Home » Reasonably true » Thorns, odds, and the impossible

Thorns, odds, and the impossible

A few years ago I was walking on a disused path in some woods near where I live, when I noticed a small branch that seemed to have attached itself to my foot. When I looked more closely, I saw about an inch of thorn sticking up through my boot just in front of the ball of my foot.

This was a genuine official hiking boot with about an inch and a half to two inches of combined Vibram outsole and orthotic insole, and a Gore-Tex and nylon upper. Needless to say, I was dumbfounded. How had a thorn managed to penetrate all that? More to the point, how had it penetrated my foot without my feeling it?

I pulled out the thorn; it was easily four or five inches long and almost a quarter of an inch thick at its base. A honey locust, I figured, although I hadn’t seen one with thorns quite that big. As I tossed the branch away from the path, it occurred to me that I’d better get a look at my injury before too long. A little way further up the path I found a convenient log, sat down, and gingerly removed the shoe, fully expecting to see a slowly expanding patch of red where the thorn had come through. When I looked, I realized why I hadn’t felt anything.

The damned thing had passed precisely between my big toe and its neighbor as far back as it could without hitting flesh. When I say precisely, I mean there was no evidence of its passage whatsoever — not blood, not broken skin, not so much as a minor scratch.

What, as they say, were the odds of that happening? Well, I maintain that, since it had actually occurred, the odds must have been 100%.

You could calculate the odds as a hypothetical exercise, taking into account such variables as the average number of dead branches small enough to go unnoticed on a disused path, the percentage of those likely to have huge thorns, the probability of such a thorn lying at the precise angle required to use the force of a footfall to penetrate a sturdy shoe. You’d also have to take into account the width of the path, the length of my stride, the size of the shoe, the total area of the sole, and so on. Then you could come up with some number, which would surely be vanishingly small.

And yet, it happened. You might be familiar with the concept of the black swan, popularized in a book of that title by Nassim Nicholas Taleb. I’m not interested in the failings of statistics which do not take all of the significant variables into account; it may be true that probability calculations can be improved by using the proper data. My point is that even when all knowable variables are taken into account, you can still end up on the wrong side of the conclusion.

Why is that? It’s simple. Statistics are descriptive, not predictive. They describe in detail past events in similar contexts to the one you’re interested in. In the end, any conclusion you draw is based on inductive reasoning, which by its nature is vulnerable to data gaps. When an event actually occurs, such as my adventure with the thorn, it becomes data, and statistical inference is irrelevant to it. The question, “What are the odds of that?” is pointless.

Does that mean that judging risk on the basis of probability is useless? Not at all. But it is why the severity of a negative outcome is so important in the decision process.

If I have a 10% chance of spilling wine on my shirt, that’s not going to stop me from drinking some. But if I have a 10% chance of dying if I get Covid-19, that’s a different story.

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