Tuesday, December 10, 2013

Better than perfect

A necessary and sufficient condition for a student to have perfect performance on a calculus exam is to correctly, perfectly clearly and with perfect elegance answer every question within the time allotted. But what if the student also includes her proof of the Riemann Zeta Conjecture on the last page? Hasn't the student done better than perfect?

Well, the student hasn't done something more perfect. But the student has taken her answers above and beyond the nature of a calculus exam. So, yes, while one cannot be more than perfect, one can go above nature. Perfection is not the same as maximality of value.


SMatthewStolte said...

When the student is writing her impressive proof, is she (in that act) taking the calculus exam? Or is she doing something else?

Alexander R Pruss said...

Good point.

Vary the case. Student is doing a graduate-level exam in number theory. She is asked to prove some known theorems about the distribution of prime numbers. She gives an elegant proof of the Riemann Zeta Conjecture and shows how the other theorems quickly follow from it.

Heath White said...

I think the general moral is that "perfect" is a partial predicate. The full predicate is "perfect at X" or "a perfect F." Then "better" is (at least sometimes) a non-partial predicate, such that a perfect F is better than a perfect G. Or maybe: "better" is a partial predicate but can be applied to wider domains, so e.g. a perfect number-theorist is better, in a mathematical way, than a perfect number-theory-exam-taker.

Dagmara Lizlovs said...

If the student is doing stuff like this in Calculus 101 then maybe she is taking a class she doesn't need to be taking. She needs to be in a way more advanced class at the graduate level, because Calculus 101 is nothing but an easy A. This is like beating up on bantam weight boxers when one should really be in the welterweight class. Either that or she really wants to impress everyone.

Alexander R Pruss said...

Or the university has bad policies and refuses to waive prerequisites.

Alexander R Pruss said...


You may be right.

If so, then the big question for perfect being theology is: What is it that the perfect being is perfect at?