Starting from the assumption of a cosmology in which Boltzmann brains dominate over evolved ones, it is not immediately obvious to me that there is a real problem, since only Boltzmann brains indistinguishable from evolved brains will be posing the question in the first place.

In other words, the vast majority of Boltzmann brains will not be troubled by the paradox because their memories will not be consistent with a stable/large physical universe, and so they would never ask such a question in the first place.

So we must only consider the subset of Boltzmann brains whose experiences would be so consistent with a universe like ours that they would pose the question "why are we not Boltzmann brains?" And in such cases, even though we may be Boltzmann brains, our experiences would be indistinguishable from evolved brains.

Is this a criticism of the Boltzmann brain paradox that has been dispatched with, or is it a legitimate cause to be suspicious of whether it is really a paradox at all?

  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$ – David Z Apr 10 '15 at 16:59
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    $\begingroup$ In Boltzmann's scenario, you would merely have to imagine that the universe is stable and whatnot. I.e. your whole memory itself would be a figment of imagination, having accidentally come together a nanosecond earlier, and soon to burst apart and rejoin equilibrium. $\endgroup$ – Ruben Verresen Jul 26 '17 at 10:29
  • $\begingroup$ @RubenVerresen, I realize this, but the question still stands. The point is that those BB's that could stand to reflect on whether or not they are in the process of rejoining equilibrium are going to be BB's from outside that reference class of observers. $\endgroup$ – user1247 Jul 26 '17 at 16:51
  • $\begingroup$ Can you please absolutely clearly state what version of the paradox you are referring to? Many people refer to the "paradox" in "Boltzmann paradox" more in the sense of a "suprising fact" rather than "contradictive statement". $\endgroup$ – Void Sep 28 '17 at 10:02
  • $\begingroup$ @Void, I'm referring to the completely canonical version of the paradox that is commonly referenced in cosmology, that in many plausible cosmological models we prima facie expect to be B brains, in which case the outcome of most physical measurements would be contrary to experience, since there would be no reason to expect, for example, for a B brain to simulate experiences that are as consistent as they are with the more usual hypothesis that we are persistent evolved animals 15 billion years after a big bang. I'm not aware of a common "surpising fact" use of the term that accepts we are BB's $\endgroup$ – user1247 Sep 29 '17 at 6:06

That doesn't solve the problem because that level of information is a trivial addition to the model. What could resolve the paradox is some concept of Shannon entropy. The rarer an event is, the more information it provides when it occurs. A large number of generic BBs floating around will not necessarily represent a proportionally large amount of information.

  • $\begingroup$ This answer doesn't have much substance to it. It's not at all clear why a "trivial addition to the model" isn't all that is needed to solve it. $\endgroup$ – user1247 Feb 27 '16 at 15:31
  • $\begingroup$ The asker wondered if brains would have memories similar to ours. This would not be major additional complexity for a brain to possess. $\endgroup$ – D J Sims Feb 27 '16 at 22:35
  • $\begingroup$ I do not understand what the relevance is of the level of additional complexity. If you are only trying to give some kind of vague "hint" it would be better served in the comments rather than as a proposed answer to the question. $\endgroup$ – user1247 Feb 28 '16 at 3:49

Here's another, simpler answer. The BB analyses (like the one above) are typically based on some very modest definition of life, like an unpressurized brain floating in vacuum. If you include all the other equipment necessary for a brain to actually function then the odds are much different.

Furthermore, the universe actually doesn't contain much information at the cosmic scale and can easily be represented by simple simulations we can do today. The bulk of the paradox is in the information required for life to develop, which is unknown, and may not be that bad if evolution is able to help out.

So no, BBs are not clearly established as a problem.

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    $\begingroup$ "If you include all the other equipment necessary for a brain to actually function then the odds are much different." I think you miss Boltzmann's point. On a purely statistical level, your scenario is even more unlikely than Boltzmann's brain, since your scenario has even lower entropy. $\endgroup$ – Ruben Verresen Jul 26 '17 at 10:25

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