Lambert’s cosine law is that the intensity of a light ray hitting a surface varies by the cosine of the angle it hits at, so light hitting at right angles to a plane gives all its intensity, but light parallel to plane gives none. In angle degree terms, light at right angles is 90º which has a cosine of one, and parallel light is 0º which has a cosine of zero, so the formula works. It also works for an in-between angle, where the cosine of that angle gives the intensity. Essentially, light projects its intensity onto a plane according to angle.
A processing model explains this rule in channel terms. A ray of light can occupy all the channels of a point on its axis, so it has full intensity on that axis. But on other axis channels, its strength projects according to their angle, so the cosine law applies. Rays of light on the same axis then share the same channels because Cos(0) is one, and rays at right angles share no channels because Cos(90) is zero. In-between, the rays share channels based on the cosine of the angle between them. In effect, the cosine law also explains how photons fill the channels of a point.
The last section explained electrons and neutrinos as extreme light colliding on a line through a point. This section explores whether a three-way collision of extreme light in a plane through a point can do the same for quarks. Can the same logic applied to a line for electrons be extended to a plane for quarks? For an electron, the photons had to fill the bandwidth of a line, which was taken to be one. Two light rays crossing at a point occupy entirely different channels, so it makes sense that the bandwidth of a plane through a point is two. It follows that if two extreme light rays are needed to fill the channels of a line through a point, four extreme light rays are needed to fill a plane though it.
In Figure 4.9, three equal-angle extreme rays in a plane meet at a point, so they aren’t enough to fill the bandwidth of a plane. Each ray fills half the bandwidth of one axis, but three times that is 1.5 not two, so the result can’t be stable because there are unfilled channels that another entity could exploit.
However the result could be semi-stable if some axes are filled completely. Dividing the plane bandwidth of two between three axes gives each one a two-thirds bandwidth, so could this interaction fill any of these axes? Three extreme light rays could fill the channels of two of the axes but leave the third unfilled.