Complexity, Probability, and God

A very old, highly intuitive, and still common argument for the existence of God is the Argument from Design.  The thrust of the argument is that the ordered complexity exhibited by the universe as a whole, and in particular by living things, is evidence that there must be an intelligent designer, since the existence of such complexity cannot be otherwise explained.The word “design” as used in this argument refers to the order and incredible complexity not just in biological systems, but also in the very intricate laws of nature that operate throughout the universe.  But, of course, “design” and “complexity” are not the same.  The theist can’t just point to an example of complexity and say, “See, it’s complex, so it is designed.”  That’s just question begging; after all, the whole question at issue in this debate is, “Does complexity imply design?”

We should clarify here what it means to say that a thing is complex.  To say a living thing is complex is to say not only that it has a lot of parts, but that the parts are arranged in a way that is unlikely to happen by chance and those same parts cooperate in a functional way.  For example, in living systems the various parts work together to do such things as run, swim, and fly—let alone live.  Complex non-living systems in the context of the design argument are usually restricted to those that appear to serve a purpose, such as the system of “parts” called the Solar System, which is so configured that the earth is kept at just the “right” distance from the sun to maintain its orbit.The flaws in the Argument from Design are several.  First, using the existence of complexity as a proof for God amounts to a self-contradiction; second, a common form of this argument (made famous by William Paley) misunderstands how humans identify intelligent design; and third, a common version of this argument that is based on probability misrepresents the role of randomness in evolution.1  Let’s look at each of these in turn.

Setting aside any appeal to Darwinism for the moment, what could it possibly mean to say that complexity in living things implies the existence of an intelligent designer like God?  One can only assume that God, whatever that term might refer to, must have at least as much complexity as anything He is supposed to have designed.  Given the theist’s assumption that complexity requires a designer, God’s own complexity implies that He also had a designer.  Either the theist is arguing for an infinite regress of God-designers and designers of God-designers, etc., or he is contradicting his own assumption that complexity requires design.  By using God as an “explanation” the theist is doing nothing more than explaining complexity (in living things) with complexity (God’s).  But this amounts to assuming what one is trying to explain, which is no explanation at all.  It just moves the mystery back a step.

This is the same logical flaw in using God to explain existence itself.  The theist often asks, “If you don’t believe in God, then how do you explain the existence of the universe?”  This question assumes that existence must be caused, and since the universe clearly exists, it too must be caused.  The theist then concludes that God must be that cause.  Now, presumably the theist supposes that God, like the universe, also exists, in which case the theist is right back to violating his own assumptions:  If God exists, and existence must be caused, then by the theist’s own assumption, God must be caused.  By using God as an “explanation” the theist is doing nothing more than explaining existence (the universe’s) with existence (God’s).  And just as before, this amounts to assuming what one is trying to explain.

Typically the theist’s reply to these criticisms is that God is the one exception: All complexity except God’s complexity must be explained, and all existence except God’s existence must be explained.  But this is blatant special pleading.  The theist is simply exempting himself from his own rules:  “Your explanation must meet these conditions; however, my explanation (God) does not.”  Of course, anyone can play this game.  Once could just as easily (and with considerably more parsimony) say all things except the universe as a whole require an explanation.

Even if one wanted to grant the theist his special exemption, other problems remain, which we can see by reviewing what it means to “explain.”  To say that something is “explained” means we’ve moved from the known to the unknown; it does not mean we moved from the unknown to the unknown.  Put simply, you cannot explain a mystery with a mystery.  If someone wants to use God to explain anything, then he would have to understand the mechanisms by which God causes something to happen, but since God is “supernatural,” then this mechanism is inherently mysterious and unknowable.   For example, to use God to “explain” complexity one would have to understand the nature of God’s supposedly uncaused complexity and the means by which it causes complexity in the natural world.  It will not do to say that such understanding is “beyond us,” forever unknowable to our limited intellects, etc.  Doing so would be no different than “explaining” rain by appealing to the mysterious properties of an unknowable rain god.  Explaining mysteries with other mysteries has all the explanatory power of saying, “It’s magic.”

We’ve seen that a supernatural God cannot serve as an explanation for anything, especially if God has the very properties His existence is supposed to explain, like the properties of complexity and existence.  But this is not the only fatal flaw in the Argument from Design.  William Paley made a rather beautiful, highly intuitive, and completely mistaken design argument when he asked us to imagine someone stumbling across a watch lying on the ground, and then carefully examining its mechanism.  He says this person would certainly observe that the watch’s

…several parts are framed and put together for a purpose, e.g., that they are so formed and adjusted as to produce motion, and that motion so regulated as to point out the hour of the day; that if the different parts had been differently shaped from what they are, of a different size from what they are, or placed after any other manner, or in any other order, than that in which they are placed, either no motion at all would have carried on in the machine, or none which would have answered the use that is now served by it…[Therefore] there must have existed…an artificer or artificers, who formed it for the purpose which we find it actually to answer; who comprehended its construction, and designed its use.

Paley then draws his eloquent and persuasive analogy:

…every indication of contrivance, every manifestation of design, which existed in the watch, exists in the works of nature; with the difference, on the side of nature, of being greater and more, and that in a degree which exceeds all computation.

One crucial problem with Paley’s argument is that it assumes humans determine whether or not something is designed by seeing if it has an accurate adjustment of parts—that is, if it shows complexity.  But this is certainly mistaken.  We know that something is designed not by its complexity, or even the degree to which it appears to serve a purpose, but by looking for ways in which it differs from nature.  In other words, nature is the benchmark against which we compare an object to see if it is designed.

For example, many naturally occurring rock fragments just happen to have a sharp edge that is well-suited for serving the purpose of chopping meat, though this does not lead us to believe that these fragments were designed.  Yet, we have found clearly manufactured prehistoric chopping and cutting stones that were designed.  How do we know they were designed and not just examples of fortuitous rock fractures?  Clearly it is not because they are sharp, since naturally occurring rocks are also sharp; and not because they are complex, since they have neither parts nor complexity; and not because they serve a purpose, since obviously random events can make a rock very sharp.  We know these stone hand axes were designed because they have markings on them that differ from what one would find in nature—that is, they have signs of manufacture.

Because the proper criterion for establishing design is difference from nature, and not complexity or apparent usefulness, we can know that something was designed even when it is both extremely simple and has no identifiable purpose at all.  This can be seen when we realize how easy it is to recognize as designed an unidentified simple part from an unidentified machine, such as an L-bracket, or a bit of wire insulation.  If Paley were right, it seems that this should be impossible, since neither purpose nor complexity is apparent.

These examples show that purpose and complexity are not the criteria we use in establishing design.  We know Paley’s watch was designed not because it is complex and/or serves a purpose, but because we recognize it as similar to other products of human manufacture, and / or because of its dissimilarity to anything naturally occurring.  So Paley had it wrong: we don’t know something is intelligently designed because it shows complexity; we know it is designed because it shows signs of manufacture, and the only way we know something is manufactured is by comparing it with nature or by having direct experience of its manufacture.  Now, if the criterion for determining design is comparison with nature, then it makes no sense to apply that criterion to nature itself since nature provides the very benchmark for making the comparison.  But this is precisely what Paley does in order to infer a super-designer.

Even if we ignore this criticism of Paley’s argument (which is decisive on its own), other problems still remain, not the least of which is the analogical form of the argument.  Paley was arguing by analogy.  In other words, since a watch shows adaptation of parts to an end and was designed and built by a designer, then by analogy we observe that nature also shows adaptation of parts to an “end,” and infer that it too must have been designed and built by a designer.  Unfortunately for Paley’s argument, if we consistently apply his analogical reasoning, then we would reach conclusions that he surely didn’t intend.  For example, our only experience with the relationship of designers to their highly complex handiwork, like watches and computers, is that there is a whole team of mortal, imperfect designers of limited power that work on one or very few complex creations—and not one immortal, perfect, and supernatural designer for all complex artifacts. So if Paley’s analogical argument were valid, we would have to conclude that living organisms were made by a team of mortal, non-supernatural, and imperfect creatures, all of whom are limited in their powers, and that different classes of complex things were made by different teams of mortal “gods.”

So far I have argued not only that a supernatural God cannot serve as an explanation for complexity or the existence of the universe, but also that His existence cannot be inferred from these.  So at this point, complexity, particularly the complexity of biological organisms and organs such as the human eye, remains unexplained.  If I were writing before Darwin’s time, I would close at this point with the comment that while we don’t know what the explanation is for the existence of complexity, we do know what the explanation is not—and it cannot be “God.”  Fortunately, however, we are writing after Darwin’s time.  For those readers not familiar with some of the basic tenets of Darwinism I would suggest reviewing the introductory article on this site, Evolution v. Creation, and then the article Evolution: Converging Lines of Evidence.

Often, the creationist will point to the genuinely awesome complexity of something like the human eye, or the bird’s wing, and argue that random chance could never have produced such engineering marvels. The creationist is absolutely correct.  To drive this point home, the creationist then quite correctly likens the odds of a structure like the eye forming by random chance to the odds of a tornado moving through a junkyard and producing a 747 passenger jet.  Again, this is an entirely appropriate analogy. The odds of chance alone producing something as exquisite as the human eye—or even single cell, for that matter—in one step is, for all practical purposes, zero.

Curiously, the evolutionist and the creationist are in complete agreement on this point. The creationist, however, seems to think that it somehow refutes evolution—much to the bewilderment of evolutionists. The reason for this is that the creationist has seriously misunderstood evolutionary theory.   Evolution’s major mechanism, natural selection, is the very opposite of random chance.  Natural selection is all about “cherry picking” and saving useful changes generation after generation.  All random chance provides is, in some sense, the “buffet” from which natural selection can select useful but slight changes.  The critical aspect of this process is that it accumulates these slight changes such that over time the accumulated change is not small at all.

The crucial point here is that there are many, many generations over which this cherry picking occurs, not just one.  To take an extremely simple example, imagine that I have a big box filled with one thousand pennies.  I shake up the box and pick out all the pennies that come up heads, which will be around five hundred (a fifty-fifty chance of coming up heads, so about half of the one thousand pennies): that’s generation one.  I then replace the missing pennies in the box and shake it up and again take out all the heads: that’s generation two.  It’s not too hard to see that in just a few “generations” I would have a pile of several thousand heads-up pennies.  The creationists’ Random Chance criticism applied to this example would amount to pointing to this huge pile of heads-up pennies and saying, “the odds of getting just one thousand pennies to come up heads is one out of a number so large it has three hundred zeros after it, and this evolutionist wants us to believe that with random chance alone he got not just one thousand heads-up pennies but several thousand!”

This imaginary critic’s calculation is absolutely correct. The odds of getting just one thousand heads in one try is so small that if we made a try every second for many billions of years it probably wouldn’t happen even once.  Yet we were able to get not just one thousand, but several thousand heads-up pennies in something like an hour.   Something is obviously wrong somewhere.  That somewhere is in the creationist’s assumption that evolution is supposed to occur in one try and with no selection, which really is analogous to a tornado going through a junkyard and producing a 747.  However, in our pennies example we had more than one try and we got our pile of heads not randomly, but by selecting them non-randomly (by cherry-picking the “good” ones) out of the random variation produced by shaking.  We then saved them up over the multiple tries – adding them to what was saved from previous generations.   Now, keep in mind that in nature, natural selection operates not over a few tries, but over many hundreds of thousands of tries (generations) and over millions, even billions, of years.

Of course, the variation produced by random chance in the pennies example is just heads or tails, and we decided that heads are “better” than tails, so only heads “survive” into the next generation.  Also, the heads-up pennies that make it into the next generation are not more likely to produce heads instead of tails—that is, they don’t reproduce by copying themselves in the way biological systems do.  This is why we won’t get anything complex out of the pennies example, though we do accumulate changes that dramatically “beat the odds.”  Natural selection in biology beats the odds in just this way, but it does so with heredity and a much, much larger range of possible variations than just heads and tails—variations that interact with each other to create many different orders of effects that also interact with each other—that is how biological complexity emerges.  How this process creates complexity is discussed elsewhere on this site, and is even demonstrated through our Freethought Debater version of Richard Dawkins’ Biomorphs program, so it won’t be repeated here.  The point of the preceding discussion is to show another fallacy underpinning the Argument from Design: the misuse of probability when criticizing the theory of evolution.

I have argued that there is no coherent way to use God as an explanation for the existence of complexity since, among other things, God himself is presumably complex.  Similarly, God cannot even be used to explain existence since God, when used as an explanation, presumably exists himself.  I have also argued that Paley’s Watch Argument mistakenly supposes that the existence of complexity and apparent purpose in an artifact are the criteria for establishing that it was designed, and it also makes an inappropriate analogical argument between man-made artifacts and nature.  Finally, I pointed out the most common misuse of probability calculations by theists in their attempts to prove the existence of God and/or attack the plausibility of evolution—namely, that of ignoring the fact that natural selection is not about the appearance of random, spontaneous complexity in one event, but about non-random cumulative selection, which occurs over many, many tries.


1Excellent discussions of the design argument can be found in Richard Dawkins, The Blind Watchmaker (New York: W.W. Norton, 1996), as well as George H. Smith’s, Atheism: The Case Against God (Amherst: Prometheus Books, 1989).  A more technical analysis of these arguments can be found in Michael Martin, Atheism: A Philosophical Justification (Philadelphia: Temple University Press, 1990).

One Reply to “Complexity, Probability, and God”

  1. Excellent article. Enjoyed the discussion, examples, clarity. Having read elsewhere about the anthropic principle which – correct me if I am wrong – claims our existence, our universe as being essentially non-random though just one of multiple other universes,while also, of course, non-creationist. Answers for just how DNA and life came about are possibly to be sought in “complexity.” I am looking for pointers to this hypothesis, or theory, if at all possible, in layman’s terms. Can you help? Many thanks again. I wish to remain on tab.

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