Re: ICT Comments

Alexander Richman <*arichman_at_babcom341.yahoo.invalid*> · Sat, 12 Apr 2003 13:11:35 -0400

At 04:19 PM 4/12/2003 +0000, you wrote:
>--- In quizbowl_at_yahoogroups.com, Alexander Richman <arichman_at_b...>
>wrote:
> >
> > Ok, I wasn't there, and I haven't seen the question, but from my
>point of
> > view, this comment is ridiculous.  Acfraud is lambasting NAQT for
>starting
> > a question with a clue which the experts will know quickly while
>other
> > people will still have a chance later by putting it in (sometimes
>advanced)
> > calculus terms or in more basic terms at the end.  Of course, the
> > "inverse-image" definition is the most general one, but very few
>people
> > meet it before their senior year as math majors, or even in grad
> > school.  I, for one, much prefer this to something with vague
>similies or
> > ambiguous characterizations at the start, which happens much more
>frequently.
> >
> > Alex
>
>Experts? Senior year as math majors? That's an exaggeration.

Maybe this is the whole root of the disagreement.  I don't consider NAQT 
(even ICT) to be a place where only grad students (or beyond) should be 
"experts" in any field for the purpose of askability of 
questions.  Certainly, I don't view an old fogey Ph.D. like me to be the 
right audience. If we disagree at this stage, then I hope we can just agree 
to disagree.

>It's not
>even as if you need to have taken a course in point-set topology to
>have seen this definition; one should at least see it in a real
>analysis class. I'm pretty sure we had that definition within the
>first week of the first math course I took as an undergraduate. I
>expect that even a good *calculus* course, say using Spivak's text,
>might mention this definition at some point.

Good for you.  VERY few people fit under your situation or used Spivak's 
book in their regular calculus course.  Even in real analysis, it depends 
whether it's done in one or several variables as to whether that definition 
will be there.  Not many schools use Baby Rudin any more.

>Even if you think only "experts" could answer the question at this
>point (if so, there were a large number of "experts" at the ICT!),
>that clue is inexcusable in the first line of the tossup. The point
>is, starting a math question with a straightforward definition is
>*always* a bad idea.

So may I ask what you would prefer in this case?  An operator based 
definition in which the most expert will be sitting asking themselves 
whether they want continuous or bounded?  Or perhaps a list of functions 
that might have to be quite long before only the only common 
characteristic, and again the most expert will likely be sitting longer 
than some who know less?  For many mathematical terms, an unfamiliar, or 
unusually formulated definition is often the best way to get an unambiguous 
clue quickly into the question.

>Even if we allow that an epsilon-delta definition
>of continuous, or a definition that says "the limit exists  and equals
>the value of the function," would be answerable by more people and
>could be a giveaway clue, the usual definition should appear
>immediately before that. I think that what I said before bears
>repeating: in mathematics, you must know the definition of a term to
>do anything with it.

No kidding.  You don't need to know all formulations of the definition, 
however.  Certainly, when I teach proofs, I'll use the epsilon-delta 
definition long before I touch on the inverse image definition.  That does 
not make my students' (or my) proofs wrong.

>  This makes definitions inherently giveaways for
>anyone who knows the subject. For almost any askable math term, the
>definition should be the giveaway, because it is the one thing that
>must be known by anyone who uses the term in doing mathematics.
>Granted, there may be rare occasions where an anecdote is better known
>than the actual definition (extending "definition" to the case
>"statement of a theorem", Fermat's Last Theorem provides an example.)
>But what clue for "continuous" could possibly be better known than the
>definition?

If a clue was something like "the absolute value of x has this property but 
the floor function does not," I would guess people who know less would have 
a better chance of guessing correctly at that stage, than people who know 
more.  This may not be better known in the sense of having been heard 
before, but IMO, that does not make it a better clue.

>If you state a less general definition as the giveaway,
>this still doesn't excuse putting the general definition first.
>

I will grant that I have been away from the circuit for a couple 
years.  Maybe the definition in question has become too much of a 
giveaway.  However, I am confident that as related here, it's a question on 
which I could have beaten any of my  (generally more quiz bowl talented) 
teammates based on my expertise of the subject matter.  In my book, that 
makes it a good question.

Alex