The Greatest Theorem

This article is part of a series on The Structure of Theorems. See also:
1. Theorems’ Almanack; 2. The Greatest Theorem; 3. Game of Theorems

Ordinary words can take on new meanings within math. Trivial, for example – though hardly part of our daily discourse – appears frequently, describing something subtly in-between “true because of definitions” and “true for reasons simpler than befitting the seriousness of this situation”. A priori is perhaps more interesting. Though it’s traditionally a philosophical term – describing facts knowable without appeal to the senses but rather to logic alone – in math, further logical investigation fills empiricism’s vacant role. “A priori, we do not know whether the following property holds,” a mathematician might explain. “But upon appeal to further (i.e., logical!) mathematical arguments, we’ll soon find out that it does.”

It should be no surprise, then, that the apparently innocuous words weaker and stronger will prove sufficiently interesting to occupy our attention for the remainder of this essay. Continue reading


Shandong Twitter


Shandong Province in eastern China, where Chin P’ing Mei was written.

Twitter – and its relatives in the world of instantaneous electronic communication, such as SMS and Facebook – have altered human communication to such an extent as to invite comparison to the advent of the printing press. “Just as the printing press may have caused a neurological re-wiring after the fifteenth century, so too may the Internet in the twenty-first,” suggests Andrew G. Haldane, of the Bank of England, in a speech he gave earlier this year. “But this time technology’s impact may be less benign,” he adds. [1] Haldane cites the work of Nicholas Carr, whose famous book “The Shallows: What the Internet Is Doing to Our Brains” makes Haldane’s warning quite explicit: “[W]hat the net seems to be doing is chipping away at my capacity for concentration and contemplation.” [2]

“Four green lights in a row. #blessed.”, tweets Aziz Ansari’s character in a recent episode of the popular TV show Parks and Recreation. Soon after, a new tweet appears on his feed: “Just hit a fire hydrant, but I survived. #Unbreakable.”

These tweets perhaps exemplify Twitter’s 160-character universe of electronic trivialities and truncated thoughts. They also, though, exhibit what, I claim, is a subtle and distinct brand of humor emerging within Twitter: the ironic and allusive use of the hashtag. We’ll see moreover that this humor finds a surprising parallel in the creative use of poetic allusion pioneered by the 1596 Chinese epic novel Chin P’ing Mei, or The Plum in the Golden Vase.

I’ll investigate and discuss these fascinating forms of humor. Continue reading