## Strauss: The coffee pot question

When I became chairman of my department a few years ago, I moved from my office far down at the end of the hall to one much closer to the center of action: the tea room! I make a lot more visits there than I used to, and began to notice a frustrating pattern:

Far more often than seems reasonable, there’s not even a full cup of coffee in the coffee pot! Once again, someone has left a nearly empty pot with no regard to the next person (me, whine)!

This seems to happen so often I began to wonder what kind of boors I’ve been working with all these years. They seem like nice people and all, but…?

And then I realized: there’s a perfectly logical reason, a mathfactor puzzle, if you will, that explains this phenomenon perfectly, no boors required, no special tricks, just sensible activity by all. My faith in my colleagues has been restored.

Why is it that on average I see an emptier rather than fuller coffee pot?

PS let us know what works for when we return…

1. ### Harry Kaplan said,

November 30, 2011 at 4:09 pm

It sounds like there is a quasi-mathematical explanation out there for the empty coffee pot phenomenon. What I have to say isn’t that clever, but it is based on actual experience with communal coffee pots.
The main point is that coffee gets stale as it sits, and stale coffee can taste pretty bad. Therefore there is not motivation for anyone who sees an empty pot to make a fresh one unless s/he actually wants a cup. So whoever takes the last cup isn’t doing anyone any favors by making more. Also, I don’t know if anyone checks in on your department’s tea room – departmental admins are probably a luxury at universities these days – but, if so s/he might just dump a pot that was obviously old and stale.
Random notes. Since anyone who makes a pot is going to take a cup, no one coming into the room will ever see a full pot. And if several people come in together to get coffee, which does happen, there you go. There are probably some specific times in the day (like right after lunch) when there is an abnormal run on coffee, and that can draw the pot down. Finally, the painful truth is that a lot of people are just too lazy, or more kindly in too much of a hurry, to make a fresh pot, so the pot will stay empty even if coffee was desired.
Since I couldn’t provide a truly clever coffee answer, I’ll present you with a good coffee question once posed by someone much cleverer than I: Martin Gardner. Suppose you have a cup of hot coffee and put an appropriate amount of cream in it. Assume the cream is a lot cooler than the coffee. Making any reasonable numeric assumptions you want, is the coffee likely to cool off at a faster, equal, or slower rate than if you had left it black?

2. ### strauss said,

November 30, 2011 at 4:14 pm

3. ### martin said,

December 5, 2011 at 8:32 pm

the coffee evaporates.
how much of a factor this is obviously depends on the temperature.
OR
with conical shaped (narrower at top) coffee pots half the volume will be concentrated near the bottom so it may look emptier than it actually is…
OR
of the people who want a cup of coffee, only a subset of those people will want it badly enough to be willing to make a new pot if they see that there’s only one cup left. so fewer people go for coffee when there’s only one cup left (or i guess less than 2)