You’re flipping a coin. How many heads in a row would it take for you to start getting suspicious?
HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH: Ninety-Two?[i]
It’s a strange question, because we generally agree that coin flips are random. Shouldn’t this mean they are also unpredictable?
If they are unpredictable, though, no outcome should surprise us – ever! After all, as maths teachers love reminding befuddled youngsters, 92 heads in a row is just as likely as getting any other sequence of heads and tails. So should we never suspect a coin of being unfair, no matter what we get?
At this point our gut takes over; it tells our mind that there is definitely something not quite right about all this – and sometimes our gut is far more accurate than we give it credit for. Our gut says that 92 consecutive heads just shouldn’t happen. Our gut refuses to join randomness and unpredictability together. Yes, it admits, coin tosses are random; but some outcomes are simply more likely than others, and that’s how it is. Why?
In the 19th century our minds caught up with our guts. Probability theory allowed a new type of physics to appear, and the link between randomness and predictability jumped straight out of the equations. Physicists Ludwig Boltzmann (1844-1906) and James Clerk Maxwell (1831-1879), amongst others, were able to see that randomness wasn’t the problem when studying the most stubborn parts of nature – instead, it was the solution.
In a series of ingenious steps, ‘Statistical Mechanics’ was born. Take, for example, the diffusion of gases. We all know that a gas can slowly spread out from a single source, mixing with other gases in the environment as it gradually progresses. Maxwell wondered about how long this process would take and what it would look like. Could it be predicted somehow?
In theory, Newtonian Mechanics (his equations which describe movement) should apply. Gas particles could be thought of as little balls bouncing around obeying Newton’s Laws of motion. Momentum could be calculated according to well-known methods. Gravity would exert a slight downwards pull. Collisions between the particles could be treated like snooker shots. The equations were all known already. They simply needed to be applied.
Except, Maxwell knew, it wasn’t simple at all. One cubic metre of air contains about 30,000,000,000,000,000,000,000 particles. At room temperature, each is moving at several hundred metres per second. Newton’s maths would have to be continually applied to countless collisions if any predictions were to be made. In short, it was impossible. A wholly different and radical approach was needed.
The breakthrough involved a most unexpected idea: randomness. What if, Maxwell wondered, we pretended we didn’t know what the particles were doing at all? What if we assumed that their motion was truly random? Ignore Newton, and then see what happens…
Amazingly, answers began to appear. Even more amazingly, they were correct when tested against real gases in the laboratory. Randomness was giving direct rise to predictability. How?
Consider a single dice roll. The outcome is random; we can’t predict it. What about two rolls? Well, we still can’t predict much, but we can do slightly better than before – we could simply guess that we will get two different numbers, and we’ll be right most of the time.
Roll six million dice, however, and we can be almost completely confident that we will get around one million 1’s, one million 2’s and so on. The outcome won’t match that exactly, but it won’t be far off at all. Extending this basic concept to encompass a thousand billion billion gas particles, it turns out, tells us exactly what will happen.
Maxwell and Boltzmann’s decision to assume gases behaved randomly unlocked our understanding of them. Diffusion could be modelled to a level of precision that means we do not need any other methods or approaches – we can work with gases in industry and in the lab and know what we are going to get. We must remember, however, that a real gas is not random at all – physicists just pretend that they are.
A few decades later, another physics revolution kicked off – that of ‘Quantum Mechanics’, the physics of the very very small. As physicists studied this bizarre new world of particles popping in and out of existence, of waves acting like particles and vice versa, and of cats being simultaneously dead and alive, they once again encountered randomness. This time, though, it was not a pretence. It was real.
It turns out that randomness is written deep into the source code of our world. Quantum particles, on their own, are wholly and genuinely unpredictable. This is not because we don’t yet understand the maths or the principles – it is because they are random by their very nature. At the most fundamental of levels in our universe, randomness rules.
This sounds disconcerting; disastrous even. What hope can there be for understanding, for progress, for meaning, for hope itself, if the foundation we are built on is so unknowable? Yet all is not lost, thanks to the lessons Maxwell and Boltzmann taught us – randomness does not mean unpredictability. When analysed according to the ideas these scientists introduced, Quantum Mechanics gives up its secrets. It becomes the area of science in which we are better able to predict lab results than any other. The randomness creates the order.
The Christian should not be at all surprised by this finding. Anything that God has written into the code of the world the Christian also expects to find written into the Biblical story. Time and again, seemingly random, pointless, and even hurtful events befall the characters on its pages. Time and again, chaos seems to reign and all sense of hope appears lost. Yet, despite all this apparent randomness, a bigger picture emerges – a picture of stability, of order, of a God on his throne who is working out his purposes for the good of those who love Him.
One striking example is found in the Exodus, in which God rescues the Israelites from abusive murderous slavery in Egypt by parting the Red Sea. How does he do it? He uses the chaos and unpredictability of the storm to form a safe path for His beloved people:
“With Your mighty arm You redeemed Your people, the descendants of Jacob and Joseph.
The waters saw You, God, the waters saw You and writhed;
the very depths were convulsed.
The clouds poured down water, the heavens resounded with thunder;
Your arrows flashed back and forth.
Your thunder was heard in the whirlwind, Your lightning lit up the world;
the earth trembled and quaked.
Your path led through the sea, Your way through the mighty waters,
though Your footprints were not seen.
You led Your people like a flock”[ii]
The God of the Bible brings order from disorder on all scales – from Quantum Mechanics to the Exodus. He has given us clues in his nature which point to his Nature. Chemists and biologists have built on the work of the physicists before them to show that even life itself is utterly dependent on the random behaviour of the very smallest building blocks God has made.
He is telling us something profound: ultimately, we can trust him, no matter what things might look like in the instant. Randomness does not mean unpredictability. God is in charge – of it all.
[i] Why 92? See Rosencrantz and Guildenstern are Dead by Tom Stoppard for the answer…
[ii] Psalm 77