When the Fibonacci number sequence is based on the number seven and its multiples, the Fibonacci sequence self-reflexively reappears when differences are calculated between it and this new number-seven-based Fibonacci sequence. The same thing happens with Lucas numbers. Can this same procedure be applied to any two numbers at the beginning of a Fibonacci/Lucas-like sequence? The answer is in the negative. This special quality of the golden proportion casts light on the fine structure constant of hydrogen, which is the unique, lightest, and most pervasive element in nature, plus other constants in nature, all of which have a dimensionless number close to the golden proportion (Phi) of the Fibonacci sequence, and provides the basis for the binary computer code as well as a uni-Phi-ed theory of mathematics and physics.