Historical images are filled of statues with broken noses from all cultures. There are many theories to explain this. Ancient Egyptians thought that a life force would enter statues through the nose, so breaking the nose from a statue would (in theory) render it useless. Destroying artifacts has long been used by conquerors to cripple a culture in order to overtake it. Damaging the likeness of a past leader was also a frequent tactic used by new leaders to elevate themselves.
There is, also, the unromantic theory that perhaps so many statues are missing noses because it’s an extremity and therefore likely to fall off by itself over time. All this debate, though, offers an entertaining conclusion about history and perhaps some instruction on how we might look at the world today.
Noticing a pattern and then following your curiosity about it is a hallmark habit of non-obvious thinkers. That same impulse which can lead you down an olfactory rabbit hole can also inspire your biggest new idea. In other words, chasing the answer to a seemingly insignificant question may not entirely be a waste of time.