Have you ever been in a situation and felt like you were reliving a scene from a book or movie? Well it happened to me the other day when I went to visit my daughter’s school. I felt exactly like I was the piper in the Pied Piper of Hamelin, because an ever-growing crowd of children followed me across the oval as I walked in.
And why were they following me? Well I had brought a Stage 4 model of the Sierpinski Sponge with me for my daughter’s Show and Tell. She had come with me to university the day before to help me make Stage 6, and we thought the other kids would be interested — and my goodness they were!
At this point I should probably tell you more about the Sierpinksi Sponge Project…
The Sierpinski Sponge is a fractal constructed in the shape of a triangular pyramid. It has a giant hole in the centre, and each of the corners around this hole is a copy of the whole thing. This means that each corner is a pyramid with a big hole in the middle, and each corner of those pyramids is a pyramid with a hole in the middle, and each … and you go on like this forever until you have an object with a great number of holes (infinitely many in fact) — hence the name “sponge”.
Of course, you can’t make a real Sierpinksi Sponge because it goes inwards forever; you can make a decent model though. What you do is you get four small pyramids and you join them together at the corners to get a bigger one with a hole in the middle. Then you take four of these bigger pyramids and you join them together to get a bigger one with a hole in the middle. And so on. The individual small pyramids are called Stage 0, then when you join four together you get to Stage 1, and then Stage 2, and so on. We made a Stage 6, which contained 4096 individual pyramids.
So back to the story… on the day after we made Stage 6, I walked through the school yard with a Stage 4 Seirpinski Sponge, and all the kids crowded around to see this remarkable thing and ask questions. And then in the classroom, the kids just couldn’t keep quiet with the questions and fought over who would be first to hold the smaller models. Their little eyes lit up as they imagined standing inside Stage 6, and imagined the awesomeness of Stage 7, Stage 8 and Stage 100.
But it did make me think: We made our Stage 6 in a public place in the Uni where hundreds of people walk past a day. Several people looked at it as they walked past, and a few came close to touch and ask questions, and a handful of those actually stopped to help make it bigger. Before construction day, I had spent every train journey sticking pyramids together, usually reaching Stage 4 by the time I got to my destination. On one particular day I finished a Stage 5 on the train and carried the metre-wide pyramid it through the crowds. Not one person stopped to look or ask about it. Yet the schoolchildren couldn’t keep themselves away.
When did all the adults lose their sense of wonder? Because even the the Stage 4 Sponge is truly wonderful to me (and to hordes of children too).
What would it take for adults to crowd around like the children in the Pied Piper of Hamelin?