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 · read in order, or start anywhere — the hub is the map.

1. 01 The Oblong on the Wall

   Newton's prism, the seven-colour convention, invisible light, and the thesis: colour is not in the light.

   Topics T1–T3 W-01, P-A ships at M1

2. 02 Smaller Than a Full Stop

   The eye as an aberrated camera, three kinds of cone, and four senses of "the same colour".

   Topics T4–T6 P-B, W-02, W-03 ships at M2

3. 03 Brown, Moonlight, and the Island of the Colour-Blind

   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

4. 04 Maxwell's Tartan Ribbon

   Maxwell's photograph, Grassmann's laws as vector-space axioms, and the negative lobe.

   Topics T10–T12 W-09 ships at M5

5. 05 The Horseshoe

   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

6. 06 The Colour of a Flame, and What "White" Means

   Blackbody radiation, the Planckian locus, the CIE illuminants, and chromatic adaptation.

   Topics T16–T18 W-16, W-17, W-18 ships at M5

7. 07 Why the Sky Isn't Violet

   Rayleigh scattering derived, why the sky is azure not violet, and the skies of other planets.

   Topics T19 W-19 ships at M5

8. 08 The Green That Isn't There

   Hering's opponent channels, after-images, forbidden colours, and the neural wiring of colour.

   Topics T20–T21 W-08, W-20 ships at M2

9. 09 Munsell's Lopsided Tree

   Munsell's perceptually-ordered colour tree and the cube-root law of lightness.

   Topics T22–T23 W-21, W-22 ships at M4

10. 10 How Far Apart Are Two Colours?

    CIELAB and CIELUV, and the patched colour-difference metrics ΔE76, ΔE94, ΔE2000.

    Topics T24–T25 W-23, W-24 ships at M3

11. 11 MacAdam's Ellipses, and the Shape of Colour Space

    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. 12 The Blog Post That Fixed Gradients

    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. 13 The Red Phosphor, and the Code in Your Pixels

    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. 14 Paint Sets, Imaginary Primaries, and Why Print Needs Black

    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. 15 The Dress

    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. 16 The Rainbow Map That Failed the Diagnosis

    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. 17 olo: The Colour No Light Can Make

    The olo experiment, impossible colours, Mary's Room, and colour as constructed not contained.

    Topics T40 W-44 ships at M4