Random thoughts

I would say that theists have a hard time dealing with randomness, but that would be misleading. Quite a few nonbelievers also dislike randomness. Randomness offends against the intuition that everything has a cause, whether this eventually means supernatural ultimate causes or a universe where every event has a natural cause.

Still, religious thinkers seem to have a particular animus against randomness, continually speaking about the absurdity of it all coming down to chance. Those parts of modern science that present random aspects of nature attract religious suspicion. Quantum mechanics is full of randomness. Darwinian evolution relies on random variation to supply the novelties selection then works upon. They create theological problems.

Creationists solve their problem by denying and denouncing randomness. But randomness, by suggesting lack of design and direction, challenges more science-friendly theists as well.

Divine Action and Natural Selection has numerous examples of what is one of the standard liberal religious responses to randomness: saying that apparent randomness is compatible with a God running the show. After all, it is possible that if we take a broader view than just physics or biology, what we thought was random might just be God’s way of accomplishing divine purposes. Rabbi Natan Slifkin, for example, points out that

One point to note is that it is impossible to ever determine whether something is truly random. One could take a string of a hundred seemingly random numbers and perform every conceivable test, and discover no pattern. Yet it could be that those numbers were actually the numbers preceding the one hundred digits that appear after the millionth digit of Pi. So, they were not actually random at all. [p. 623]

Indeed, this is absolutely correct. Randomness is, strictly speaking, a property of infinite sequences. By looking at a patternless (algorithmically random) finite sequence, we can guess that the finite data is part of a random sequence. But this inference is always fallible.

But that misses the point! Mere compatibility between science and God is very cheap and easy to obtain. A creationist who declares that God placed fossils in the earth to test the faith of believers is also achieving compatibility, in much the same way. The real question is what is the best model, the best explanation to account for the finite but patternless data. In that context, bare compatibility is not all that relevant. It’s still possible that what we thought was random was only apparent randomness, but we cannot infer this on the basis of the patternless data. We need further information. It may be that an intelligent designer is responsible for quantum fluctuations or the contingencies of evolution. But we cannot infer this from present-day physics or biology. We need some other reason to think there is a God behind the scenes, pulling the strings of what is apparently random. For example, a clear and convincing revelation expressed in some kind of scripture might work. Good luck with that. In the absence of a pattern revealed by bringing in a wider range of data, scientists are perfectly correct to say that they’re dealing with actual randomness.

I don’t want to pick on Slifkin; he’s just the easiest one to quote. There are others in Divine Action and Natural Selection who make the same error, even when they should know better. For example, Stephen M. Barr, who is a legitimate and respectable particle physicist, but who is also a conservative Catholic with ambiguous intelligent design leanings. Indeed, Barr has become a favorite among some conservative Catholic intellectuals in the US, such as Michael Novak.

A shorter exposition of Barr’s thoughts on randomness and evolution can be found in his First Things article, “The Design of Evolution.” After Barr’s paper in Divine Action and Natural Selection, you can find my critique, as part of a dialogue between us. But in short, it’s the same mistake, made worse by errors in Barr’s technical understanding of randomness. (Why does a physicist, when reflecting on randomness, not refer to the relevant mathematical literature, rather than drowning the concept in theological gobbledygook?)

I’ll stop here before this turns into even more of a rant. In any case, randomness is one of my personal hobbyhorses, and one of the major themes in my books. If you’re interested, read them to find out more.

About Taner Edis

Professor of physics at Truman State University

  • http://www.blogger.com/profile/12763971505497961430 Jeffrey Shallit

    In the Kolmogorov theory, it is not correct to say (as you did) that randomness is a property only of infinite sequences.

    In fact, one of the very first results proven in any book on Kolmogorov complexity is that there exists a random binary string of every length. Here “random” is a synonym for “incompressible”.

    While it is true that we cannot explicitly produce such a string (except perhaps for some small values of n, depending on your model of universal machine), we know that they exist.

  • http://www.blogger.com/profile/10778996187937943820 Taner Edis

    Jeffrey Shallit: “there exists a random binary string of every length. Here “random” is a synonym for “incompressible”.”

    We don’t disagree. That’s algorithmic randomness, which applies to finite strings. Randomness is the n -> infinity limit.

    Making the distinction can be useful. For example, for finite n, the compressibility of a sequence depends on the language you’re using. That dependence goes away at the infinite limit.

    My view of how randomness comes into play in physics is roughly like this. We make a long series of observations, such as that of a quantum two-state system, and find a patternless string of data. That is, as far as our ability to tell (we may be wrong, especially since there is no algorithm to test for algorithmic randomness), algorithmically random. But we want to model this data, asking what sort of function we see fits the data. After all, we can keep taking data indefinitely. A function is an infinite string. So we say that our best guess is that the finitely-random data was generated by a random (in the infinite sense) function. So in this context, the finite/infinite distinction is useful.

    Again, I don’t think we disagree. At least I hope not.

  • http://www.blogger.com/profile/13562135000111792590 RBH

    I’ve never quite understood why theists have a problem with randomness. After all, in the Bible what can only be seen as random events are treated as routes by means of which Yahweh conveys his wishes to humans, as for example Joshua casting lots in the Old Testament to divvy up Canaan among the tribes of Israel and the disciples in the New Testament casting lots to decide between candidates to replace Judas.

  • http://www.blogger.com/profile/10778996187937943820 Taner Edis

    RBH: “I’ve never quite understood why theists have a problem with randomness. After all, in the Bible what can only be seen as random events are treated as routes by means of which Yahweh conveys his wishes to humans”

    My impression is that they don’t have any problem with apparent randomness in exactly that sense. The outcome can’t be predicted by mere humans, but in the deeper reality, it is determined by the gods. By casting lots, or trial by combat, or whatever mechanism of uncertain outcomes you use, what you’re doing is surrendering to the divine will.

  • http://www.blogger.com/profile/09925591703967774000 Dianelos Georgoudis

    Taner Edis writes: “I would say that theists have a hard time dealing with randomness, but that would be misleading.” Well, I don’t personally have any problem with randomness; quite on the contrary I think the best way to make sense of evil is to recognize it is random. Of course one can accept that some events are random, without believing that all events are random. So, why do you think that theists have a hard time dealing with randomness? You write that randomness creates “theological problems”. What problems do you have in mind?

    You write that randomness “suggests lack of design and direction”, but that’s not necessarily the case as evidenced by algorithms that use randomness to achieve their ends. You write that “Quantum mechanics is full of randomness”, but this is only true of its modeling of phenomena. An ontological interpretation of QM need not use randomness, as evidenced by the various deterministic interpretations. (I always find useful to think of Plato’s model of the shadows in the cave; the shadows themselves may be random but the reality that produces these shadows may not be.) You write that “Darwinian evolution relies on random variation” but I think that’s false, for Darwinian evolution will work fine using a sufficiently good pseudo-random (and hence deterministic) source too.

    Perhaps you mean that if true randomness exists then God could not have guided Darwinian evolution to an end-result that God has designed. But as we saw phenomenally true randomness may exist while ontologically it doesn’t. In any case, if a theist is a dualist here is an idea for guided natural evolution that Alvin Plantinga proposed in one of his lectures: Suppose that God first designs us in His/Her mind as it were. Then God, again in His/Her mind considers Everett’s many worlds, and of these considers the huge number of worlds in which the desired design obtains. Of all of them God chooses the one whose statistical probability is greatest (no detectable hocus pocus there) and actualizes this one into material reality.

    You write that it is easy to obtain “mere compatibility between science and God”. I agree of course, but I wonder whether Richard Dawkins would agree with that. I understand he strongly believes that that theism cannot be compatible with science. (In comparison I question whether ontological naturalism can be made compatible with science, but that’s another question.)

    You write: “The real question is what is the best model, the best explanation to account for the finite but patternless data.” I agree, but would like to point out that 1) not all our data are patternless and that’s why knowledge including scientific knowledge is possible, and 2) we have more data in our disposal than science deals with, namely we have the whole experience of life and not just our observations of physical phenomena. To me one of the strongest reasons for believing in God is that theism works much better as an explanation for all our experience of life than naturalism.


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