One of my earliest memories of mathematics goes like this: I’m three or four. I’m sitting on the driveway at home. My sister Ava tells me that if you walk around the world, your head will travel further than your feet. This seems … possible to me, and also alarming. I grab a basketball, and see how many finger lengths it takes me to walk my finger around the surface of the basketball. I imagine shrinking the ball down, and see that it would take fewer fingers to make it all the way around. I imagine blowing the ball up much bigger, and see that it takes more fingers to move around. I imagine a little boy walking around the earth as if his feet were on top of one ball, and his head were inside a different, larger ball. It takes more fingers to go around the foot-ball than it does the head-ball. There’s a pattern here! If I know how big the ball is, can I tell how many finger lengths it takes to go around the ball?
I head to the oracle: I ask Dad when he gets home from work.
He puts down his briefcase on the table, and then goes to the whiteboard in the kitchen. This whiteboard normally had lists of groceries, and grandma’s phone number, and whose turn it was to empty the fish-smasher – which is what you call the dishwasher after your older brother gets a hold of the marker. Dad starts talking and draws some squiggles involving the letter “r”, the number 2, and a weird number called π.
It’s difficult to remember much about this story, because memory is a fault mechanism. I’m not sure how much of that ‘fingers moving around the basketball’ went. I do, however, vividly remember seeing that squiggly letter up there on the board, and being told that it was another number, like the old favorites 3 and 4, except it was different because it was squiggly and you couldn’t count it on your fingers. The little 2, hanging out over that letter r – what was that all about? That was just the icing on the cake of … what is this? What on earth is this?
I had to learn more.
At some point in my childhood – i’m not sure where it was in relationship to learning about this strange number ‘π’ – the number 100 stopped being a stand-in for ‘infinity’ and just started being a hundred, the result of 10 times 10, the number of dots on the yellow Kumon board with the brown-and-green magnets, or the number of seconds in just over a minute and a half.
Before that point, a hundred dollars was a crazy amount of money, enough to buy a helicopter or a castle or a dinosaur with a harness that you could ride. After that point, a hundred dollars was still a lot of money, but with a bit of math you could figure out that it would take a few months before you had that much in allowance by doing chores. It was not enough to buy a Sega Genesis, but it was enough to buy two new games for the computer. It was not enough to buy a car, or a house – those things cost much more. There were much bigger numbers than a hundred, you see, and a hundred was just one small step of a giant sequence that went on forever.
That difference – one hundred starts out as ‘infinity’ and then ends up being just a simple number you can count to in a few minutes – that’s kind of how Dad showed the world to us. At first it was this impossibly large place, and so many things in it were so massive and insurmountable, like walking all the way around the world on your own, just to see how much farther your head would go than your feet. Either way at the end, you’re exhausted, even if it’s just in your imagination. But Dad broke those things down for us into concepts, typically involving numbers, that made the world seem much more tractable.
We drove up the 1 highway, from LA to SF, in the late summer of 2006. I’d spent all summer at Harvey Mudd College outside LA, and wanted to visit my friend in San Francisco. Dad happened to be in Pasadena for work that Friday, and needed to be at a Conference in SF the next day. He travels all over the world for business, and has for years. Strangely enough, there are only two times I can remember him needing to be in San Francisco, and both of those times happened to line up perfectly with my schedule when I happened to be there. How lucky!
On that drive through the August fog, on windy California roads between the mountains and the sea, we talked. We talked about business, about life, about work, and I started to understand just how big the adult world really was, and how much of it this man had seen. He talked passively about how he’d been in line to be promoted to a high position than he was at currently, but at the last minute his company’s CEO was replaced by someone else, someone he went to high school with and had better grades than – and this guy turned the promotion over to someone else.
He was this close to making a million bucks a year, and he described this passively, with no sense of regret or anger or frustration, just the same calm matter-of-fact tone you’d use to explain to someone else that you could factor a polynomial using the process of synthetic division. The lack of passion with which he described that fleeting encounter with a chance at big money – that stuck with me. He said you could spend your whole life regretting the various way things didn’t work out, and it wasn’t really constructive. He’s right.
Not only does mathematics help us understand the world better – it can let us prove things. Certain proofs are done not so much with words but with actions. I can prove that I have access to your private key by the action of signing something with your private key.
Dad showed his love for us with his actions – with the sacrifices he made in his career to keep us near our cousins and grandparents, and with the piggyback rides he gave us when we were little. He ran out on the court to tie my shoes when I played basketball in grade school, and he drove two days across the country to pick me up when I really needed help a few years ago. Through his actions, much moreso than anything else, this man is proof of the power and resilience of love.