moments of sheaf 🐚 Mi 23 Juli — point, morphism, wave
hypnagogic mathematics #
I experience having nice ideas form while dreaming, but when I wake up they seem to fade.
The other day I had a nap, and I kept thinking while half asleep: "I should record this idea, I even know how to write it down!" then when I woke I did not know how to write it down or express it, nor remember what it was about...
I could remember a dot, a line, and a wavy line:
• - ~
and that they somehow connected meaningfully!
Yes, this is quite meaningful already, a generative seed, a foundational structure.
• → object, - → morphism, ~ → natural transformation/functor flow.
point, line, wave
• → - → ~
Today I had a similar experience, it was logical connectives somehow connecting to a common core, maybe ∀ was in the middle of, ∃ outside, further away, ∨ and ∧ had structural meaning, but these were somehow connecting things, a fusion.
When I awoke I had these thoughts:
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∀ in the middle, gravity
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thinking of gravity as negative ~ positive, presence ~ absence #maybe
∀ F ∃ -F,∀ 1 ∃ ø, every absence has its presenceI thought: why towards the center of the Earth is gravity, when maybe it is as meaningful to think "away from the center is …". There are many centers, there is a pull towards black holes, disappearing, so maybe it is more meaningful to think "away from" ~ existence. Wow, ∀ pulls ∃ resists? - Oh I don't yet know relativity! (but this inspires me to learn basic physics 🐬) #perhaps Everything rolls toward 🕳, and everything has it's own 🕳? Recursive rolling towards holes?
∀ x : Obj, ∃! h : Hom(x, 🕳 x)hole(x) := kernel (id_x : x ⟶ x)- #maybe everything glides 🪶 - Does everything has its own geodesic? maybe it matters how we think about things, so instead of forces of push pull, maybe everything glides, a crane flying by -
mathematics as a way of thinking:
¬gravity, Hom(cat, Earth)sort of applying / fusing mathematical patterns with everyday concepts- Oh I could do this, sitting in the garden looking at things I noticed I could look at / draw a bunch of things, so instead of focusing on a single leaf, I can look at a plant, and the stone near it and the frog, and a reflection, etc and draw the bunch of things, instead of fixating on a single object or point, which has to do with mindfulness and actively noticing things.
Blog : Stress → Play
• - ~
∀, ∃, 🕳
🌳 ⊣ 🌿