>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.
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.