mystery of two and three

Number one symbolises uniqueness. It is prevalent in both mathematics and physics. Beyond number one, mathematics and physics diverge in a mysterious way.

In mathematics, if you have three examples of a given structure, then it is extremely likely that there are infinitely many other examples as well. In other words, beyond uniqueness, the only finite number mathematics favours is the number two.*

In physics, number three plays the same role that number two plays in mathematics.** It underlies all plural ontologies.

• There are three spatial dimensions.

• There are three gauge theories corresponding to the three fundamental forces.

• There are three generations of leptons and quarks.

• Only the first three fundamental representations of the double cover of the Poincare group matter for calculating the spins of fundamental particles.

• Only the first three orders of the generic Lagrangian matter for describing the dynamics of non-interacting particles.

* Hat tip to Prof. George Janelidze

** Hat tip to Physics from Symmetry by Jakob Schwichtenberg