Additional Math Pages & Resources

Monday, September 26, 2011

Majoring in Arithmetic

Arithmetic is the most fundamental realm of mathematics, used for counting and calculations. It involves number sense, quantity, combining numbers and separating numbers - the traditional operations of addition, subtraction, multiplication and division. These lead to integers, fractions, decimals and related concepts like factors, powers and roots.
This definition of arithmetic comes from a useful book called The Words of Mathematics.

arithmetic (noun, adjective): from the Greek arithmos "number", from the Indo-European root ar- "to fit together." A related borrowing from Greek is aristocrat, presumably a person in whom the best qualities are fitted together. Arithmetic must once have been conceived of as fitting things together, or arranging or counting them. An arith-m├ętic (emphasis on 3rd syllable) series is one in which each term is a fixed number apart from adjacent terms, just as the counting numbers of arithmetic are equally spaced.

It's ironic that the word is related to aristocrat, when today it means basic, or common. It's not really a respectable discipline. We think of the word as child-like, primitive, trade-oriented. It's like Home Economics. Auto Shop.  (Please don't take offense, home-ec and shop teachers!)

Telling your friend that your daughter is at Harvard and "she's majoring in arithmetic" would come across badly, like saying "my son is in the 95th percentile of wood shop students".

In most of our educational system, we prize the high achievers. We want everyone to be in the Gifted class. All students to be College-Prep. All our children to be above average. Garrison Keillor has exploited this tendency in his comedy about a mythical Midwestern town:

where "all the women are strong, all the men are good looking, and all the children are above average," has been used to describe a tendency to overestimate one’s achievements and capabilities. The Lake Wobegone Effect, where everyone in a group claims to be above average, is observed among drivers, CEOs, stock market analysts, college students, parents and education administrators.

A more grandiose term for this human tendency is Illusory Superiority. If you follow this link to the Wikipedia page on Illusory Superiority, you see that we educated folk ought to speak like this:

Illusory superiority is a cognitive bias that causes people to overestimate their positive qualities and abilities and to underestimate their negative qualities relative to others. This is evident in intelligence tests, performance on tasks, and the possession of desirable characteristics or personality traits.

Thus we see ourselves as better than others - not that they are bad, mind you - but just not as good as we are. If we are being gracious, we might not claim to be smarter than anyone else, but:
  • "primus inter pares" (Latin: the first among equals)
  • "All animals are equal, but some animals are more equal than others" (George Orwell, Animal House)
Around thirty-five years ago, just after I graduated from college, an SAT survey was given to about a million students. A full 70% classified themselves above the median in leadership ability, 85% put themselves above the median in their ability to get along well with people, and 25% rated themselves in the top 1% of students.

Optimistic, the positive thinkers would say. Delusional, the pessimists would say. Who is right?

I graduated first in my class in college, the valedictorian, yet for the last 10 years I have been "majoring in arithmetic". Woe is me.