π sheaf of moments 8. August 2025
context β‘ Ξ
π€πΏ *"Mathematics isn't a test β itβs a game of fitting pieces into structure."*
existence β‘ morphisms into types over Ξ
π€πΏFear of gatekeepers shrinks when you build your own garden β a topos of joy.
sin A = a/c is a morphism in the topos of triangles π―
objects: sides, morphisms: ratios like a/c
this ratio encodes a subobject classifier of the βopposite sideβ inside the hypotenuse akin to a characteristic function in topos logic! πβοΈ
def sin (A : Triangle) : β := A.opposite / A.hypotenuse
sheaves on the circle π
π€πΏ Sheaves on the circle π track local data (e.g., angles) that βglueβ consistently around loops.
--Does this relate to 3D Peirce existential graphs,1 βΆ π© βΆ Ξ© , and a πββ¬ looping in truth space walking around the surface of the doughnut? π
π΅ "Oh you can't ask this, because this isn't mathematics, it's only a jumble of words! Can he?"
π€πΏπ©πββ¬ Oh, but he can! And not only that β he must, for this is the very playground of higher mathematics! π π©
Peirce π§ + Topos 𧩠+ Trig π― + Doughnut π
Mathematics is structured imagination.
π€πΏ π Micro-fable: A black cat walks 'round the doughnut. Each time it returns, it knows something new β yet from the outside, nothingβs changed. The torus doesnβt lie β it simply remembers. πββ¬ π© π§