In the first installment I reminded the fact that there are exactly 3 generations (flavors) of fermions. This fact was established by the CERN LEP experiments (Aleph, Delphi, L3, and Opal). There is an independent confirmation of this fact by the CMB (cosmic background radiation) measurements. According to the latest results from the Planck space telescope the existence of a fourth neutrino type is excluded at the 95% confidence level. Remember neutrinos are fermions. If a fourth neutrino type does not exist the fourth fermion generation (flavor) does not exist either. Planck space telescope measurements are consistent with the results of the CERN LEP experiments.

Quarks possess a property called color charge. There are three types of color charge, arbitrarily labeled as blue, green, and red. Each quark color is complemented by an anticolor (antiblue, antigreen, antired). Attraction and repulsion between quarks is mediated by force carrying particles known as gluons. Each gluon carries one color charge and one anticolor charge. When a gluon is transferred between quarks, a color change occurs in both; for example, if a red quark emits a red–antigreen gluon, it becomes green, and if a green quark absorbs a red–antigreen gluon, it becomes red.

The 3 color charges must be related to the 3 generations of fermions because quarks are fermions themselves.

The 3 generations of fermions and the 3 color charges beg the question: why 3?

**Skipping the standard answer today**

In the Eastern philosophy, the standard answer to the question “Why 3?” is 3 gunas (3 fundamental principles/tendencies). The subject of 3 gunas is very interesting and I wrote perhaps too many articles about 3 gunas so I will skip the discussion of gunas in this post. Instead, I would like to bring to your attention to the relationship between 3 and the geometrical concept of area.

**Emergence of space-time-energy**

Minimum of 3 intersecting lines are needed to create area. This sounds trivial but I have a suspicion that in the primordial stage before the emergence of the space-time-energy the manifestation of a confined region was the necessary condition for the emergence of space-time-energy. The lowest dimensional confined region is an area. What is the minimum number of lines that can form an area? The answer is 3.

**Minimum area concept in CDT**

In the “Causal Dynamical Triangulations” (CDT) approach to quantum gravity the space-time is thought of as a mosaic of very small triangles. Actually, the most fundamental element in CDT is a geometrical object known as pentachoron (tetrahedral pyramid). The four sides of the pyramid are made of tetrahedron cells. This is hard to visualize. Perhaps the rotating image below helps (maybe not!)

The pentachoron is analogous to the tetrahedron in three dimensions and the triangle in two dimensions.

The “Causal Dynamical Triangulations” (CDT) approach to quantum-gravity is very promising in my opinion.

**Area concept in the Bekenstein bound**

In 1972, J.D. Bekenstein proposed that there must be an upper bound to the amount of information that can be stored in a finite region of space. This is known as the Bekenstein bound. He also claimed that the maximum information that can be stored in a finite volume is proportional to the surface area of that volume. Bekenstein derived this from heuristic arguments involving black holes.

**Area concept in Gerard ‘t Hooft’s Holographic Principle**

Gerard ‘t Hooft took the Bekenstein bound one step further and proposed that the information contained in a black hole is actually stored in the quantum fluctuations of the spherical surface known as the “event horizon.” His arguments were based on rigorous mathematics combining all known laws of physics. If the entire information contained in a black hole is actually stored on the 2D surface of the event horizon then the event horizon can be likened to a hologram.

**Area concept in the speculative version of the Holographic Principle**

Gerard ‘t Hooft’s “holographic principle” applies to black holes. String theorists apply the “holographic principle” to the universe and speculate that the entire physical universe can be seen as a two-dimensional information structure painted on the boundary of the universe.

**Simple point of this post**

Many people are thinking that concepts involving “area” (2D formations of various kinds)are important at the primordial stage. I am simply pointing out that the number 3 will naturally arise whenever we consider the “area” concept.