Where are we going to hang? That's the essence of the hanging problem. And it's different for every person, and, because of this, for every group of people it is defined by its constituent members and milieu within a macrosystem. In this post I will be talking about collective hanging, but reverse engineering to individual theory isn't hard.
To formulate the hanging problem in any given environment at any given time, we can represent the constraints as a series of monadic formulae, the possible locations as variables, and the satisfactions of those formulae as sets of those variables.
This is less imposing than it appears. Take the following example, chosen to illustrate the timelessness of the hanging problem.
Julian W. W. Coddleswarth: I say!
Jean-Pierre-Claude Frogelé: Indeed! Where shall we ang to-day, ma eenozently Eenglish frond?
JC: Well, of course, one must consider the certainly unsportsmanly modern pricing of suitable tobacco due to the entire globe not being presently subjugated by Her Majesty's Empire.
JF: Ah, ah, but ov caurse. On zee ozzer'and, tobacco eez ardly not a nezzezzitee, wouldn't you zay?
JC: Hardly incorrect, dear chap! And let us not forget that our mutual acquaintance Ozzel will be dropping in this tea time's antecedent hour!
JF: Ozz-elle? Oh dear, we moost caunzeedar a chezzbard.
JC: He will most unequivocally not allow our souls to go unchallenged on the board this day.
All that text, and all it boils down to is this:
- They want to hang at a place that sells tobacco.
- They would prefer to hang at a place that sells tobacco cheap.
- They need to hang somewhere they could play chess when Ozzel shows up.
Of course that's hardly a problem. Frequently, there will be no item that satisfies every condition, and this is when the tough, touchy, friendship-annihilating, morality-wrenching questions start flying like flying fish that can and do actually fly. Does the high price of tobacco warrant that our two fellows reconsider their consideration of that clause? Will Ozzel definitely show up? And why are they bending to his will anyway? Have Ozzel bring his own chess set!
(It's because he's just so cool. I heard he joined the Royal Society at age fifteen... and wears sunglasses to meetings. Sunglasses! I wish I was as cool as Ozzel.)
And so, why am I so interested in this? Consider this modern dilemma. (For the purposes of example, we can use the old stalwart standby, the Venn.)
A, B, and C are, respectively, the set of places that are open late, that have wi-fi, and have soft drinks in free-refill form. My comrades and I have still not managed to track down what place, if any, goes in the center that I have marked with the off-putting green question mark. For instance, the 'H' is the Herman B Wells Library in Bloomington, which is in A because at least part of it never closes and B because it has wi-fi but not C, because it's no restaurant, it's a library, silly. The 'P' is Panera, which is in fact not a library, but closes at 9 pm or earlier daily and so though in C it is not in A. Both, though, are and always will be members of D because, well, I'll get to that in a minute.For the most part, we don't need wi-fi, so unless someone needs to study or we need to work on an internet-integral investment, we can count the intersection of A and C as universally available. With one exception...
See the big red 'S'? That's Steak 'n Shake. Arby's (the 'A'), Donato's, Pizza King, and many other places are open until 11 or 12 or even 1, but only 'S' stays open for 24 hours a day, every day (it would be helpful to have in this analysis included a distinction between "late" and "hella late" but I didn't). In fact, Steak 'n Shake is so exclusive in their owlhood that they've acquired a reputation for it. Before you know it, you can't hang out at Steak 'n Shake. It's just... formulaic. Or, well, I guess. I'm not the one that has the allergy to blasé (though the reaction I have to unoriginality approximates it in this case, I suppose).
So, we can add D, which is the set of all places to go that are not Steak 'n Shake. I should probably have considered this before I drew the diagram because, since 'S' is already placed and it can't go in more than one spot, all that extra space out there is assured to be eternally empty. Indeed, why don't we just go ahead and use this replacement chart. It's marginally less correct, significantly more informative, and on the whole just darn sad.
What a...
