“We answer that …” a proper updating of the scientific worldview, one that incorporates the findings of quantum mechanics and chaos/complexity theory, brings us “into a wider world” indeed. In this world, it is not so hard to conceive of God’s divine action having a place, and it is perhaps impossible to rule such action out. Once again, the scientific and religious accounts may not be as conflicting as we thought. Our first task, then, is to fast-forward in our account of the history of science and take note of two discoveries that changed, perhaps forever (though that remains to be seen) our understanding of causality and history from a scientific perspective.

Science update, part 1: Quantum mechanics

Those of you who have studied quantum mechanics in a course on, say, modern physics, physical chemistry, or molecular biology know that it is an exceedingly difficult subject, full of counter-intuitive behavior and challenging mathematics. Never fear: the understanding necessary for our purposes is minimal.

One way of narrating the emergence of quantum mechanics in the history of twentieth-century physics is by considering a motivating question about the nature of light. Since the mid-nineteenth-century, physicists had been sure that light was a wave. Indeed, James Clerk Maxwell and others had developed a theory (based on four elegant equations that have come to be known as Maxwell’s Equations) that showed very convincingly that visible light was a special kind of electromagnetic radiation that, like all such radiation, travels through the universe in waves.

However, in the first few years of the twentieth century, mathematical physicists started treating light like a particle (a quanta) in an attempt to explain some strange experimental results. Their intuition that light might behave both as a wave and as a particle was later confirmed by subsequent experiment. A further strange finding followed: tiny particles behave the exact same way. At the subatomic level, the level of electrons and even smaller building blocks of the universe, particles can behave like waves. The universe appeared to be stranger than we’d thought.

The strangest of all these phenomena, and the one that most interests philosophers and theologians, is known as Heisenberg’s Uncertainty Principle. The easiest way to understand this idea is to think about how you would measure the position and velocity of, say, an electron. Stephen Hawking writes,

The obvious way to do this is to shine light on the particle. Some of the waves of light will be scattered by the particle and will indicate its position. However, one will not be able to determine the position of the particle more accurately than the distance between the wave crests of light, so one needs to use light of a short wavelength in order to measure the position of the particle precisely … [O]ne cannot use an arbitrarily small amount of light; one has to use at least one quantum. This quantum will disturb the particle and change its velocity in a way that cannot be predicted … Heisenberg showed that the uncertainty in the position of the particle times the uncertainty in its velocity times the mass of the particle can never be smaller than a certain quantity … Moreover, this limit does not depend on the way in which one tries to measure the position or velocity of the particle, or on the type of particle: Heisenberg’s uncertainty principle is a fundamental, inescapable property of the world. [1, 56-57]

Hawking also describes what he believes this picture meant for Laplace’s grand visions: “The uncertainty principle signaled an end to Laplace’s dream of a theory of science, a model of the universe that would be completely deterministic: one certainly cannot predict future events exactly if one cannot even measure the present state of the universe precisely” [1, 57]. All of a sudden, there was a chink in the armor of the purely mechanical universe. Through the lens of quantum mechanics, the world looked a little fuzzier than it did before.

Science update, part 2: Chaos and complexity theory

In our opinion, the strange world of chaos and complexity theory is even harder to understand. Unfortunately, as we will see, these newer disciplines are also important to modern discussions about the causal joint problem.

Perhaps the easiest way in to chaos theory is through the eyes of one of the first researchers to stumble upon it and understand what it meant: Edward Lorenz. Imagine for a moment that Laplace was somehow transported to the early 1960s. He might have tried exactly the experiment Edward Lorenz was up to, which was an attempt to learn how to predict the weather by simulating it on a computer.

“Ah, but what about about the Uncertainty Principle?” you rightly ask. Well, our transformed Laplace might have been relatively undeterred, despite Hawking’s warnings above. “I don’t care about predicting the behavior of electrons,” he might have said. “I only want to study systems I can see, systems whose macroscopic behavior shouldn’t be affected by quantum-level fuzziness. Systems like the weather.” The mechanical worldview of Laplace was in many ways still operative for Lorenz.

Journalist and early popularizer of chaos theory James Gleick describes a subtle assumption in this thinking, the error of which Lorenz was about to discover:

There was always one small compromise, so small the working scientists usually forgot it was there, lurking in a corner of their philosophies like an unpaid bill. Measurements [even macroscopic measurements unaffected by the Uncertainty Principle] could never be perfect. Scientists marching under Newton’s [and Laplace’s] banner actually waved another flag that said something like this: Given an approximate knowledge of a system’s initial conditions and an understanding of natural law, one can calculate the approximate behavior of the system. [2, 14-15]

This assumption turns out to be wrong. Lorentz discovered this fact one day when he got impatient with his computer and re-entered the simulation’s initial conditions by hand. In doing so, he slightly changed them, because he was entering them from an old printout that rounded the numbers off. So he ended up with two simulations, one where a starting variable had the value 0.506127 and one where that same variable was rounded to 0.506000. [2, 16]

If the above assumption is correct, it shouldn’t have mattered. Such a small change in the initial conditions should only have had a small effect on the weather simulation that followed. But it didn’t; it had a large effect (this introduction has a picture of the two weather patterns mapped over time). As it turns out, the weather can only be modelled using what mathematicians call nonlinear equations. And nonlinear equations like the ones Lorenz was using exhibit “sensitive dependence on initial conditions.” Lorenz went on to name this phenomenon using a helpful analogy. He called it the butterfly effect:

The flapping of a single butterfly’s wing today produces a tiny change in the state of the atmosphere. Over a period of time, what the atmosphere actually does diverges from what it would have done. So, in a month’s time, a tornado that would have devastated the Indonesian coast doesn’t happen. Or maybe one that wasn’t going to happen, does. [3, 129]

The science of chaos theory developed in fits and starts over the next twenty years. With its younger sibling complexity theory, it has discovered a strange and beautiful world (a Google Image Search for “chaos theory math” should give you some idea). We don’t have time for a more systematic treatment, but Gleick’s Chaos [2] is a fascinating and accessible introduction. (Math geeks will also almost certainly enjoy the video some Cornell students made of Jonathan Coulton’s song, “Mandelbrot Set.” Warning: there’s a small amount of profanity in the lyrics.)

We will let sharper thinkers than us make some careful points about the implications of chaos and complexity theory for the idea of divine action and the causal joint problem. For this introductory sketch, we’ll leave you with the following evocative summary:

There is order in chaos: randomness has an underlying geometric form. Chaos imposes fundamental limits on prediction, but it also suggests causal relationships were none were previously suspected. [4, 35]

Implications for divine action: Causal joints revisited

What have we learned from our updating of the scientific picture of the world? Robert John Russell, who edits the journal Theology and Science sees in this picture the possibility for “a new view of special providence which holds both that God acts in the world objectively, and yet that such action is not by intervening in or suspending the laws of nature” [5, 84]. On the theological side, Haught sees as the key to understanding this claim the idea of a personal God whose “mighty acts” are nonetheless gently performed:

[T]he universe of complexity and chaos suggests an understanding of God’s power as gentle and persuasive rather than coercive. A world which, as a whole, is so sensitive to the initial conditions from which it has evolved is one that seems to be guided more by tenderness than by brute force … God apparently does not force the world into some final shape in an instantaneous display of magic. Nor is God a linear mathematician, deterministically directing the world in the manner of a cosmic ruler. But still the universe does exhibit, from its very beginning, the character of being influenced by some gentle, noncoercive quality of self-ordering … The kind of creator we might associate with this spectacle is not the same as the narrowly conceived divine mechanic of classical natural theology. [6, 157]

On the more scientific side, Polkinghorne believes that the causal joint by which God can bring these gentle acts about may lie somewhere in the interaction between the material and the mental, an interaction that cannot be ruled out of our current physical picture of the universe:

Read from the bottom-upwards, physics provides us with no more than an envelope of possibility, within which future development is constrained to lie. Within that envelope, the path actually taken depends upon the realization of a specific set of options selected from among proliferating possibilities. These different possibilities are not discriminated from each other by energetic considerations … but by something much more like an information-input … One sees the opportunity for using this information-input, necessary to resolve what actually occurs, as the vehicle for a downward operating causality, a role for the “mental” (information) in the determination of the material. [7, 25-26; see also 8, 33]

That’s a mouthful. What he’s saying is that it doesn’t actually look like God would have to “inject” energy into the apparently closed system that is the universe in order to have a noticeable effect on it (because most real physical systems are so sensitive). Thus, God’s will (here Polkinghorne calls it the “mental”) doesn’t need to violate a physical law such as the conservation of energy in order to have an effect on the material world (such a violation would be what Russell calls “intervention” and Haught calls “coercion”). Just as our mental powers can bring about a change in the physical world (such as when we decide to move our own bodies in some way), so can God analogously participate in the physical world. In both cases (not just the latter), the causal joints are “hidden within the unpredictability of process” [8, 34]. Hidden, but not imaginary.

Of course, we need to be modest in our claims. The “contrast theologians” would be quick to remind us that our theological tasks are quite distinct from the scientists’ and that the two should not be conflated. Moreover, a careful examination of what has been put forth shows that we’re certainly not dealing with a recapitulation of those famous “proofs” for God’s existence which have fared so poorly on the philosophical scene.

No, at most we have what Markham and many others call “pointers” to God [9, 39]. But at the very least, we can say something like this: “Of course, we don’t know, and never will, how God interacts with the world. But the supple and open-ended picture of the universe that has arrived in science suggests that it is by no means unreasonable to suppose that God might do so.” For those wishing to state this conclusion a bit more strongly, you could do worse than a phrase Polkinghorne used in a recent personal conversation with us at a gathering of Christian scholars: “The defeatists have been defeated.”

Miracles: A case study

It’s interesting to apply what we’ve learned above to the mightiest of God’s acts, those occurrences we call miracles. Notice right away, though, that there is a continuity between miraculous acts of God and more mundane ones if we subscribe to the outdated model of the clockwork universe. If it’s supposedly impossible for God to interact with the physical world, then what does it matter if the supposed interaction is raising the dead or redistributing the rain in Spain? Conversely, if we take the findings of more current science seriously, and are open to the various proposals about possible causal joints, then a certain cautious openness to the reality of miracles doesn’t sound quite so absurd.

We can no more make a systematic study of miracles here than we could attempt to pin down an exact answer to the causal joint problem. However, we can once again share a few helpful comments from two important (and mutually appreciative) thinkers in this area of theology.

Both Polkinhorne and Ward are careful not to assent to a sloppy definition of miracle in light of our conversation above. Language of interference with or intervention in nature or its laws will not do within our picture of the surprising suppleness and flexibility in nature. Ward’s definition of “extraordinary events that show spiritual power” [9, 105] seems in this respect a helpful choice. A further advantage of this definition is that it reminds us of the religious purpose of miracles, which the Biblical witness insists is wrapped up in their ability to serve as a sign for us of the reality of God [8, 45].

This purpose also then points to limitations. Polkinghorne writes, “God is no celestial conjurer, doing an occasional turn, but his actions must always be characterized by the deepest possible consistency and rationality” [8, 45]. Thus, seemingly senseless “acts of God” in the sense that we often use that word are anything but. God does not go around capriciously spinning off hurricanes or other disasters.

“But why aren’t there more miracles of the opposite variety?” we might well ask. Why not more prevention of such disasters. Putting aside the difficulty of ruling them out (how would we know, if the disasters never went on to take place?), Polkinghorne thinks the answer lies in God’s reliability:

People say that they cannot at all believe in a God who acts if he did not do so to stop the Holocaust. If God were a God who simply interferes at will with his creation, the charge against him would be unanswerable. But if his action is self-limited by a consistent respect for the freedom of his creation … and also by his own utter reliability (so that he excludes the shortcuts of magic) it is not clear that he is to be blamed for not overruling the wickedness of humankind. [8, 53-54]

You’re perhaps noticing that whenever we talk about how God interacts with the world, a visit from the theodicy question is seldom far behind.

Polkinghorne goes on to summarize his position on miracles with the following statement: “miracles are neither ruled out by scientific knowledge that the world is a relentlessly inflexible mechanism (it is not) nor by theological knowledge that God is just the deistic upholder of general process (he is more than that). That there may have been miracles is a coherent possibility” [8, 54]. However, neither he nor Ward would want to let that comment stand without a word of caution. Ward’s is appropriately sober: “Legends readily multiply, and human imagination is strong. It is, therefore, reasonable to be very cautious in affirming that a [particular] miracle has occurred” [9, 105-106]. Obviously, fidelity to the reality of certain miracles, such as the resurrection of Christ, is an important part of Christian faith.

Closing remarks

We hope the foregoing material has been sufficient to whet your appetite. There’s so much to learn about both the science we’ve discussed and its relevance to current theology. Perhaps for this topic in particular, about the best we can do is get you thinking and reading. Ward’s chapter on miracles in The Big Questions in Science and Religion [9, 83-106] is particularly accessible and treats miracles from a variety of religious perspectives. Haught’s chapter “Why Is There Complexity in Nature” in Science and Religion [6, 142-161] is a careful (and moving) exploration of some intriguing aspects of chaos/complexity theory that we’ve given short shrift here.