A pigeonhole problem

Posted on 11/04/2013 by Peter Cameron

Pigeonhole

The simplest form of the pigeonhole principle says

If n+1 letters are put into n pigeonholes, then some pigeonhole must contain more than one letter.

This result can be quantified, extends naturally to Ramsey’s Theorem, and lies at the base of diophantine approximation and other things.

But it was borne home to me last week, when I chaired a public lecture by Colva Roney-Dougal on the mathematics of communication, that there are in fact two kinds of mathematicians: those who put letters into pigeonholes, and those who put pigeons into pigeonholes.

Which kind are you?

It seems vitally important not to mix the two kinds!

About Peter Cameron

I count all the things that need to be counted.

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5 Responses to A pigeonhole problem

Jon Awbrey says:

11/04/2013 at 11:14

Moi?

I’ve always had more trouble with the communication of mathematics than the mathematics of communication.

Reply
Ursula Martin says:

17/04/2013 at 19:29

They are doos, and they live in doocots….
http://ihbc.org.uk/context_archive/109/dovecote/dovecote.html

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- Peter Cameron says:
  
  18/04/2013 at 10:04
  
  Excellent! Next year I shall lecture on the doocot principle …
  
  Reply
Jon Awbrey says:

18/04/2013 at 01:50

Pidgins in Pidginholes?

Although it was well understood that linguistic processes are in some sense “creative,” the technical devices for expressing a system of recursive processes were simply not available until much more recently. In fact, a real understanding of how a language can (in Humboldt’s words) “make infinite use of finite means” has developed only within the last thirty years, in the course of studies in the foundations of mathematics.

— Noam Chomsky, Aspects of the Theory of Syntax (1965)

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