Weasels: So after all the talk this week, I find myself puzzled by the logistics of the circular firing squad. What am I supposed to be picturing? Is it an everybody-shoots-the-guy-to-his-left thing or are you aiming at whoever’s across from you through some poor bastard in the middle?
Basmati: Maybe it’s a variation on the handshake problem? Or that scene from Wanted?
Weasels: No, a Mexican standoff traditionally involves 2n handguns where n is the total number of participants, and your linear firing squad generally has n-1 rifles, and in some cases n-2 bullets.
Weasels: Besides which Trump is almost certainly opposed to importing standoffs from Mexico.
Weasels: It’s only a handshake problem if every member of the circular firing squad has to shoot every other member, which seems medically implausible. Presumably it’s the other way round and what matters is that everybody gets shot at least once.
Basmati: Well if everyone has to get shot once we could talk about spanning trees on K_n.
Basmati: What’s the Minkowski sum of firing squads?
Weasels: I’m not interested in a general equation, just the two-dimensional circular case.
Weasels: Well ok, we know that the daisy chain method works for both n=2k and n=2k+1 where n is the members of the firing squad and k is an integer. The crossfire method only works for n=2k and that’s before you’ve accounted for the odds of bullets colliding.
Weasels: Is this backstopped in some way? Doesn’t anyone care about civilian casualties?
Basmati: What if instead we take a lattice firing squad? Or a lattice of firing squads??
Basmati: What if they aren’t arranged in a convex fashion?
Weasels: I think we might be able to solve this as a lattice for any case in which there is an enemy to be executed at the center of the polygon, but I think once the firing squad is no longer convex we’re onto the general case again (circular is obviously a misnomer, except for cases where n—>∞).
Basmati: What if they’re in hyperbolic space?
Basmati: I think that would be appropriate.
Basmati: They can’t shoot each other. They’re all on the edge of the hyperbolic plane.
Weasels: That’s what we do to any journalist caught using analogies without thinking them through.
Basmati: What are they using the analogy for? The election as a whole?
Weasels: The Republicans, typically.
Basmati: So the circular firing squad are armed with elephant guns?
Weasels: Get out of my car.