27 March 2009

What is "classical"?

John Cook quotes a definition of "classical", due to Ward Cheney and Will Light in the introduction to their book on approximation theory. Basically, something is "classical" if it was known when you were a student.

The problem with this definition is that it depends on the speaker, which is really not a good property for a definition!

6 comments:

Anonymous said...

My feeling is that "classical" is a term that is (and should be) deliberately vague. In any case, it surely depends on the field, no? In computer science, results from the 60's and 70's are "classical", whereas I don't think one would necessarily call results in number theory from the 60's and 70's "classical" (unless we are talking the 1860's or 1870's :)).

unapologetic said...

I go with Baez, Kauffman, and that lot. "Classical" deals with Cartesian categories. Other non-Cartesian monoidal structures get lumped into "quantum".

Michael Lugo said...

John,

I'd argue that that's a different word "classical" (even though it's the same sequence of letters) -- it's the "classical" of "classical physics".

unapologetic said...

But it gets used in general mathematics. Like, "classical" vs. "quantum" topology. Which has almost nothing to do with c-vs-q physics.

Anonymous said...

So you don't think the definitions of the words "I" and "my" are good?

Anonymous said...

What's wrong with depending on the speaker? It means it's not an abstract mathematical definition, but that's true of most words. For example, "interesting" is a useful word that depends very much on the speaker.