Does God Play Dice?
Does God Play Dice?
Or, Towards a Theology of Chance
The one really excellent book I have read on this topic, to which the present article is heavily indebted, is David J. Bartholomew’s God, Chance, and Purpose: Can God Have it Both Ways?. Bartholomew is an Emeritus Professor of Statistics at the London School of Economics and Political Science, and was the President of the Royal Statistical Society from 1993 to 1995. His writing is extremely clear and accessible. The late Revd. Canon Arthur Peacocke MBE has produced further theological reflections, especially in Theology for a Scientific Age: Being and Becoming – Natural, Divine, and Human, pp.115-121.
God, Einstein quipped, does not play dice. Or so it seemed. Now, however, our current scientific picture of the world seems to involve a significant element of chance, in such diverse areas as the origins of life, evolution by natural selection, and mainstream interpretations of quantum mechanics. This observation prompts some of the most difficult questions at the intersection of theology and science. What does it mean to uphold the traditional creedal claims of God’s goodness, omniscience, sovereignty (i.e. omnipotence), and purpose for the natural world He created if that world seems to have chance built into it?
When we say that a possible event E is due to chance, what we mean is that there is nothing in the world that would allow us to predict whether E actually occurs at time t. Now there is an ambiguity here: is the occurrence of E unpredictable because we simply don’t (or couldn’t) know all the relevant information, or is it in some sense intrinsically unpredictable – the product of a truly random process? The latter possibility is the theologically troubling one. For a truly random process would be unknowable even by God. And does the theist really want to say that not even God knows whether (say) this uranium-238 atom will decay in the next ten seconds? Is such a God still “in control” of His creation?
Certain theologians (typically in the Reformed tradition) have argued against construing chance as evidence of actual randomness in the world. These Reformed theologians prefer a totally deterministic doctrine of divine sovereignty, in which God controls the outcomes of even the “chance events” of the physical universe. Under this view, chance is not an agent or entity; there are no random processes; and chance events are unpredictable only from a human point of view.
But, as David J. Bartholomew argues in God, Chance, and Purpose, the Reformed position may be unsatisfactory in light of the empirical fact of chance. In the quantum arena, Bell’s theorem shows that all deterministic, non-probabilistic interpretations of quantum mechanics (e.g., “hidden variables” theories) must give up the principle of locality, which is a rather unappealing move (cf. Bartholomew, p.199, fn.3). This strongly suggests that the deterministic route is not the way to go.
Furthermore, and less technically: even if chance events aren’t actually caused by random processes, they still look as though they were. This in itself is theologically significant: “something indistinguishable from pure chance is being used” by God in the structure of His creation (Bartholomew p.204). If God’s character and intentions are supposed to be reflected in the structure of His creation, then it would seem a little odd for God to be causally micromanaging the universe “somewhat furtively under cover of randomness,” as Bartholomew puts it; one might wonder whether that is “a God-like thing to do” (p.130). If this is what God were doing, it would be very impressive, but also rather misleading, to say the least. So what are we to do?
It seems that, especially in light of the quantum revolution, we are stuck with chance in a way that former generations were not. In the classical, Newtonian scientific picture of the world, it was much easier to find a place for God. The Christian God has always been understood to be the transcendent Creator and sustainer of the universe. The universe is his handiwork, his craftsmanship. The order and beauty of the natural world is under- stood to reflect that craftsmanship. Classical Newtonian laws like the law of universal gravitation seemed a fitting expression of that providential order and beauty: elegant, simple, unchanging, universally true throughout all spacetime, immaterial, transcendent, yet actually governing the behavior of physical things. Thus could Isaac Newton say, “This most beautiful System of the Sun, Planets, and Comts, could only proceed from the counsel and dominion of an intelligent and powerful being.”
As an aside, I should emphasize that in the classical picture, God is not thought of as a “God of the gaps” whose miraculous intervention is to be invoked as an explanation of the extraordinary, irregular, or mysterious. Rather, He is the God of the ordinary, regular, and therefore entirely suspicious lawful- ness and intelligibility of the universe. The theist tends to look at the world in a kind of perpetual wonderment that it should be essentially orderly at all, and, what’s more, that it should admit of (relatively) simple description by a few elegant physical laws knowable by humans. The authors of Scripture saw the personality and character of the Judeo-Christian God in that very orderliness. Thus the psalmist could write, “The heavens declare the glory of God, and the sky above proclaims his handiwork” (Ps 19:1, ESV). The psalmist goes on to draw a close parallel between the perfection of God’s natural order and that of His moral order. Similarly, in Jer 31:35-37, the regularity of the “fixed order” of the heavens is likened to the divine faithfulness in human affairs, that is, God’s faithfulness in keeping his covenantal promises to Israel.
Returning to our main topic, chance does not seem to offer any such prospect of being understood as the purposeful handiwork or craftsmanship of a good, wise, powerful Creator. Not at face value, anyway. What, then, are we to do with the current probabilistic interpretations of quantum mechanics, which posit that certain subatomic phenomena are in fact random processes? What about the randomness of genetic mutation that underpins all of evolutionary biology? What do these physical processes tell us about God’s orderly design and authority over His creation?
Bartholomew makes several helpful points. In the first place, the relationship between chance and order is in fact exceedingly complicated, and depends also upon the scale at which you look at things. What is chaotic at one level may well be orderly at a higher level, and vice versa. The emergence of order from chaos is seen in something as simple as the eventual conformity of the number of heads out of ten fair coin tosses to a binomial distribution B(10, 0.5). Or, for a slightly more sophisticated example, the ideal gas laws (along with all the other thermodynamic laws) are fundamentally statistical: they are derived by starting from the assumption that particles move about at random, and then deducing facts about the aggregate of all the particles. Conversely, chaos theory studies how even a system governed by a few simple and deterministic rules can exhibit chaotic, unpredictable behavior in the long-term and at the grand scale. For instance, even deterministic mathematical models of weather systems exhibit the same eventually chaotic (turbulent) behavior that we find in real-life weather systems. Such systems are so sensitive that long- term predictability, in the deterministic sense, is impossible. (See Bartholomew ch. 3-4.)
Two ideas emerge from this discussion. On the one hand, it might turn out that chaos at some scales is an inevitable consequence of order at other scales: chaos emerges from order. (This is admittedly a highly speculative and tendentious way of putting it.) On the other hand, chance is not without laws of its own: order emerges from chaos. There are precise and orderly laws that arise from the operation of random processes; we may call them statistical laws. The laws of thermodynamics are an example already mentioned.
It seems that these statistical laws help to explain the world in a way not reducible to laws of the merely classical type. The statistical laws are in a sense complementary to the classical kind of investigation. Whether the relevant laws are classical or statistical depends, in part, upon the level you are considering within the system. If this is correct, then chance would feature as an integral part of the scientific explanation of the world. If you try to leave statistical laws out of the picture, you will be neglecting to describe some of the orderliness and intelligibility that exists in the world.
Bartholomew regards statistical laws as part of God’s providential and orderly design for physical phenomena. Perhaps God wanted His creation to satisfy some or other of those laws, and decided to use random processes as a way of bringing this about. In fact this is not such a far-fetched idea, since we ourselves do the very same thing. Humans, as Bartholomew notes, use chance in a variety of soberly practical applications (e.g., Monte Carlo simulation, genetic algorithms, and so forth; see his ch.10).
The Reformed theologian may object (as Bartholomew notes, pp.216-20) that, whilst humans can take advantage of random or pseudo-random processes that already exist in the world and co-opt them for human purposes, it is quite another matter for God to create and sustain truly random processes. Is it even coherent for God to create and sustain a random process? How could He (knowingly, deliberately) create a process that brings about outcomes that He Himself does not know and cannot predict? If God doesn’t make the tossed coin come up heads, then what does? Is God supposed to tell the coin, “Come up heads or tails. I don’t really care. Your pick.”? Bartholomew suggests (p.220) that God might use the mechanisms of pseudo-randomness, the sort that we use in pseudo-random number generators; but this response is not entirely satisfying. It is difficult to know what to say. I imagine that all efforts (whether theistic or non-theistic) to account for why an event due to chance actually occurs or does not occur will run into similar philosophical trouble.
Finally, to all these points, Bartholomew adds an aesthetic consideration. In addition to soberly practical applications, humans also use chance just for fun. Whether it be a game of pitch-and-toss, or throwing paint at a blank canvas, chance introduces a pleasant kind of variety and novel- ty into the world. You might think that this would be a desirable thing. This is eloquently expressed by Bartholomew, p.34: “what could be more elegant than to conceive and get going such a simple and beautiful system? A universe which makes itself. A universe burgeoning with potential. Surely God could have done no other.” Or, as Peacocke puts it, “God the Creator explores in creation” (Peacocke p.121).
The real worry in all this is, what are theological implications of considering random processes to be part of the divine design? Bartholomew is willing to bite the bullet and propose the rather radical thesis that God is a risk-taker: that He does in fact play dice with the universe, and the unfolding possibilities are in fact genuinely open possibilities. If God is a risk-taker, then He takes actions where “the outcome was intrinsically uncertain and which might turn out contrary to His intentions” (p.225).
This thesis, Bartholomew is well aware, requires a somewhat radical reinterpretation of traditional Christian teaching on God’s sovereignty and omniscience. Of particular worry for Bartholomew (pp. 228-9) is the doctrine of the Incarnation. The eternal second person of the Trinity entered into time as Jesus Christ, fully man and fully God, so that His perfect human life and innocent death might rescue the sons of Adam and daughters of Eve from our exile. Under Bartholomew’s proposal, entering into time means entering the domain of chance, and outside the domain of God’s total control. Choosing Incarnation as the means of bringing about our salvation therefore seems like a tremendous risk. Is it impious to ask whether things could have gone wrong with Jesus, such that God might have had to try again a second time?
Then again, our Jesus was the second attempt, or perhaps the umpteenth attempt, at God’s first and riskiest venture. It is a venture familiar to every parent, in a way: the venture of raising free, responsible, intelligent children to love what is good and avoid what is evil, children who are able to make choices and take risks of their own. Things did go wrong in that first and riskiest venture, and they have been going wrong ever since; and God has not yet grown weary of us.
One might be wary of too hastily re-interpreting traditional doctrines to fit God to the science of the present age. Yet, equally, it would be naïve to suppose that the traditional Christian doctrines were not themselves influenced by the science of their days. (The Newtonian picture of the world has always flirted with theological determinism, which no doubt informed the Reformed tradition in its theological reflection.) Each age will have to re-interpret the depositum fidei for itself, as responsibly as it is able. Should we therefore accept Bartholomew’s proposal? Perhaps we should at least give it a sporting chance.
1 Bartholomew (p.2) cites the example of the prominent Calvinist theologian R. C. Sproul’s Not a Chance: The Myth of Chance in Modern Science and Cosmology (1994), whose thesis is “to show that it is logically impossible to ascribe any power to chance whatever.”
2 This discussion was inspired by pp.18-19 of Vern Poythress, Redeeming Science: A God-Centered Approach. Wheaton, IL: Cross- way, 2006.
3 General Scholium to the Principia. Andrew Motte’s English translation (1729) is available on the page “Newton’s General Scholium.” Newton Project Canada. http://isaacnewton. ca/newtons-general-scholium/.
4 This discussion is influenced by Bernard J. F. Lonergan’s Insight: a Study of Human Understanding. New York: Philosophical Library, 1970.
Stephen Mackereth ’15 is a Mathematics and Philosophy concentrator living in Mather House and is a staff editor for the Ichthus.confession, David J. Bartholomew, Einstein, evolution, mathematics, philosophy, science, theology