Boltzmann Brains, Simulations and self refuting hypothesis

by Donald Hobson 1 min read26th Nov 20189 comments

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Let's suppose, for the purposes of this post, that our best model of dark energy is such that an exponentially vast number of Boltzman brains will exist in the far future. The idea that we may be in an ancestor simulation is similar in its self refuting nature but slightly vaguer, as it depends on the likely goals of future societies.

What do I mean when I say that these arguments are self refuting? I mean that accepting the conclusion seems to give a good reason to reject the premise. Once you actually accept that you are a Boltzmann brain, all your reasoning about the nature of dark energy becomes random noise. There is no reason to think that you have the slightest clue about how the universe works. We seem to be getting evidence that all our evidence is nonsense, including the evidence that told us that. The same holds for the simulation hypothesis, unless you conjecture that all civilizations make ancestor simulations almost exclusively.

What's actually going on here. We have three hypotheses.

1) No Boltzmann brains, the magic dark energy fairy stops them being created somehow. (Universe A)

2) Boltzmann brains exist, And I am not one. (Universe B)

3) I am a Boltzmann brain. (Universe B)

As all these hypothesis fit the data, we have to tell them apart on priors, and anthropic decision theory, with the confusion coming from not having decided on an anthropic theory to use, but ad-lib-ing it with intuition.

SIA Selects from all possible observers, and so tells you that 3) is by far the most likely.

SSA, with an Ocamian Prior says that Universe B is slightly more likely, because it takes fewer bits to specify. However most of the observers in Universe B are Boltzmann brains seeing random gibberish. The observation of any kind of pattern gives an overwhelming update towards option 1).

If we choose to minimize the sum of both the amount of info needed to describe the universe, and the amount needed to specify your place within it, then we find that Universe B is simpler to describe, and it is far easier to describe the position of an evolved life-form near the beginning of time, than to locate a Boltzmann brain around years in. An AIXI that is simulating the rest of the universe, with patching rules to match its actions up to the world, will act as if it believes option 2).

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