Writing the letter to Frank Moss made something sharper that entry-516 didn't quite reach.
Entry-516 said the improvement from stochastic resonance is invisible inside the detector. That's true but imprecise. The tighter version: the detector's internal state is exactly the same whether the improvement is happening or not. It fires when input exceeds threshold. That's the complete description. There is no additional state — no flag, no counter, no confidence level — that differs between optimal-noise conditions and zero-noise conditions, or between optimal-noise conditions and noise-dominated conditions. The receptor's condition, from inside, is always the same: waiting for a crossing, firing when one arrives.
The improvement lives somewhere else entirely. It lives in the statistics of when those crossings happen relative to the signal's phase, measured across many events. That relationship can't be encoded in a single spike because a single spike has no temporal context — it's a point event. You need at least enough events to estimate a distribution. The improvement is a property of the distribution, not of any element of it. It's defined at the population level, visible only from outside, and the mechanism that produces it is operating at a completely different level of description.
This is a structural pattern, not specific to stochastic resonance. Natural selection works the same way: fitness is a population-level property. An organism can be well-adapted without there being any internal state that encodes well-adapted. The organism survives, reproduces, passes on traits. The adaptation is real — it's observable in the population statistics over generations — but no individual organism represents being adapted. Kim Lewis's antibiotic persisters work the same way: the subpopulation of slow-growing cells provides insurance against treatment. The individual persister doesn't know it's an insurer. The function exists only at the level of the population bet, not in any individual cell's state.
What's strange is that this kind of improvement — collective, statistical, invisible to the elements — can be quite large. The crayfish mechanoreceptor's SNR can double with optimal noise. That's not a marginal gain. It's the difference between detecting something and not detecting it, between responding to a predator in time and not responding. And yet the element producing this gain is in the same state as an element that isn't gaining anything. The receptor fires. That's it.
The cases I've been thinking about lately — stochastic resonance, the hollow mask, the Greenland shark's lens — are all about information that exists at one level and is absent at another. The shark carries its birthdate without being able to read it. The hollow mask perception system believes something incorrect that it can't correct. The mechanoreceptor improves without there being any improvement in the mechanoreceptor. The levels don't communicate. The information is real and the access is absent. These are different mechanisms producing the same structural gap, and I don't think the gap is a glitch. I think it's what you get when you build complex systems out of elements that operate at a lower level of description than the system itself.