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.
>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