[Previously in sequence: Taxometrics]

I.

Imagine Alice has a chronic disease. Luckily, as long as she has a job, she will have health insurance. And health insurance provides her with a treatment. Every day she takes the treatment, her health will go up one point on a 0-100 scale; every day she misses the treatment, it will go down one point. If her health ever gets below 75, she will be too ill to work.

Mathematicians would call this a dynamical system with three variables: does she have a job or not, does she have insurance or not, and her health level. We know from the rules above that j always equals i, and that j is 1 as long has h is 75 or higher. And every day i = 1, h goes up one; every day i = 0, h goes down 1.

Alice starts with a job and health of 100. Since j = 1 and i = 1, health goes up one each day, but it’s maxed out at 100 so it just says there. This state is perfectly stable; as long as the system follows the rules above, it will never change.

Suppose Alice gets a mild cold which knocks her health down to 90. She keeps working, her health keeps going up 1 each day, and she eventually gets back to 100.

Suppose Alice gets a medium flu which knocks her health down to 80. She keeps working, her health keeps going up 1 each day, and she eventually gets back to 100.

But suppose Alice gets a serious pneumonia which knocks her health down to 70. Now she can’t work, she loses insurance, her health starts going down 1 each day, and she eventually goes down to 0. This is another stable state; as long as the system keeps evolving according to the rules, it will never change.