OK, you've suckered me to step a little further along this path that I've always regarded as the high road to madness...
I get the feeling (from me and others) that circles are more likely to cause people to comment on their feelings than are other types of monuments. Ergo, the more complete the circle, the more potent it's... whatever it is...

I wonder if I'm Austin McSherry, condemned through my sins, to be imprisoned by rationality...