Today, I came across a curious blog by author Rudy Rucker, who argues that it is impossible to fully simulate the Earth. That to do so would require grinding up the entire Earth into computronium, which is pointless since the result is a simulated world exactly like the real world, so why bother?
But my question is: why would we want to create a perfect duplicate of the Earth, all the way down to the tiniest pebble and blade of grass? Rucker argues that to completely simulate the entire Earth, we would need exactly this amount of matter since “there are no shortcuts for nature’s computations”, and why bother since the result of said simulation already exists. I would agree with this assessment, but we can drastically cut back the required amount of computer power needed to simulate a virtual environment.
Let’s put in some numbers here: the Earth masses 5.972 x 1024 kg. To fully simulate the entire Earth, right down to single atoms, we would 1 Earth, or 5.972 x 1024 kg. The thing is, though, our senses cannot sense atoms. Our visual and tactile systems cannot sense very much below 0.1 mm in size. So why would we have to make our virtual world with such a tiny “pixel resolution”? Instead, let’s make our virtual world have a pixel resolution of 0.01 mm. Basically, our virtual world’s “atoms” are pixels 0.01 mm in diameter. These virtual atoms (or, V-atoms) are bound together with simulated forces in order to accommodate being manipulated in various ways (touching, lifting, tearing, breaking, etc.). Real world atoms, however, have diameters on the order of 10-10 m or, 0.0000001 mm. So, you might think that each V-atom could stand in for 100,000 real world atoms. Ah, but both V-atoms and real atoms are three-dimensional. If you were somehow transport a V-atom into the real world and stuff it full of real atoms, would find that a V-atom holds 100,0003 or 1015 atoms. This means that you could simulate any physical space and use 1015 times less matter than it would take in the real world. For the Earth, that would be 5.972 x 109 kg.
That’s still a lot of matter. The computer system that would simulate the entire Earth would mass roughly the same as the Pyramid of Giza. But why would a person need to simulate the entire Earth? If you’re a normal person with their own personal computer made of computronium, you’d like to be comfortable and have lots of space in your virtual environment, but simulating an entire planet seems like overkill. Instead, what if we were to simulate a volume only 5 km x 5 km x 5 km? The entire volume of Earth (including 100 of atmosphere), is around 1.14 trillion km3, whereas our imagined virtual environment is only 125 km3. This again reduces the amount of needed matter by a factor of about 10-10, so that our imagined virtual space would require only 0.6 kg of mass (about one-and-one-third pounds). This is smaller than a modern-day desktop computer. In fact, it is likely to be much small since a virtual world like this would likely be mostly skybox. Simulating air would likely be much easier to simulate since it is far less dense than the ground. You might have maybe a few dozen to a hundred meters of ground depth, and then 4.9 km of virtual air above. Lots of people like to fly, not as many like to dig. Of course, it’s up to the user what they want, but the point is there is definitely enough matter around to distribute such computers to each and every person in existence.
Not to mention that the whole point of a virtual world is that it can be made different than the real world. In physical reality, we are stuck with physical law. But in virtual reality, physical law become limited only to what is imaginable. Feats impossible in the real world (for example, humans flying like Superman) become trivial in the virtual world. Deconstructing the Earth to make a perfect virtual duplicate which requires the entire Earth anyway makes no sense, but using tiny parts of it to make coarser, smaller, but ultimately indistinguishable, virtual fantasy worlds makes enormous sense.