Go look at http://thismight.be/offensive/uploads/2007/09/04/image/attraction.gif -- a chart of different types of attraction, from thismight.be/offensive. (The site doesn't allow external referrers; when I posted the link I thought it just didn't allow inline links to images.)
The chart has an x-axis "physical attraction" and a y-axis "mental attraction", and then the square is divided into regions corresponding to different types of relationships: Zone of Pain, Just Friends, One Night Stands, F Buddy, Awkwardness, Dating Potential, Dating Zone, Marriage Potential, and Null. ("Null" is in the extreme upper right, corresponding to a very high level of both physical and mental attraction; I take it that the creator of this image finds this impossible.
What I immediately noticed is that the chart is basically symmetric across the diagonal, which implies some sort of symmetry between mental attraction and physical attraction. I don't think I believe this, but what sort of hidden symmetry is there in human interaction in general?