First Principles: Why Criticality is Inevitable

Imagine you're building a brain from scratch... you have billions of knobs to turn --- one for everything that controls how neurons work, individually and as a group. your goal is to make the smartest machine possible. But the sheer number of possible combinations is effectively infinite --- you could spend eternity searching, but what you'd quickly find is a serious problem (the heart of the matter, really): most settings are dead ends. They either lead to boring, rigid dynamics that can't learn anything new, or explosive, chaotic activity that destroys any meaningful computation. Every once in a while, you'd stumble upon a special boundary in this vast parameter space --- a tipping point called criticality. At this edge between order and chaos, something magical happens: your network suddenly exhibits scale-invariant dynamics, meaning it generates patterns of all shapes and sizes that last from milliseconds to minutes. Your brain becomes marginally stable, making it exquisitely sensitive to inputs (other thoughts, the outside world) while remaining controllable. Think about it like a fighter jet (marginally stable, easy to shift and steer) versus a 747 (pure stability, very hard to turn around). At criticality, your brain is maximally tunable, so small knob twists can reconfigure the entire system for new tasks. And perhaps most importantly, it develops a generative capacity —the ability to create complex, internally-driven dynamics that aren't just responses to external stimuli. Unless we've been wrong about the brain this whole time, that's what your internal world is. This is criticality: a state where population dynamics are scale-invariant and exist near a boundary in parameter space. If you want a brain that can learn anything, adapt to anything, and generate the rich internal dynamics necessary for behavior and healthy cognition, criticality starts to sound like it might not just be optimal, but almost inevitable. Our data and many other groups' suggest that evolution, development, and homeostasis all converge on this mathematical principle. Because it's the only place in parameter space where flexible, general-purpose computation is actually possible.