the leghorn theorem

On a more recent trip to Chicago (this is now a Portland-based food diary about Chicago-based food) I read The Man Who Loved Only Numbers, a biography of Paul Erdös. Who was, in addition to being an under-sexed ampethamine addict, just your garden variety mathmetician. Of particular interest, to me, was his work with combinatory logic rooted in a generalization of Dilworth’s Lemma – “the partial order width of a set P is equal to the minimum number of chains needed to cover P.”  This can be expanded to a node-based model called the Theorem on friends and strangers — a simplification of F.P. Ramsey’s great work, who Erodös absolutely adored

It’s also excellent airport fodder; if the line at the Concouse C Starbucks has more than 6 people you can consider any pair, at least three pairs will either be mutual acquaintances OR at least three pairs will be mutual strangers. The fun doesn’t stop, try parsing the entire crowd huddled around United’s baggage claim. But you have to use a set of at least 6 people or else the theorem does not hold.

  For when there are too few pairs for the theorem, I present Leghorn chicken.

  Leghorn Café is empty at 7am, except for yourself and the cook, with whom you are mutual strangers. The cook is a bit suspicious of you until you announce, to the silence, that you do not Yelp.

  A pair of maple-sage house made sausages, who are mutually acquainted.  

The spicy chicken is absolutely acquainted with a side of verde ranch but they are so, so bad with hot coffee. You order a Mexican Coke at 7:15am. The biscuit is a vision, it belongs in The Book!, which is where Erdös put all of the proofs that were heavenly and perfect.

Leghorn Cafe

600 N. Lesalle St.

Chicago, Illinois

The Man Who Loved Only Numbers: The Story of Paul Erdös and the Search for Mathematical Truth by  Paul Hoffman (1998)


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