Knowing that this number, the golden ratio, is present not just in mathematics, but may also be present within your own brain and body (at the atomic or subatomic level), what do you think it means? is this number evidence of a grand design, a massive freak coincidence or something else?

Golden ratio (Golden proportion, the division in extreme and middle ratio, harmonic division) — the ratio of the two values b and a, a > b is true when a/b = (a+b)/a. 
For practical purposes, limited to the approximate value of the ratio of a and b = 1,618 or approximately = 1,62. In percentage rounded value of the Golden Ratio is the division of any quantity in relation to 62% and 38 %.

The world have very much different values which often can have ratio like  62:38. However, we can say that many images with the Golden ratio, really looks nice.