Let me give one very simple example. Starting from a universe consisting of a finite number of bits, i.e., either 0 or 1, a basic operation is introduced, viz., to make a “discrimination”. To express this operation, another operation is needed: addition modulo 2: \(0 + 0 = 1 + 1 = 0\) and \(0 + 1 = 1 + 0 = 1\). If the outcome is 0, then the elements of the sum are not distinguished, else they are. Look now at sets that contain 0 and/or 1, and such that, if two elements are distinguishable, that element belongs to the set as well. There are exactly 3 \((= 2^{2}-1)\) such sets: \(\{0\}, \{1\}\) and \(\{0,1\}\). If these 3 elements are now taken as a new basis instead of 0 and 1, a clever construction shows that 7 \((= 2^{3}-1)\) such sets exists and, in a next step, 127 \((= 2^{7}-1)\) pops up. Now \(3 + 7 + 127 = 137\) and that number is close to the electromagnetic coupling constant.