1.2.2 Colour mixture by addition

In 1853, Grassmann4 formulated a set of axioms, empirically 4Herman Gunther Grassman
(1809–1877), German
mathematician, physicist and
linguist.
validated, which are now known as Grassman’s laws of colour
perception. They are, framed in terms of lights which may or may
not be mixtures,
Additivity: adding a third light to each of two lights perceived as
equal produces equal mixtures. Algebraically, x = y ⇒ x + z = y + z.
Proportionality: altering the luminances of two equal lights by
equal factors produces two equal lights. Algebraically,
x = y ⇒ αx = αy.
Transitivity: equality of light mixtures implies that the equal lights
can replace each other in all contexts. Algebraically,
(x = y) ∧ (y = z) ⇒ x = z.
Note that these laws break down at very low luminances, where
stimulation of rods is more important than cones; they also are not
strictly true over changes in luminance even at ordinary levels,
though for practical purposes they are sufficiently accurate over a
wide range of illumination that they can be used without significant
error.
Grassman’s laws imply that if we have two coloured lights
representable as mixtures of certain primaries (whether those
primares are fundamental to the eye or simply chosen as points of
reference), then the mixture of the two colours is also representable
as the mixture of those primaries. Specifically, if light X matches
aA + bB + cC, and light Y matches a�A + b�B + c�C, then the
mixture X + Y will match (a + a�)A + (b + b�)B + (c + c�)C. This rule
of mixture by addition, coupled with the assertion that three
primaries are enough to match any colour, is the basis for much of
digital colour production.