Lambert’s cosine law is that the intensity of light hitting a surface varies by the cosine of the angle it hits at, so light at right angles to a surface gives all its intensity, but light parallel to it gives none. In angle terms, light at right angles is 90º which has a cosine of one, and parallel light is 0º which has a cosine of zero and in general, light projects its intensity onto a plane according to the cosine of its angle.
In processing terms, a ray of light at a point can access all the channels on its axis, but also spins to project onto other channels on other axes according to angle by the cosine law. Rays of light on the same axis then compete for the same channels, while rays at right angles don’t compete for channels at all. In-between, rays compete for channels based on the cosine of the angle between them.
For electrons, two extreme light rays overloaded the channels of a line through a point, so can three extreme rays do the same for a plane? Can quarks then arise in the same way that electrons did?
Previously, the line axis bandwidth was taken to be one, so the bandwidth of a plane through a point is two. Hence, if two extreme light rays fill the channels of a line through a point, four rays are needed to fill a plane through it.
In Figure 4.9, three equal-angle extreme rays meeting at a point can’t fill the bandwidth of a plane. Each ray fills half of its line axis bandwidth but three times a half is 1.5 not two, so the result isn’t stable, as there are unfilled channels that another entity could exploit. Dividing the plane bandwidth of two between three axes gives each a two-thirds bandwidth.
Yet three rays could fill two axis to be semi-stable, as quarks are, so could a quark be when a three-way interaction fills two axes but leaves the third unfilled?