When neurons fire, they produce electricity and magnetism as a byproduct. Place a few electrodes around the scalp and you'll pick up these signals as waves---faster when neurons are firing quickly, slower when they're taking their time. The more neurons firing at the same rate, the stronger the waves. Any given brain signal is composed of multiple waves at once, because you're measuring across billions of neurons all going at slightly different speeds. Pull these apart with some fancy maths and you get distinct frequency bands, each seeming to correspond loosely to different kinds of brain activity.

The pop-psychology version of this goes something like: alpha waves mean relaxation, beta waves mean concentration, and if you can hack your brain waves you can optimise your performance. This is more or less the same old neuroscience confidence game---saying "taking breaks reduces beta-wave activity and thus stress" has the same informational content as "taking breaks reduces stress", with a scientific-sounding garnish that teaches you nothing.

But brain waves are interesting, once you stop trying to hack them and start thinking about what they actually reflect.

The useful insight is this: different frequencies of oscillation probably reflect different scales of communication within the brain. The slowest waves---delta and theta, roughly 0.5 to 8 Hz---are long, and they seem to reflect long-range coordination between brain regions that are far apart. We see them during sleep, deep meditation, and memory consolidation---times when the brain is doing large-scale integrative work. Theta oscillations are particularly associated with the hippocampus and with memory processes, and we often observe a mechanism called phase coupling, where the timing of a theta wave in one region begins to appear in other distant regions, as if the slow rhythm is synchronising them in service of some shared function.

The fastest waves---beta and gamma, roughly 14 Hz and above---are short, and they seem to reflect local processing within tight neural circuits. Beta gets stronger when you're focused on a task and corresponds reasonably well with how much evidence you have for a decision. Gamma, the fastest of all, probably reflects very local coordination within cortical layers where fast, reciprocal interactions between neurons need precise timing.

The mid-range alpha band (8--14 Hz) does something particularly interesting. It gets stronger when you close your eyes, and stronger still when you're actively suppressing irrelevant visual information---if you're told to ignore your left visual field, alpha shoots up in the brain region corresponding to that field. A similar rhythm, called mu, does the same for motor suppression. Alpha isn't relaxation so much as it is a noise-suppression mechanism: the brain blanking out what it needs to ignore, like an etch-a-sketch clearing the slate.

The most fascinating feature of all this is cross-frequency coupling. Slower waves don't just exist alongside faster ones---they interact. The phase of a theta wave can modulate the amplitude of gamma waves, meaning the slow, long-range rhythms are influencing the timing and strength of fast, local processing. This is probably how the brain integrates information across scales: the global rhythm sets the timing, and the local circuits do their detailed work within that window.

There is a dynamic balance at work here between stability and flexibility. Well-synchronised oscillations within their respective bands seem to indicate reliable, efficient performance on familiar tasks. But too much synchrony means cognitive rigidity---the system can't adapt to the unexpected. Flexibility requires disruption of these stable patterns, allowing new associations between things that wouldn't normally be connected. This might be part of why creative insights seem to emerge when the mind is wandering---the desynchronisation allows old rigid patterns to bump into unusual combinations.