Could One Physics Theory Unlock the Mysteries of the Brain?

Critical phenomena arise at transitions.

The idea is that when the system is  just at this edge of order and disorder,  

interesting complex dynamics can arise.

As a physicist, critical phenomena is  extremely appealing because it appears  

in many phenomena — from the evolution of the  universe to the properties of superconductors,  

flocks of starlings, networks of brain cells,  tectonic plates, social interactions among humans,  

all these types of things. Any time I can  see one equation apply to lots and lots of  

different things, I think that’s beautiful. It’s  economical. It’s insightful. Which raises a really  

profound question: Why? Why are so many things  in nature operating near the critical point?

When physical systems go through phase  transitions, such as when water transitions  

from a liquid into a vapor because of a  change in temperature, the system moves  

through what’s known as the critical point  – a fleeting moment of transition from one  

phase to another characterized by exotic emergent  properties that have long intrigued scientists.

Critical systems have this property  of changing phase. Small changes in  

some critical environmental variable lead  to drastic changes — almost discontinuous  

changes — in the function. And it’s that  kind of observation that leads us to believe  

that the study of critical  transitions is valuable.

Critical dynamics are best demonstrated in a  simplified system known as the Ising model,  

which visualizes the individual iron atoms making  

up a magnet with arrows to indicate  the direction of each atom’s spin.

You can imagine a lattice. And on this lattice you  

get all these little spins that  can point either up or down.

And when this lattice is really cold,  what will happen is all the spins will  

line up together. So the nearest  neighbor interactions will cause  

them all to point in the same direction.  This piece of iron — BING! It would stick  

on your refrigerator because all the  bar magnets are in the same direction.

But now if you heat this up — if you took  a little Bic lighter and you put it under  

it — what would happen is these little  spins would start moving. They start  

going in different directions. And then they  would eventually cancel. Some of them would  

point up and some of them would point down, and  then it would fall off of your refrigerator.

So you get a phase transition from being  very ordered to being totally disordered.

As it passes from order to disorder, the system  moves through the critical point and clusters of  

similarly oriented spins form throughout the  lattice. If you were to measure the sizes of  

these clusters at various scales, the data would  reveal what’s known as a power law, where dynamics  

at one scale mirror the dynamics at other scales.  This phenomenon is also known as scale invariance.

Scale invariance is another way of saying that  there is self-similarity or fractality. These  

kinds of properties are spectacular because indeed  everything simplifies at the critical point.

When a system reaches the critical point,  

it displays a telltale peak in what is known  as the correlation length — an indication of  

how sensitive the system as a whole is to  the activity of any one of its components.

What happens is the system behaves in ways that  

allow fluctuations to occur over  the scale of the entire system.

If it was too cold, you’d have no correlation  because they’re just pointing. They’re not  

moving. And when it’s too hot, they’re  moving a lot, but they’re not correlated.

So only at that sweet spot right in the  middle do you have interactions at all scales.

Now, what that means is something very weird.  That means that the distance over which these  

spins might interact is technically infinite.  I could take a spin over here and flip it,  

and there’s some nonzero probability that  another spin very, very far away would flip  

also as a result of it. So in other words, I  can initiate a cascade of events that would  

propagate through the system, and it would have  some nonzero probability of affecting that.

In 1987, the physicist Per Bak wondered if  many different types of complex systems in  

the natural world might self-organize  around critical points. To illustrate  

his theory of “self-organized criticality,”  Bak used the familiar example of a sandpile.

As the pile gains mass, friction can no  longer hold the grains of sand in place,  

and a single grain added to the pile  will trigger an outsized effect,  

sending avalanches cascading down its sides.

And it turns out that if you look at the  distribution of avalanche sizes — the big ones,  

the small ones, the intermediate  ones — they follow power laws.

And so Per Bak’s idea was that, hey, here’s  a natural system that self-organizes to the  

critical point. You don’t need to tune it  there. You don’t need to get just the right  

control temperature to put the Ising  model. It will evolve into that state.

And so when he came out with this  concept of self-organized criticality,  

he was claiming that many natural  systems fall into that category,  

like earthquakes, like stock  market crashes, like piles of sand.

Now, he was a pioneer, and it  was amazing that he did that,  

and it inspired many people from  other areas to enter into the  

field of criticality and to take a look at  this concept and apply it more generally.

And I would say basically it’s had  huge amounts of traction. However,  

there have been people who  have been quite skeptical.

Bak’s equations only account for one grain of  sand hitting the pile at a time. In nature,  

things are more complicated, and researchers have  found it difficult to simulate true criticality.

This is a general problem of mathematical models  just to be always aware of: At what point have you  

overextended that simple abstraction and  applied it in a way that’s inadmissible?

And so SOC is just one mechanism for tuning to  critical points. It’s a very interesting one,  

but perhaps it will turn out to be a rare one.

Despite the criticism, Bak’s work  inspired interest in criticality  

throughout the 1990s and into the early  2000s, when neuroscientists began to probe  

a new question: whether brains might  exhibit self-organized criticality.

Per Bak’s work opened up the concept that  criticality could apply to many different things,  

and that made me think: We’ve got lots of  neurons that are interacting in this network,  

so, hey, why not? So we just started  to apply that framework to the data.

The idea that the brain is at the  transition point — for example,  

at criticality, at the transition between order  and chaos — has been around for a while. I think  

the real avalanche of criticality research was  triggered by John Beggs and Dietmar Plenz in 2003.

We isolated the gray matter. The cortex has a  piece of tissue. When it was young, we grew it on  

a microelectrode array in a dish. We let it grow  for about four weeks and we measured the activity,  

how these cells would interact with each other.  And we found that in layers II, III, they start to  

form groups like just these cascades that were  predicted by the Per Bak sandpile model. And  

plotting avalanche science distributions  and sure enough, they were power laws.

It was the first paper that claimed that the brain  was probably functioning at a critical point.

The question for scientists then became:  

Why? Why might functioning at a  critical point be helpful for brains?

Can you show that operating near the  critical point actually increases  

behavioral performance? And when you’re  not near the critical point, it doesn’t?

So why would being at the critical  point be to your evolutionary advantage?

So let’s say you’re at the side of a river and  there’s a bunch of reeds and they’re blowing in  

the wind. And then you notice that, hey, this is  different from yesterday. I think there’s a tiger.  

So you want to be very sensitive to inputs. The  system is most susceptible to slight changes  

in inputs when it’s near the critical point. It  has these large fluctuations that can take off.

According to the critical brain hypothesis,  when the network is right at criticality,  

it’s perfectly balanced between two extreme  states: super-criticality, in which networks  

of neurons display the highly ordered runaway  excitations seen in epilepsy, and sub-criticality,  

in which signals fail to trigger larger cascades  and stall out, as seen in comatose states.

By hovering near the critical point,  

the theory goes, networks of neurons would  be optimized for information transmission.  

Just like in the Ising model, tiny inputs could  result in big, complex behaviors in the network. 

Proving that such a measurement  of optimal brain activity exists  

would give researchers a new scale to  interpret just about everything brains do.

When we first got our results back from  the 2003 paper, I was just enamored with  

the idea of criticality. I was in love  with it. I’d go to bed thinking, “Oh,  

it’s optimal information transmission. We get  the — just the right exponents. It’s all cool.”

And then over time, people started  to question this in various ways.

Just as with Per Bak’s sandpile model,  

scientists began to question whether the  physics of criticality could neatly apply  

to such a chaotic biological system with  so many variables interacting all at once.

In simpler systems like the Ising model, a  single variable like temperature can be adjusted  

to bring the network right to the critical  point. But in complex biological systems,  

the prospect of tuning to the exact point  of criticality would be much more difficult.

The brain is constantly receiving inputs from  outside that could, you know, blow it off of  

the critical point. So for those reasons alone, it  can’t really be exactly critical. Then what is it?

One of the options of many on the  menu about how the brain is actually  

operating is that it’s slightly  sub-critical, and that it doesn’t  

really get to the critical point  because that might be dangerous.

Another plausible idea is that it’s quasicritical.  

And what that means is that it gets as close to  the critical point as it can. But then there’s  

this activity that’s basically going to push  it away from being right at the critical point.

As research continues to reveal  tantalizing signatures of criticality,  

what was once a fringe theory has begun to  attract more mainstream attention in the field,  

with researchers now hunting for what kinds of  

mechanisms might be responsible for  tuning brains to the critical point.

The big question that is unanswered so far is  what is the homeostatic mechanism bringing back  

the brain to this quasi-criticality region?

That’s a big question — a big open question.  That’s the million-dollar question.

Neuroscience has been and continues to be very  hesitant and reluctant to agree on a theoretical  

idea of the kind that criticality offers. Most  neuroscientists are very hard-nosed empiricists.  

They don’t believe that there is an overarching  theory that explains most — or, you know, god  

forbid — all of what the brain is doing in  one handy concept such as critical state.

I personally think that what does not  play well with neuroscientists is if  

criticality is portrayed as the answer to  everything. I think that is overselling it.

And yet I have no doubt believing  that a system like the brain almost  

requires us to be in a critical state for  it to function well or optimally, even.

There might also be one equation that explains how  the whole thing works. That’s the idealized dream.  

We may never, ever get there, but the hope is  that there might be some general principles  

that really explain how intelligence  functions in this world that we live in.

The field wasn’t there 20 years ago when we had  just one idea, a sandpile model or an Ising model,  

that would guide us. We are way beyond that. And  we are at the point now where the technological  

advance in neuroscience to record the individual  spiking activity for many, many thousands of  

neurons…. These are the precision tools that we  need in order to test new ideas on criticality.

How is the collective coming together to  produce outcomes that are way beyond what  

an individual could do? And I think this is  how our society is organized. This is how  

our brain, our body is organized. And  any understanding of the richness that  

we gain when we operate as a collective, I  think, is just beautiful scientific insight.