With the "swastika" I've become unsure whether cultures shared this symbol early on, or whether it was simply reinvented over and over because it's a simple and pleasing symbol. You have it as the fylfolt in Northern Europe, you have it in India...I even saw it on churches in Ethiopia...Totally neat if all 3 made it up independently, and not really that unlikely given it's simplicity and geometric-goodness...
Ah! Now you're talkin' a language I understand! The Collective Unconscious! Carl Jung! The Archetypes! The Hundredth Monkey! It's Ubiquitous!