The critical brain
The brain works when information flows
Last week I wrote about the allure of the critical edge - the zone between order and chaos, where visual intrigue lies.
It turns out that this critical edge holds more than just aesthetic charm. When a system is near the critical point of a phase transition, special dynamics reign. And it may just be these special conditions which allow our brains to operate.
According to the critical brain hypothesis, the brain functions right on a critical edge between order and disorder. The brain is a giant network of neurons, each of which is capable of receiving and producing electrical signals. If the connections between neurons are strong, then neuronal activity gets amplified and builds up over time. But if the connections are weak, then neuronal activity rapidly dies down. It’s in the careful balance between these two states where the brain can operate most effectively.
To an extent, this feels intuitive. The brain is complex, and complex things probably need to exist in some goldilocks zone to thrive. But the critical point is not your typical goldilocks zone. The reason it gives rise to optimal brain activity is quite deep, and relates to ideas about information, fractals, and emergence.
The idea of brain criticality is typically explained by returning to the Ising Model, the model of magnetization I mentioned last week. While not the same system (our brain isn’t a magnet), the Ising model is good at illuminating certain features of criticality, and you can draw analogy between how something similar would look in the brain.
Picture a grid of objects, where each one is either spin up or spin down (this doesn’t have to mean much to you, the important thing is just that there are two possible states for each point in the grid, much like how a neuron can either fire or not fire). If a majority of the spins are in the same direction, they generate a net magnetic field. If the spins are all randomly oriented, then there is no net magnet effect.
If you start with a Ising Model that is magnetic (aka ordered) and add heat, the extra energy will cause the spins to fluctuate. If you add enough heat, you eventually reach a phase transition where the spins are so overwhelmingly randomized that the magnetization is lost. The critical temperature at which this happens for a magnet is its Curie temperature.
But if you pause the system right this critical point between magnetization and non-magnetization, what do you see? In the in-between stage, you’ll find a clumpy mess. There’s an overwhelming sense of randomness, but with recognizable patches and clumps of order.
If you start at a small patch of your critical Ising Model and zoom out, you’ll notice that no matter how far out you move, the pattern looks the same. In fact, if I gave you a screenshot of a critical Ising Model, you would have no idea what scale the image was taken at. That’s because at the critical point, the Ising Model is scale-invariant, just like a fractal.
This video shows it well: compared to the low and high temperature states of the Ising Model, only the critical point has this feature of symmetry across scales. This fractal-like nature is a telltale sign that you’re looking at a system at a critical point.
And sure enough, in 2003, measurements of neuronal activity in the brain revealed this fractal-like scale invariance that characterizes being at a critical point. But why would the brain evolve to exist at this strange state?
It’s important here that the states of individual elements are not independent of each other. The magnetization of one atom has the ability to affect the one next to it. With this in mind, imagine that you flip the spin of one of the atoms in the critical Ising Model. It then goes on to flip a few neighboring atoms, but not all. Those atoms go on to affect their neighbors, and so on.
You can imagine an analogy in the brain. If one neuron firing caused all nearby ones to fire, the brain activity would be out of control. Think of the feedback from a speaker - if it keeps amplifying itself, the original sound signal is completely distorted. But if that neuron caused too few connections to fire, then signals die down before making much of a trip around the brain. It’s right at the critical point that a neuronal signal can travel to where it needs to go without wreaking havoc.
At the critical point, local interactions naturally lead to long-range communication. As someone who’s always had a curiosity about how the act of storing and communicating information emerged in biological systems, this was a bit of a revelation for me. There are necessary conditions for the organic movement of information, and the critical point satisfies them.
I just read about a new discovery that shows a certain amount of heat can transition a quantum system from being entangled to not-entangled. This means there is a phase transition between quantum and classical states! I haven’t looked closely enough to determine whether this is a continuous or discontinuous phase transition (or if we can even know yet). But if it’s continuous, and systems can persist at this quantum critical point, then I’m very curious to see what special phenomena exist there.