One of the very small details that has tripped me up on my rereading of Infinite Jest is the name controversy of the Great Concavity (as the U.S. calls it) or Great Convexity (as Canada calls it). A wide set of motives are given for the events that lead up to the territory being ceded to Canada, but the gist of it is that territory in northern New York, Vermont, New Hampshire, and Maine was discovered in the late nineties to be heavily polluted and subsequently given to Canada.
The problem is that the line described in the text looks like this:
So the border looks like a convex curve from the U.S.’s side and a concave curve from the newly-Canadian side. So why are U.S. citizens adamant about calling the polluted territory the Great Concavity and the Canadians equally adamant about calling it the Great Convexity?
The answer lies in the question of whether either nation wants the disputed territory: as the land in the Great Concav-exity is polluted and irradiated beyond rectification, neither the U.S. nor Canada want the land. Therefore, the U.S. views the territory like this:
And Canada like this:
Simply put, this territory dispute differs from most other disputes by the fact that neither nation wants the territory at dispute. The names they give the territory, therefore, refer not to their relationship to it, but to the other‘s relationship to it. I.e., the U.S. refers to it as the Great Concavity because, from their perspective, it is a concave curve in Canada’s border, and Canada refers to it as the Great Convexity because it is a convex curve in the U.S.’s border. Most territory disputes are inclusive, so in naming the territory in question nations make it appear that the territory is already in their possession, and to disagree with them would be to enact a contradiction in language. But as neither the U.S. nor Canada want the desolated land in the Great Concav-exity, so in naming the border, they refer to the other nation’s land, not their own.
It’s confusing at first but completely plausible once you get your head around it, just like all the other little downplayed effaced jokes in Infinite Jest.