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I tried GPT4-turbo in the minutes following its announcement and it was blazingly fast.

>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.

>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.

This is basically what I tried this morning at the prompt level (awful results), but the sketchy idea I had in mind went further by introducing control-flow "meta-tokens" to help the LLM renavigate its context. In this perspective the context would be rethought as a self-editing structured mind-map, with the linear aspect of the context at a time T standing for the execution trace of the exploration of this mind-map so far. Some of those meta-tokens would be able to have side effects on the context, to highlight, give structure, summarize, forget and so on, some of its parts. This could allow for native structured output without using a syntactic format such as json, programmatic constructs in the style of LMQL, implementing memory, etc. The goal: not just to give logical/reasoning abilities to a LLM, but to give it the means to come up with its own cognitive architecture. Implementing structured output (using a <label name="stuff">...</label> token) to also implement memory/scratchpads, would also bring inspectability of those cognitive structures for free. Of course I have no idea how to implement this (I'm a ML tourist).

>So far, all of the work on AGI has been the result of brute forcing. We've tried to develop a structural understanding of how the human brain works, and we've failed. So we've fallen back to torturing circuits into reorienting themselves into compression algorithms for human knowledge. The mechanisms that these tortured circuits used for doing so, the structures they produced in N-dimensional space to embody that knowledge -- we have very little understanding of how these things actually work under the hood.

And this is the way. (Machine) learning theory is in some way a meta-science about how to do science from facts in order to construct theories that effectively explain these facts. What you are asking for will never amounts to a short set of equations. There is not elegant theory of how to perceive numbers and this is why symbolic artificial perception, rule engines, spam detection, RDF ontologies, etc never took off. You're idealizing knowledge as a set of representations without ever reifying how these representations come into existence. We're departing a world of representation toward a world driven by "incarnations": you can't make sense of a how a brain works without the help of another brain, and this is why there is so many things being researched at the intersection of deep learning and neuroscience. I'd even go as far as considering this is in fact how brains work: they can be composed and decomposed monoidically.

In short:

>a structural understanding

There is no such thing

>the structures they produced in N-dimensional space [...] this brute force approach

This is a contradiction. I'm not saying there won't be "structural insights along the way" nor that throwing categories into the machine learning mix won't be useful, but the learning-like aspect that you denote by "brute force" is more fundamental, and in some way above the very processus of science.

Why don't you give it a try ? A text in the first-person to mock the following comment:

>Honestly I’ve not encountered an author I resonate with yet

Surely, you'd know how to make it better than a smart 4th grader.

I recently had an introspective dream revealed to be based on a literal prompt at the end: "Game to learn to talk about It and its player." When I asked GPT to craft a plot from this prompt's title (and the fact it is revealed at the end), it reproduced the dream's outline, down to the final scene:

GPT reconstruction:

The dream reaches its peak when you meet the "final boss" of the game: an entity that embodies the ultimate barrier to communication. To overcome this obstacle, you must synthesize everything you've learned about "it" in the dream and present a coherent vision that is true to yourself. As you articulate your final understanding of "it", the maze dissolves around you, leaving you in front of a giant mirror. In this mirror, you see not just your reflection but also all the characters, passions, and ideas you encountered in the dream. You realize that "it" is actually a reflection of yourself and your ability to understand and share your inner world. The dream ends with the title revealed, "Game to Learn to Communicate about It and Its Player", meaning the whole process was a metaphor for learning to know and communicate your own "it" - your personality, thoughts, and emotions - with others, and that you are both the creator and the discoverer of your own communication game.

My note:

The continuation of the dream corresponds to an abrupt change of scene. I find myself in my bed, in the dim light of my room, facing a mysterious silhouette. As I repeatedly inquire about its identity, I stretch my hands towards its face to feel its features as I cannot clearly see them. Then, a struggle begins, during which I panic, giving the dream a nightmarish turn. Noticing that the dark figure mirrors my movements, I realize it's myself. Suddenly under my duvet and as I struggle to get out, I feel jaws and teeth against the sheets. I call out for my mother, whom I seem to hear downstairs, and that's when my vision fades, and I see the dream's source code displayed behind. It consists of ChatGPT prompts shared on the lime green background of an image-board. At the bottom, I then see the dream's title: "Game to learn how to communicate about It and its player."