The Eleatic hangover cure (from MIT's open courses online)

[The Straight Story]

It’s well known that one way to cure a hangover is by a “hair of the dog”—another alcoholic
drink. The drawback of this method is that, so it would appear, it cannot be used to completely
cure a hangover, since the cure simply induces a further hangover at a later time, which must in
turn either be cured or suffered through.

But, if you think about it, there is a way to completely cure a hangover using a hair of the
dog. Suppose (1) that there is a simple and direct relationship between the amount of alcohol
consumed and the duration of its effects, so that, for example, a pint of beer induces an hour’s
drunkenness, followed by an hour’s hangover, with smaller quantities of alcohol corresponding
to proportionally shorter periods of drunkenness followed by shorter hangovers. Suppose also
(2) that a hair of the dog works because drunkenness masks the pain of a hangover. I will speak
loosely: when a hangover is masked in this way, I will say that the hangover is “cured”, though
perhaps it would be fairer to say only that its symptoms have been relieved.

To cure a hangover using a hair of the dog, start drinking at a time when you are not drunk,
and have no hangover. Drink a half a pint of beer, and wait for half an hour until you are just
about to get a hangover. Then drink quarter of a pint of beer. Wait quarter of an hour, until you
are just about to get a hangover. Then drink an eighth of a pint of beer. And so on... After an
hour, you have drunk a pint of beer and it has not given you a hangover. Every incipient hangover
you might have had was cured by a further drink.

Objection: No publican will sell you the infinite number of drinks that you require, or stock
1/64th pint glasses!

Reply: You don’t have to buy an infinite number of beers, just take an infinite number of sips
out of an ordinary pint.

Objection: But seriously, somewhere along the line you’ll have to do something physically
impossible. You’ll have swallow beer ever faster, until beer passes down your throat at greater
than light speed. For that matter, owing the atomic nature of beer, eventually you’ll reach a point
where you can’t divide the remaining beer in two without ending up with something that is no
longer beer, or no longer contains alcohol.

More here:
http://www.otago.ac.nz/philosophy/Staff/JoshParsons/papers/hangover2.pdf

MIT courses online here:
http://ocw.mit.edu/index.htm

[Cirque du So-What]

1. I went to high school with the executive director of MIT's OpenCourseWare program

She was class valedictorian (natch) and a heckuva nice person. I was surprised to see her name when I visited the OCW site, but not TOO surprised.