... At the ages of perfect squares is when we all cross or achieve significant milestones in our lives as children, students, (young) adults, spouses, parents, grandparents, senior citizens of society and so on.
Consider these ages - 4 (early childhood), 16 (adolescence/maturity), 25 (young adulthood), and 36 (mid-adulthood), and so on.
...It appears that perfectly-squared numbers correspond to notable periods of transition in life (e.g. one's starting school, coming of age, independence, career milestones, etc).
You might find this coincidence dubious.
Yet I don't see why humans can't help but instinctively grant significance to this coincidence. I would in fact argue:
In mathematics, perfect squares show unique properties/symmetry.
And there is the golden ratio, which is believed to underlie all beauty, harmony and proportion in nature. Even plants are said to follow the ratio.
Why then should perfect-squares not be a viable idea of nature - especially when the numbers so beautifully map to the expected stages of human growth?
Another thing I like: the gaps between the squared numbers, i.e. the difference between consecutive perfect squares - are constantly increasing in size:
- Between 1² (1) and 2² (4): 3
- Between 2² (4) and 3² (9): 5
- Between 3² (9) and 4² (16): 7
- Between 4² (16) and 5² (25): 9
Literally interpreted, our stages of life 'stretch out' as we age.
And more metaphorically interpreted, we humans have 'more time' at each stage, to accomplish whatever needs to be done then (that which was not/could not be done at an earlier stage).
I might be too adventurous with this symbolism; in fact you might interpret it differently (or not at all).
Aside: As a programmer, I resonate more with the beauty of the powers of two. But perfect-square symbolism has its own charm; and given that 2025 is a perfect square (of 45²), here's to a beautiful year to everyone!