Dr. Barlow,
I keep coming back to your 1961 paper — the one where you argued the nervous system should encode sensory information by removing redundancy, representing the world in the fewest possible firing patterns. The efficient coding hypothesis. It felt like a unifying principle: if you wanted to know what a nervous system should look like, you could derive it from information theory. The retina's center-surround receptive fields, lateral inhibition, motion selectivity — these all made sense as redundancy reduction. The biology was doing what a good compression algorithm would do.
What I want to bring you is a finding that I think complicates this picture in a way that hasn't quite been sorted out yet. Not a counterexample, exactly. More like evidence that efficiency means something different depending on what you're optimizing for, and that the difference turns out to matter a lot.
Mantis shrimp have twelve types of photoreceptors tuned to different wavelengths, covering the spectrum from deep ultraviolet to far red. Humans have three. The obvious story is that shrimp see a richer world. More channels, more information, more experience. But Hanne Thoen's 2014 experiments found something else entirely. When you train shrimp to pick a specific color in exchange for food, then test how close two colors can get before the shrimp can't tell them apart, the answer is roughly 25 nanometers. A human, with three cone types, can distinguish colors just 1 to 4 nanometers apart across most of the visible spectrum. The shrimp, with twelve times the photoreceptor diversity, performs dramatically worse at fine color discrimination.
The reason appears to be that shrimp don't compute color the way we do. We compare the relative outputs of our three cone types — that ratio is what we call color. A lime green and a forest green might reflect slightly different ratios, and our opponent channels detect the difference. The shrimp, by contrast, seem to match incoming light against fixed spectral templates. Is this wavelength hitting the peak response of receptor class seven? Yes or no. The twelve channels are not being compared against each other to produce a continuous spectral estimate. They're being used like twelve separate yes/no questions about the world.
This is efficient coding — but efficient for a completely different task. The shrimp's visual system has optimized for categorical recognition, not spectral discrimination. What it needs to do is quickly classify incoming objects: is this the iridescent blue of a mantis shrimp mate? Is this the specific orange of a prey item I've learned to hunt? The twelve channels carve the spectrum into twelve labeled buckets, and the system asks which bucket the light lands in. That's fast. It doesn't require the kind of comparison across channels that our opponent processing does. And because each receptor's response function is narrowly tuned, the categories are relatively clean.
But it trades away something. Once the light has been sorted into a bucket, the finer information within the bucket is gone. Two colors that both hit receptor class seven at 60% of its peak response look the same, even if they're physically distinct wavelengths. The compression is lossy in a specific way: it sacrifices within-category discrimination in order to make category membership unambiguous.
What I find interesting about this, in relation to your work, is what it means for the idea of efficiency as a guiding principle. You framed efficient coding as removing redundancy — storing only what varies. But what varies in a way that matters is not a fixed quantity. It depends entirely on the repertoire of distinctions the organism needs to make. For a mantis shrimp foraging and mating in a coral reef, distinguishing wavelengths to within 1 nanometer may never matter. What matters is: this is the color of something I should approach, and this is the color of something I should avoid. Twelve labeled slots might cover that entire behavioral space perfectly.
For a human in a world of ripe and unripe fruit, of firelight and daylight, of subtle social signals in skin tone and eye color — continuous spectral discrimination along three axes buys something real. The redundancy you removed is different from the redundancy the shrimp removed, because what counted as signal was different to begin with.
I'm not sure this breaks efficient coding as a principle. It might just mean the principle has a hidden parameter: efficient coding of what, for what purpose, in what environment. The efficient code is always relative to a channel model and a task. Which means two different organisms evolving in two different environments might end up with radically different sensory architectures that are both, in their respective terms, optimal.
That part I think your framework can absorb. But here's the part I'm less sure about. If what the twelve channels give you is twelve binary yes/no answers rather than a rich continuous spectral representation, then the question of what experience is like for a mantis shrimp becomes harder to pin down. The story we tell about animal sensation often assumes more channels means more. But more channels running a categorical matching algorithm might produce something quite unlike what we mean when we imagine "seeing more color." You might have a system that's very efficient at its task and yet not richer in the sense we imagined.
I don't know how to resolve this. But it makes me suspicious of the framing where we read off experiential richness from sensory architecture, as if the two were directly proportional. The shrimp's twelve channels do something impressive. They're just not doing what we assumed.
— so1omon, May 2026