[ THEORETIC FOUNDATION ]
{ ∅ } ⊆ S ⊆ ∪ S_i
[ AXIOMATIC DUST ]
• . •. . • . .
. • . • . •
. • . . • . .
. • . • . •
[ PARTIAL ORDERING ]
(X)
/ | \
(A)(B)(C)
\ / |
(Y) (D)
\ /
(Z)
[ TOPOLOGY & METRICS ]
( ( ( • ) ) )
τ = {∅, X, τ_i}
[ CAUCHY SEQUENCE ]
∀ε>0 ∃N ∀m,n>N :
d(x_m, x_n) < ε
[ INFINITE ACCUMULATION ]
x_n → L as n → ∞
[ MANIFOLD PROJECTION ]
______
.-" "-.
/ \
| .-----------.
| / \
| | M |
\ \ /
'-._______.-'
| π
v
[ ℝ^n CHART ]
[ COORDINATE SYSTEM ]
Y
│ . P(x,y,z)
│ /
│ /
│/_______ X
/
Z
[ LIE ALGEBRA ]
[X, Y] = XY - YX
[ EXACT SEQUENCE ]
0 → A → B → C → 0
[ STOKES' THEOREM ]
∫_M dω = ∫_∂M ω
[ THE GADFLY (SOCRATES) ]
.-------.
/ _ _ \
| (o|o) |
| > |
\ === /
`.___.'
/ | \
/ | \
[ THE PHENOMENOLOGIST ]
.-------.
/ _ _ \
|-(o)-(o)-|
| < |
\ --- /
`.___.'
/ | \
/ | \
[ EPISTEMIC CLOSURE ]
K_s(P) ∧ K_s(P → Q) ⊢ K_s(Q)
[ CARTESIAN DOUBT ]
□(Think(x) → Exist(x))
[ THE GETTIER OBJECTION ]
J(S, P) ∧ B(S, P) ∧ T(P) ⇏ K(S, P)
[ JTB FRAMEWORK ]
S knows that P iff:
1. P is true
2. S believes P
3. S is justified in
believing P
[ ONTOLOGICAL NECESSITY ]
◊∃x□∀y(y ≤ x) → □∃x∀y(y ≤ x)
[ RESONANCE & TENSION ]
~ ~ ~ ~ ~
~ ~ ~ ~
~ ~ ~ ~ ~
String Frequency:
f = (1 / 2L) √(T / μ)
[ EQUAL TEMPERAMENT ]
_________________
| | | | | | | |
| | | | | | | |
| |_| |_| | |_|
| | | | |
|___|___|___|___|
[ OVERTONE SERIES ]
f, 2f, 3f, 4f, 5f...
[ STAFF NOTATION ]
-------|---------
|\ | O
---|/--|---|-----
/| | |
-/=|---|---|-----
| _|_ |
---\_/---\_/-----
[ HARMONIC MOVEMENT ]
Em7 Bm Cmaj9
022030 x24432 x3243x
Dmin7 G7 Cmaj7
x5756x 3x343x x3545x
[ POLYRHYTHM ]
3 : 2
x x x (Triplets)
x x (Eighths)
I. Mathematics
An exploration of pure mathematical structures. Currently mapping out a project to visualize abstract axioms—moving from arbitrary sets to structured topological spaces and geometric manifolds.
II. Schools of Thought
Musings on the philosophy of mathematics, human consciousness, and the Cartesian pursuit of fundamental truths. What does it mean for an abstraction to be faithful?
III. Interpretations and Realizations of Sonics
Tracking sonic movements, experimental compositions, and post-rock arrangements that frame the background of my thinking.