[andresgemilsson]

Why not? If you get good at it, you can learn to quickly tell which wallpaper symmetry group a given tiling has. On most psychedelics the hallucinations are easily identifiable as belonging to one of the 17 wallpaper Euclidean symmetry groups. It turns out that on DMT you see symmetry groups that are none of those... and then you realize... wait, I'm seeing a flat surface tessellated by heptagons! This means... the space is hyperbolic! What's the epistemological issue here? :-)

[Jeff_Brown]

I can't tell whether you're seriously asking, but just in case:

Geometry requires the ability to precisely measure angles and distances. Subjective hallucinatory experiences permit the witness to feel like they're seeing just about anything -- a sphere partitioned into five congruent squares, an ant that is an even number of ants, the square root of irony. But they don't admit any kind of measuring stick.

Although I guess if impossible-outside-of-hyperbolic-space tesselations were universal experiences of the users of DMT, that would do it. But I know a few, and they never mentioned repeating patterns. One talked about Gumby people a lot. Which, to be fair, probably involved some cool geometry, but I doubt it violated the parallel postulate.

[andresgemilsson]

One of the most fascinating things about DMT is that you get to experience the same level of visual resolution that you experience in your fovea but across your visual field. I'd say that for a trained observer/phenomenologist, we can know with the same level of trust that yes, they saw the *442 wallpaper symmetry group on DMT as we can trust that someone is seeing a square under normal conditions. And indeed, symmetries are already widely reported (see: https://psychonautwiki.org/wiki/Symmetrical_texture_repetiti...). It's a core effect. Next time you try DMT just pay attention... you'll see it all over the place.

Why are not more people reporting the hyperbolic features I've identified (e.g. hyperbolic folding of the worldsheet at the Magic Eye level, as described in the article)? And why instead do we mostly hear about reports of entities? The reason is simple: it's not what people are trying to bring back. We don't yet have a rational culture of inquiry for the structural analysis of psychedelic phenomenology.

As explained in the following article, currently people focus on the semantic content (the narrative) rather than the phenomenal character (the texture). But as we gather more rational, intelligent, and dedicated psychonauts, consistency of reports and consilience will increase: https://www.qualiaresearchinstitute.org/blog/rigorous-report...