What can Occam’s razor tell us about God?

It is a sensible rule. If someone says your car doesn’t run because an internal combustion engine turns a drive shaft which turns the wheels, but because it’s pushed by magical goblins, you can say “but you can’t see the goblins”. He might say, they’re invisible. You say, well, I’ve run my hand around the car, and I can’t feel them either; he says they’re undetectable by touch. The engine looks like it’s running? The magic goblins make it look as though it’s running. The drive shaft is turning? The goblins turn the drive shaft.

The evidence – a car with no visible goblins – supports both hypotheses. No amount of evidence will falsify the ‘invisible magic goblins’ hypothesis, because it’s unfalsifiable. But Occam’s razor provides a way out: “Sure, the evidence supports both hypotheses. But I can explain it without undetectable goblins, and that is simpler, so I will choose the first hypothesis until you give me a better reason to choose the second.”

Debates like this have really happened. In 1857, the naturalist Philip Henry Gosse wrote a book called Omphalos, in which he argued that all the evidence that the Earth was older than Biblical tradition claimed – all the fossils, and layers of sedimentary rock, and ancient canyons apparently carved by millions of years of erosion – had been created by God already looking ancient.

Again, it’s impossible to falsify this claim with evidence. But we can say “OK, but ‘the universe looks old because it is old’ is simpler than ‘the universe looks old because God wanted to make it look old’.”

But there’s a problem: I’ve just asserted that A is simpler than B in both cases. It’s not always obvious what simple means. For instance, the Christian philosopher Richard Swinburne, in a 2010 paper, deployed Occam’s razor when he suggested that God is the simplest explanation for the universe, because God is a single thing. “God did it” is certainly simpler to say than “the universe emerged from quantum fluctuations in space-time”. But I would say that Occam’s razor is an argument against the existence of God. Who’s right?

Conveniently, in the 1960s, the mathematicians Ray Solomonoff and Andrey Kolmogorov developed a mathematically formalised version of Occam’s razor. One version of it is known as ‘minimum message length‘, and it asks: what is the shortest computer program that could produce what we’re seeing?

Let’s start with a simpler example than the creation of the universe: producing a string of numbers. I’ve taken this example from a Czech mathematician/computer scientist called Michal Koucký. He gives three strings of numbers: 33333333333, 31415926535, and 84354279521. If you wanted to write a program that carried on those strings for a million digits, what’s the shortest it could be?

The first you could do very easily: a simple bit of code saying “print the number 3 a million times”. You could do it in four lines of the beginners’ programming language BASIC.

The other two look random. But, in fact, the second string is simply the first 11 digits of pi, and you could print it out to a million digits by using one of the many quite simple algorithms which determine the digits of pi.

The third, however, is truly random. To write it out to a million digits you would need the program to specify all one million of them.

According to the ‘minimum message-length’ version of Occam’s razor, the first string is the simplest; the second is nearly as simple; and the third is the most complex.

So what does this mean for Swinburne? Well, the equations needed to describe the Big Bang are certainly complex. But they are sufficiently simple for humans to have written them. The algorithms needed to describe God – an all-powerful, all-knowing being – are not. We haven’t even managed to write software that’s as powerful as a human brain yet. From a minimum message-length perspective, God is much more complex – and therefore unlikely – than physics.

The same is true of evolution – you can quite easily write a program that approximates evolution by natural selection. But an intelligence sufficient to design all the creatures that evolution has made would be amazingly hard to program.

It also has implications for arguments within science. The “many worlds” interpretation of quantum theory, which says that every fraction of a second the universe splits into billions of parallel universes, sounds complex. The alternative, the “Copenhagen” interpretation, which says that quantum events aren’t resolved until they are observed, needs only one universe, and so sounds simpler.

But the program you’d need to create millions of universes would be pretty much the same as a program needed to create one universe – just have an extra line in it which says “do that again”, essentially – while a program that had to keep track of what every human in the world was looking at would be much more complex. According to minimum message-length Occam’s razor, a cosmos consisting of infinite universes can be ‘simpler’ than one that contains just one.

None of this means that these arguments are correct. The Copenhagen interpretation might be right despite being more complex. God might still exist; if the evidence shows that intelligent creation is more likely than the Big Bang, then it doesn’t matter how simple the theories are. But it means that you need more evidence for them.

William of Ockham was by all accounts one of the finest philosophical minds of his time, but he was also a friar and a Christian. I don’t know if he would be pleased to see me using his razor as an argument against the existence of God. But I think he would appreciate the simplicity of Solomonoff and Kolmogorov’s update of his argument for simplicity.

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Tom Chivers is a science writer. His second book, How to Read Numbers, is out now.

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