A friend of mine keeps a sleep log in which he monitors exactly how many hours he sleeps every night. He told me the logs taught him something interesting. While he used to worry that some nights he didn’t get as much sleep as others, he noticed that even if there were deviations from his usual sleep pattern, when looking at this pattern over a larger time window, his average sleep would always return to the same number of hours.
My head jumps immediately to an analogy in probability theory: the law of large numbers. As the window over which we examine our behavior increases, the average tends to converge to what we expect. Of course, there’s a problem with taking this analogy too seriously because it assumes one’s behavior is roughly stationary. Indeed, I can look at my sleep pattern over the past twenty-seven years, but my daily routine now is much different than it was when I was giving my parents grief with wet diapers (I cause grief in other ways now). For the analogy to work, the time scale should be small enough that it is roughly stationary but not so small that the statistical averaging does not sufficiently converge.
Curiously enough, for the past four weeks, I have been keeping a log, as well. Every Friday, I have to compile a list of my accomplishments from the work week along with my goals for the upcoming one. In an effort to help me remember what I had done during the week, I have tried to keep a daily log of my accomplishments along with my goals for the upcoming day. Something interesting happened: while there would be days in which I would fall significantly short of my goals or make no progress, when averaged out over the course of a week, I would be closer to my weekly goals.
I observed a similar phenomenon sans logs in graduate school but on a much different time scale. In information theory, there are arguably two major conferences every year: one with a deadline in January and the other with a deadline in July.* These deadlines served as the markers of progress. The scary thing about having markers spread so sparsely was that there would be weeks, sometimes even a month or two, in which I would fail to make progress, and the thought of having to make and meet the looming deadline caused me stress.
Was I doing something wrong? Should I change my behavior? To avoid panic, I learned to perform a simple test: how significant was the progress I had made relative to a few months ago with respect to my expectations? When it failed to meet expectation, I would make changes. However, more often than not, I could concretely identify progress made on this larger time scale, and it would roughly match where I expected to be.
So while there may come an especially bad day or a night in which I get barely any sleep, as long as these are not systemic problems, I can rest easy knowing that they should balance themselves out in the long run. And rest easy I should… I’ve accumulated quite the sleep deficit recently!
*I would be tempted to think there is only one since I never met the July deadline.