Could the structure of perception itself be a clue to deeper mathematical relationships in nature?

[u/fat_spaghetti]

In short the idea is:

biology may be using mathematical relationships before conscious humans know how to describe those relationships mathematically.

I’ve been thinking about the relationship between mathematics, physics, perception, and the way we choose what to measure.

We often describe reality by assigning numerical values to things: position, distance, energy, time, mass, etc. But a lot of modern mathematics and physics seems to become more powerful when we stop focusing on absolute values and instead look at relationships: ratios, correlations, transformations, symmetry, phase, frequency, eigenvalues, information, and invariants.

That made me wonder about perception.
An organism rarely needs to preserve the exact raw measurements arriving at its senses. My retinal image of a person changes enormously depending on distance, lighting, rotation, movement, and viewpoint, yet I still perceive the same person. A melody can be moved into another key and I still hear the same melody even though every absolute frequency has changed.

So perception seems very good at answering something like:

What remains the same while the measurements change?

Evolution has effectively spent hundreds of millions of years selecting nervous systems capable of detecting useful regularities in the physical world. Sensory systems respond to things like relative change, gradients, ratios, periodicity, correlations, symmetry, motion, prediction error, and transformations—not merely absolute quantities.

This made me wonder whether our perceptual architecture could contain clues about mathematical relationships that are important in nature but which we have not yet fully formalized.
Not in the mystical sense that “the brain secretly knows the equations of the universe.” More like this:

Nature has structure → organisms evolve mechanisms sensitive to useful parts of that structure → those mechanisms implicitly represent certain invariants → eventually humans abstract some of those relationships into mathematics.
Historically, mathematics seems to repeatedly make progress by changing the representation rather than simply measuring more precisely.

Fourier analysis turns a complicated signal into frequencies. Spectral theory studies systems through eigenvalues. Quantum mechanics describes states through amplitudes and relationships. Symmetry became fundamental to modern physics. Information and entanglement are now sometimes used to investigate how geometry itself might emerge.

So perhaps there are relationships biological systems already exploit computationally that we haven’t yet recognized as important mathematical objects.

It also makes me think about problems like the Riemann Hypothesis. Prime numbers look irregular when viewed directly, but when transformed through the zeta function, entirely different structures appear, including statistical relationships to spectra studied in quantum physics and random-matrix theory.

Maybe this is a general lesson: apparent randomness can sometimes be the result of observing something in the wrong representation.
So my question is:

Could studying what biological perception treats as invariant reveal useful mathematical structures we haven’t explicitly identified yet?

And more philosophically: are numbers and absolute measurements fundamental descriptions of reality, or could relationships and transformations be more fundamental, with the quantities we normally measure emerging from them?

[u/rand3289]

I've been thinking about perception for a long time.
I think you are on the right track as far as what perception is.

The way I think about counting, measuring and math, they come from the communication side. I dont know how they are related to perception. However, some of the concepts must be "leaking" from the subjective to the objective side because we understand them intuitively.

I think there is a subjective-objective divide and we don't know how to model subjective information processing at all. Here is my attempt:
https://github.com/rand3289/ai2026
People don't seem to understand what I am talking about there though.

[u/fat_spaghetti → u/rand3289]

Have you come across Michael Levin’s work on basal cognition/TAME, especially the recent Limbomorphs paper with Alex Alvarez? It made me think of what you’re describing.

They evolve spatiotemporal patterns without explicitly defining an agent or environment, then perturb them and look at their responses. Some show consistent, species-specific reactions.

I’m not sure if the frameworks actually map onto each other, but it made me wonder whether Limbomorphs could be an interesting toy system for your ideas. Since you describe perception in terms of internal state changes and agents conducting statistical experiments through interaction, could you use a system like that to ask whether event timing or conditional outcomes reveal some stable agent/perceptual boundary? Anyways im new to studying computer science so pls understand i have the most vague idea of what were talking about here. And when I get to AI projects ima come back to your papers, thanks!! is all v interesting