Four Forces

 There are four fundamental forces of Physics;

(Gravity, Electromagnetism, Weak, Strong)

The study of these and their charges are at the foundation of Physics. The (Charge, Field) duality is the governing duality since these forces are fields. The numbers that correspond to the forces are;

(?, 1, 2, 3)

The last three are obvious because the corresponding groups are;

(?, U(1), SU(2), SU(3))

The group numbers refer to the entry numbers of the complex matrices that govern the corresponding interactions.

The obvious number that corresponds to Gravity is Zero, but there is no group called ?(0). Quantum Gravity studies the symmetry of Gravity but apparently "QG can not tolerate global symmetry groups". Since QG is not a mature theory, this remains a mystery. According to Gemini, "the primary mathematical field that studies the structure of "the very small" is Noncommutative Geometry".

The symmetries of the number 4 may shed some light into this;

((2+2), (2*2), (1+3), (3+1), (1+1+1+1))

This may look trivial but all these exist in the fields. For example;

(2+2); ((Gravity, Electromagnetism), (Weak, Strong))

(1+3); ((Gravity), (Electromagnetism, Weak, Strong))

Electromagnetism enters General Relativity directly, making them a strong duality. The (1+3) symmetry is obvious since Gravity stands apart from the other 3.

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From another more fundamental view, there are four fundamental categories of Physics;

(Energy, Time, Mass, Gravity)

The (2+2) and (1+3) symmetries are obvious here too.