— Dr. Chanda Prescod-Weinstein π π½ββοΈ π§π§π³οΈβπ (@IBJIYONGI) August 9, 2019

After seeing the first tweet from Kayley Brauer I was hoping to find a way to talk about this new result with the boys, but didn’t really know what to do. Thanks to the tweet from Dr. Chanda Prescod-Weinstein, I learned that the LA Times had put together a terrific presentation that was accessible to kids.

First, I had my older son read the article on his own and then we talked through some of the ideas he had after reading it.

I thought that reading the article on his own would be a little too difficult for my younger son (he’s about to start 8th grade) so instead of having him read it on his own, we went through it together:

Obviously I’m not within 1 billion miles of being an expert on anything related to this new image of the Milky Way, but it was still really fun to talk about it with the boys. I’m very happy that advanced science projects like this one are being shared in ways that kids can see and experience.

Today my older son was back from camp and I thought it would be fun to try an experiment that is described in the first part of chapter 3 of the book. The experiment involves a ball rolling down a ramp and is based on an experiment of Galileo’s that Strogatz describes.

I started by having my son read the first part of chapter 3 and then tell me what he learned:

Now we took a shot at measuring the time it takes for the ball to roll down the ramp.

I misspoke in this video – we’ll be taking the measurement of the distance the ball travels after 1 second and then after 2 seconds. I’m not sure what made me think we needed to measure it at 4 seconds.

Anyway, here’s the set up and the 5 rolls we used to measure the distance after 1 second.

Here’s the measurement of the distance the ball rolled after 2 seconds. We were expecting the ratio of the distances to be 4 to 1. Unfortunately we found that the ratio was closer to 2 to 1.

We guessed (or maybe hoped!) that the problem in the last two videos was that the ramp wasn’t steep enough. So, we raised the ramp a bit and this time we did find that the distances traveled after two seconds was roughly 4 times the distance traveled after 1 second.

This is definitely a fun experiment to try out with kids. Also a nice lesson that physics experiments can be pretty hard for math people to get right π

[sorry for mistakes – this one was written up in a big hurry]

I’m a big fan of the Mathematical Objects Podcast hosted by Katie Steckles and Peter Rowlett. Their most recent episode talked about Newton’s law of cooling and I thought it would be fun to try the project at home. Here’s link to the specific podcast:

— Mathematical Objects (@mathsobjects) July 5, 2019

Note that this project does require some adult supervision because it involves boiling water.

The idea in this project is to explore Newton’s law of cooling two different ways. The first way is to talk about the law, observe some water cooling for a bit, and then make a prediction about how that cooling will proceed. The second way is to take two cups of hot water and compare the temperature when you add cold milk to one initially and to the other 10 min later.

Here’s how we got started:

Next we took two glasses of hot water and measured the initial temperature:

5 min later we returned to measure the new temperatures and then use Newton’s law of cooling to predict the temps 5 min later. This part of the project was a little hard to do on camera, but you’ll get the idea of the things you have to keep track of. Hopefully we did all of the calculations right!

Next we moved on to the “tea” experiment. Here we started with two cups of hot water and added milk to one of them. We are going to wait 10 min and then add milk to the other glass and compare the temperatures of the two cups. Both kids mad a prediction about what would happen:

Finally, we returned to the cups and finished the 2nd experiment. Both kids guessed right on the relative temperatures, but I’m not 100% sure that we got the amount of water and milk exactly equal in the two cups. Still a fun experiment, though.

A saw a really neat twitter thread last week thanks to a re-tweet from Chanda Prescod-Weinstein:

Thinking about brightness of a moving object in magnitudes is complicated, so hereβs a brief tutorial with some calculations at the end. Imagine a telescope with one arcsecond pixels, excellent seeing, and some idealization, and a 4th magnitude satellite.

The thread explained why thinking about the (astronomical) magnitude of an object moving through a telescope’s field of view is a little difficult. It was neat to learn that something I didn’t realize was hard is actually pretty hard (though it feels like basically everything in astronomy is like that!), but another thing that jumped off the page for me in that twitter thread was that it was an excellent example to show to kids learning about logarithms.

For reference, here’s the Wikipedia page we used in the project to learn about the concept of magnitude and also get a few examples:

My younger son (in 7th grade) is just learning about logarithms now and my older son (in 9th grade) has a bit more experience with them. We started by talking about the relative magnitude formula and working through a short calculation to show why the number 2.5 shows up in the formula:

Next we looked at the Wikipedia page linked above to get some examples of magnitudes of a few objects we recognize:

Now we talked through Bruce Macintosh’s twitter thread. I wanted to go through the thread carefully to make sure the kids had a basic understanding of the concepts he was discussing (arcseconds, for example). We talked about some of the calculations, but did not do any calculating ourselves in this part. One question for the kids here was why did Macintosh use a + sign in his formula when the Wikipedia page has a – sign in the formula?

Finally, we did the calculations and found the answer to the mystery of the + and – sign from the last video. Happily, we match the answers from Macintosh’s thread:

This project was really fun. It was a really happy accident that just as my younger son was learning about logs a neat (and “new to me”) example of where logs are used showed up in my twitter feed!

The first ever image of a black hole was released last week, and it blew my mind! For our Family Math project this morning I decided to try to share some of the ideas relating to that image with my younger son. He’s in 7th grade and had not heard about the announcement, so it was especially fun to hear his off the cuff reactions.

I started by simply showing him the picture and asking him to describe what he saw and if it looked like what he expected a picture of a black hole to look like:

Next we watched Katie Bouman’s Ted Talk video (published in 2017) about the black hole imaging project. This video is fantastic and great to share with students because the explanation of the project, and especially why the project is so difficult, is done at a level that kids can appreciate even if they can’t understand all of the details. Here’s that video:

After we finished watching, I asked my son to tell me some things from Bouman’s talk that caught his eye:

Next I had my son read through two great twitter threads from when the announcement happened last week. Those threads are from two physics professors – Katie Mack from North Carolina State University and Chanda Prescod-Weinstein from the University of New Hampshire. Those two twitter threads are here:

— Chanda Prescod-Weinstein π π½ββοΈ π§π§π (@IBJIYONGI) April 10, 2019

First ever direct image of a black hole! The supermassive black hole in the galaxy M87 — 6.5 billion times as massive as the Sun! #EHT#BlackHole The image is better than I expected! pic.twitter.com/Tv7I36v4xQ

Here are two of the tweets from those threads that caught my son’s eye and his explanation of why he thought those two tweets were interesting:

Now I had my son play with a on online program that Leo Stein made a few years ago that shows the amazingly beautiful paths light can take orbiting a black hole. You can find the program here:

Unfortunately our camera was having a strange fight with the computer screen at the beginning of this video, so I cut that part out. Because of that cut the video starts mid conversation, but you’ll still be able to see that Leo’s program is really great to use with kids. I love his comment at the end: “Black holes seem pretty mysterious and neat and have weird properties.”

Finally, I showed him a picture from one of the papers about the black hole image that was published last week. The link to the paper with the image is here:

(2/2) Take this picture, for example, which shows what the pic would look like leaving out one of the telescope sites. It really does a great job of illustrating the deep level of care that went into the final work. pic.twitter.com/UqHtqPcWZE

Here’s our quick discussion about that image and what my son thought about it. Talking a little bit about this image can help younger students see and understand some of the statistical work that went into producing and checking the image:

It was really incredible to see the announcement of the black hole image last week. It is equally incredible that so many people in the physics community take time to share their ideas about discoveries like this with the public. I’m super grateful for the public-facing work those people do because it makes sharing new discoveries with kids possible (and fun!).

I saw some really neat tweets from John Carlos Baez and Greg Egan on Penrose-Terrell rotation last week:

A cube whizzes past at nearly the speed of light, c. What do you see? Lorentz contraction squashes the cube. But you *see* it as rotated and bent, since light from different parts of the cube take different amounts of time to reach you – and it's moved a lot by then!

[1/3] At @johncarlosbaezβs suggestion, I made some animations showing how Terrell Rotation [the distortion in the *appearance* of an object moving sideways https://t.co/vyt148Znut ] looks for both relativistic physics and Galilean physics with a finite speed of light. pic.twitter.com/jptwIJey5K

[Correction] I missed some of the true weirdness in the faster-than-light non-relativistic version. In that case, an objectβs world-line can cross the incoming light cone twice, so parts of the cube can have two distinct images at the same time. pic.twitter.com/7RaXu7NAsd

Even though even the most basic ideas from relativity are far outside of what kids can grasp, I thought it would be fun to share these animations with my younger son. The animations in the above tweets are definitely something that kids can appreciate, and I was excited to hear what my son would have to say.

So, I started out the project today asking my son to describe anything he knew about relativity and then what he thought he’d see if a cube passed by him really fast:

Next we talked about some simple ideas from relativity and what impact those ideas might have on a cube passing by. Also, since he’s just starting to learn about square roots and quadratics in school, I showed him the Lorentz contraction formula and we did one simple calculation:

Finally, we went to the computer to look at the tweets and animations from John Carlos Baez and Greg Egan that I linked above. As always, it is really fun to hear a kid react to and describe ideas from advanced math (and physics!):

Have you ever fantasized about simulating binary black holes on your computer? Who hasn't? We made the next best thing:https://t.co/eGYbfocf2J. This example demonstrates the superkick; the final black hole flies away at 1/100 the speed of light! pic.twitter.com/fB2XDpaWYb

The link goes to the “Binary black hole explorer” made by Vijay Varma, Leo Stein, and Davide Gerosa, and it is one of the most amazing computer visualizations I’ve ever seen!

Even though the math and physics going in in the background is way way way too advanced for kids, I thought it would be fun to hear them describe what they were seeing. Imagine having the opportunity to see simulations of rotating black holes when you were in 7th and 9th grade!!

My younger son went first:

My older son went next – we’ve just finished up the section in his calculus book on parametric equations and polar coordinates, so I thought he’d find these simulations to be especially interesting:

I loved showing these simulations to the boys. Even if they can’t totally understand what’s going on, it sure is a nice peek at what can come down the road if they find physics to be interesting.

And, as always, it is so fantastic to see scientists sharing amazing work like this on twitter!