On the bus the other day, as I was rolling past waiting commuters on Marquette Ave in downtown Minneapolis, I saw a yawn traveling along through the crowd. Or at least, that was the appearance- it may have just been that people were randomly yawning as I passed. Regardless, that got me thinking: what is the propagation speed of a yawn through a given crowd?
We should be able to express that as an equation, if we choose our parameters wisely. First, let's define "speed", for the purposes of this exercise, as the time required for a yawn to travel a given distance through a crowd in any direction. The reason for that wording will become clear later.
So, that brings us to the equation:
V = d * q * (m / r) * f(C)
d is the average delay between when a person sees a yawn start and starts yawning themselves
m is some distance factor (it can be observed that someone closer is more likely to inspire a yawn than someone farther away- m will have to be determine experimentally)
r is the average distance between crowd members
f(C) is a function of the crowd shape, orientation of individual members to each other and crowd activity
f(C) can be thought of as a "crowd quality" metric, and it will be different for linear crowds (people waiting for the bus, but all facing the sreet), crowds where there is no orienting factor (people waiting for a concert, for instance, who may be facing any direction based on where their friends are), queues, or spectating crowds. It is also likely that by being similarly primed mentally will factor into f(C)- a room full of bored college students is more likely to propagate a yawn quickly than people waiting for a bus, all with different degrees of boredom and internal mental activity.
Now, let's consider directionality. If we pick two arbitrary points and attempt to measure the propagation time between them, we will get a false sense of the travel time because of the meandering of the yawn through the crowd. It is thus better to simply pick a "patient zero" and then watch for a yawn to occur in any person at a given radius away from that person. The resulting scalar value is the speed of a yawn, or perhaps the "speed of lassitude".