearly any other part of the world. The distinguishing factor is meaning. It isn't that we could pile a bunch of rocks in any particular way and have it happen to be unlikely how it turns out, but it is that it is incredibly unlikely that such a pile would be the carrier of a message (in whatever form this message may take) that has meaning for a specific group of people. The issue is whether the unlikely event is of no particular meaning, that is, it could easily have been different with no substantial impact ("noise") or whether it makes a considerable impact (a "tune").

This raises the key question. How can we tell whether what seems to us at first glance as random is a tune or whether it is just noise? That is to say, how can we know if there is a message, whatever that message may be, embedded in the details or whether it is nothing more than random facts with no significance? This is a real question (though the example is somewhat trivial) for those who cannot see the hidden images contained in Magic Eye puzzles. Everyone around them proclaims that there is an image to be seen; they can independently verify what it is and can even trace it out with their fingers, but, so long as the individual in question cannot see it, the dilemma remains: Is there really an image that I cannot see, or is everyone around conspiring against me?

Another example might be that of Stonehenge. Such a huge monument has attracted attention for years. If we were to forget everything we knew about the function of Stonehenge, we would have to ask the question, "Were these stones placed here for a reason, or is it merely random?" We might be inclined to the former conclusion because it might seem impossibly improbable to explain how the rocks ended up where they were merely by chance, but, since chance is not convincing evidence in and of itself, as we have noted above, it is not sufficient to tilt the argument decisively in one direction or another. It is only when we begin to say, "These rocks are here as a calendar," when we notice how it charts the solstices, that we are fully convinced, beyond all reasonable doubt, that the rocks are meaningful.

The problem still remains. How can we judge whether the object of our study is truly random, that is, purely coincidental or meaningful in a way we cannot yet understand? How do we know that what seems to be nothing more than white noise does not contain a message we have simply not yet learned the language to understand? The fact of the matter is that there simply is no surefire way to judge ahead of time which is the case. What is more, there is no way to ever prove that there is no message, even after countless trials. One can only prove, or make a strong case for, a message bring present; never that one is absent. After all, a message may emerge one day after years of fruitless research. Projects to understand a given reality may even be abandoned and yet be pregnant with a meaning that we have not yet been able to grasp.

This does not mean, of course, that we should operate with the assumption that every seemingly meaningless thing has a hidden, deep meaning. We simply cannot function if we look at every arrangement of rocks or grass as holding a deep truth about the universe. Sometimes things that appear meaningless are precisely that. Among scientists, there is only so much grant money available, there are only so many pages in a given journal, there are only so many lab technicians, which means some selection must take place. Not every lead can be followed; not every pattern can be analyzed in every possible way. Decisions must be made and they must be made knowing full well that by doing so, important discoveries that have hitherto been just beyond reach, might be missed.

So, to return to the question raised by apologists in our modern world, is the universe an accident or is it created? The decisive point in the argument is not on the improbability of the universe being precisely what it is and not otherwise, but on whether the universe being what it is is full of meaning that would be destroyed if it were not what it is. This often takes place around the issue of the so-called "anthropic principle." I do not mean to suggest that this observation will solve this or other problems easily, but that it must be taken into account and realized that the battlefield upon which much debate has raged is a false one and should be abandoned by both parties, so that we might start again and have more authentic, more fruitful, more honest discussions. The question is (we might say always) one of meaning. Not just "What is it?" but "What does it mean?"