TOTD 2018-04-28: “The Surprisingly Solid Mathematical Case of the Tin Foil Hat Gun Prepper”

Here is an article you should read and think about: “The Surprisingly Solid Mathematical Case of the Tin Foil Hat Gun Prepper”.  The author is a stormwater hydrologist—what he does for a living is study the behaviour of water as it moves through the Earth’s ecosystem and, in particular, extreme events such as floods.  It is he and his colleagues who draw the red lines on maps which determine whether you can get flood insurance at an affordable price and, in many cases, obtain a long-term mortgage on a property.  Those in his profession think deeply about “tail risks”: events which occur rarely but which have major, or even catastrophic, consequences when they happen.  Humans have evolved in an environment which has selected them to apply a number of heuristics that, in most cases, get a good enough answer without a complete understanding of the problem or an exhaustive analysis of the situation.  But evolution, biological or cultural, is poor at selecting for heuristics which apply for events which happen less frequently than the lifetime of most members of a species.  We use our intuition, and often we get the wrong answer.

There is some math in the cited paper, and in what follows, but nothing more complicated than multiplying numbers, which you can do with a calculator if you wish to work it out for yourself.  The only other thing you need to know are some very basic facts of probability and statistics: I’ve written an “Introduction to Probability and Statistics” which, while aimed at other applications, may help if you’re rusty and want to review the details.  All you really need to know is that if a series of events are independent of one another (the outcome of one doesn’t affect the others), and that they have a given individual probability, you get the probability of a series of events occurring one after another by multiplying their probabilities together.

If your eyes are beginning to glaze over, consider a simple case.  When you flip a fair coin, it’s equally likely to come up heads or tails—a statistician would say the probability of heads (or tails) is 0.5 (or ½).  What’s the probability of two heads (or tails) in a row?  You just multiply the probabilities and get 0.25 (¼).  The flips are independent because each flip has a probability of 0.5, regardless of the previous flips.  Even if you’ve flipped nine heads in a row (probability 0.00195, one in 512 times), the probability of the next flip being a head is still 0.5.

What does this have to do with floods, or prepping, or heuristics?  Just that we aren’t very good at understanding how these numbers behave when the probabilities are small and the consequences are dire.

You’ll often hear of a “hundred year flood”.  This is sloppy terminology which many people take to mean a flood that only happens once a century.  That’s wrong.  What it means is that it’s a flood, defined by the extent of flooding, which has a probability of 1/100 (0.01) of happening in a given year.  That is a very different thing.

Now let’s do that little bit of math I warned you about.  If your house is located within the red line of the “100 year flood”, then each year you’re rolling a 100 sided die and if it comes up zero, you lose everything (or almost).  Now, the chance of a flood in any given year doesn’t depend upon what happened in previous years so the probabilities are independent, and we can multiply them.  But now we’re going do to a little arithmetic and look at, not the probability of a flood, but the probability of no flood.  Well, that’s just one minus the probability of a flood (1−0.01 = 0.99).  Now, if we want to know the probability of going n years without a flood, we need only compute \(0.99^n\).  Remember thirty year mortgages?  I do—I had one.  Let’s plug in 30 for n.  Tap-tap-tap on the calculator, or a little fiddling with the slide rule, and we get 0.74 or, of you like, around ¾ probability there will be no flood.  But that means there’s a 0.26 probability there will be a catastrophic flood before the mortgage is paid off.  Is it any wonder it’s hard to get a mortgage for a house in a “100 year” floodplain?

With this background and perspective, the author moves on to consider an event far more catastrophic than a flood (whose effects are local on a continental scale): a violent conflict over the government of a large territory.  Plugging in the numbers for the United States, he finds two such events in 340 years (the American Revolution and the War of Secession), and taking the mean lifespan of a person today as 78.7 years, calculates a probability of 37% that such an event will happen in their lifetime.  This is substantially higher than that of the flood, and will have consequences far more widespread and serious.

And the U.S. has been far more stable than most other countries in the world.

It’s fashionable to mock “preppers”, but taking the basic precautions against the collapse of our comfortable lives and the infrastructure which supports them is, based upon on a statistical calculation, no less reasonable than preparing for events such as a flood, hurricane, tornado, or earthquake.  And the well-equipped prepper is in a good position to ride out any of these events as well.

The zombie apocalypse is obviously pure fiction, but it has an allure to a few tongue-in-cheek preppers because of its functional completeness. If you are prepared for zombies, you are literally prepared for anything.

Read the whole thing.

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