Color: Two Revolutions — Newton (1704) and Wittgenstein (1950)

Isaac Newton made color a problem of physics — light broken into rays. Ludwig Wittgenstein, 250 years later, made it a problem of language — color as grammar. Both were right, but about different things.

Newton Opticks, 1704

Historical Overview

In 1666, during the plague year at Woolsthorpe, a 23-year-old Isaac Newton darkened his room and let a narrow sunbeam pass through a triangular glass prism. Instead of a round white spot, he saw an oblong spectrum. In his experimentum crucis (crucial experiment), he isolated a single color with a slit, sent it through a second prism, and found it could not be split further — but could be recombined with others to make white again.

Published in Opticks (1704), Newton argued that white light is heterogeneous: a mixture of rays "differently refrangible." Color is not in objects, but "in the mind" — a sensation produced by the disposition of light to excite certain motions in the sensorium.

Different refrangibility: Each spectral hue bends by a fixed amount in glass. Red least, violet most.
Seven colors: Newton chose red, orange, yellow, green, blue, indigo, violet to match the musical scale — a cultural choice, not physics.
Experimentum crucis: A second prism proves colors are not created by the glass, only separated.
Recomposition: All spectral colors recombined produce white light again.
Color circle: Newton bent the spectrum into a circle, joining red to violet with non-spectral purples/magentas — colors that exist only in the brain, never in a single wavelength.

Prism angle / dispersion: 32° ← drag to see Newton's first prism split white, second recombine

GNU Octave — Simulate Newton's Spectrum

% Newton: spectrum 380-750 nm to approximate RGB
lambda = 380:5:750;
cols = zeros(length(lambda),3);
for i = 1:length(lambda)
  l = lambda(i);
  if l < 440
    r = (440-l)/60; g = 0; b = 1;
  elseif l < 490
    r = 0; g = (l-440)/50; b = 1;
  elseif l < 510
    r = 0; g = 1; b = (510-l)/20;
  elseif l < 580
    r = (l-510)/70; g = 1; b = 0;
  elseif l < 645
    r = 1; g = (645-l)/65; b = 0;
  else
    r = 1; g = 0; b = 0;
  endif
  cols(i,:) = [r g b].^0.8;  % gamma correction
endfor
figure(1); imagesc(lambda, [0 1], cols'); axis tight off;
title('Newtonian spectrum - refrangibility mapped to color');

% Newton's color circle (1704) - joining ends with purple
theta = linspace(0, 2*pi, 8);
spectral = [1 0 0; 1 0.5 0; 1 1 0; 0 0.7 0; 0 0.3 1; 0 0 0.6; 0.5 0 0.8];
figure(2); polar(0,1); hold on;
for k = 1:7
  plot([0 cos(theta(k))], [0 sin(theta(k))], 'linewidth', 8, 'color', spectral(k,:));
endfor
% non-spectral purple closes the circle between violet and red
plot([cos(theta(7)) cos(theta(1))], [sin(theta(7)) sin(theta(1))], 'color', [0.7 0 0.7], 'linewidth', 8);
title('Color circle: magenta exists only by mixing ends');

Wittgenstein Remarks on Colour, 1950–51

Historical Overview

Written in the last 18 months of his life and published posthumously in 1977, Ludwig Wittgenstein's Remarks on Colour was not physics but philosophy. He was responding to Goethe's Theory of Colours (1810), which had attacked Newton for ignoring how we actually see and talk about color.

Wittgenstein asked: why can't we imagine a "transparent white" or a "reddish green"? It's not because our eyes lack receptors — it's because our language forbids it. Color words form a system of internal relations, a "grammar." He borrowed Philipp Otto Runge's color octahedron (1810) to map these logical oppositions: white vs. black, red vs. green, yellow vs. blue.

Language-games: "White is the lightest color" is not an empirical discovery, but a rule for using "white."
Logical impossibilities: "There is no reddish green" (III §106). Not forbidden by optics, but by grammar — we have no practice for it.
Transparent white? We can imagine clear glass, but not something that is both white (opaque) and transparent. The concepts exclude each other.
Critique of Newton: Physics explains wavelengths, but cannot explain why "yellowish blue" is nonsense while "greenish blue" is fine.
Color octahedron: Not a scientific model, but a map of conceptual distances — white at top, black at bottom, four primaries around.

Interactive: Runge–Wittgenstein Octahedron

Click a vertex. Wittgenstein uses this shape to show logical, not physical, relations.

White — Top

Select a color to see Wittgenstein's remark on its grammar. Start with white: "White is the lightest colour" — this is part of what we mean by 'white', not a fact we discovered.

Language test: Is "reddish green" possible?

Wittgenstein: Correct. We can mix red and green pigment and get brown, but we cannot see a color that is both fully red and fully green at once — unlike reddish-yellow (orange). It's not retinal opponent processing (though Hering later described that); it's that our color concepts are built on oppositions. "Reddish green" has no place in our language-game; we wouldn't know what to point to.

GNU Octave — Plot the Color Octahedron

% Wittgenstein / Runge color octahedron - logical relations
white  = [0 0 1];
black  = [0 0 -1];
red    = [1 0 0];
yellow = [0 1 0];
green  = [-1 0 0];
blue   = [0 -1 0];

V = [white; black; red; yellow; green; blue];
% faces: white to equator, black to equator
F = [1 3 4; 1 4 5; 1 5 6; 1 6 3; 2 4 3; 2 5 4; 2 6 5; 2 3 6];
C = [1 1 1; 0 0 0; 1 0 0; 1 1 0; 0 0.6 0; 0 0 1];

figure; patch('Vertices', V, 'Faces', F, ...
  'FaceVertexCData', C, 'FaceColor', 'interp', 'EdgeColor', [0.3 0.3 0.3]);
hold on;
text(0,0,1.08,'white','HorizontalAlignment','center','Color','w');
text(0,0,-1.08,'black','HorizontalAlignment','center','Color','w');
text(1.05,0,0,'red'); text(-1.05,0,0,'green');
text(0,1.05,0,'yellow'); text(0,-1.05,0,'blue');
axis equal off; view(35, 28);
title('Color Octahedron - grammar of color, not physics (Wittgenstein after Runge)');