“Honey, how long before they get hurt?” — Wikimedia Commons

All the parents have been there. You arrive at a birthday party and discover the hosts rented a trampoline or bouncy house. You’re both excited and concerned at the same time. You know it will be fun for your child, but also a big safety risk… I myself have a fake front tooth in the place of one claimed by a trampoline in the second grade.

Before sending little Johnny or Jenny in, you take a quick scan to see how many other kids are on the bouncy surface, how fast they are moving, how empathic the big ones are to the little ones, and how many other parents are on the sides keeping things in check. You inherently know when the conditions cause the likelihood of an injury to go through the roof. This is a phase change problem. Contrary to our Social Thermodynamics: Creativity post, we’re trying to prevent phase change here. Let’s break it down by the Gibb’s energy:

g = u + Pv – Ts

where u is values, P is stress, v is inverse density, T is resources, and s is empathy. If the change (g2-g1) in Gibb’s energy is negative (the value for g is less after something happens then before) phase change will spontaneously occur. In other words, to prevent phase change, the goal is to make g2 greater than g1 to prevent things from going crazy. Let’s go term by term:

u (values): the reason the kids go in to begin with is that you want them to have fun with friends. But before you send them off you add another value layer by whispering in their ear, “Be very careful  to stay safe and not hurt little Debra.” A number of parents put in the work to stick around the sides offering constant safety reminders to keep the values high.

P (stress): The constant reminders often come with an ultimatum: “if you can’t keep from bumping into Debra you’re going to have to come out.” The kids feel it too. If the bumping gets to hard, they don’t want to get hurt either, “anybody cries and the ‘rents will shut ‘er down.” The more tight the packing, the higher the stress.

v (inverse density): Remember this is inverse density, the lower the density, the more space between people. The lower the number in the bouncy house, the higher the space between people, and the lower the chance that things change for the worse. What’s also interesting is we can estimate a physical volume or area where a phase change starts to occur relative to the energetics of the bouncy surface. My estimate is that for a bunch of 3-5 year olds, the threshold area is about 2-3 square meters per child. But this depends on the energetics of the situation.

T (resources): Don’t send them in full of sugar and caffeine! The key resource being used here is ATP. Just like in classic thermodynamics, temperature is a measure of the average speed of particles. The faster they’re moving the higher the likelihood of injury. If things start to get dicey, slow it down to prevent phase change. Things will eventually slow down as ATP is burned up. One of the best ways to slow it down quickly? Get your kid talking to you on the outside (Qout).

s (empathy): Math says try to reduce the connections in order to inhibit phase change. Intuition says the opposite. A minimum amount of empathy is required commensurate with the values needed for safety. Blindfolding the children before sending them in would be a disaster. A minimum awareness of others, speeds, direction, and intent is required. But it’s easy to saturate this ability with three or more kids. We’ll come back to this with the topic of natural group/cohort sizing. In short, lock eyes and bounce with one -fun, more though and your in for a blow.

Remember, all of these properties are related for a situation, and we still need a surface of state that shows how these change relative to each other. It’s very possibly to increase Gibb’s energy through the other properties even though entropy/empathy increased. In this case I’d guess that the fastest way to prevent phase change is reducing the number of kids. I stood outside a bouncy house for awhile one afternoon trying to predict how many more kids could get added before the system spontaneously changed. Parents were always aware enough to step in and dampen the change before it happened. Many of the kids felt the pressure too and removed themselves.

Trampolines and bouncy houses are fun. They give us the ability to defy gravity and entropy for a short time. Another way to think about this — they give us new ways and abilities of interacting with the world and our friends and thereby increases our connections. I never thought about fun as a quality measure for empathy generation.

(Note: this post is one chapter of what could become a book someday. The other chapters can be found here: https://hydrogen.wsu.edu/dr-jacob-leachman/ )