Our favorite Bookworm has one of her illustrated editions posted this morning. I snagged two items as particularly relevant to a phenomenon I’ve known about for some time, but which other people have a hard time digesting. Here they are:
Let’s overlook, just for the moment, that any Gentle Reader of Liberty’s Torch can and will easily grasp the import of the numbers in those two graphics. Rather, let’s reflect on the huge number of people who’ll look at those numbers and utterly fail to understand them. You can trust me on this one, friends: upon confronting those graphics, the great majority of Americans would simply scratch their heads and say “So what?”
The problem isn’t stupidity. Neither is it ignorance. It’s a far simpler thing:
Our lives are lived within a relatively narrow numerical range: countable objects that have perceptible dimensions. We have a feel for those numbers. We lack such a feel for the much larger or the much smaller. It’s what makes the probabilities in the graphics above difficult for most people to appreciate.
Astronomers have that problem too. We don’t use the units that apply to terrestrial distances when speaking of the distances between the planets, or the spaces between the stars. We use units that bring the numbers attached to them into our comfort zones: AUs and parsecs. Those “oversized” units wouldn’t fit anything in normal, terrestrial life, but they’re eminently suitable to astronomical operations.
They who study the very small use special units as well: the Angstrom (Å) and the Electron Volt (eV) are two examples. Indeed, even in the realm of the relatively small, such as genetic studies, we use units normal people doing normal things would not grasp: the micrometer (μm) and microgram (μg) being the most relevant. The point, as previously, is to bring the numbers attached to those units into the realm of the easily grasped and manipulated.
This is something to keep in mind whenever you seek to introduce very large or very small numbers into an argument.
Consider an argument about automobile safety that I encountered long ago: the probability that some individual American will die in an auto accident. Back then, there were about 50,000 road deaths in an average year. That number has considerable emotional impact – My God! 50,000 corpses per year! — but just how threatening is it to the average commuter?
A little arithmetic changes the picture from one that looks like an undertaker’s dream to something the ordinary American driver can – and does – tolerate. Let the total population of the U.S. be set at 250,000,000, just for round number convenience. In a given year, of 50,000 of those Americans will die in a road accident, that’s 50,000 / 250,000,000 == .0005 or 0.05% of the population. In other words, 99.95% of all Americans will escape death by auto that year. (Something else might get you, but that’s for another day.) That should make the average guy feel pretty safe, no?
Well, maybe and maybe not. A lot of people have difficulty with percentages of that sort. Also, there are always custard-heads out there who’ll say something stupid such as “Yes, but the probability of dying from AIDS is 100% if you catch it!” So I did a little more figuring, based on the average number of miles driven per American per year, and it worked out that John Q. Public, to have an even-money chance (probability 0.50) of dying in a road accident, would have to drive 47,000,000 miles: nearly 2000 times around the world at the equator.
The busiest salesman I’ve ever known didn’t quite log 10,000,000 miles over a fifty-year career…and he did almost all of that by air. Stretches the mind, doesn’t it?
I wrote the above partly for your amusement, but also for your perspective. To reach the average person with an important fact, you have to bring any figures important to it into the realm with which he’s comfortable. Numbers with a lot of digits, whether before of after the decimal point, usually don’t qualify. They might seem comprehensible to you, you bulging egghead, you, but the person to whom you’re talking might not share your perspective. Indeed, he probably doesn’t and never will.
Just a few thoughts for your Holy Thursday morning.