Just another seemingly flawed but plausible logic on the net. For your everyday dose of thinking..

"How long will I live for?" Most people want to know the answer. Let's call this answer X; that's what a mathematician would do. X is a variable, some number; let's measure it in years. We would like to know what X is. Is it 60, 80, 100? It's hard to give a good estimate - there is too much uncertainty. When mathematicians are faced with uncertainty, they whip out a tool called probability theory. Sounds fancy, but it's just a way of dealing with things we don't know exactly.

A mathematician would call X a random variable - something whose value we don't know exactly. But we have some rough idea of what the value of of this random variable is. We know it's bigger than 0 and smaller than 200 (assuming no one invents an immortality serum any time soon). There is still a lot of room between 0 and 200. Can we narrow it down a bit more? Well, what probability theory would say is that we are looking for the expected value of X - "How long can I expect to live for?"

There are many ways of getting a good estimate of this expected value. I could, for example, find the average life length of all the people who have died, or just those who have died in the past year and have lived in the same country as me. I could even throw out the women's numbers and just average the men's. (Women seem to live longer for some reason.) That's what I would call computing my life expectancy - another name for the expected value of X.

So what is this number good for? Well, I would like it to be larger, if possible; wouldn't you? Most of the decisions you make in life have an effect on this number - your life expectancy. If you run across the road on a red light, there is a small probability that you will get hit by a car, so you decrease your life expectancy slightly. This change is so small that you probably don't even give it a thought. For example, if you are 20, and your life expectancy is 80, and there is a probability of 1 in 10 million of getting hit by a car while running across the road, then you have just decreased your life expectancy by about a minute an a half. If running across the street has saved you 2 minutes of waiting for a green light at the crosswalk, then you have made a good choice. Of course, I pulled the probability of 1 in 10 million out of... thin air, so judge for yourself. My point is - lots of decisions affect your life expectancy every day.

So what does the TSA have to do with any of this? I'm glad you asked. I have just had the privilege of going through airport security in North America. (Somebody from Europe, please tell me you don't put up with this idiocy over there.) I had to take off my shoes. If that's not annoying enough, they confiscated my toothpaste, all 1/2 a tube of it. Silly me for forgetting that carrying toothpaste onto a plane is illegal.

Let's think about why they took my toothpaste. One way to look at it is to realise that the TSA's job is ensuring my safety. In our mathematical language, their job is to keep my life expectancy high. There once was a vague threat of a terrorist attack on a plane that involved a vague mention of a liquid explosive. Even though the plot was debunked as implausible, some TSA officials have made a mental connection between "liquid explosives" and "toothpaste" and enacted a rule banning toothpaste from planes. The reasoning probably went something like this - if this rule manages to prevent just one terrorist attack and saves just one life, then the minor inconvenience of having to surrender toothpaste at the gate has been worth it. In other words, this rule increases the life expectancy of at least one person, which is good. (Or so they must have thought.)

If this is the reasoning that they used, then I claim that they are quite wrong. Let's imagine that there is a homicidal maniac who is smart enough to cook up a liquid explosive so powerful that half a toothpaste tube of it could do terminal damage to an airplane. Let's also imagine that this individual is willing to destroy an airplane and kill himself in the process. Let's also imagine that he manages to pass through security and just happens to end up on the same flight as me. What do you think are the chances of all of this happening? One in a million? One in a billion? Less than that? I don't know; let's call this probability P for now.

Now consider a completely different scenario. A TSA employee confiscates my toothpaste at the airport. I spend 3 days on a trip brushing my teeth without toothpaste. I get back home, and there are emails to read, bills to pay and work to do, so I forget to buy a new tube of toothpaste for another 3 days. That's almost a week of poor dental hygiene. So I get a cavity, and a tooth infection, which spreads to my brain and kills me. Unlikely, you say? Sure. But how unlikely? What are the chances of that? One in a million? One in a hundred thousand? In other words, if a hundred thousand people did not use tooth paste for a week, do you think one of them would get a serious tooth infection? A fatal one? I don't know; let's call the probability of this turn of events Q.

If P is larger than Q, then the TSA's rule increases my life expectancy. If Q is larger than P, then the rule hurts my life expectancy. We can argue about this, but there is a more fundamental observation. Is P large enough for me to even care? Think back to crossing the street on a red light. The probability of getting hit by a car was so small that you didn't even care to think about it. Crossing the street illegally shortens your life expectancy by a minute and a half. How many seconds do you think the hypothetical toothpaste maniac would shave off of my life expectancy? I claim that P is so small that the time that the TSA's stupid toothpaste rule has added to my life expectancy is much, much smaller than the time it would take me to go to Safeway and buy a new tube of toothpaste. Mathematically, the rule makes no sense.

I can make the same argument against the take-off-your-shoes rule and the super-sensitive metal detector rule that makes me empty my pockets and take off my belt.

So what is the price of saving one person's life, as measured in toothpaste? It's probably much smaller than you think, if you think in terms of probability.

-GordaN

Labels: Logic