> More seriously, I hate those arrows exactly because I never know what
> they mean.  I think it's just like the "split window
> vertically/horizontally" issue: it's a bad UI and the right solution is
> to choose neither of those options.


There actually is an icon that is unambiguous: the "a-z" or "z-a" one:

https://www.iconfinder.com/icons/905641/ascending_az_filters_sort_sorting_icon
https://www.iconfinder.com/icons/905640/descending_filter_sort_sorting_za_icon

I'd be happy with that or Clément's stacked layers' solution.

Philippe