The Mathematics of Colour

Colour is a lossy, three-dimensional projection of an infinite-dimensional spectrum. Light arriving at the eye is a function of wavelength — a point in an infinite-dimensional space — and three kinds of cone collapse it to three numbers. Almost every difficulty in this series is a consequence of that one projection: that two different spectra can look identical (metamerism), that the matching primaries go negative and the standard ones turn imaginary, that no triangle of real primaries can ever cover the horseshoe of visible colour, and that there exist colours — like olo — that no spectrum can produce at all. One fact, told seven ways.

17 posts · ≈4 h 54 min total · read in order, or start anywhere — the hub is the map.

01 The Oblong on the Wall ≈16 min
Newton's prism, the electromagnetic spectrum, and why colour is not in the light.

Topics T1–T3 W-01 ships at M1
02 Smaller Than a Full Stop ≈15 min
The eye as an aberrated camera, three kinds of cone, and four senses of "the same colour".

Topics T4–T6 W-02, W-03 ships at M2
03 Brown, Moonlight, and the Island of the Colour-Blind ≈17 min
The edges of colour vision: anomaly and dichromacy, tetrachromacy, the birth of brown, and the Purkinje shift.

Topics T7–T9 W-04, W-05, W-06, W-07 ships at M3
04 Maxwell's Tartan Ribbon ≈16 min
Maxwell's photograph, Grassmann's laws as vector-space axioms, and the negative lobe.

Topics T10–T12 W-09 ships at M5
05 The Horseshoe ≈26 min
The XYZ construction, the chromaticity horseshoe, the LMS↔XYZ link, and metamerism.

Topics T13–T15 W-12, W-13, W-15, W-11, W-14, W-10 ships at M5
06 The Colour of a Flame, and What "White" Means ≈20 min
Blackbody radiation, the Planckian locus, the CIE illuminants, and chromatic adaptation.

Topics T16–T18 W-16, W-17, W-18 ships at M5
07 Why the Sky Isn't Violet ≈13 min
Rayleigh scattering derived, why the sky is azure not violet, and the skies of other planets.

Topics T19 W-19 ships at M5
08 The Green That Isn't There ≈14 min
Hering's opponent channels, after-images, forbidden colours, and the neural wiring of colour.

Topics T20–T21 W-08, W-20 ships at M2
09 Munsell's Lopsided Tree ≈17 min
Munsell's perceptually-ordered colour tree and the cube-root law of lightness.

Topics T22–T23 W-21, W-22 ships at M4
10 How Far Apart Are Two Colours? ≈16 min
CIELAB and CIELUV, and the patched colour-difference metrics ΔE76, ΔE94, ΔE2000.

Topics T24–T25 W-23, W-24 ships at M3
11 MacAdam's Ellipses, and the Shape of Colour Space ≈20 min
MacAdam's ellipses as a Riemannian metric, Resnikoff's dichotomy, and Bujack breaking additivity.

Topics T26–T28 W-25, W-26, W-27 ships at M4
12 The Blog Post That Fixed Gradients ≈16 min
OkLab by construction, the family of modern perceptual spaces, and the Abney and Bezold–Brücke effects.

Topics T29–T30 W-28, W-29, W-30 ships at M2
13 The Red Phosphor, and the Code in Your Pixels ≈17 min
Display gamuts and the red-phosphor bottleneck, gamma encoding, and why sRGB is a code not an intensity.

Topics T31–T32 W-31, W-32, W-33 ships at M3
14 Paint Sets, Imaginary Primaries, and Why Print Needs Black ≈20 min
RGB working spaces and ACES, HDR transfer (PQ/HLG), and additive versus subtractive mixing.

Topics T33–T34 W-34, W-35, W-36 ships at M5
15 The Dress ≈17 min
Colour constancy and "the dress", the channel-swap proof, and photometry through V(λ) — the candela.

Topics T35–T36 W-37, W-38, W-39 ships at M5
16 The Rainbow Map That Failed the Diagnosis ≈20 min
Why the rainbow/jet colormap fails, modern perceptual colormaps, and the three palette jobs.

Topics T37–T39 W-40, W-41, W-42, W-43 ships at M5
17 olo: The Colour No Light Can Make ≈14 min
The olo experiment, impossible colours, Mary's Room, and colour as constructed not contained.

Topics T40 W-44 ships at M4