This morning I saw a nice twitter thread about herd immunity from Tim Gowers. In that thread I learned about a NYT opinion article written by Carl Bergstrom and Natalie Dean. Here’s Gowers’s twitter thread which has a link to the article:

A thread to explain point 1) in more detail. (A similar explanation is in the v.g. article by Natalie Dean and Carl Bergstrom that is linked to — the one I give below is not importantly different, but is slightly more mathematical than would be appropriate for the NYT.) 1/ https://t.co/NZynuyrTtM

I thought that both the article and the twitter thread would be interesting reads for the boys this morning. We started with the article – here are a few things they found interesting:

[before diving in – our regular camera stopped working, so I filed this project with my phone. Sorry that the film quality is poor]

After talking about the article a bit, we dove into exponential growth. I think they’d understood the exponential growth ideas in the article at a high level, but going a little deeper really did help them understand the ideas about growth rates better. It was particularly interesting to hear them talk about what happens when 1 person infects 1.5 other people on average:

Next I had them read through Tim Gowers’s twitter thread (while I learned how to download videos from my phone to iMovie 🙂 ). They looked at the thread for about 10 min – here are their initial thoughts:

Finally, we took a close look at the infinite series that Gowers used in his twitter thread. My older son was already pretty familiar with infinite geometric series, but my younger son is not as used to them. Here we talked through the ideas behind the general formula for the sum. My younger son had some good ideas for how to sum the series, so this turned out to be a really worthwhile discussion:

This project was really fun. I’m glad that so many scientists and mathematicians are sharing their ideas with the public. I’m especially thankful for ideas that are presented so clearly that they can be understood by middle and high school kids.