This time (which was actually presented way back in November) I wanted to discuss more about the thinking of the ancient Greeks. I wanted to talk about the two main beliefs of the basic constituents of the world. I presented the four elements view along with the indivisible particles (or atomist) view.
I spoke with the kids about how serious the Greeks were about figuring out the world around them. They tried to understand what everything around them had in common and how it was different. Again, the big focus was on "why." What could be the difference between leaves, dirt, sky, and animals?
The four elements theory was originally proposed by Empedocles [em-ped-uh-kleez]. Empedocles believed that all things were made of four elements (things that cannot be broken down further); Earth, Air, Fire, and Water. He believed that they could combine because of a force called Love. Love, like between people, was supposed to be able to draw things together. Strife, which I told the kids was like war or fighting, made the elements separate.
I talked a bit about Zeno's [zee-no] famous paradox of the arrow in flight. After explaining that Zeno proposed that an arrow could never reach it's final destination because it always had to go half-way. If shooting the arrow across the table, first it had to go to the middle of the table, then to the middle of what was left, then to the middle of the next space left, and then to the middle of that. I pointed out to the kids that if we used a magnifying glass, we could still make lots of middles. And then we have to imagine that the middles can continue so that there was always a middle to reach. So Zeno's paradox was that an object could never reach its destination--and yet it does. And for those reasons, Zeno's paradox was really interesting to think about.
I had each of the kids stand and play the part of the arrow. I asked them to move to the middle point of the table. Then to the middle of what was left. Then again, the middle between their current position and the end of the table. In only two more moves, there was no physical way to see a distance between parts of themselves and the table--and there they were at the end of the table. I purposefully did not ask them to imagine themselves having a center-line of no size. How come they made it when Zeno's Paradox would say they couldn't? I pointed out that they take up more space than the middle.
That was the thinking that spurred Leucippus [lyoo-sip-us] to try to discern the nature of matter. I handed the kids each a sheet of paper. I asked them to rip it in-half. Then rip one of those halves again. And to keep taking a half and ripping. I allowed them to do this until I paper confetti all over my table. Eventually they all had some tiny portion of paper that they couldn't rip using their bare hands. I then stated that Leucippus thought there must be some really small piece that could never be divided (which would explain how they, and the arrow, get where they want to go). So Leucippus rejected the idea of the four elements in favor of everything being made of these particles and nothing else; particles and empty space.
Democritus [dem-ah-crit-us], learning from Leucippus, also propounded the particle idea and gave it the name atomos for 'indivisible'. He believed that the different sizes and movements of the particles could account for all of the differences we see around us. It turns out that he was remarkably correct, but that the thought experiments of Democritus and Leucippus were, somewhat correctly, ignored in favor of an element theory that other great thinkers felt was more grounded in evidence of the senses.
Aristotle came along later and described the elements in terms of complementary physical properties, like soft and hard, hot and cold, or wet and dry. Aristotle added ether because, in his thinking, the heavens could not be made of the same materials as Earthly things because they behaved completely differently, so he added ether as a fifth element. Each thing behaved a certain way because of the elements it was made of. Earth-containing items moved down until they reached something they couldn't move through and things. Things made of the element Air would rise up to Air's natural place above the Earth. We know now that Aristotle was mistaken, but his views were so convincing and matched people's observations so well that they lasted a really long time.
I then introduced our next topic: Archimedes. Archimedes was the pioneer of the science of statics--using math to understand systems in equilibrium. For the kids I said he was the first guy to use math to represent the real world. I also told the Archimedes "Eureka" story to describe Archimedes' love of thinking.
On the board:
Empedocles ~450 BC
Everything is made of Earth, Water, Air, Fire (Aristotle adds ether)
Love and Strife were forces that changed things.
Leucippus ~440 BC
There must be something tiny that is indivisible.
Democritus ~420 BC
The smallest indivisible particles: atomos
First to use mathematics to describe laws
The Stomachion This is a very famous puzzle from Archimedes. Apparently he was using it to determine how many unique ways the pieces could be combined to make a square. It was called stomachion (stomach-yon) because it could be so frustrating that it could give you a tummy ache. We ran out of time to actually work on it in class, but I printed the first page on card stock so the kids could cut it out and experiment with making the shapes.