Saturday, February 27, 2010

The Fifth Episode of Happiness

It WAS the calculus lecture! Tied with the chemistry class! Proof that truly exceptional and exciting teaching can reach even the dullest and most unpromising student. Both teachers had remarkable energy and clarity and a clear gift for engaging everybody in the room, even when the room was a large lecture hall.

Now, when I say "the dullest and most unpromising student," that truly is me. I got a C in Algebra II and never got past trig. I have no memory of learning anything at all in high school chemistry and never studied chemistry in college. My mission was to see if I could learn something from both classes yesterday - preferably something life-transforming - and I did!

In the calculus class, Mary Nelson put up on the board some (to me) hideously long equation. I may have written this down wrong in my notes, but it was something like:

5 + (2n to the 4th power)
(6n to the 4th power) + (2n to the 3rd power)
where the limit of n is infinity.

Are you all with me so far??

Dr. Nelson then asked the class how many of them could see instantly that the answer was 1/3. Certainly I hadn't seen this! The reason why is something called "dominance of powers." Dr. Nelson said, and these were the words that changed my life: "Infinity to the 4th power is huge compared to 5."

This means (I think) that when you are dealing with something as big as infinity to the 4th power, you can just not bother with the part of the equation that has 5 in it. Indeed, you can not bother with the part of the equation that has infinity to the 3rd power in it.

Now, she also said that "Dominance of powers only applies to polynomial over polynomial." But I think she was wrong there. I think it applies to everything.

What are the really big things in your life, your infinity to the 4th power? THOSE are the things you need to be focusing your energy on, and your worry, and your delight. You can just skip worrying about 5 at all. Or even infinity to the 3rd power. You could say (I could say) that the basic point was "Don't sweat the small stuff" - but it's only because the big stuff, infinity to the 4th power, matters SO MUCH.

Dr. Janet DeGrazia in the chemistry class was also truly exceptional. There they were studying thermodynamics, and I did have the edge there, over the calculus class, that at least I had HEARD of entropy (and actually knew, sort of, what it was). Dr. DeGrazia showed a video of a car being blown up by something called (I think) thermite, and as she turned to a discussion of gases later in the hour, she had balloons in liquid nitrogen that changed size amazingly when released into room temperature air.

Here was her life-changing comment. In talking about some chemical reaction, she said, "You have to put energy in to break bonds." Hmm. I went up after class to tell her how great the class had been, but also to ask her, "What happens when you MAKE bonds?" She said: "When you make bonds, you get energy back."

Ooh! Let me repeat: "When you make bonds, you get energy back." So: breaking bonds TAKES energy. Making bonds CREATES energy. (Well, I guess there is conservation of energy, so it would be more like: Making bonds RELEASES energy. Anyway: gives you energy back.)

So maybe making bonds is like infinity to the 4th power! It's what really matters in life. Maybe the only thing that matters.

Or so concludes this philosopher and children's book writer upon observing her first chemistry class in forty years and her first calculus class, ever.


  1. Amazing. I'm completely with you. (BTW, I never got TO trig -geometry was the last of it for me).
    Connections...yes, absolutely what really matters. And speaking of connections, I married a mathematician...

  2. Thank you for writing this, Claudia. SW