Powers of 10 website

Source: Eames Powers of Ten website

When my daughters were little, we discovered an amazing book of photographs from a movie made by Charles and Ray Eames called Powers of Ten. It was a very cool way to introduce powerful mathematical ideas.

When sharing it with schoolchildren, we always started in the middle of the book, where there was a photo of a man lying on a square of grass in Chicago. The grassy square was ten meters by ten meters. (Ten to the first power!)

Each time you turned the page towards the beginning of the book, the linear scale got bigger by a factor of 10. Turn the page once, it's 100 x 100 meters and you saw a larger expanse of grass surrounded by adjacent roadways. Turn the page again, 1000 x 1000 meters, and you saw a square kilometer of Chicago lakefront. And so on through sequential powers of ten.

What amazed the children was that it only took six page turns (six powers of ten) to go from the human everyday scale of seeing the man lying on the ten by ten meter grassy square to a scale where you could suddenly see almost the entire earth. And we didn't stop there. Another two page turns and we could see the entire moon's orbit around the earth. Another three page turns after that and we could see the orbits of the inner planets around the sun. Another page turn after that and we could see essentially the whole solar system.

We would keep going, we could see the nearest star, then the Milky Way, then other nearby galaxies, and after a total of 25 page turns from the center of the book, we were at a scale of 10 to the 25 meters across, roughly a billion light years.

Then we would turn back to the center of the book again, and we would find the man lying on the grass, and start turning pages towards the back of the book, instead of the front. Going in that direction, the scale would shrink. From a one meter scale, we go down to a tenth of a meter scale, a one hundredth of a meter, and so on. We zoom in on his hand, the skin cells in his hand, the molecules in those cells, the atoms in those molecules, the subatomic parts in those atoms. We stop after 17 page turns, on the scale of a quark.

The first part of our exploration had introduced the positive powers of ten. The second part of our exploration had introduced the negative powers of ten (which naturally led to the idea of 1 as the zero-th power of 10.)

The book is still available and I recommend it highly, but today's kids can also explore it all for free at the very cool and interactive Powers of Ten website. They can watch the classic Powers of Ten movie on the website (free registration required) or play an interactive Powers of Ten game and explore more on the website.

In addition to the website version of the movie, there's also a DVD version, which science museums like to show on big screens. Since this coming Friday is October 10 (10/10), also known as "Powers of Ten Day," there might be some good opportunities to catch this movie on a big screen then. There's also a great travelling museum exhibit as well.