My goodness, haven't even noticed that mine were missing. Some sixty five years back I did a training course as a manucurist When I was working in a hairdressers), and can remember that we used to push down cuticles on those hands we were working on - but even then cannot remember anything specifically which dealt with half-moons. Much to my despair, my own nails were always bad, no matter what I did, breaking and peeling. The only time I had good nails was each time I was pregnant, but as soon as baby was born, they reverted back. Then, I was put alendronic acid, and lo and behold, my nails all grown nicely - but still only those half-moons on my thumb nails