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By Root 2130 0

a computer to generate all possible computable universes than it is to program individual computers to generate them one by one. To see why, imagine programming a computer to simulate baseball games. For each game, the amount of information you’d need to supply is vast: every detail about every player, physical and mental, every detail about the stadium, the umpires, the weather, and so on. And each new game you simulate requires you to specify yet another mountain of data. However, if you decide to simulate not one or a few games, but every game imaginable, your programming job would be far easier. You’d just need to set up one master program that systematically makes its way through every possible variable—those that affect players, the environment, and all other relevant features—and let the program run. Finding any one particular game in the resulting voluminous output would be a challenge, but you’d be assured that sooner or later every possible game would appear.

The point is that whereas specifying one member of a large collection requires a great deal of information, specifying the entire collection can often be much easier. Schmidhuber found that this conclusion applies to simulated universes. A programmer hired to simulate a collection of universes based on specific sets of mathematical equations could take the easy way out: much like the baseball enthusiast, he could opt to write a single, relatively short program that would generate all computable universes, and turn the computer loose. Somewhere among the resulting gargantuan collection of simulated universes, the programmer would find those he’d been hired to simulate. I wouldn’t want to be paying for computer usage by the hour as the turnaround time for generating these simulations would similarly be gargantuan. But I’d happily pay the programmer by the hour since the instruction set to generate all computable universes would be much less intensive than that required to yield any one universe in particular.11

Either of these scenarios—a great many users simulating a great many universes, or a master program that simulates them all—is how the Simulated Multiverse might be generated. And because the resulting universes would be based on a wide variety of different mathematical laws, we can equivalently think of these scenarios as generating part of the Ultimate Multiverse: the part encompassing universes based on computable mathematical functions.*

The drawback of generating only part of the Ultimate Multiverse is that this downsized version less effectively addresses the issue that inspired Nozick’s principle of fecundity in the first place. If all possible universes don’t exist, if the entire Ultimate Multiverse is not generated, the question resurfaces of why some equations come to life and others don’t. Specifically, we’re left wondering why universes based on computable equations hog the spotlight.

To continue along this chapter’s highly speculative path, maybe the computable/noncomputable division is telling us something. Computable mathematical equations avoid the prickly issues raised in the middle of the last century by penetrating thinkers like Kurt Gödel, Alan Turing, and Alonzo Church. Gödel’s famous incompleteness theorem shows that certain mathematical systems necessarily admit true statements that can’t be proved within the mathematical system itself. Physicists have long wondered about the possible implications of Gödel’s insights for their own work. Might physics, too, necessarily be incomplete, in the sense that some features of the natural world would forever elude our mathematical descriptions? In the context of the downsized Ultimate Multiverse, the answer is no. Computable mathematical functions, by definition, lie squarely within the bounds of calculation. They are the very functions that admit a procedure by which a computer can successfully evaluate them. And so, if all the universes in a multiverse were based on computable functions, they all would also do an end run around Gödel’s theorem; this wing of the Library of Mathematical