In a comment on a prior post my friend Amy told me about this Carl Sagan talk about the 4th dimension:
I decided to have the boys watch the video and then talk to start our Family Math project for today. After they watched it we discussed the parts they found interesting.
My younger son thought these two things were interesting:
(1) How the apple appeared as it fell through “Flatland”, and also how the creatures in Flatland interacted with the apple.
(2) The other 2D world that was curved.
My older son found these parts interesting:
(1) The discussion of projecting images from one dimension to a lower dimension, and
(2) The idea that lower dimensional things would have a hard time, but not an impossible time, noticing higher dimensions.
Right at the end we talked about the similarity between Carl Sagan walking around the sphere and (i) Vi Hart’s “Wind and Mr. Ug” video and (ii) a bicycle trip around a Klein Bottle. These are two of my all time favorite videos – sadly, though, the Klein Bottle video is no longer on youtube 😦 Luckily Wind and Mr. Ug remains:
Definitely a fun little project today – always fun to hear the boys’ ideas about complicated math topics 🙂
Mike's Math Page 
This series of yours has been such fun for me – especially today’s Flatland references. I just finished working my way through “The Annotated Flatland” by Ian Stewart, which includes Abbott’s original text, plus notes on changes Abbott made in the second edition, lots of biographical and historical info about Abbott and Boole and Hinton, connections to HGWells etc, sociohistorical commentary on Victorian England as seen through Abbott’s eyes, and, of course, lots of geometry and math.
Then, too, I just happen to be taking a mooc on the philosophical, historical, artistic, and scientific impact of Einstein, and higher dimensions play into that as well (though I only “get” a tiny sliver of the physics).
Nice synergy! it’s been a very four-dimensional spring. Thanks!
By the way, Wind and Mr. Ug is the first Vi Hart vid I ever saw… and remains one of my favorites.
And by the way by the way, it’s sad that kids are growing up in a world without Carl Sagan.
(for the boys)
Guys, that was extremely cool, hearing your reactions to that video. As it happens, all the same things interested me about it, too. Also the fact that as the square fluttered through space, he was able — after some initial confusion — to recognize what was going on. I wonder whether we’d be able to do the same in a fourth dimension — or fifth, or sixth.
If you want a challenge, you might be interested in the video I showed my (college) students right after this one — except that this guy goes to eleven.
My students aren’t math or physics students, by the way — they’re going to be doctors and dentists, mostly. But they need to know how to explain complex health problems to patients who don’t know much about bodies or diseases. So just like Sagan used Flatland and the apple to get across the idea of dimensions you can’t sense, my students will have to use images and stories to help patients understand their own diseases. I wanted my students to see that even very strange and difficult ideas like the fourth dimension (or 11th!) can be shown to people this way — so we can do the same with, say, diabetes, or epilepsy.
-amy
I’m having them watch the video this morning and we’ll do a similar project tonight