Process journal of learning by Attila Vajda

fragments 2025-07-09

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ChatGPT conversation, this is useful in my experience:

desc

a LOT of cool things are happening, in my experience, maybe it's normal...

cool_things := mindfulness × growth mindset × mathematics × recovery

or is it:

c ≈ m × g × 𝑚 × r

𝓒 ≅ 𝓜 × 𝓖 × 𝕄 × 𝓡

Oh this is nice: ⊥───⊤ ⟶ ⊢───⊣

A continuous interval of truth? I find this theme fascinating, but I still struggle to understand how this is. Yesterday I learnt quantifiers ∀ ∃ can be arranged geometrically. Eg ∀∀ ∀∃ ∃∀ ∃∃ is a square with coordinates 00 01 10 11

∀∃╭────╮∃∃  
  │    │  
  │    │  
∀∀╰────╯∃∀

for three quantifiers it's 2^3 = 8 quantifier shapes: ∀∀∀, ∀∀∃, ..., ∃∃∃ — logic genome 🧬, or Quantifier Cube 🧊.

Which somehow is analogous to Ω^3 ⟶ Ω (flax seeds?) 256 logical ternary operations, 256 in colors, 256 in audio, so there seems to be sort of shades to truth, which I find fascinating! Pixelated truth. I don't yet know, but I wonder, what do the edges mean, what do the outside/inside of the cube mean?

def logic_fn := (Ω × Ω × Ω) → Ω

Are the logic functions, so are the quantifier shapes

({∀, ∃} × {∀, ∃} × {∀, ∃}) ⟶ {∀, ∃} ? #unsure Even the logical functions as shape, what does logic to have shape mean?

Then can you #maybe have quantifier / logic shapes ℕ ⟶ ℤ ⟶ ℚ ⟶ ℝ ⟶ ℂ ⟶ Ω^n ?

∀∀∀ = 000  
∀∀∃ = 001  
∀∃∀ = 010  
∀∃∃ = 011  
∃∀∀ = 100  
∃∀∃ = 101  
∃∃∀ = 110  
∃∃∃ = 111