Ten conspiracy theories for nerds (or conspiracy theory theory)

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Ten conspiracy theories for nerds (or conspiracy theory theory)

Not your usual cup of tea, here is one of them:

The Simulation Argument. This is legion in popular culture from “The Matrix” and “Inception” and other sci-fi, so we’ll just refer you to Nick Bostrom’s formulation of it. In theory we could tell the difference if something happened in the manner of The Truman Show where a light labeled “Sirius” falls from the sky. But are there any such events?

We offer one complexity-related observation. Although it is routine to say that classes like ${\mathsf{P}}$ and ${\mathsf{BQP}}$ have universal simulation, this isn’t strictly true. The universal function for ${\mathsf{P}}$ doesn’t belong to ${\mathsf{P}}$ —if it did, then ${\mathsf{P}}$ would be in some fixed polynomial time bound, which it isn’t. Although proving this is technically murkier for “random” or “promise” classes like ${\mathsf{BQP}}$ , the essential idea holds for any reasonable complexity class. Thus a universal simulation involves dropping down to a lower grade than the resources on which you draw. If our universe is convincingly universal, perhaps this is a well-motivated reason to reject the argument.

Perhaps the conspiracy is that so many people are intent on getting us to believe the simulation hypothesis. Here is another one:

${\bullet }$ Factoring Really Is Easy. This is similar to the last, but now they can factor in polynomial time on a laptop, rather than need a quantum computer. Ken and I think this one has a much higher prior, almost on the order of “Breaking Engima Really Is Easy” in 1939.