< God's Rule Over Chance and Chaos
May 4, 2024
"I saw something else under the sun: The race is not to the swift, nor the battle to the strong; neither is the bread to the wise, nor the wealth to the intelligent, nor the favor to the skillful. For time and chance happen to all." (Ecclesiastes 9:11 BSB)
This article is the first in a series on miracles and science. One definition of a miracle, though a rather unsatisfactory one, is when a highly improbable event. But I am afraid that we cannot really even talk about miracles and science because we don't have the prerequisite vocabulary. This and the following primer articles address that issue. There are four definitions we need to understand: Randomness, chaos, chance, and probability. In a second paper we will try to understand entropy, though entropy will be a tougher hill to climb.
Randomness
Do random things happen "by chance"? The answer is "semantics", or, it all depends on your definition. In common speech yes, but technically we have never found it. Let's explain with an example.
You flip a fair coin and make the claim that it was totally random whether it came up heads or tails. Let's evaluate that claim with a critic's eye.
Could you predict anything about the coin? Yes, you could predict that it very likely would not stop and rest on its edge. You could also see that if it was flipped 100 times before, and almost every time was heads, then the assumption that it was a fair coin was false. But you cannot predict if it would be heads any more than you could predict it would be tails. So it is random, if and only if by random you simply mean "unpredictable".
But was the cause of it being heads or tails really random, without any cause whatsoever? Actually you might predict if it would be heads or tails, based on the starting position (heads or tails of at an angle), the exact force you applied, the air currents, and any imperfections on the coin, down to the nth degree. But all your calculations would be worthless if you forgot to include the exact height about the ground that you tossed the coin. But with all that information, you could model each flip of the coin, and come up with the answer. So it is not really random at all, if by random if by random you mean "without any cause".
So if we cannot predict an event, it does not mean there was no causes (perhaps plural) for the event, only that we are not able to predict the outcome from the causes.
Chaos
Let's go back to attempting to predict the coin toss again. Let's say we included all of our variables, and we put them through our equations. Wait a second, how do we know that our equations are correct? Do we need to take account our latitude, because of the earth's rotation, the air pressure, the temperature (which makes metal expand or contract, etc.), and the alignment of the stars? Well, it turns out that we don't have to get the equations right, or even know the equations for some problems. We can use AI (Artificial Intelligence) machine learning to create a model. We can simply flip that coin thousands of times, meticulously recording all the conditions each time. Then we can run all that data through a machine learning computer program and it will create a model that will be able to predict heads or tails based on the input. It will also show us variables that have no effect at all, such as the alignment of the stars. It will also show us how good the prediction is; will it predict with only 70% accuracy, 90%, 99%, or other? But let's say that our measurements were not very good, they were only correct within 4%. Then we might expect the predictability to be rather poor. A rule with data is "garbage in, garbage out". But we would expect that as we incrementally make our measurements more precise, (and we re-flip the thousands of times), our predictability would incrementally improve.
And for many systems we would be totally wrong! For any system, there is a point of imprecision, below which measurements are totally useless; you have to be above that point to have any predictability work at all. But for many systems, called chaotic systems, there is no point at which even perfectly precise measurements can give you perfect predictions. If your measurement of the force you flipped the coin with was a tiny bit off, and there were enough flips, your predictability would go out the window. Think of a roulette wheel, where the tiniest error measuring when a ball is dropped means the ball lands in a totally different slot, and the number of that slot might not be close at all to the predicted number.
So it turns out that many systems, including weather, ocean currents, and stock markets, are chaotic. For the weather, we can "accurately" predict that tomorrow will not be -100 degrees, and not +200 degrees, and we can even do better than that, but even the largest supercomputer, running the most sophisticated algorithm cannot accurately predict the temperature tomorrow down to any better than 1 degree F. So when we talk about coin flips, roulette wheels, weather, accidents, cancer, etc. it is more accurate to call all those things "chaotic", rather than random.
So what things are truly random, in the sense that they have no cause whatsoever? With the exception of particle decay (including radioactivity), which scientists know little about, science has not discovered a single thing that is random. How have the leaves landed on your lawn this fall? – chaos. Why are the stars in the night sky arranged the way they are: - chaos. Why did your particular car, and not other of the same year and model, break down at exactly this moment in time – chaos. The fact that we cannot predict those things, even with the very best measurements, does not mean they have no cause, only that they have chaos.
An excellent book that is highly recommended on this is Chaos: Making a New Science, by James Gleick, published in 1987.
Chance
Probability is the "chance" that something will occur. What is the chance that flipping a fair coin will land heads twice in a row? There is 50% chance that it will be heads on the first flip, and 50% on the second flip, so 0.5 * 0.5 = 0.25 = 25%. But wait a second. Let's say the first coin toss was already done, and I saw that it was tails. The situation has not changed, but the probability has changed, solely because the information I have has changed. Now the chance is 0%. Or what both coin tosses have occurred, and I saw both. Then the probability is either 0% or 100%. On the other hand, if both coin tosses have already occurred, but I did not know the outcome, then the chance is still 50%. So the chance of the coin landing heads twice depends not only on the force of the flip, the air currents, the height before it lands, etc., but the "chance" of two heads depends on what I know.
There was a story of two men who went into town to see a movie, and at the climax of the movie was a horse race between a white horse and a black horse. One man said to the second, "I bet you ten dollars that the white horse wins." The second said "you're on". The white horse one, and at the end of the movie the second man was about to pay up, and the first man said, "I can't take your money, because I saw the movie before." The second man said, "I aw the movie before too, but I did not think he would win twice in a row!"
Similarly, you could flip a coin in another room, see the result, and ask me my prediction. I would see a "chance" of 50%, but you would see either 0% or 100%. So I see "chance", and you don't, and what we both see is not deceptive. But paradoxically, I see something, chance, that you don't see, and it is due to my lack of knowledge.
So does chance exist with God? In a way more certain than any movie, God already sees everything, so from God's ultimate perspective no: everything is either 0% or 100%. However, there is genuinely the appearance of chance for us, not because the outcome has not already been determined, but because in the horse race we haven't seen the movie yet. Thus, due to our limited sight and lack of foreknowledge, we live in a world where we see chance everywhere. But our limitations in no way limits God.
So we might conclude that since God knows everything with certainty, God and probabilities have nothing to do with each other. – and we would be totally wrong, as the next section shows.
Probability Distribution
Let's go back to coin tosses again, or rather, lots of coin tosses. Let's say we flipped a fair coin three times. We would think we would be most likely to get an outcome of two heads once, two tails once, and heads and tails twice. It might not turn out that way, but if we repeated this enough time the average would be very close to this. Now let's say we flipped the coin 1,000 times. We would get a sort of bell-shaped curve of the results. And if we repeated then experiment many, many times, we would get curves that are almost identical to each other. So while we still are no good at predicting the outcome of an individual coin toss, we actually are quite good at precising predicting the probability distribution of a large number of coin tosses. The name for a curve of this shape is a normal distribution. There are other distributions, such as Poisson (where there is a hard minimum such as 0,) binomial, and others. But the fact that we can reliably predict and use probability distributions is a foundation of statistics. How can we tell if something occurs randomly (or more precisely, chaotically) or not? If it is a normal distribution (and a Poisson distribution can look like a normal distribution for a sufficiently large range), an f-test or other methods can show things like, you employee getting sick almost every time a new video game comes out might not be random. Likewise we can play detective, looking at numbers, and if certain digits show up in the ones and tens column with far more than average frequency, or certain percentages do not match a percentage of a greater population, there might be a non-random cause, and you might have just discovered evidence that someone faked the data.
God of course knows probability distributions, and it appears that God regularly used probability distributions in nature. Let's see you see rocks arranged in a distribution on a field. Or let's say an artist wanting to put small, colored specs on a piece of furniture, flicks a paintbrush to get the right density of specs. The artist did not place each individual dot, but the artist decided on the density of the specs. Of course if the artist did not like the result, she would just wipe it all off with a cloth and do it again. What is to stop God from being able to do what an artist does?
God's Role (and Rule)
God is sovereign: He rules over all. Ps 103:19
Nothing happens beyond what God allows. Job 1:12; 2:6; Jms 4:15
People do some things on their own initiative. 2 Cor 8:17
However, God knows everything in advance. Ps 139:16
He knows and sees all. 1 Jn 3:20; Ps 139; Pr 5:21; 15:3; Heb 4:13; Isa 46:10
Everything God decrees happens. Isa 14:24,27;43:13;55:11; Jn 10: 29; Heb 6:17; Mt 28:18; Examples: Dan 9:26; 11:27,35,36; 12:1
God does as He pleases.-Mt 20:15; Ps 115:3; 135:6; Rom 9:20; Dan 4:35
Nothing is too hard for God. Gen 18:14; Job 42:2; Jer 32:17; Mt 19:26
God rules over chance in Scripture
"The lot is cast into the lap, but its every decision is from the LORD." Proverbs 16:33 (BSB)
When Joshua and the Israelites were defeated the first time they attacked Ai, God told them it was because someone sinned in keeping gold they should not have. In Joshau 7:11-19, they cast lots to find out who it was. The casting of lots appeared to be a random result, but God used casting lots to reveal Achan and his family had taken the forbidden loot.
God directed with a random action
God used chance or casting lots to direct the king of Babylon. Here is what scripture says. "Then the word of the LORD came to me, saying, "Now you, son of man, mark out two roads for the sword of the king of Babylon to take, both starting from the same land. And make a signpost where the road branches off to each city. Mark out one road for the sword to come against Rabbah of the Ammonites, and another against Judah into fortified Jerusalem. For the king of Babylon stands at the fork in the road, at the junction of the two roads, to seek an omen: He shakes the arrows, he consults the idols, he examines the liver. In his right hand appears the portent for Jerusalem, where he is to set up battering rams, to call for the slaughter, to lift a battle cry, to direct the battering rams against the gates, to build a ramp, and to erect a siege wall. It will seem like a false omen to the eyes of those who have sworn allegiance to him, but it will draw attention to their guilt and take them captive." (Ezekiel 21:18-22 BSB)
The Random arrow of God
"So the king of Israel and Jehoshaphat king of Judah went up to Ramoth-gilead. And the king of Israel said to Jehoshaphat, ‘I will disguise myself and go into battle, but you wear your royal robes.' So the king of Israel disguised himself and went into battle. Now the king of Aram had ordered his thirty-two chariot commanders, ‘Do not fight with anyone, small or great, except the king of Israel.' When the chariot commanders saw Jehoshaphat, they said, "Surely this is the king of Israel!" So they turned to fight against him, but Jehoshaphat cried out. And when the chariot commanders saw that he was not the king of Israel, they turned back from pursuing him. However, a certain man drew his bow without taking special aim, and he struck the king of Israel between the joints of his armor. So the king said to his charioteer, ‘Turn around and take me out of the battle, for I am badly wounded!' The battle raged throughout that day, and the king was propped up in his chariot facing the Arameans. And the blood from his wound ran out onto the floor of the chariot, and that evening he died." (1 Kings 22:29-35 BSB)
Conclusion
With our limited sight, we observe the phenomenon of random chance. But our restrictions are not God's. God does not experience randomness, and from His ultimate perspective, being all-knowing, randomness and chance do not exist. Yet God can direct and use chaos, probability, and probability distributions towards His creation as He pleases. And Scripture has given a number of examples where He has done so.
In the next article we will move to a organize our thinking on a more difficult concept: entropy does not limit God.
By Steven M. Morrison, Ph.D.
www.biblequery.org/doctrine/change/GodRulesOverChanceAndChaos.html.