## Orthogonality

Mathematics is the language of reality, and so eight or nine times a day I find myself casually using a word I learned in topology or linear algebra in a completely different setting. My friends are threatening not to speak to me anymore. But these are good words! If only I had a way to explain the words I’ve come to love without asking my friends to take a math major first—oh right. I have a blog. (The post proper is aimed at an audience with maybe high school math. The footnotes are for mathematicians or an interested reader who wants to know more. The exercises are for anyone with the listed prerequisite.)

Two things are orthogonal if they are perpendicular. But why don’t I just use the word “perpendicular” with retail customers and at the bar? Why roll to lose an audience with a slightly harder word that means effectively the same thing?

Shade of meaning is everything, but where perpendicular lines are going in the opposite direction on a piece of paper, orthogonal objects are going in the opposite direction on everything. There is no setting in which these two objects are connected, correlated, or drift-compatible.