[xmcqdpt2]

Most elements are stable, especially most of the ones we deal with, and they fall in clear periods and rows based on chemical valence. This is true for main group elements and mostly true for transition metals.

I think the periodic table was discovered, not invented. My guess is that whenever we communicate with some advanced alien species, the periodic table is going to be one of those things we share.

[TeMPOraL]

Periodic table is recording multiple different patterns in atoms. Some better than others. By nature, its a dimensional reduction. There are many alternative renderings of the periodic table (or spiral, or cube, or ...) emphasizing different regularities. The one you refer to is just the most popular rendering.