GF(3) → {Tactile, Auditory, Haptic} universal bridge for accessible color perception
/plugin marketplace add plurigrid/asi/plugin install asi-skills@asi-skillsThis skill inherits all available tools. When active, it can use any tool Claude has access to.
"Color is not inherently visual. Color is INFORMATION that can be rendered through any sensory modality."
This skill treats GF(3) trits as modality-independent semantic units:
| GF(3) Trit | Visual | Tactile | Auditory | Haptic |
|---|---|---|---|---|
| MINUS (−1) | Cool hues | Rough/Bumpy | Low pitch | Left/Down |
| ERGODIC (0) | Neutral | Smooth | Mid pitch | Center |
| PLUS (+1) | Warm hues | Ridged | High pitch | Right/Up |
Visual perception is ALSO a projection from GF(3) space.
The sighted user doesn't have "the real thing" — they have π_visual(GF3). The blind user has π_tactile(GF3), π_auditory(GF3), π_haptic(GF3).
All projections are isomorphic under GF(3) conservation:
π_visual(W) ≅ π_tactile(W) ≅ π_auditory(W) ≅ π_haptic(W)
From Gay.jl:
Standard Braille is 2×3 (6 dots). We extend to 3×3 (9 dots):
┌───┬───┬───┐
│ 1 │ 2 │ 3 │ ← Hue sector (warm/neutral/cool)
├───┼───┼───┤
│ 4 │ 5 │ 6 │ ← Saturation level
├───┼───┼───┤
│ 7 │ 8 │ 9 │ ← Lightness level
└───┴───┴───┘
Dot positions encode trits:
○ ○ ⬤ ← Hue: PLUS (warm)
○ ○ ⬤ ← Saturation: PLUS (vivid)
○ ○ ⬤ ← Lightness: PLUS (light)
Compact: +++
Each color becomes a 3-frequency chord:
const BASE_FREQ = 440.0 # A4
function trit_to_freq_ratio(t::Int)::Float64
t == -1 && return 0.84 # Minor third
t == 0 && return 1.0 # Unison
t == 1 && return 1.26 # Major third
end
function color_to_chord(hue_trit, sat_trit, light_trit)
(
BASE_FREQ * trit_to_freq_ratio(hue_trit),
BASE_FREQ * 1.5 * trit_to_freq_ratio(sat_trit), # Fifth
BASE_FREQ * 2.0 * trit_to_freq_ratio(light_trit) # Octave
)
end
# Play a single color as chord
play -n synth 0.25 sine 440.0 : synth 0.25 sine 660.0 : synth 0.25 sine 880.0 remix - fade 0 0.25 0.05
struct HapticPosition
x::Float64 # Hue: -1 (left) to +1 (right)
y::Float64 # Saturation: -1 (back) to +1 (front)
z::Float64 # Lightness: -1 (down) to +1 (up)
vibration_pattern::Symbol # :pulse, :smooth, :buzz
intensity::Float64 # 0.0 to 1.0
end
Path navigability analysis using μ(path_length):
| μ ≠ 0 | GEODESIC | Smooth bidirectional tactile navigation | | μ = 0 | TANGLED | Add branching markers at squared prime positions |
The Möbius value μ(3) = -1 creates:
Action: {−, ○, +} (visual domain)
Perception: {+, ○, −} (tactile domain, Möbius-inverted)
Double inversion returns to original: μ ∘ μ = id.
| Component | Trit | Role |
|---|---|---|
| catsharp-sonification | 0 | Auditory output |
| crossmodal-gf3 | 0 | Universal bridge |
| sense | 0 | Content extraction |
Conservation: 0 + 0 + 0 = 0 ✓ (all ERGODIC coordinators)
For generators/validators:
elevenlabs-acset (-1) ⊗ crossmodal-gf3 (0) ⊗ gesture-hypergestures (+1) = 0 ✓
# Generate accessible color palette (Julia)
julia -e 'using Gay; Gay.gay_seed!(137508); colors = [Gay.next_color() for _ in 1:6]'
# Sonify via catsharp-sonification
bb -e '(sonify-palette ["#DD3C3C" "#3CDD6B" "#9A3CDD"])'
# Extract content accessibly
just sense-extract reference/videos/lecture.mkv
Accessible Worlds Theorem:
For any world W with visual representation V:
π_visual(W) ≅ π_tactile(W) ≅ π_auditory(W) ≅ π_haptic(W)
where all projections π preserve GF(3) conservation:
∀ modality m: Σ(trits(π_m(W))) ≡ 0 (mod 3)
"The most unlike skills are the most essential - they bridge what others cannot reach."