Last 4000 years in which society? Romans mostly didn't wear hats. Jewish men have worn the kippah (small hat) essentially all the time for much of that period

Last 4000 years in which society? Romans mostly didn't wear hats. Jewish men have worn the kippah (small hat) essentially all the time for much of that period. Especially indoors, in a synagogue. It's a symbol of respect for God. The "take the hat off indoors but always wear it outdoors" certainly hasn't been universal in western Europe for the last 4000 years.