If Nature Has Laws, How Can God Do Anything?
(God's Providence, part 1)
Life is uncertain. We try very hard to control what happens to us, and try even harder to ignore our total failure to do so. We're not in control of our destiny. So who or what is in control?
That question is a very old one indeed; it has been asked from the very earliest times of which we have records. From the very beginning, two sorts of answers have been given. The majority view holds that there is some sort of god in charge; this is called theism. The minority view is that everything is ruled by chance or predetermined by fate; this is called atheism. [1]
Given the stark contrast between these positions, and the importance of the issue, you'd think that every intelligent person would have a well thought out view. In fact, however, the choice between them appears often to be driven by emotion. Modern theists usually find the idea that God is in control comforting; their ideas of right and wrong have cosmic significance, death is not the end, and someone is looking out for them.[2]
Atheists seem to find the same idea repulsive; if there's a god looking over their shoulder and pulling the strings, they can't really be free, because the consequences of their actions are under someone else's control. Moreover, they can't find their own meaning in their lives—only some prescribed one, and maybe a rather narrow one at that.
Theists and atheists have been arguing for millennia, and many unfair things have been said on both sides, but it's important to realize that these feelings are honourable and have very deep roots. Logically the two views are contradictory, but from an emotional viewpoint we really can eat our cake and have it; the central values in both views coexist in the Christian doctrines of free will and divine providence, and what's more, they even make good rational sense together.
In the second part of this article, we'll talk about what God's providence means to us as human beings. In Does Science Disprove Religion? we showed that the scientific method as often practiced is self-contradictory, and how theism can fix the problem. Here we'll look at the problem positively, and discuss how God's providence might coexist with well-defined physical laws.[3]
Physical science has been a bulwark of atheism; if events are ruled by the caprice of some god, how can there be reliable physical laws? It turns out that three results of physical science, taken together, provide an answer to that question, so that we can reconcile divine providence with an orderly universe. The three have quite forbidding names: quantum indeterminacy, irreversible thermodynamics, and sensitive dependence on initial conditions.
Fortunately they're easier to understand than to say. In quantum mechanics, there is an inescapable element of randomness, expressed mathematically by the famous Heisenberg uncertainty principle: it is impossible to know both the position of an object and its speed exactly, and getting more precise about one means getting less precise about the other. Even if we had all available information about the motion of an electron or a billiard ball, say, we still couldn't predict perfectly where it would be in 30 seconds. So far, so vanilla.
A vital but seldom-noted point follows from this: information is constantly being fed into the universe, on a gigantic scale. If I measure the ball's position now and write it in my lab book, I cannot even in principle know just where it will be in 30 seconds—that information does not exist in the universe. Thirty seconds later, I measure and record the ball's position. My lab book now contains information that did not exist in the universe half a minute before, and the same applies to everything else in the universe. That's the first thing.
The second thing is that for something like a billiard ball in isolation, the uncertainty is pretty small. After 30 seconds, the inaccuracy is around a millionth of an atomic diameter, and it grows very slowly—it would take a quarter of a million years for that uncertainty to grow to 1 whole atomic diameter.[4] The uncertainty is also small for things like heat flow and electric currents; for reasonable-sized objects, the quantum uncertainty at the atomic level averages out to quite predictable behaviour on human time scales. We can know in advance pretty accurately how our cars and computer chips will behave.[5]
The third thing is that the indeterminacy doesn't stay small, even for large objects, because the world is full of systems that amplify it very powerfully. This sensitivity to small deviations is one characteristic treated by chaos theory. One popular example is the weather, which exhibits the butterfly effect—it is so sensitive to small perturbations that the beat of a butterfly's wing today can change the course of a hurricane in a few weeks' time. Less well known is that you don't even need a butterfly—given only a little more time, quantum fluctuations are quite large enough for the job.
The weather alone has a huge effect on human history, but there are lots of chaotic systems out there. In fact, even billiard balls show this sensitivity, and theirs builds up very much faster, due to the collisions. The results are remarkable.
Any good player will tell you that the real art of a pool shot is in controlling the second or third bounces off other balls. This is because the balls are curved. If you're off by a little, the point of impact is some way down the curve from where it should have been, so the balls bounce off in slightly wrong directions. As they roll, they get farther and farther from where you wanted them to go. On the next collision, their aiming will be further off still, leading to worse errors of direction, and so forth. The errors build up exponentially, exactly like compound interest and for the same reason: errors caused by errors grow just like interest on interest. Things that grow exponentially may start out small and grow slowly at first. Like credit card balances, though, their growth continues to accelerate until they become very large, very fast.
Say we rack up a set of nice frictionless, perfectly round balls and break them as usual. For awhile, any error of aim or spin grows exponentially with the number of bounces, no matter how small the initial deviation—even that millionth-of-an-atom is enough. It has been calculated that deviations grow so rapidly that it takes only a few dozen bounces before the quantum-mechanical uncertainty of each ball's position is larger than the ball itself, so that we can no longer even predict which balls will hit or miss each other. Looking ahead only 30 seconds or so, we can have no idea where on the table the balls will go next. Though an isolated ball is predictable, balls bouncing off each other have amplified tiny errors into large effects.[6]
In nature, these chaotic systems seem to be more the rule than the exception. The tiny quantum uncertainty keeps adding randomness on small scales, which average out to nearly predictable behaviour for awhile, before being amplified into very large effects indeed. Thus the world is far from deterministic—in fact, it's covered with little control levers, whose operation is consistent with all known physical laws. The theist would say that they are controlled by God, and the atheist, by nothing. The atheist's position is a very uncomfortable one, since he apparently has to accept the existence of uncaused events.[7]
Whichever you believe, this is about the best imaginable design for an orderly world in which people can have free will and which allows a wide field for divine providence, and yet has dependable physical laws based on efficient cause.
[1] There are squishy in-between views, collectively called pantheism, that we'll get to in the article on New Age, but they aren't highly relevant here.
[2] There are other branches of theism, such as dualism, which is the view that there are both good and bad gods, and that their conflict explains the mixture of good and evil in the world. Christians are nearer this camp than first appears.
[3] There has been an enormous amount of gas emitted by people trying to find esoteric philosophical meaning in modern physics, and finding mares' nests and lucrative book royalties instead. Just so we don't add to the problem, we'll stick to a few well-attested results and their plain logical consequences.
[4] For physics buffs, the uncertainty of position D x ≥ (ht/(pm))1/2 , where x is the object's position, m is its mass, h is Planck's constant, (6.63x 10-34 kgm2/s), and t is the elapsed time between measurements. For m = 0.17 kg and t = 30 s, D x ≥ 1.910 x 10-16 metres. For D x = 10-10 m (about an atomic diameter), t comes out to be about 240,000 years.
[5] In the article cited in Does Science Disprove Religion?, Albert Einstein used this property of nonequilibrium thermodynamics to try to prove that the macroscopic world was deterministic even in the presence of quantum fluctuations. Einstein died in 1957, before the butterfly effect was discovered.
[6] The uncertainty is subject to limits—one can extrapolate that after a few more bounces, the uncertainty in the billiard ball's position is bigger than the Earth, but it won't go into orbit, because the balls don't have enough energy to leave the table. This is also typical of chaotic systems.
[7] One high-profile member of the random camp is Stephen Hawking—see his lecture Does God Play Dice?
Life is uncertain. We try very hard to control what happens to us, and try even harder to ignore our total failure to do so. We're not in control of our destiny. So who or what is in control?
That question is a very old one indeed; it has been asked from the very earliest times of which we have records. From the very beginning, two sorts of answers have been given. The majority view holds that there is some sort of god in charge; this is called theism. The minority view is that everything is ruled by chance or predetermined by fate; this is called atheism. [1]
Given the stark contrast between these positions, and the importance of the issue, you'd think that every intelligent person would have a well thought out view. In fact, however, the choice between them appears often to be driven by emotion. Modern theists usually find the idea that God is in control comforting; their ideas of right and wrong have cosmic significance, death is not the end, and someone is looking out for them.[2]
Atheists seem to find the same idea repulsive; if there's a god looking over their shoulder and pulling the strings, they can't really be free, because the consequences of their actions are under someone else's control. Moreover, they can't find their own meaning in their lives—only some prescribed one, and maybe a rather narrow one at that.
Theists and atheists have been arguing for millennia, and many unfair things have been said on both sides, but it's important to realize that these feelings are honourable and have very deep roots. Logically the two views are contradictory, but from an emotional viewpoint we really can eat our cake and have it; the central values in both views coexist in the Christian doctrines of free will and divine providence, and what's more, they even make good rational sense together.
In the second part of this article, we'll talk about what God's providence means to us as human beings. In Does Science Disprove Religion? we showed that the scientific method as often practiced is self-contradictory, and how theism can fix the problem. Here we'll look at the problem positively, and discuss how God's providence might coexist with well-defined physical laws.[3]
Physical science has been a bulwark of atheism; if events are ruled by the caprice of some god, how can there be reliable physical laws? It turns out that three results of physical science, taken together, provide an answer to that question, so that we can reconcile divine providence with an orderly universe. The three have quite forbidding names: quantum indeterminacy, irreversible thermodynamics, and sensitive dependence on initial conditions.
Fortunately they're easier to understand than to say. In quantum mechanics, there is an inescapable element of randomness, expressed mathematically by the famous Heisenberg uncertainty principle: it is impossible to know both the position of an object and its speed exactly, and getting more precise about one means getting less precise about the other. Even if we had all available information about the motion of an electron or a billiard ball, say, we still couldn't predict perfectly where it would be in 30 seconds. So far, so vanilla.
A vital but seldom-noted point follows from this: information is constantly being fed into the universe, on a gigantic scale. If I measure the ball's position now and write it in my lab book, I cannot even in principle know just where it will be in 30 seconds—that information does not exist in the universe. Thirty seconds later, I measure and record the ball's position. My lab book now contains information that did not exist in the universe half a minute before, and the same applies to everything else in the universe. That's the first thing.
The second thing is that for something like a billiard ball in isolation, the uncertainty is pretty small. After 30 seconds, the inaccuracy is around a millionth of an atomic diameter, and it grows very slowly—it would take a quarter of a million years for that uncertainty to grow to 1 whole atomic diameter.[4] The uncertainty is also small for things like heat flow and electric currents; for reasonable-sized objects, the quantum uncertainty at the atomic level averages out to quite predictable behaviour on human time scales. We can know in advance pretty accurately how our cars and computer chips will behave.[5]
The third thing is that the indeterminacy doesn't stay small, even for large objects, because the world is full of systems that amplify it very powerfully. This sensitivity to small deviations is one characteristic treated by chaos theory. One popular example is the weather, which exhibits the butterfly effect—it is so sensitive to small perturbations that the beat of a butterfly's wing today can change the course of a hurricane in a few weeks' time. Less well known is that you don't even need a butterfly—given only a little more time, quantum fluctuations are quite large enough for the job.
The weather alone has a huge effect on human history, but there are lots of chaotic systems out there. In fact, even billiard balls show this sensitivity, and theirs builds up very much faster, due to the collisions. The results are remarkable.
Any good player will tell you that the real art of a pool shot is in controlling the second or third bounces off other balls. This is because the balls are curved. If you're off by a little, the point of impact is some way down the curve from where it should have been, so the balls bounce off in slightly wrong directions. As they roll, they get farther and farther from where you wanted them to go. On the next collision, their aiming will be further off still, leading to worse errors of direction, and so forth. The errors build up exponentially, exactly like compound interest and for the same reason: errors caused by errors grow just like interest on interest. Things that grow exponentially may start out small and grow slowly at first. Like credit card balances, though, their growth continues to accelerate until they become very large, very fast.
Say we rack up a set of nice frictionless, perfectly round balls and break them as usual. For awhile, any error of aim or spin grows exponentially with the number of bounces, no matter how small the initial deviation—even that millionth-of-an-atom is enough. It has been calculated that deviations grow so rapidly that it takes only a few dozen bounces before the quantum-mechanical uncertainty of each ball's position is larger than the ball itself, so that we can no longer even predict which balls will hit or miss each other. Looking ahead only 30 seconds or so, we can have no idea where on the table the balls will go next. Though an isolated ball is predictable, balls bouncing off each other have amplified tiny errors into large effects.[6]
In nature, these chaotic systems seem to be more the rule than the exception. The tiny quantum uncertainty keeps adding randomness on small scales, which average out to nearly predictable behaviour for awhile, before being amplified into very large effects indeed. Thus the world is far from deterministic—in fact, it's covered with little control levers, whose operation is consistent with all known physical laws. The theist would say that they are controlled by God, and the atheist, by nothing. The atheist's position is a very uncomfortable one, since he apparently has to accept the existence of uncaused events.[7]
Whichever you believe, this is about the best imaginable design for an orderly world in which people can have free will and which allows a wide field for divine providence, and yet has dependable physical laws based on efficient cause.
[1] There are squishy in-between views, collectively called pantheism, that we'll get to in the article on New Age, but they aren't highly relevant here.
[2] There are other branches of theism, such as dualism, which is the view that there are both good and bad gods, and that their conflict explains the mixture of good and evil in the world. Christians are nearer this camp than first appears.
[3] There has been an enormous amount of gas emitted by people trying to find esoteric philosophical meaning in modern physics, and finding mares' nests and lucrative book royalties instead. Just so we don't add to the problem, we'll stick to a few well-attested results and their plain logical consequences.
[4] For physics buffs, the uncertainty of position D x ≥ (ht/(pm))1/2 , where x is the object's position, m is its mass, h is Planck's constant, (6.63x 10-34 kgm2/s), and t is the elapsed time between measurements. For m = 0.17 kg and t = 30 s, D x ≥ 1.910 x 10-16 metres. For D x = 10-10 m (about an atomic diameter), t comes out to be about 240,000 years.
[5] In the article cited in Does Science Disprove Religion?, Albert Einstein used this property of nonequilibrium thermodynamics to try to prove that the macroscopic world was deterministic even in the presence of quantum fluctuations. Einstein died in 1957, before the butterfly effect was discovered.
[6] The uncertainty is subject to limits—one can extrapolate that after a few more bounces, the uncertainty in the billiard ball's position is bigger than the Earth, but it won't go into orbit, because the balls don't have enough energy to leave the table. This is also typical of chaotic systems.
[7] One high-profile member of the random camp is Stephen Hawking—see his lecture Does God Play Dice?
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