[karmakaze]

Reminds me of the saying about a poet vs mathematician, the first gives different names to the same thing and the latter the same name to different things. Maybe that's why I can't stand highly descriptive prose (aka describing the water while I'm drowning over here).

Now what if you're a poetic mathematician (or mathematical poet), what's that mind map look like?

[LargoLasskhyfv]

Well... what about that palace of mind thing, and the ability to rewind into almost all older memories at will, and on demand being able to look up things from there, like reading, without having it memorized at all? Also full stream of consciousness, like smells, tastes, light wind on your skin, 'silken air' at just the right temperature and humidity.

All of that arranged in something like 'eigengrau', represented by glitterlike points connected by graphs, mostly in 'phospene' colors, but not exclusively so.

Sometimes very non-euclidean, moving/warping.

KNOWING what's behind every glitter point, like small cinema, large home theatre, from several points of view at the same time.

No words involved. Just visuals.

Thinking, like juggling/weighing blobs, like that glowing stuff which moves slowly up and down in a lava-lamp.

Somehow 'knowing' what each blob, its size/form/viscosity/weight/speed/color/brightness/'feel'/smell represents.

Slowly emerging new 'visuals' from this. Which are then translated into 'language', if ever.

[kjqgqkejbfefn]

>phosphene color

Not sure whether you talk about the uranium yellow/green color, or the brief hallucination of a light spot (happened to me just a few minutes ago, hadn't had one in a long time).

I don't have such an hyperbolic mental palace, and this doesn't really give me the ability to establish a global map but I relate a lot to what you wrote. Sometimes as I reach the climax of a long deep thought, I'm thinking via vision exclusively to the extent I don't even pay attention to what my outer eye sees and I stumble upon some insight that is sometimes almost impossible to convey in language, not because it lies beyond, but because the intrusion of language causes the idea to collapse: words points to dangling shapes that mean barely anything because the rest of the painting has gone away.

To those that have read this far and can't relate to this way of thinking, this isn't a superpower, those are rather rare experiences of altered states.

Talking about this is a kind of taboo and may cause some smiles, and indeed if there is a deeper truth to these experiences about the computational or geometric nature of the mind, maybe in the same way synaesthesia mirrors spectrograms, it won't help people working in machine learning a lot (even though some like Lecun seem to use their own visual introspective abilities as a source of inspiration).

However they may prove to be crucial in conceiving what kind of use brain chips should be put too. For now it seems we're walking through a thick fog in that direction with envisioned application being confined to interfacing to external computers or increasing cognitive abilities quantitatively, such as perfect memory and so on. If I could sustain such experiences durably, with a high level of control and enhanced geometric/mathematical understanding, I believe this would be akin to a superpower, yes.

[mistermann]

Like (parts of) this sort of thing maybe?

https://youtu.be/BLmAV6O_ea0?si=OdPbwBXs6mOR5Xj2

[LargoLasskhyfv]

No. That's too dense and organic. Mine are rather abstract, much padding, empty eigengrau between 'loci', and more 'geometric'?

edit: I knew about mandelbulbs before. My inner mindscapes are not like that.

[kjqgqkejbfefn]

>Now what if you're a poetic mathematician (or mathematical poet), what's that mind map look like?

Well look at the drawings I posted below: mathematical notions mixed with ad-hoc diagrammatic distinctive elements such as colors and marks. With maybe a theorem that posits that every mixed representation like theses matches a colorless, unannotated, rigorous mathematical object ?

In fact I come from a structural linguistics background, and when I pictured how one could extrude a semiotic square into another one, I felt like I understood the vague intuition behind homotopy type theory: the metaphor goes like this – the extrusion volume must be water tight for the squares to make sense.

Suppose you read Dostoyevsky's short story "Another Man's Wife and a Husband Under the Bed." In that case, you might notice that the protagonist's vertical position, as he eavesdrops on what he believes to be his wife through the wall of another man's apartment while standing alone in a corridor, mirrors the horizontal position he later assumes when hiding under the bed of his wife's presumed lover. This physical positioning reflects his moral descent, particularly as he is not alone this time. Beneath the bed with him is another man, clandestinely involved with yet another man's wife. This leads to help us picture that our protagonist is just as disconnected from his wife as the man lying next to him under the bed or the husband unknowingly sleeping above them—if not more so.

Granted I don't have the detailed vision of this semiotic diagram, but coming up with the skeletal structure is exactly what the job of a semiotician consists in (which I'm not). What matters is that all these equivalence classes the writer lays down, just like in mathematics, allows meaning to flow. His vertical loneliness must match his horizontal promiscuity for the story to operate this crescendo. Clog theses connections, and the inner structure of the object they tie together disappear too. Digging into Saussure and Voeivodsy one can realize they shared a common obsession about identity, for it is precisely when physical objects become indistinguishable that they can be referred to with the same terms and that conceptuality arises (Aerts, 2010s and onward).

"Different names to the same thing" and the "same name to different things": the two directions on the homotopical ladder.

Note: I'm 100% in postmodern mode here, this goes way above my head of course.