Funny Word Order in a Poster Advertising a Study on Word Order

I like linguistics, although I don't know much about about it. (Much of what I know comes from reading Language Log, which should be on your blogroll.)

A few weeks ago I was at McMaster University, and I saw this poster advertising for participants in a study about word order:


Mastering the correct word order in English often seems one of the hardest tasks for German and French speakers. French mathematicians, for example, often write things like "We study here the case x > 2" instead of "Here we study the case x > 2".

The funny thing is the bizarre word order in the sign itself! Maybe it was deliberate, but I still found it amusing.

In case you can't read the text, here it is:

We are seeking German language speakers from Austria, Switzerland, Liechtenstein or Germany for a linguistic study on the relation between word order and articles currently living in the Hamilton area...

I had to read it three or four times before I realized they were seeking German language speakers currently living in the Hamilton area.

"Any" Considered Harmful

Edsger Dijkstra wrote a famous letter in the Communications of the ACM that appeared under the heading "Go To Statement Considered Harmful".

I'd like to make a case against the use of "any" in mathematical discourse.

The problem with "any" is that it can mean both "for all" and "there exists", and it's not always clear what is meant. "It's true for any x" probably means "for all x". But "The theorem is true for S if any element of S is a square" probably means "it's true if S contains at least one square".

I was just attending a meeting at Dagstuhl in Germany where one speaker said something like "If L is regular, then u is equivalent to v if and only if for any state q of the minimal DFA for L we have δ(q,u) = δ(q,v)". Now if you know the theorem, the meaning is clear. But if you don't, you might be left wondering, does he mean "u is equivalent to v if there exists some state q such that δ(q,u) = δ(q,v)" or "u is equivalent to v if for all states q we have δ(q,u) = δ(q,v)"?

Because of this ambiguity, I think we should avoid the use of "any" in mathematical discourse. We can replace it by "all x" or by "some x", according to what we mean.

Who's with me?