Euclid’s first common notion is this: Things which are equal to the same things are equal to each other. That’s a rule of mathematical reasoning and its true because it works - has done and always will do. In his book Euclid says this is self evident. You see there it is even in that 2000 year old book of mechanical law it is the self evident truth that things which are equal to the same things are equal to each other.
It’s so difficult to describe [depression] to someone who’s never been there, because it’s not sadness. I know sadness. Sadness is to cry and to feel. But it’s that cold absence of feeling — that really hollowed-out feeling. That’s what Dementors are. - J.K Rowling