Wednesday, March 2, 2016

Acalculia, innumeracy, or numerophobia?

I think there's an epidemic of number-induced brain paralysis going around.

There are quite a few examples of quant questions in interviews creating the mental equivalent of a frozen operating system (including this post by Sprezzaturian), but I think that there's something beyond that, something that applies in social situations and that affects people who should know better.

Here's a simple example. What is the orbital speed of the International Space Station, roughly? No, don't google it, calculate it. Orbital period is about 90 minutes, altitude (distance to ground) about 400km, Earth radius is about 6370km.

Seriously, this question stumps people with university degrees, including some in the life sciences who necessarily have taken college level science courses.

And what college-level math do you need to answer it? The formula for the circumference of a circle of radius $r$. Yes, $2\times\pi\times r$. The orbital velocity in km/h is the total number of kilometers per orbit ($2\times\pi\times (6370+400)$) divided by the time to orbit in hours ($1\frac{1}{2}$), that is around $28\,000$ km/h, which is close to the actual value, $27\, 600$ km/h. (The orbit is an ellipse and takes more than 90 minutes.)

Can it possibly be ignorance, innumeracy? Is it plausible that college-educated professionals don't know the circumference formula?  Nope, they can recite the formula when prompted.

Or is it acalculia? That they have a mental inability to do calculation? Nope, they can compute exactly how much I owe on the lunch bill for the extra crème brûlée and the expensive entrée.

No, I think it's a mild case of numerophobia, a mental paralysis created by the appearance of an unexpected numerical challenge in normal life. This is a problem, as most of the world can be perceived more deeply if one thinks like a quant all the time; many strange "paradoxes" become obvious when seen through the lens of numerical (or parametrical) thinking.

For example, some time ago I had a discussion with a friend about strength training. The gist of it was that powerlifters are typically much stronger than the average athlete, but they are also much fewer; because of that, in a typical gym the strongest athlete might not be a powerlifter, but as we get into regional competitions and national competitions, the winner is going to be a powerlifter.

"That's because on the upper tail the difference between means is going to dominate the difference in sizes of the population." That quoted sentence is what I said. I might as well have said "boo-blee-gaa-gee in-a-gadda-vida hidee-hidee-hidee-oh" for all the comprehension. The friend is an engineer. A numbers person. But apparently, numbers are work-domain only.

The awesome power of quant thinking is being blocked by this strange social numerophobia. We must fight it. Liberate your inner quant; learn to love numbers in all areas of life.

Everything is numbers.