Mathematical Wool

Posted on by Owen Lynch

In Scott Alexander’s Unsong, there is a theory about the creation of the universe that goes something like this. (some discursive paragraphs removed)

“Today I will expound unto you the kabbalistic theory of the creation of the world,” said Ana. “It all starts with Leibniz…”

“See, there’s this idea called divine simplicity. People keep asking, okay, so God created the Universe, but who created God? The answer is that God doesn’t need creating. He’s perfectly simple. He’s just a natural thing for there to be. People act like you need God to explain why the universe isn’t just nothing. But why should the Universe be nothing? Why shouldn’t it be, I don’t know, a piece of bread? The only reason people think ‘nothing’ needs no explanation, but a piece of bread does need an explanation, is that nothing is simpler than bread. Well, God is just as simple as nothing. So there.”

“How is this Leibniz?” asked Eli Foss.

“I’m getting to Leibniz! Right now we’re at information theory. A well-defined mathematical explanation of simplicity. We can measure the complexity of a concept in bits. The number of binary digits it would take to specify the concept in some reasonable encoding system. We can do it with numbers. The numbers 0 and 1 are one bit. Two is 10, three is 11; those are two bits. Four is 100, five is 101, six is 110, seven is 111; so three bits. And so on. We can do it with computer programs; just count how many bits and bytes they take up on a computer. We can do it with images if you can get them into a format like .gif or .jpg. And we can do it with material objects. All you have to do is figure out how long it would take to write a program that specifies a description of the material object to the right level of complexity. There are already weather simulators. However many bits the most efficient one of those is, that’s how complex the weather is.”

“And God?” asked Zoe Farr.

“God is one bit. The bit ‘1’”.

“I find that…counterintuitive,” was the best Zoe could answer.

“Well, it’s easy to represent nothingness. That’s just the bit ‘0’. God is the opposite of that. Complete fullness. Perfection in every respect. This kind of stuff is beyond space – our modern theories of space take a bunch of bits to specify – but if it helps, imagine God as being space filled with the maximum amount of power and intelligence and goodness and everything else that it can hold, stretching on to infinity.”

“Leibniz was studying the I Ching, and he noticed that its yin and yang sticks, when arranged in hexagrams, corresponded to a new form of arithmetic, because he was Leibniz and of course he noticed that. So he invented binary numbers and wrote a letter to the Duke of Brunswick saying that he had explained how God could create the universe out of nothing. It goes like this. You’ve got God, who is 1. You’ve got nothingness, which is 0. And that’s all you need to create everything. 1s and 0s arranged in a long enough string.”

“The kabbalistic conception is that God withdrew from Himself to create the world. I, for example, am beautiful and intelligent, but not so physically strong. God is perfectly beautiful and intelligent and strong, so by withdrawing a little bit of His beauty and intelligence, and a lot of His strength, and some other things, we end up with an Ana.”

“How did God decide which 1s to change to 0s?” asked Erica.

“And there’s the rub,” said Ana. “To change any 1s to 0s at all is making the world worse. Less Godly. Creation was taking something that was already perfect – divinity – and making it worse for no reason. A wise woman once said that those who ask how a perfect God create a universe filled with so much that is evil miss a greater conundrum – why would a perfect God create a universe at all?”

In math there is a similar conundrum. Leopold Kronecker once said that “God created the natural numbers, all else is the work of man.”

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