Triangles

If you take an equilateral triangle and bisect the base, you can make an infinite number of triangles by simply extending two lines in any direction from the base to touch any of the other two sides (will these lines radiating out from the bisected base themselves always be equal in length?).

This is what my first grader told me, I think, when he came home today. I thought to myself, no way! I had really better get busy with my Cliff's Notes and brush up my knowledge of geometry!

The triangle is a finite area, but since it is imaginary, I should think it would possess an infinite number of imaginary points along each side, especially as we can now get into supertiny measurements. Just as our numbers never reach infinity as they enlarge, but can get larger any time we wish, so there must be an equal amount of endless diminishment that is possible such that we can never reach a smallest line-length.

I suppose I should think about more practical things.

Any attempt to get from mathematics toward any real-life problem always reminds me of the medievals and their questions concerning how many angels can dance on the head of a pin.

I don't think quality can be measured very precisely, since no two people will agree.

Probably a consensus of opinion will be reached throughout a school that such and such is a "good" teacher, or that such and such is a "good" student.

If there were three variables that determined the notion of the good, what would they be? In a student or teacher, I'd look for -- a. gusto in terms of their attitude toward the topic, b. experience c. general intellectual ability as correlated by IQ. Multiply this result by the number of good students in a class, and then divide by the number of mediocre students in the class, and you will have a number that has no relation to whether the class was any good.

Classes that were good, generally everybody in the class agreed that they were good. It's not just the students and the teacher and the subject, but sometimes also the room. One bad student can wreck a class for me. Two bad students (even if I am another student) and the class is just a mess. An ugly room always spoils an experience for me, especially if there are tattered papers and broken maps attached to the walls.

A student's life is reduced to a GPA. Teachers' lives are reduced to a number as well (Rate My Professor). But mediocre classes are rarely ranked in Rate My Professors. Students who loved and hated teachers want to rank. No one else is motivated.

Voting works too in this way -- it comes down to a number of partisan votes for each. Few can be bothered to get out and vote unless they're really fired up. Reviews generally go that way, too. If you just hate a poet, you let them have it, and if you love a poet, you want everyone to know, but if you're just bored, you say nothing.

A poet or teacher or student may be an idiot, but tell one joke that you remember the rest of your life. These are the black swans of an experience that aren't put into the overall rating.

If a vote is valid (unlike the recent vote in Myanmar), this is supposed to give us a sense of the electorate's perception of the quality of the various candidates. Aung Suu Kyi was released JUST AFTER the election, which is supposed to be a sign of the election's fairness.

Numbers help us to represent things (approval ratings), but they don't catch the entirety of an experience, and may distort it. Most Republicans think Bush has a high IQ, and think BO is an idiot. Most Democrats think Obama's IQ is stratospheric, and Bush can barely feed himself. By reducing an experience to a number, it helps us to grasp it more clearly, but too often it's just a prejudice. Numbers are no more objective than feelings, when they're based on feelings.

Love triangles are generally a mistake in life, but often the motor behind good novels. Ranking a novel however has nothing to do with a numerical ranking. It has to do with a feeling. But, it seems, we can give this feeling a number. What does giving a feeling a number really mean? Can you feel a number?