Flattening the curve! Flattening the curve!
We shall come rejoicing, flattening the curve!
Our whole country is playing limbo with hospital capacity as the bar.
I do love a curve. One of my earliest memories was seeing Koko Head Mountain in Oahu, Hawaii, from the coast. To your left the mountain rises steeply toward a summit, just like the curves of infected numbers observed in a pandemic, such as ours.
At the summit it flattens off, reaching a highest point. After that, it drops off just like it rose up, and the whole curve looks like the familiar bell curve we’ve seen so often.
I just lied. No, it doesn’t drop off the way it rose up. The curve isn’t symmetric about the peak. What you actually see is a slower descent than the rise. You see what appears to be a gently sloping plateau.
Which, if you’ve paid attention to what various experts have said regarding the spread of the novel coronavirus, is just the sort of curve they predict. Their statistical models show a steep rise to a peak, followed by a slow descent as more and more people survive the disease with some immunity, and their presence in the population gradually reduces the rate of spread of new cases.
I love math but can’t stand statistics. I hate statistical modeling.
My favorite statistics story: In World War II, the Royal Air Force became alarmed at how many of their planes were getting shot down by the Germans. They thought maybe the planes needed more armor. But too much armor, and the planes couldn’t fly. Someone got the idea to look at planes returning from raids and see where all the bullet holes were, thinking, “We’ll add armor only where the planes are getting hit.”
Sure enough, there was a clear pattern to the bullet holes. The Germans couldn’t seem to hit the nose of a plane. Mostly, they punctured the wings. So, they added armor to the undersides of the wings.
The punchline: A mathematician stepped up and pointed out that, since they were only seeing the planes that returned, their sampling was incomplete. Planes were getting hit those other places, and not coming back.
That story illustrates a great pitfall of statistical reasoning. Statistics is about measuring what you don’t know. Get too good at it and you can easily forget to keep looking for new knowledge.
Take “grading on the curve.” Above, I alluded to the bell curve, aka, the truncated Gaussian distribution.
Teachers love tests that result in scores that fall along a bell curve. It’s a cinch to grade such tests. Grade by percentiles. Let the top 10 percent get A’s, the bottom 10 percent fail, the next highest and lowest 20 percent get B’s and D’s respectively and the remaining 40 percent clustered in the middle get the C’s.
The problem with all this is analogous to the problem with counting bullet holes in bombers. The very fact you succeeded in getting a Gaussian distribution means you can’t see what, if anything, the students learned from your teaching. For all you know, the scores are randomized because your students came to you with random knowledge of the course material, and all you’re seeing is their demographic randomness.
I had a math teacher in middle school who taught nothing whatsoever. He assigned homework, collected previous assignments and spent the remaining class time, 45 minutes, talking about improvements he was making to his Mercer Island house. He was so proud of the nice bell curves he got on his tests. He was oblivious to the fact that his test results were a test of his teaching; the fact that he always got such nice bell curves consistently demonstrated his failure to teach.
All my life I’ve had people say to me, “Hey, you’re good at math, right? Help me win at gambling.” They want tips on beating the odds.
Usually, I say to bet on horses, the stock market or elections, where you can get an edge up on others by knowing things.
But, really, the best approach is to start your own casino or insurance company, or become a bookie or stock broker — those profit most from gambling profit on other people’s risk-taking.
Not everything is random. We learned last week that up to four times as many Black Americans as white Americans who tested positive for the coronavirus have died from it. I’m betting that’s not random.
Dr. Wes Browning is a one time math professor who has experienced homelessness several times. He supplied the art for the first cover of Real Change in November of 1994 and has been involved with the organization ever since. This is his weekly column, Adventures in Irony, a dry verbal romp of the absurd. He can be reached at drwes (at) realchangenews (dot) org
Read more in the Apr. 15-21, 2020 issue.