This is my post for day 24 of the Inkhaven writing retreat.

Imagine you’re in the ancestral environment. (People do that, right? That’s normal?) The only thing you know about the shape of the world is what you’ve seen with your own eyes. You and your tribe have roamed around quite a bit, so you’ve seen meadows, rivers, and mountains, and you know the earth can change a lot. But there’s always a horizon. If you actually sat down on a log and thought about it, what would the options be?

I feel like I’ve heard a lot of cultural myths about the sky. About what would happen if you somehow went up and up and up. About how the gods live there or whatever. It also seems pretty common for people to interpret the sky as a dome. Thinking of it as a dome gives you some sense that the edges might be walls or barriers of some kind, and I guess that might lead you to think of the surface of the earth as a disk of a fixed size.

Presumably one reason people think of the sky as a dome is because they can see the stars rotate smoothly. And, of course, they rotate smoothly because the earth is a sphere rotating in space, and the stars are approximately fixed and infinitely far away.

But does this actually look different than if the earth was flat, and the stars infinitely far away, and rotating around the north star? This is kind of hard to intuit, but my sense is that it would actually look the same. So why does it look so much like a dome?

Oh, right — the sun and the moon also seem to travel on the dome. Since you can see their diameter, you can tell they’re not infinitely far away, and so if they were traveling in straight lines, you’ll see them get smaller on the horizon. So maybe the sun and moon are the main reason people thought of the sky as a dome.

Let’s put that aside, and assume we have no reason to think the sky is a dome. What would people think about the horizon? If you keep walking for days on end, and new, random landscapes keep coming over the horizon, I feel like it would be very reasonable to assume that it just went on forever. (The oceans are compelling evidence for an end, but if land can suddenly turn into ocean then it stands to reason that ocean can suddenly turn into land.) And as you walked around, you would occasionally find more people. And the more you walked the more people you would find. I think it would be reasonable to conclude that the earth is filled with infinitely many people!

As a small digression, some people think that Occam’s razor means that each postulated physical object requires evidence; that the burden grows with the number of objects. They would say that, maybe seeing a few trees is evidence for a few more unseen trees, or that seeing a thousand stars is evidence for around a thousand more unseen stars, but surely infinitely many trees or stars is infinitely unlikely.

I think this is reasonable but wrong. Nature is not out there manufacturing new objects one at a time, using up some kind of finite resources, like you or I would be. Nature just is a way. And being the way of “filled with thirty trees” is not tremendously more likely than being the way of “filled with endless trees”. My formal stance on this is based on descriptive complexity; longer description length means lower probability. Since you can formally well-define “infinity” with a very small number of logical symbols, that to me makes it actually quite likely. In contrast, most specific finite numbers take a long time to describe. So the more objects you see, the more likely there are to be infinitely many.

Going back to the question of how many people there are, can you imagine how crazy the world would feel if you believed there were infinitely many people? I have grown up always knowing that the earth was finite and so were its people. It’s obviously huge and detailed, but in some sense, there’s a comprehensible limit. You can look at globes and see all the continents. You can start to memorize the names of countries, and the layout of the largest cities. But if an infinite earth was roughly evenly populated forever and ever, you would never know what might be about to come over the horizon. You could find a utopian city of gold, or a nest of dragons. If some army or plague was spreading across the land, you would just not be able to do anything about it. Presumably this is in fact how many people felt throughout history, or still feel.

There’s one more direction we could speculate about; down. This seems to be far less popular. But like, really truly, if you knew nothing about physics or the nature of matter, and all you had was a few decades of experience running around on the earth — what would you think was down there? What would you expect to happen if you just… started digging?

The sky has the really weird property that you can see right through it. And it kind of seems easier to go up. You can throw stuff pretty high. You can go climb a mountain. You can see that birds and clouds got up there somehow. But the ground is way more unforgiving, if you try to go down. Holes collapse pretty easily, so you’d have to dig out a huge cone.

I think it would be reasonable to believe that it’s just dirt and rock for miles and miles, way more than you could ever practically dig. But there would still be a fact of the matter about what’s below that. Would you believe in infinite rock? Would you believe that space itself stops? Sure, you could believe in hell, but hell has a floor. What’s under the floor? One has to wonder what a Solomonoff inductor predicts.

I’d love to read speculative fiction where some prehistoric rationalists use their spare resources to pursue a deep understanding of the universe by digging a really deep hole. And where, in that universe, the earth is an infinite flat plane, and the answer to what lies below is not the same as in our world.