Set Phasers on “Wedgie”
I just half-read a recent article, which points out that people who are really good at math tend to be good at ballpark estimates.
This is not news. Everyone who goes past second-semester physics knows this. How many piano tuners are there in Chicago (here’s a hint: divide the number of community organizers by ten)?
Here are a couple of things people who are ignorant about math and science don’t realize. First, once you get past your first year of college, all hard science is math. Second, no real scientist cares much about exact figures until it’s time for a real-life application. Scientists estimate all the time.
I say this with some irritation, because I’m a former scientist, and I’m very used to making ballpark estimates, and I get “corrected” a lot by people who don’t know anything about using numbers. For example, when making a practical calculation in real life, I might say, “Let’s say the tread length of a tire is three times the diameter.” And some…helpful person…will pipe up and say, “Actually, it’s more like 3.1428!” Like I have never heard of pi.
I’ve forgotten most of what I know about science and math, but I’m not stupid. I can calculate sines and cosines with a pencil, to any number of decimal places you want. I know what pi is. I know what radians are. I know what a unit circle is. You’re not helping me when you tack 0.1428 onto 3 for me. It’s like offering training wheels to a professional bicycle racer. Okay, a fat retired professional bicycle racer. You get the idea.
In the real world of science, nobody is impressed when you know the value of something to ten decimal places. That’s grunt information. Let the entry-level engineers worry about that; it’s what calculators and computers are for. The highest and best use of the human brain, with its capacity for all sorts of abstract thought, is not calculating silly figures any six-year-old with a ten-dollar calculator can generate. The hard work is in understanding complicated concepts and manipulating them in your mind. Variables are for thinkers. Arabic numerals are for people who work on assembly lines.
If you’re in a room full of scientists, you can round eight hundred and thirty-seven up to a thousand, and nobody will even cough. They understand. When exactitude matters, it matters. The rest of the time, it’s a hindrance and a pain in the butt. If scientists liked getting bogged down in difficult numerical calculations, they would never have invented algebra or the metric system.
This is why, in the movie Rain Man, Dustin Hoffman was not working for NASA. At NASA, nobody cares if you know how many toothpicks are on the floor. They are not going to give you a job just because you can calculate square roots instantly. That stuff is useless. It might have been important in 1944, when we were using clunky IBM machines to do calculations to help us build the atom bomb, but probably not even then. Nobody wants to hear about the trees. What matters is being able to see the forest.
I remember back when liberals were lying about Saddam Hussein’s uranium ore. They claimed it didn’t exist, but there were actually 500 tons of it. Using ballpark figures, I came up with a guess as to how many bombs you could make with that much ore. And I was wrong. But I was so close, it didn’t matter that I was wrong. My point was that it could make somewhere around a hundred bombs, and the actual figure was not far from a hundred. A real nuclear engineer, Ward Brewer, did a more exact calculation, which is how I know I was wrong, and also how I know my answer was useful and sufficient. ONE bomb would have been a lot, to the people in the vicinity when it went off. The most fundamental point was to show that that ore could do a lot of damage, and I’m pretty sure I succeeded.
When my grandfather died, and I was sitting on the runway, getting ready to fly to his funeral in Kentucky, I thought about all the cigarette tobacco he had grown in his life, and in a few minutes I was able to calculate that my family had probably given about ten people lung cancer. I thought about that, because the family was going through a lot of misery, and it seemed as though we were being repaid for something. If I were obsessed with exact figures, I would never have been able to do the calculation. Maybe the real number is five. Maybe it’s twenty. If you want to get philosophical about it, there is no real answer. But ten is a useful estimate.
There are many examples in science where a result that is off by a factor of two is perfectly acceptable. If you’re a smarty-pants who loves correcting people with exact numbers, that will probably depress you. Well, it should. You ought to know whether or not you’re a scientist by now. If you’re not…shut up.
Many of the figures we spout and use with confidence are approximations. The sun isn’t really 93 million miles away. The population of the US isn’t really 300 million. Come on. For crying out loud, pi is an approximation, even if you take it to three thousand decimal places.
Scientists have a word for the numerals in a number, which they consider meaningful. They call them “significant figures.” What does that tell you about the ones they leave out?
I think Star Trek is one reason people get overly excited about highly accurate figures, which are what real scientists and mathematicians call “trivial.” Back in the day, very often, Kirk and Spock would find themselves in a pickle, and Spock would say something ridiculous, like, “Our chances of survival are approximately 1 in 3457,329.02304730979.” And Kirk, who never thought about anything more complicated than scoring with alien babes without revealing his girdle or losing his wig, would buy it. And of course, there was no way Spock could back up that figure, and even if he had, there is no way you could have called it “approximate.” When he said “approximately,” he was just being an ass. Like, “I could give you ten more decimal places, but it would do you no good, because you would still be the descendant of a monkey.”
You have to remember: Star Trek was not written by scientists. It was written by chain-smoking TV writers with big hard livers, liberal arts degrees, and deadlines. Even TNG, which seems to have gotten some occasional input from scientists, had some pretty unscientific dialogue. I remember somebody on the bridge saying the temperature of something was like 7 million Kelvins below zero, or something like that. You can have a positive temperature of 7 million units. In the negative direction, there’s a floor. Off the top of my head, I think 0 Celsius is +273.15 Kelvins. Zero Kelvins is the absolute bottom. You can’t get any colder than that, even in February with the windows open and your hand down Hillary Clinton’s blouse.
You’ll notice I’m not checking the Kelvin thing, any more than I checked to see if the first four digits of pi, past the decimal sign, are .1428. That’s because IT DOESN’T MATTER. The concept is what matters.
So no, I’m not surprised that a good estimator might turn out to be a good mathematician. It’s probably surprising only to the kind of people who write newspaper articles.