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On the Utility of Mathematics

I just had an interesting exchange with the grandmother of one of my PreCalculus students. She came into the classroom and looked at all the symbols and whatnot on the board. Then she said, "So tell me, how does all this math help you in your life?"

I said, How does music help you in yours? They are the same thing.

Math thinking

Stand by...

old guy thinking

When I was young I knew everything.

Now I'm old and I know very very little. Replacing knowledge is opinion. I had opinions when I was young, as well as certainty, but they weren't the same opinions I have now.

To my children I apologize for the blunders their father made that they had to live through.

Here's what I have learned after 36 years of being a father, 33 years as a teacher...

It doesn't matter if you eat all your beets. All that matters is that you share food with people who love you, and who you love. Same with veggies in general. When the time is right you will develop a taste for them.

You don't have to eat with a fork when you're little. It's a handy tool and when you're ready you'll pick it up. All that matters is that you share food with people who love you, and who you love.

Doing well in school is nice because learning is fun. It is the brain's endless hobby. But if you are in a setting where learning isn't fun, it's perfectly reasonable for you to ask to be excused. That's not the same thing as refusing to rise to a challenge or to overcome a barrier, but learning is fun and if that is not your experience in school then something is wrong with school, not you.

Until high school, homework is irrelevant and steals time away from more important learning - unless it's some sort of project that you embrace and that your parents or friends embrace with you. Learning is a social activity primarily. From time to time it is a great solitary process, but not as a rule. When you're in high school the value of homework is that you take the time to reflect on neat stuff that class periods don't give you the time to reflect on. Homework is best done jointly with a friend. Doing endless pages of rote calculations (I teach math) does not make you a better person, student, or doctor. Doing repetetive boring work does not build charcter, it crushes it.

Question authority, just like the bumper stickers say. Not because authority is wrong but if it can't answer your questions properly then it's not authority but bullying.

Rules are agreements we make with one another. Most often life is easier if you share agreements with those around you. But there is no rule that says "Daddy knows everything" (sorry, you guys) or that if you're the guy or the dad or the woman or the mom that you have to be obeyed. Leadership does not mean telling people what to do, but making agreements with them about how we will all do it together.

Just because you start something does not mean you have to finish it. You don't. You can change your mind, or take a breather. That's fine.

That said, don't make promises you don't intend to keep.

"Nice" is better than "smart" any day. And if you have a clever wit don't ever use it to make yourself look good at the expense of others. Laughter can be vicious and cruel when used in this way and nobody likes that no matter how hard you make them laugh.

You are here first and foremost for yourself, not for other people. The trick is that you only become yourself or grow to like yourself by giving yourself to other people. It's a strange thing but true.

Love is not just a feeling. It's an active verb. Don't ever forget that.

You don't owe anybody anything that is burdensome unless carrying the burden makes your heart sing. Having one's own children makes the heart sing, in my experience. A life best lived is, in fact, lived for others. This is a conundrum, at least on the surface.

Here's a funny thing I have learned that I cannot explain or even articulate very well - you must learn to listen to your heart rather than your mind. Your heart knows truth, while your mind is easily confused.

These are true statements, in my heart's opinion.

Alex-less thinking

Alex the African Grey parrot is dead.

This is a loss to many people, and a loss to me. For 31 years (out of an anticipated lifespan of 50-70 years) Alex has been blazing trails in science. He was purchased in a pet store in Chicago on July 5th, 1977 by a researcher named Irene Maxine Pepperberg. She deliberately allowed the store manager to pick out the bird from a group of 12-15 month old African Greys. She wanted the selection to be reasonably random as she wanted to study the ability of such birds (renowned for their ability to communicate since the time of Aristotle) to actually do so under scientifically controlled conditions in order that she might understand their cognitive abilities.

Lots of birds can learn to imitate sounds. I have heard that if you split the tongue of a crow it can learn words, although I have never seen such a thing and cannot understand how such a discovery could ever be made. Myna birds talk, in the sense of reproducing sounds they have heard, although there is no apparent communicative intent. I own an eclectus named Charlie who says "I love you," "Gloria" and a bunch of other stuff mostly in Korean. (He spent his formative years in the house of a Korean friend of Gloria's.) None of what he says seems to have communication as its intent, although some may disagree. Charlie, when I challenge him, has yet to do so.

I heard about Alex several years ago from my friend Liz Lee. Alex, she told me, could use words to communicate ideas, and could put together words he already new to express new thoughts. I'm not sure I entirely believed her at the time, but it really stuck in my mind. An example (true) is this: Alex had learned to describe objects by color, shape, size, number and several other attributes (read the book.) One day he was given corn on the cob to eat without being given its name. The next day he asked for "more long yellow... more long yellow...'

I like ideas. I love math and teach it because it is the study of the interplay of pure ideas stripped of the mundane reality of specific meaning. (My interest is evidently in what is called pure mathematics rather than applied mathematics in which I have little interest. I don't wish to debate the relative merits of either. I'm old and can love whatever I want. Forgive me Mr. Kite, for thinking your very astute intelligence will have the necessary counter-examples. Logic will no longer change my mind, completely overcome by my affection.) To examine the thinking processes of a bird seems to me to be examining the interplay of pure ideas, and of ideas formed in a very alien brain. (Think T-Rex. That alien a brain.)

So Alex enthralled me and I bought and studied Dr. Pepperberg's very scholarly book, The Alex Studies. It is wonderful, although it ain't casual reading.

It's fascinating and I immediately understood that it was necessary for me to get an African Grey to live with me. Last Christmas I got one as a gift for Gloria. I called her to give her the good news. She declined the gift, sensibly enough, so I bought the bird as a gift for my dog Vinnie. I named the bird Scipio after Vinnie declined to offer any name other that "Arf," which isn't right for a bird.

Scipio, now known as Skippy, is a male. I learned this by paying big bucks for a DNA test, the only way to kn ow for sure short of watching who gets on top under the right conditions, which are not about to be offered.

I planned a sabbatical during which it was my intention to teach him everything that Alex knew, and more. Alex was my ideal, the goal, the dream. He set the bar and he set it very high.

The night before dying he said something approximating this: "Will you be in tomorrow?" to which the answer was "Yes', Ill be in tomorrow." But tomorrow morning, he was dead in his cage. Nobody yet knows why but his vet is returning early from vacation to try to figure it out.

I find the world a smaller place without him. Skippy seems relieved.

Lazy Thinking

I'm on vacation. Sleep, eat, surf (the web), sleep, eat, surf (the web.)

Fin de Siecle Thinking

Alright, fin de siecle is an exaggeration... It might be fairer to say simply "turning a page" but somehow it feels a bit more consequential than that.

I just finished a four year stint as director of a summer school. Capital S summer school. 4200 students, K - 12. SIx weeks, 3 million dollars gross, the most outstanding programs and teachers I have ever seen.

Directing it was exhilarating, but exhausting. The six weeks are the easy part, the really fun part. Staffing it, looking after the logistics, that's the hard, tiring and stressful part. Faced with some health issues that gave me pause to reflect on the meaning of my life I decided to step down, take a year's sabbatical and go back teaching, which is what I love to do.

So I was expecting that yesterday would be my last day at work for a year. But it won't be. I was asked to fill in for a math teacher who was transferred at the last minute. I was delighted to agree to do so. (But keep it secret. Conventional wisdom is that I am making a huge sacrifice and "taking one for the team." That's not the case at all. I was almost dreading the sabbatical and wasn't entirely excited by the projects I had undertaken to complete while on sabbatical.)

So I have 3 weeks off and then back into the classroom.

Here's the kicker. I will be teaching pre-calculus, and I haven't looked at that stuff in 40 years.

Heads up.