Rudy Rucker, in a post titled Fundamental Limits to Virtual Reality, argues that a virtual version of our planet, if it used the same computing resources, could never be as rich in phenomena. His main argument:
This is because there are no shortcuts for nature’s computations. Due to a property of the natural world that I call the “principle of natural unpredictability,” fully simulating a bunch of particles for a certain period of time requires a system using about the same number of particles for about the same length of time. Naturally occurring systems don’t allow for drastic shortcuts.
For details see The Lifebox, the Seashell and the Soul, or Stephen Wolfram’s revolutionary tome, A New Kind of Science—note that Wolfram prefers to use the phrase “computational irreducibility” instead of “natural unpredictability”.
Granted, a full simulation at the level of atoms or elementary particles would not be doable. But there’s no reason you need one. Vidar Hokstad nails it in the comments:
We can’t predict the arrangement of individual atoms in a large object. Why would a simulation even try? If someone do point an electron microscope at an object in the simulated world, the simulator can pick any random arrangement and we wouldn’t know better.
The notion of leaving the details up to randomness is an interesting move. But maybe they aren’t random. Wolfram sometimes claims the whole kaboodle comes out of some, like, ten-bit rule that’s run for a really large number of cycles. Here’s the number of cycles that’s the thing that won’t fit on your desk.
When people talk about a substitute being “just as good,” I think of the Who song. [lyrics omitted]
But if all the stuff that Rucker shows on his photos — snow, fields, clouds, rocks — can be recreated qualitatively from humongously lossy statistical mechanics models and it’s only details like what you see through an electron microscope that have to be made up on the spot, doesn’t that already contradict his original point, which is that VR surroundings would look noticeably impoverished? It’s true that in a chaotic world, if you go to a lossy VR version, it will diverge pretty quickly from what it would have been. But then, in a chaotic world, the world diverges from what it would have been every time you blink.
Also, it seems like there should be some sort of principle that says it doesn’t take much more computing power to run a convincing virtual world for a mind to live in than it takes to run the mind itself. There’s only so much you can process in a second. I suppose that if you want a world to naturally factor huge numbers, computational complexity theory says that doing so takes much longer than it takes a mind in it to recognize that the numbers have indeed been factored. Most features of the world don’t seem to me to be like that, but my thinking here isn’t clear at the moment.
If I’m right and Rucker is wrong, the world takes up much less room in VR than will be available on future real-world computers. That means virtual worlds could be much bigger than Earth; it’s interesting to think about the implications if people lived there. In fact, if a there’s a not-too-expensive algorithm determining what a new piece of the world looks like, as well as how other pieces would have affected it until that time, and the algorithm gets run only as needed, then in a sense the world is infinite. (This doesn’t have any real function, and I’m not claiming people will choose to create this; just that they could if they wanted to.)