Boltzmann-brain argument against multiversal fine-tuning

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Brian Tomasik
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Boltzmann-brain argument against multiversal fine-tuning

Post by Brian Tomasik » Sat Dec 17, 2011 9:03 am

The problem of fine tuning is often addressed by appeal to a multiverse hypothesis. The idea is that in an infinite multiverse, some universes will be fine-tuned for observers, and by anthropic selection, we'll only find ourselves in those universes. So the probability of fine-tuned universes conditional on a multiverse is very high. If I read Chapter 2 of Anthropic Bias correctly, it seems to me that Nick Bostrom agrees with this type of reasoning.

However, Robin Collins raises an interesting counterargument in "The Fine-tuning of the Cosmos: A Fresh Look at its Implications":
Because [Boltzmann Brains] BBs have a finite probability of occurring in any region of space-time with a positive energy density, in a sufficiently large universe that has some lower-bound to its mass-energy density, many BBs are almost certain to occur. This is true even if the constants and parameters of physics are not fine-tuned – for example, if the dark energy density is too large for galaxies and stars to form. Furthermore, in standard versions of the multiverse – such as promoted by Stephen Hawking (reference_, Alexander Velnkin (reference), and Leonard Susskiind (reference), the bubble universes that are produced are infinite in size and meet this minimal mass-energy density condition. Such infinite universes will have an infinite number of BBs, whether or not their constants are fine-tuned. [pp. 6-7]
Therefore, even if we could explain why, in our own universe, Boltzmann Brains are more rare than non-Boltzmann Brains, non-fine-tuned multiverses will still lead Boltzmann Brains to preponderate by cosmic orders of magnitude.

However, we have reasons to think we're not Boltzmann Brains:
  • Empirical: Our experience is ordered. For almost all brain fluctuations, even a momentary experience is chaotic.
  • Prudential: Only if we're not Boltzmann Brains will our actions have lasting impacts on the universe in terms of reducing suffering, etc. So we should act as though we're not Boltzmann Brains.
What do you think? Does this argument make any errors or oversights?

As a disclaimer, I should say that I find most of the remainder of this article by Collins unconvincing. His god hypothesis -- even if it can be made coherent and explanatory of anything -- is far more extravagant than what's needed. Or else, if one defines "god" as merely certain principles of physics that makes fine-tuning true, then the relation of this "god" to ordinary religion crumbles away. That said, it does seem to me at first glance that the specific portion of Collins's argument cited above weakens the conventional multiverse explanation for fine-tuning and therefore strengthens the suggestion of some more targeted principle of nature that gives rise to orderly observers.

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Re: Boltzmann-brain argument against multiversal fine-tuning

Post by GregoryLewis » Sat Dec 17, 2011 3:03 pm

This is one bit of phil of R I follow somewhat closely.

Most of the surprise of being in an 'agent structured universe' vanishes if most observers are agents. BBs will be singularly rare occurences (perhaps one for a second or two out of a trillion universes, and the odds climb higher as I think we need to specify this observer needs to be able to do some sort of observation/inference on the conditions of the universe). In contrast, each life permitting universe can spawn a vast number of observers/interacting-agents.

With infinitely many worlds, you get both options infinitely many times. So you get infinitely many BBs, but also infinitely many observers/interacting agents. It seems the best fudge to work out the fraction of all observers that are embodied agents is to multiply the (very small) 'life permitting region' by an approximation of how many lives will exist per life permitting universe universe, compared to 'BB permitting region' by an approximation of how many BBs will exist per universe (likely to be an infinitesimal fraction). It strikes me the fraction of agents/total observers has a not too low central measure with massive error bars, so an FTA is not rescued by appeal to widening the reference class to observers.

A bigger problem with the fine tuning argument is that we have negligible evidence to believe life permitting universes are rare, even assuming a single universe hypothesis. Although Life permittingness is rare in our region of epistemic illumination, our epistemic illumination is so pathetic compared to the space of possibility it gives us next to no insight. So observation of fine tuning gives at best trivial evidence to believe life permittingness is rare.

I've written about it here and here, for the interested.

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Re: Boltzmann-brain argument against multiversal fine-tuning

Post by CarlShulman » Sun Dec 18, 2011 1:05 am

As the size of a Boltzmann brain increases, the probability that it will be generated by a fluctuation declines exponentially: with each additional atom that needs to randomly alight to construct a minimal BB we multiply the probability by some tiny p of the atom so alighting. A human brain has on the order of 10^26 atoms, so the probability of it being generated at a given suitable site would be p^(10^26). If p is 1/1024 (ridiculously high), then 1 in 2^(10^27) sites would have a brain of a given ordered/evolvable configuration.

That provides quite a lot of "breathing room," i.e. even if universes or regions that can support the evolution of intelligent life are fairly rare or low-measure, plausible ways of taking limits will give a small share to BB rather than evolved creatures.

Say that we penalized laws of physics according to their Kolmogorov complexity, so that a universe with basic laws that require an extra bit to specify takes a 50% probability penalty. Some very simple programs would produce human brains by generating pseudorandom worlds, e.g. placing atoms initially using the digits of pi. But the atoms would wind up in brain-like configurations only astronomically rarely, as stated above.

Evolution combined with laws of physics that produce large bubbles of low entropy (like eternal inflation) could produce intelligent life exponentially more frequently, e.g. by specifying that bones would be contiguous, DNA molecules working, etc. This might require a more complex program than BB-world, but we would have have a good chunk of 10^27 bits to specify this more complex world.

So, if there is something like a Tegmark IV multiverse, one can see how this BB issue could be defused. A more perplexing problem would be if we thought there was but one universe, and had a complexity prior over its laws of physics: then we would think the world was probably mostly populated by BBs and we were the ludicrously rare ordered ones.

However, note that the Self-Indication Assumption would address this: in the Tegmark IV multiverse there can be a ludicrously higher population density so SIA would convince us we were not BBs. A similar argument could be made from total consequentialism combined with a one-boxing decision theory: in a multiverse that includes non-BB-dominated laws of physics there can be a higher density/measure of experiences like ours, and we should think of ourselves as controlling the decisions of a class of systems physically identical to us (at least), so maximizing expected utility involves acting as though there are many of us (and thus universes where evolution is possible exist).

I'm actually more skeptical of the argument that we can't do anything if we're BBs, so we can ignore the possibility under causal decision theory. One could still choose to think about flowers, or otherwise have a happy thought in the instant before one dissolves into chaos. That might be sensible if it really were ludicrously more likely that one was a BB rather than an evolved being.

Edit: fixed number of sites and bits.
Last edited by CarlShulman on Sun Dec 18, 2011 3:12 am, edited 1 time in total.

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Brian Tomasik
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Re: Boltzmann-brain argument against multiversal fine-tuning

Post by Brian Tomasik » Sun Dec 18, 2011 1:44 am

Thanks, Gregory!

So I guess you're challenging this premise: "Therefore, even if we could explain why, in our own universe, Boltzmann Brains are more rare than non-Boltzmann Brains, non-fine-tuned multiverses will still lead Boltzmann Brains to preponderate by cosmic orders of magnitude." I would have assumed the opposite, because fine-tuning for life instead of just Boltzmann Brains involves combined probabilities on the order of 10^-100 or 10^-1000, and it seems intuitively that the probability of a (very small) Boltzmann Brain reflecting on its existence as an observer is higher than that. [Edit: In light of Carl's envelope calculation, I guess I was wrong about that. :) Even a brain much smaller than a human brain would be much less probable than fine-tuning is.]

Of course, all of this is on the supposition that there aren't simpler laws or agents to explain why the constants are as they are, which I find to be most plausible.
GregoryLewis wrote: A bigger problem with the fine tuning argument is that we have negligible evidence to believe life permitting universes are rare, even assuming a single universe hypothesis. Although Life permittingness is rare in our region of epistemic illumination, our epistemic illumination is so pathetic compared to the space of possibility it gives us next to no insight.
Claire elaborates on this in your second link:
I don’t think we can see enough of the relevant possibilities to pass any judgement on whether life-friendliness is surprising given Atheism. Among the space of all possible worlds, we can surely inspect very few of them: it seems likely that the number of worlds we can examine is a tiny subset of these. Why not worlds where there are no physical parameters, and just filled with consciences? Or any number of things I can dream up (and, further, knowing that will be still other possibilities I can’t). Yet inferring from our tiny subset of possible worlds of which barely any are life-friendly to infer that it’s life-unfriendly across the board is an outrageous extrapolation.
But if there were other universes where life-permittingness were not so much on a knife's edge, then we should overwhelmingly expect to find ourselves in those universes. The fact that we find ourselves here suggests that our universe has many more observers than even the average observer-containing universe. Claire makes this point later on:
In this case, we aren’t confirming the aiming hypothesis over the random selection because our result is life-friendly: given your example, the vast chunk of possibilities are so it would be no surprise to find one ‘at random’. What’s surprising here is there seems something special about this lone universe – this lone fly: that it’s on it’s own in a field. So it’s no longer the fact that our universe is life friendly that’s causing the surprise, but rather that it’s tuned to be in a locality of non-life-permitting universes.
I haven't yet gotten a chance to read your first link, but I see that it has a lot more discussion, so I may need to read that before commenting further.

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Re: Boltzmann-brain argument against multiversal fine-tuning

Post by Brian Tomasik » Sun Dec 18, 2011 2:15 am

By the way, what do you think of the Biocosm hypothesis? I read about it years ago while researching lab universes (which I don't support :( ), but I guess it's also a way out of the Boltzmann-Brain problem with the plain-vanilla multiverse scenario. While I assign this particular theory low-ish probability, it may be the single-best concrete explanation I know of, rather than just saying "there are more fundamental principles/processes leading to this type of universe that we don't yet know."

Edit again: In light of Carl's calculation, I see that this isn't necessary.

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Re: Boltzmann-brain argument against multiversal fine-tuning

Post by Brian Tomasik » Sun Dec 18, 2011 2:55 am

Thanks, Carl!
CarlShulman wrote:A human brain has on the order of 10^26 atoms, so the probability of it being generated at a given suitable site would be p^(10^26).
What's the smallest possible brain having my current thoughts? Much smaller than 10^26 atoms. But however small it is, it likely won't matter: 10^20, 10^10, etc. would all likely give enough breathing room. Fine tuning is more like 2^(-10^3) or 2^(-10^5) or something.

Also, p in your argument should in reality be much smaller than 1/1024. (How small exactly? In the ballpartk of 10^-35?)
CarlShulman wrote: However, note that the Self-Indication Assumption would address this: in the Tegmark IV multiverse there can be a ludicrously higher population density so SIA would convince us we were not BBs. A similar argument could be made from total consequentialism combined with a one-boxing decision theory: in a multiverse that includes non-BB-dominated laws of physics there can be a higher density/measure of experiences like ours, and we should think of ourselves as controlling the decisions of a class of systems physically identical to us (at least), so maximizing expected utility involves acting as though there are many of us (and thus universes where evolution is possible exist).
That falls under the scope of my "prudential" point, right? I can't tell if you're disagreeing with this reasoning in your last paragraph about causal decision theory or if you're just playing devil's advocate there by suggesting what CDT would say.

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Re: Boltzmann-brain argument against multiversal fine-tuning

Post by CarlShulman » Sun Dec 18, 2011 3:33 am

I agree brains could be smaller than human, and that the probability of the right kind of fluctuation is lower (as I implied). Wikipedia throws around numbers like 10^(10^50) years for a Boltzmann brain to be produced, citing "Sinks in the landscape, Boltzmann brains and the cosmological constant problem" (http://arxiv.org/abs/hep-th/0611043).
That falls under the scope of my "prudential" point, right?
The SIA is not a prudential argument. The "total consequentialism plus one-boxing, approximating the SIA in many situations" point is a prudential argument, which I presented as a devil's advocate. Without some separate reason to assign substantial probability to non-BB worlds (SIA, the simplicity of a multiverse, etc) the probabilities would be in Pascal's Mugging territory.

I happen to think we do have independent a priori reasons to place credence in a multiverse.

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Re: Boltzmann-brain argument against multiversal fine-tuning

Post by Brian Tomasik » Sun Dec 18, 2011 4:08 am

CarlShulman wrote: The SIA is not a prudential argument.
Yeah, that's right. I have much intuitive sympathy for SIA independent of prudential considerations, but "total consequentialism plus one-boxing" is IMO an even better argument for acting as though SIA is true.

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