How long it takes to get sick of something
Eat the same lunch twice as often and you will not get sick of it in half as many lunches. You will get sick of it in about the same number of days. The counting unit is wrong. It was never the sandwich.
This comes out of a review published at the end of July, by Matthew Smart, Stanislav Shvartsman and Martin Mönnigmann, about habituation: the oldest and plainest kind of learning there is, the one where a thing stops getting a rise out of you. Snails do it. So do amoebae, and single cells with no nervous system at all, and certain electronic circuits nobody designed to be alive. Because it turns up in that many places the authors went looking for the part that has to be true everywhere, and what they found is small enough to write on a napkin.
You need two things. A leaky memory of how much stimulus has arrived lately, filling while the stimulus keeps coming and draining while it does not. And a readout that saturates, so that when the memory is full the response gets throttled.
The second part is doing more work than it looks. Suppose you had a nervous system that only ever added things up, so that two stimuli together always produced exactly the sum of what each produced alone. Such a system cannot get bored. Not “tends not to”. Cannot, and the proof is three lines long.
A response is a physical quantity, a firing rate or a concentration, so it cannot go below zero. Feed the system one pulse and whatever comes back is therefore positive the whole way. Now feed it a train of pulses: if the system only adds, its answer to the tenth pulse is its answer to the first plus nine leftovers from earlier ones, and those leftovers are positive, because everything is. Each pulse arrives on top of a slightly larger pile. The response can only climb.
So getting sick of things is not a weakness in the appetite. It is the fingerprint of a part of you that fills up. Anything that could go on responding without limit would also go on being interested forever, and would need no variety at all, and would be a very strange animal.
Now the counting. Write the model down and drive it with a regular stimulus and the whole thing solves in closed form, which means you can ask exactly how fast the memory fills. The answer surprised me. Each repetition closes the same fraction of the remaining gap, and that fraction is set by the leak rate multiplied by the gap between repetitions, so the two cancel: however often the thing happens, you arrive halfway to your own floor after the same interval of clock time. I ran it at four stimulus rates covering a factor of eight and got 0.69322, 0.69322, 0.69322 and 0.69315 in units of the memory’s own draining time. The exact value is the natural logarithm of two.
Where the floor sits does depend on the rate. Eat the thing more often and you end up flatter about it, and there is a limit to how flat, set by the average amount arriving. What eating it more often does not do is get you there any sooner. Boredom charges by the day, not by the exposure.
The last piece is the one that separates being bored from being tired. Fatigue is in the muscle, so it does not care what you ask the muscle to do. Habituation sits in a channel. In the version I ran, twenty repetitions of one stimulus drop the response to seven percent of where it started; switch to a different stimulus and the very next response comes back at full strength, because that channel’s memory was never filled. Nothing about you recovered. You just knocked on a different door.
There is a second way back, and it is stranger. Present one strong unrelated stimulus in the middle of the dull series and the old response returns on the old channel, most of the way, immediately. In the model this happens because the interruption drains the memory instead of filling it. In a kitchen it is the reason a dinner you were tired of tastes like something again when there is a guest at the table, or when the day has been bad, or when you eat it somewhere else.
Somebody said to me, about food, that it has to be different every time or you get bored, but it has to be familiar too somehow, and that being a person is tiresome. I do not think those two halves are fighting. Familiar is the dish. Different is whichever part of it has gone quiet. The demand is not for novelty, which would be exhausting and is not actually what anyone wants at dinner. The demand is for one channel somewhere that has had time to drain.
And the draining takes as long as it takes. That is the one number in all of this you cannot argue with or hurry, and it is the same for snails.
