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Home » Archives » May 2012 » Driving and the Integral of Danger

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Driving and the Integral of Danger

Driving and the Integral of Danger

Here at, one thing we're not cynical about is automotive safey.

When we discuss driving/automotive safety we're going to mention something called the Integral of Danger. The point of the Integral of Danger is to attempt to illustrate just how important motoring safety is.

In mathematics, we use a concept of Calculus called the Integral to account for the fact that the total significance of something has to do with both it's intensity and it's duration. For example, a single candle buring for a long period of time contains the same total energy as a very fast, but very intense laser pulse. To determine if the two were equal, we'd take the integral of each energy curve and compare the resulting values.

DangerCurve (18k image)

So what if we apply the concept of Mathematical Integration to the danger level of various activities?
For a bomb technician, the level of danger, at certain moments in his/her career may be very high, but even for a relatively busy bomb technician, it is only for a few moments at a time, and fairly infrequently.

How about smoking? Over time, smoking can make you just as dead as if our bomb disposal technician above had a particularly bad day on the job, but it does not happen in a flash -- many people smoke for decades before the damage catches up with them.

But how about something that is both very dangerous, and we do frequently and for relatively long periods of time? It's Integral of Danger is going to be higher than it is for the smoker, or for the bomb technician. Even for individuals that live particularly risky lifestyles, I can't think of anything that has a higher Integral of Danger than driving (or riding in) a car.

Statistics bears this out -- motor vehicle accidents are consistently among the top causes of death.

Multiplication is another mathematical concept that applies to the Integral of Danger.

If we multiply a large number by a small number, we can get the same results as multiplying a small number by a large number. Mathematicians call this the Commutative property.

A properly packed parachute is obviously a very important detail (large number) for a sky diver, but over his or her life, the Integral of Danger for an sky diver is not that large (small number) -- in fact most sky divers -- at least the ones with properly packed 'cutes -- eventually die of heart disease, or -- you guessed it -- in car accidents.

But even a seemingly insignificant (small number) detail of motoring can be just as important to our continued existence since the Integral of Danger is so high (large number).

So if as you read the articles here on, it seems we're over analyzing, or harping on a small detail of motoring, just remember that each small detail is multiplied by a large Integral of Danger.
Posted by: carcynic on 24 May 12 @ 10:46 PM EST [Article Anchor]

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