Do you have a second?

Every 15 minutes, someone averages a sum of events over an arbitrary period of time. No, I don't have a citation for that. It's standard practice to assume that frequencies are infrequently constant yet are much easier to understand if we can apply some kind of linear assumptions to them. That's perfectly fine, especially when we don't really know when the event in question is more or less likely to happen. This approach is used in science and medical journalism with the intent of breaking down impossibly huge numbers (i.e., 50 thousand deaths due to Ocelot Fever) into something more human-readable.

The problem arises when the level of granularity imposed by averaging over time obfuscates the reasons why the events happen at all. If MADD tells us that "In 2011, 9,878 people died in drunk driving crashes - one every 53 minutes", what do we really learn? That single number, (9,878 deaths / 53 minutes) is so specific that it disregards critical time-related factors like the weekend.*

I was planning to do an XKCD-inspired bit of Googling** and search for results of a few arbitrary frequencies to find out what happens at those times, every time. The results are too ghastly to share as most of the assumed events involve death, dismemberment, or assault. So, for the sake of diversity, I'll pull a few numbers from instead:

  • Every second, Johnny Depp makes $2.92. The guy makes $92 million a year. Economists do use hourly pay or yearly salary to estimate how much an individual's time is worth, such that any period of time is "worth" however much they would have earned had they spent it working for pay. This can lead to some rather ludicrous estimates when inappropriately applied. We know Johnny Depp isn't actually working continuously despite his numerous sources of income. Even so, a number like $2.92/sec doesn't really provide us with any context to Mr. Depp's economic situation.
  • Every second, 194 videos are watched on Myspace. What a perfect example! The statistic is from 2009. Some big changes have happened since then. Even so, it's fun to imagine Myspace users draining what's left of their attenuated attention spans on single-second videos. Hundreds of them every second!
  • Every second, cows emit 250 kgs of methane in the United States. It's already difficult to imagine what a single kilogram of methane looks like,*** much less how what happens to it when the next second's round of methane arrives. Even so, cows don't continuously emit methane and they may emit more or less of it depending on what they're eating. Those factors can't even be considered when we break things down into seconds or even hours. If I observe a cow swish its tail three hundred times in an hour, perhaps I can safely claim 5 tail swishes per minute. Expanding the observation to a thousand cows over the course of months or years would render per-minute or per-second estimates useless without a greater knowledge of the relationship between cow tails and time.

All I'm saying is that averaging massive numbers over time is misleading at best and dangerously myopic at worst. These are situations best handled by probabilities, not solid quantities and linear relationships. Averaging such an immense quantity over such a small period of time distorts our understanding of both quantities.

*This paper's thesis in brief: young people like to drink for fun on the weekends. To be fair, the study subjects were Swiss rather than the usual Americans. I'll refrain from griping about social science research for now.

**I have this nagging suspicion that this actually was an XKCD piece at some point. If so, go read that again too. It was probably pretty entertaining.

***250 kg of methane is 375 thousand liters, if that helps.