Why 4 is cool

4 = 2+2 = 2x2 = 2^2

Where ^ represents exponentiation. In fact if we use ^ to stand in for Knuth's up-arrow then we can go even further with four:

4 = 2+2 = 2x2 = 2^2 = 2^^2 = 2^^^2 = 2^^^^2 = ... = 2^^...^2 = ...