# 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.

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## Author: John Walker

Founder of Ratburger.org, Autodesk, Inc., and Marinchip Systems. Author of The Hacker's Diet. Creator of www.fourmilab.ch.

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

1. Magnificent post, John.  I understand the fallacy of the frequentist argument, and yet I still fall prey to it on a routine basis.

Equally valuable is the bald assertions of the reasonableness of reasonable things — in the face of unreasonable opposition, more so.

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2. I remember using these kind of statistics back in the early 1980s to explain why the Soviets (not Russia – it was still the Soviet Union back then) found even a porous anti-missile system so threatening. My basic assumption was that a Soviet first-strike needed to destroy enough US missiles to ensure the subsequent counter-strike did not cripple the Soviet Union.

For my purposes I assumed the Soviet Union would survive without serious damage if no more than 50 US nukes survived a first strike. Given the number of warheads we had back then, it was amazing what an SDI system that even nailed 1% of incoming missiles would due to reducing the effects of a successful first strike taking out a US response.

I argued this meant that Reagan was right to offer the Soviets US ABM technology.  A porous ABM system would reduce the odds of either nation launching a first strike if both sides had it, but it suited the Soviets better to keep MAD in place because they assumed the uncertainty would eventually wear the US down.

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3. I was told I was going to be able to buy a parachute on the way down.

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4. 10 Cents:
I was told I was going to be able to buy a parachute on the way down.

A true libertarian is somebody who jumps off a cliff confident the market will supply a parachute.

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5. 10 Cents:
I was told I was going to be able to buy a parachute on the way down.

A true libertarian is somebody who jumps off a cliff confident the market will supply a parachute.

I believe in a fair country gravity should be outlawed. Think how many lives would be saved. #gravitysucks

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6. 10 Cents:
I was told I was going to be able to buy a parachute on the way down.

A true libertarian is somebody who jumps off a cliff confident the market will supply a parachute.

Now, you KNOW I like this sort of joke.

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7. Excellent! @johnwalker

I understood all of this article.  Why is this a big deal?  Well, when confronted with my first statistics class in graduate school , it required me to supplement my textbook with three borrowed library books on the subject just to get a B grade  (I did not take statistics in undergrad; hadn’t taken a math class in 20 years.  I used to sit at my study table with all four books opened to the same topic <smiling>)

Thus, I say again, Excellent!  So, well explained.

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8. I admit to being one of those who reads ‘prepper’ material (just always made sense to me to do so), although I’m not a prepper in any big sense.   However, that said, we are always prepared for a hurricane (prepared for up to at least 3 weeks of self-sufficiency).

Only problem, we forgot to find a solution for, is addressing the fact that we are no longer ‘young’, no longer quite so fit/strong/flexible as we used be.

But I hadn’t really thought about it, that is the ‘physical’ preparedness needed, until it was brought home to me last year when one of our large trees was pulled up during a hurricane and some of the huge branches ended up in the road.

Knowing it was my responsibility to move the tree/branches, I went over to ask a neighbor I saw with some thick rope if I could borrow it when he was done.  I had planned to tie it to the tree and its large branches to make it easier for me to pull it off  the road.  The neighbor, said yes, he would bring the rope over to my house in a bit.  I went inside to change clothes.

When I came back out just a short time later to see if he was on his way yet, I was surprised to see, the tree and all its big branches had been moved to the end of the block and onto the cul de sac circle.   Turns out he had gotten another neighbor to help him.  They tied it to his truck and towed it all away without saying a word to me.   I’m guessing I did not look to him quite up to being able to move the big tree myself, although it hadn’t occurred to me that I would not be able to; I’ve always been ‘able’.   (PS.  Thank you again, Jonathan)

In hindsight, not sure how I thought I was actually going to get the job done, but it never occurred to me for a second that I wouldn’t.

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9. Great article, with very straightforward math.

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10. 10 Cents:
I was told I was going to be able to buy a parachute on the way down.

A true libertarian is somebody who jumps off a cliff confident the market will supply a parachute.

I believe in a fair country gravity should be outlawed. Think how many lives would be saved. #gravitysucks

I agree 120.37%.  After all, gravity is just a social construct anyway.  And a racist and classist one, too, owing to height differences among various peoples, implying an entirely unequal vulnerability to dangerously rapid, uncontrolled depletions of gravitational potential energy (known to some as “falling”).

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11. 10 Cents:
I was told I was going to be able to buy a parachute on the way down.

A true libertarian is somebody who jumps off a cliff confident the market will supply a parachute.

I believe in a fair country gravity should be outlawed. Think how many lives would be saved. #gravitysucks

I agree 120.37%.  After all, gravity is just a social construct anyway.  And a racist and classist one, too, owing to height differences among various peoples, implying an entirely unequal vulnerability to dangerously rapid, uncontrolled depletions of gravitational potential energy (known to some as “falling”).

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12. My one quibble is that we frequently don’t know enough to say that a certain flood is a 100 year flood.  The joke is that we get a 100 year flood very five years.

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13. Off topic.

FYI, this is with my iPad in landscape. If I had it in portrait I would see even less of the notification. 🙂

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14. Richard Easton:
My one quibble is that we frequently don’t know enough to say that a certain flood is a 100 year flood.  The joke is that we get a 100 year flood very five years.

A 100 years doesn’t buy you as much time as it used to, Richard.

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15. Richard Easton:
My one quibble is that we frequently don’t know enough to say that a certain flood is a 100 year flood.  The joke is that we get a 100 year flood very five years.

A 100 years doesn’t buy you as much time as it used to, Richard.

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16. Garbage In, Garbage Out.   There are lots of places with poor or missing rainfall data, with the result that the estimates are based on non-representative information.   The guys that develop the flood maps have every incentive to get it right, and they keep getting better, but there are limits.

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17. Richard Easton:
My one quibble is that we frequently don’t know enough to say that a certain flood is a 100 year flood.  The joke is that we get a 100 year flood very five years.

A 100 years doesn’t buy you as much time as it used to, Richard.