Tuesday, January 15, 2008

The Sleep Formula

Running low on sleep turns up the suck on everything, especially
intelligence and mood. Sleep deprivation sucks in any job, but is
especially disastrous in a self-motivated, creative-type job like being a
grad student. I can easily lose a whole day of sciencing if I screw up
that night's sleep. What's confusing though is the sense that the night
*before* last night plays a big part too. So how can I predict for how I'm
going to feel on a given day? (the non-geek may wish to skip
to the punchline at this point.) As a simple model, I will call the lack
of sleep deprivation, or the amount of well-restedness, my "sleep charge",
and it will be a function of the last n nights' hours of sleep. Let's make
it a linear function then at time t it's x(1)*s(t) + x(2)*s(t-1) + ... +
x(n)s(1+t-n). So what are the x's and the n? How far back do I look at my
sleep pattern, and what weightings do I give them?

This will differ for different people. But for myself I've decided and
tested the model of going back only 2 nights. And they will be equally
weighted. (so this is a 2-point simple moving average) The formula I now
use, and which has been remarkably successful in predicting how much I get
done and how I feel about it is this then:

Sleep charge = number of hours slept last night * 0.5 + number of hours
slept the night before * 0.5

As an example, 6.5 hours one night and 8 hours the next, equals a sleep
charge of 7.25. Now all I need is interpretation. Using intuition, for me
I think it goes something like this:

Sleep charge < 7: Zombie like.
Sleep charge 7-7.5: Ok
Sleep charge >= 7.5: Shiny and full of pep, cleverness and creativity.

This rule has been astoundingly accurate at predicting my days over the
last week and a half. Just as the formula predicts, one bad night affected
two days and then I was fine. And knowing that showed how it's useful: by
knowing I was going to havee a zombie day, I could stop panicking about
being too scattered and slothful, take it easy on myself, and plan for
what I *can* do - there are always a few zombie jobs around that I've been
putting off. And it becomes ultra-clear what the benefit of getting that
extra bit of sleep is, and when to plan to exploit that burst of willpower
and inspiration (like I had sunday).

What have you figured out about how your sleep works?