[giva]

Well, this sound weird to me in the sense that I don't feel that I think in _words_. I only convert my thoughts into words when i need to speak or write them down; So when I need to communicate them to others, when I need to remember them for later, or when I am stuck and I need to clear things up.

I was actually convinced it was the same for most people, and that for this reason "Rubber duck debugging"[1] is a thing.

1) https://en.wikipedia.org/wiki/Rubber_duck_debugging

[kjqgqkejbfefn]

Am I the only one visualizing some of my most creative thoughts in a mental palace that is formed by many distinct (euclidian) spaces, whose axis connect to each other through a graph ? Closest thing that can describe this I found are simplicial sets:

picture: https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcRx5Xam...

It seems it's used by cognitive models, although I'm not formally trained enough to tell exactly how:

https://arxiv.org/pdf/1703.08314.pdf

[mewpmewp2]

I wish I had something like this in my head to tie things in together. Right now I feel like my understanding of things is so disorganised and "lucky" in a sense. I feel lucky that I have grasp of anything.

[endofreach]

Wow, well expressed. That's exactly hoe i feel. Not momentarily, but with everything. Though i am actually not intelligent, i just have good intuition and luck to grasp some of what i need to "unddrstand".

[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.

[giva]

I don't know what a simpilician set is and wikipedia didn't really helped me. However I could roughly describe my "mind" as many mental maps where concepts are laid out and connected in different ways. Learning means putting new things on these maps a thinking is navigating through them.

[kjqgqkejbfefn]

This is just a deleuzian metaphor for the weird kind of space I perceive certain abstract thoughts with.

>many distinct (euclidian) spaces, whose axis connect to each other through a graph

Imagine having pictures hanged on the walls of your mental palace that act as portals to others rooms and corridors within that palace, and that must exist parallelly to each other, in different "universes" otherwise their volumes would intersect. The kind of geometry the Antichamber video game features.

Or picture this: a representation that relies on its axis to convey meaning, for instance the political compass meme. Walk along an axis long enough and it will connect orthogonally to another axis, for instance, authoritarianism may connect to anger from the emotional compass.

Simplexes: a generalization of triangles to n dimensions. A 2-axis representation (the political compass for example) could connect to spaces with 3 axis (the ascended political compass: https://external-preview.redd.it/UQgZCVQ4OLg_Hz16FGdu9-qxfq9...).

To represent this you could connect one tip of a segment (a 1-simplex) to the tip of a triangle (a 2-simplex), each vertex in these figures representing an axis. This is where my deleuzian metaphore collapses because I'm conflating the notion of axis with the notion of the "left" and "right" part of an axis. And I'd also be tempted to consider that planes should be allowed to connect to axis (to support that portal through a painting I mentioned above).

So this is just a sketchy thought, but this seems legitimate as it's not something I conceptualize but something I perceive (sometimes). But I think there may be something interesting behind these perceptions because it seems they deal with separate concerns through some kind of orthogonal geometry that is structured: putting a concept in a dimension orthogonal to another concept doesn't lead that dimension to be orthogonal to all other dimensions/concepts in your mental palace, as that would be the case if it took the shape of a n-dimensional space. And because the orthogonality is structured, it allows to deal with more than 3 concepts spatially at the same time and embed them within something your eye can picture in 2D or 3D, using diagrammatic annotations (colors, marks, etc). Finally it allows to put a concept C in several orthogonal relationships to distinct concepts, for instance A and B, and to keep these different instantiations of concept C orthogonal to each other.

This is what my mind pictured as I was explaining this ; colors and graduation marks/boxes faithfully representing what I just perceived: https://pasteboard.co/kMecyenyZdzg.png

Note that the two colors, the green of the axis and of red of the sticks could be thought as two individual concepts of their own, orthogonal to each other.

https://pasteboard.co/3VYEyepnVouQ.png

If a mathematician is reading this, please accept my deepest apologies. Here's another paper that seems thematically related to this: https://ieeexplore.ieee.org/abstract/document/10008602

[jiggawatts]

https://mymodernmet.com/inner-monologue/

[giva]

Really interesting. I could guess that people that "think in words" are more likely to share their thoughts on social media, since they don't need to translate them into text/speech like people that "think in concepts"

[idiotsecant]

I guess from the results of this thread a larger percentage of HN has this condition, but my understanding from reddit threads is that it is quite abnormal. I also lack an internal narrative, and I was quite shocked to find out that most people literally have a voice that they 'hear' internally.

[giva]

I'll paste my reply to another comment on this thread:

> I could guess that people that "think in words" are more likely to share their thoughts on social media, since they don't need to translate them into text/speech like people that "think in concepts"

So, maybe word-thinker are just over represented in "mainstream" social networks, and concept-thinker are over represented in engineering circles?

[JoBrad]

Same. If I try to visualize my thoughts it’s like a cloud that coalesces into various forms, to show different scenarios. It definitely isn’t word-based until I decide to actually translate it into that mode.

[mewpmewp2]

Interesting. I think all of my thoughts are this record I'm listening to as if it's an audiobook almost. Sometimes, it's like multiple parallel streams of different thoughts at different strengths that I can observe, like a thought line that is going on, on a more subconscious level, and it's something that if I notice, I might want to pay attention to.

Like multiple LLMs are generating tokens in my head in parallel, but like in my field of view, some I can only listen/see barely because I'm not focusing on them.