The herring shoal: message passing without a messenger

A herring shoal turns as one. A predator lunges at the edge, and within a moment the whole school — thousands of fish, spread across water no single fish can see — has wheeled away. No fish is in charge. No signal crosses the shoal. Each herring watches only its nearest neighbors and reacts to them; the reaction propagates neighbor to neighbor as a wave, and the wave moves through the school faster than any individual fish can swim.

That is message passing, and it is the deepest computational pattern in our reasoning machine.

A factor graph — our diagram of quantities and the arithmetic linking them — is a shoal. Each variable knows only its immediate neighbors: the constraints it appears in. When one variable’s value becomes known, the news propagates: every constraint touching it tightens, which pins other variables, which tighten further constraints. No global coordinator ever sees the whole problem. Just local rules, applied everywhere at once, and a wave of implication sweeping the graph.

Our early experiments measured the herring property directly. When we ran deduction as breathing cycles — every part of the graph updating in parallel each cycle — solving depth scaled the way a shoal’s wave does: a problem requiring D sequential steps of reasoning resolved in roughly D/4 breaths, because the wave propagates from every known value simultaneously, meeting in the middle. Deduction is not a chain. It is a flood.

The same pattern lives at every scale of the machine. Inside a breath, slots attend to slots — each committed fact is a fish that flinched, and its neighbors react. Inside the solver, constraint propagation is the wave run with exact arithmetic. And between the two, the alternation: the neural side commits a few facts, the symbolic side floods their consequences through the graph, and the returning wave changes what the neural side looks at next.

What a message actually needs

Watch the shoal closely enough and you can factor out what any message passing system requires. Three things:

1. A channel — a medium the signal travels through. The herring have water and the lateral line; our slots have attention edges; the solver has the port.
2. A language — a form both ends understand. The herring’s language is motion itself; ours is typed structure: factor roles, committed edges, phase-bound wires. A channel without a shared language carries noise, not news.
3. A time interval for the handoff — and this one is the sleeper. Sender and receiver almost never act at the same instant. A message must survive between being sent and being read.

That third requirement may be the quiet reason attention works as well as it does. Attention is not a phone call — it is a parking garage. A fact gets written into the residual stream or a notebook slot and simply parked there, addressed by its content, until some later cycle’s query comes looking for exactly that shape of thing and picks it up. Sender and receiver never need to meet. We learned this as a design law the hard way: dropping a passenger at the airport is easy, timing a pickup is hard — so build systems around drop-offs. Every organ in our machine that works well works this way: the notebook parks facts across breaths, the solver’s port parks derived values for the next cycle, the committed structure parks itself in the masks. The wave through the shoal is fast precisely because no fish waits for a reply.

There is a lesson in the herring for anyone building reasoning systems: you do not need a general to move an army. You need good local rules, honest neighbors, a medium the wave can travel through — and a garage where messages wait, content-addressed, for whoever comes needing them. Most of our architecture is just that medium and that garage, kept clear.