If you’ve been following me on Twitter you’ve seen reports of the Great Migration. This is the pompous name I give to the process of bringing the goldfish who were in tanks in the basement for the winter back outside again. This to let them enjoy the benefits of the summer, like, not having me poking around testing their water every day. (We had a winter with a lot of water quality problems. I’m probably over-testing.)
My reports about moving them back — by setting a net in that could trap some fish and moving them out — included reports of how many remained in each tank. And many people told me how such updates as “Twelve goldfish are in the left tank, three in the right, and fifteen have been brought outside” sound like the start of a story problem. Maybe it does. I don’t have a particular story problem built on this. I’m happy to take nominations for such.
But I did have some mathematics essays based on the problem of moving goldfish to the pond outdoors and to the warm water tank indoors:
- How To Count Fish, about how one could estimate a population by sampling it twice.
- How To Re-Count Fish, about one of the practical problems in using this to count as few goldfish as we have at our household.
- How Not To Count Fish, about how this population estimate wouldn’t work because of the peculiarities of goldfish psychology. Honest.
That I spend one essay describing how to do a thing, and then two more essays describing why it won’t work, may seem characteristically me. Well, yeah. Mathematics is a great tool. To use a tool safely requires understanding its powers and its limitations. I like thinking about what mathematics can and can’t do.