Season Transition

I love this time of year, when it's starting to feel cool and fall-like in the morning. The mountains are just barely starting to turn color. I'm feeling a now-familiar longing for cider mills. I have candy corn in my candy dish.

But even as the mornings cool down, it's been warm in the afternoons - almost too warm to feel like fall. A couple days ago I looked at the 10 day forecast and saw that the temperatures are about to drop a good twenty degrees or more this coming, and I felt happy. Which maybe never happened before I moved away to a colder climate and then came back.

In spite of the beautiful afternoon temperatures, there are fewer children playing on my street this year than there were last. I don't know why. A couple families with lots of kids moved out, but a couple more families with lots of kids moved in, and the kids and the parents all seem to get along with each other. Back in August when the kids were still playing together some parent installed one of those yellow Children At Play signs in front of their house, and the signs quickly proliferated. One day there was one sign, the next day there were two, and within a couple of weeks I counted eleven of them, on our block alone. I'm all about slow traffic in places where children play, but eleven signs seemed a bit out of hand. It was kind of funny, and also a bit eerie. The more yellow Children at Play children there were lining the streets, the fewer real children there were actually out playing.

I feel like you could take that thought and run with it and wind up with a good B horror movie.

One of the consequences of this cool-in-the-morning, hot-in-the-afternoon weather is the Great Jacket Pileup. It's chilly enough when I go to campus that I wear a jacket, and hot enough that I frequently forget to take the jacket back with me when I leave in the late afternoon. This means that, unless I'm unusually vigilant, my jacket collection gradually transfers itself from my apartment to my office, which is a problem because most of the time when I need a jacket, I need it from my apartment.

I think it could make a good math problem, though. Suppose that I begin with no jackets on my coat rack at school. Suppose also that, on a given day:

• The probability that it is cool enough to wear a jacket in the morning is 80%.
• The probability that I bring home the jacket I wore, if it is the only jacket on my coat rack, is 10%.
• The probability that I bring home only the jacket I wore, if there are multiple jackets on my coat rack is 30%.
• The probability that I get ambitious and bring home all the jackets on my coat rack, if there are multiple jackets on my coat rack, is 15%.
• The probability that I forget to bring home any of the jackets on my coat rack, if there are multiple jackets on my coat rack, is 55%.

Question 1: What is the expected value of the number of jackets on my coat rack at school after four weeks of this weather?

Question 2: How many jackets do I need to own for this probability pattern to be sustainable for an entire month?

I don't know the answer to either of those questions, except that the answer to Question 2 is probably more jackets than I have. So I've forced myself to become unusually vigilant, which completely disrupts the probability scenario but leaves me with a jacket at home if I need it.