19th October, 2009
There’s only one thing that fascinates me more than big numbers (we’re talking 10^10^10^10^2.08 years big here) and that’s space. And they only just beat really big science theories to it.
So you can probably imagine how happy I was when while reading about some pretty big numbers on Wikipedia, I discovered a concept called the Boltzmann Brain.
This concept is of course named after Ludwig Boltzmann, the Austrian physicist, and I thought I’d share a little bit about the idea with you. I found the combination of physics, probability, and philosophy incredibly interesting.
Boltzmann proposed that we and our observed low-entropy world are a random fluctuation in a higher-entropy universe. Even in a near-equilibrium state, there will be stochastic fluctuations in the level of entropy. The most common fluctuations will be relatively small, resulting in only small amounts of organization, while larger fluctuations and their resulting greater levels of organization will be comparatively more rare. Large fluctuations would be almost inconceivably rare, but this can be explained by the enormous size of the universe and by the idea that if we are the results of a fluctuation, there is a “selection bias”: We observe this very unlikely universe because the unlikely conditions are necessary for us to be here, an expression of the anthropic principle.
This leads to the Boltzmann brain concept: If our current level of organization, having many self-aware entities, is a result of a random fluctuation, it is much less likely than a level of organization which is only just able to create a single self-aware entity. For every universe with the level of organization we see, there should be an enormous number of lone Boltzmann brains floating around in unorganized environments. This refutes the observer argument above: the organization I see is vastly more than what is required to explain my consciousness, and therefore it is highly unlikely that I am the result of a stochastic fluctuation.
The Boltzmann brains paradox is that it is more likely that a brain randomly forms out of the chaos with false memories of its life than that the universe around us would have billions of self-aware brains.
The rationale behind this being paradoxical is that, out of chaos, it is more likely for one instance of a complex structure to arise than for many instances of that thing to arise. This ignores the possibility that the probability of a universe in which a brain pops into existence, without any prior mechanism driving towards its creation, may be dwarfed by the probability of a universe in which there are active mechanisms which lead to processes of development which (given a starting state that is unlikely but not as unlikely as the spontaneous appearance of a brain with no precursor) offer a reasonable probability of producing a species such as ourselves. In a universe of the latter kind, the scenarios in which a brain can arise are naturally prone to produce many such brains, so the large number of such brains is an incidental detail.