# Calculating the probability of a Boltzmann Brain

1. May 26, 2013

### lukesfn

Can anybody point me to a rough calculation of the probability of a disembodied brain appearing from a random fluctuation vs the probability of a brain evolving in a vary large random fluctuation?

I'm an eternalist. I find it easier to accept the ridiculous idea that the universe was always here, and has always been in equilibrium but we exist in a random fluctuation then ludicrous idea that the universe popped into existence with no cause apparently violating the 2nd law of thermodynamics.

I have however just learned about the Boltzmann brain paradox. Or at least learnt the name of it.

It suggests that a small fluctuation containing an isolated brain is much more likely then a large fluctuation with many brains. Some assume this means they are a most likely a disembodied brain, others think because we see a self consistant world, this is unlikely, however there is likely physical reason to make our observed universe more likely.

I've been reading in quite a few places that the Botlzmann brain paradox is a problem for many models with an eternal universe, but the handwaving arguments are completely unconvincing to me. I'm wondering what the probabilities are when people sit down and calculate it.

I'm wondering if a lot of people make the assumption that all configurations of similar apparent complexity are equally likely. But, I would kind of expect that at any time you are more likely to find a spherical plannet then a square one, I would also expect that you are much more likely to find a planet that formed from the collapse of a some other distribution, then one that appeared randomly. Similarly, I would assume that a brain is more likely to evolve in a large fluctuation then appear perfectly formed in a small fluctuation. It seems intuitively obvious to me, and simply solves solves the Botlzmann paradox, however, I've read from many sources, people still taking it as a serious problem, as I assume my like of thought is obvioius, so I'm curious about how the probabilities are actually calculated.

I imagine the probabilities would be calculated something like below.

disembodied probability = (Probability of a brain sized amount of matter appearing randomly) × (Probability of it being a conscious human like brain) x (mean time of brain existence)

evolved probability = (Probability of enough matter randomly appearing to produce our big bang ) x (Probability of a brain evolving from this matter) x (mean number of brains) x (mean time of each brains existence)

Can anybody help me filling values for these things? The probabilities only need to be relative to each other, so that makes life easier.

2. May 26, 2013

### Simon Bridge

The Boltzman brain is not considered to be a literal brain ... human brains could be thought of as one way that a Boltzman brain may manifest. The definition does not presuppose a particular form though.

The idea that many-brains are less likely than single brains assumes that the single-brain has higher entropy.
But it may be that self-aware entities can only form in concert with other self-aware entities as a kind of feedback mechanism ... such a model would be consistent with evolutionary thinking and avoids the need for the entity to appear spontaneously from a single fluctuation.

It's not something you can compute the probability of - since the requirements for self-awareness are not known.

It's more a qualitative philosophical device that can be used comparatively ... we don't know what the probability is in absolute terms of P(brain)=<some number> but we can rank in order of likelyhood quite a wide range of things assuming that higher entropic conditions are more likely to arise spontaneously from a single fluctuation.

3. May 26, 2013

### lukesfn

Already understood, and the same is true for an evolved brain. However, suck things are more unknown so harder to estimate probability off.

I assume there are many reasons that would prevent the probability being accurately calculated. I can easily think of a few.

However, I can see some room for numbers to be useful. For example, if it more likely for my exact brain to spontaneously form, then for the same amount of matter visible in the universe to spontaneously explode, then, that would leave the paradox in tack. Those numbers would be much easier to calculate.

Perhaps it is even not to hard to calculate weather a brain similar to ours would appear. That would also be a useful calculation.