I had a recent conversation that went something like this:

“Hey, you know about brains. What about Boltzmann brains? Can they exist?”

If, like me, you are not versed in statistical physics, you might as surprised as I was. Boltzmann brains? are we talking about 19^{th} century physicist Ludwig Boltzmann’s actual brain, or some crazy AI project?

As it turns out, neither. Boltzmann brains are a logical argument that speak deeply to cosmology, stochastic systems and our intuitions about the universe – and very little about actual brains.

The argument goes like this: you have a universe around you governed by the laws of thermodynamics. Specifically the second law stipulates that in a closed system, any physical process leads to an increase in entropy; in other words, disorder amongst the component atoms inside the system. The universe is a closed system (i.e. it is finite) and therefore it tends to increase in entropy. Therefore, the ideal state for our universe is of thermodynamic equilibrium, in other words, high entropy. However, the world that surrounds us is not like that, we observe order everywhere, from stars and galaxies to the presence of life, which indicates low entropy in the system. So we are left with a sticky situation: thermodynamics predicts high entropy, and we observe low entropy.

One solution would be to theorise the universe as *mostly* being in a state of high entropy, which occasionally fluctuates into a low entropy state and gives rise to our reality, before being quickly ushered back into chaos. This is when Boltzmann comes in – while he sees the universe as fundamentally statistical system, fluctuating between states of varying entropy, the idea of our perceptible reality being a statistical fluke appeared to him as nonsense.

The problem is, every increasing step of complexity requires a increasingly rare statistical fluke of low entropy to give rise to it. So a bit of dust clumping together is more likely than a planet forming. Similarly, a star or a galaxy are increasingly more improbably scenarios in our thermodynamic balanced universe. Taking this argument to the extreme, if you wish to create a scenario where a series of unlikely stochastic processes from a maximally entropic starting point lead to a sentient being, it would vastly more probable that a) such sentience would be made up from the minimum number of components necessary, for example a lonesome brain without a body and b) that such sentience would exist for the smallest amount of time possible. It therefore follows that in this universe any sentient being is far more likely to be a single, floating brain immersed in the a chaotic universe flickering in and out of existence by sheer randomness, rather than the complex pastiche of order we see in our low entropy universe.

Boltzmann brains are therefore, a *reductio ad absurdum* of the argument for our observable universe being a statistical fluke from thermal equilibrium. More fundamentally however, it’s also a paradox – the second law of thermodynamics holds in virtually every conceivable scenario covered by classical physics and yet our universe is ordered and low-entropic.

In essence, Boltzmann brain can’t exist – it is in fact a tool in cosmological theory for arguing a theory is flawed, if it predicts their presence. And as I promised, they have little to do with actual brains. But they do speak of some fundamental concepts about the way we think about the physical universe. Firstly, and probably most appealing to Ludwig Boltzmann, that entropy is fundamentally statistical and our universe follows its rules. Secondly, that our current understanding of the universe is not reconcilable with fundamental thermodynamics, at least not without considering some more exotic theories about how the universe works, which is what physics is all about. And finally, it allows us to consider how unlikely sentience is, in the ‘high-entropy stochastic process’ sense; it is perhaps the most unlikely of all the observable things we see in the universe.

So cheers to you, you vanishingly unlikely statistical fluke atop a high-entropy universe.

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An awful lot has been written about Boltzmann’s brain including a great series of articles for Discover Magazine, and in the New York Times. There’s even a video, if that’s more your thing. Sadly, I could not find any literature on Boltzmann’s actual brain.