N.3 Na­ture and real eigen­val­ues

The ma­jor dif­fer­ence be­tween real and com­plex num­bers is that real num­bers can be or­dered from smaller to larger. So you might spec­u­late that the fact that the num­bers of our world are real may fa­vor a hu­man ten­dency to­wards sim­plis­tic rank­ings where one item is worse” or “bet­ter than the other. What if your grade for a quan­tum me­chan­ics test was $55+90{\rm i}$ and some­one else had a $70+65{\rm i}$? It would be log­i­cal in a world in which the im­por­tant op­er­a­tors would not be Her­mit­ian.