“Mom! Give me your phone, and I also need the iPad!”
Excuse me? Before I flipped out on the 10-year-old, I suggested he rephrase his “requests” and put some explanation to it all.
“Oh. Right. May I please* use your phone and the iPad? I was telling Johnny** about that Zeno’s Paradox thing, and I want to send him information about it.”
Well, of course he can use my phone and iPad to share mathy stuff!
While elementary school math is rooted in mastering the basic operations of arithmetic (making it a rather one dimensional subject…ha!), the study of math is so much more broad and deep and colorful. Yes, math is about manipulating numbers, but it is also about using solid logical thinking. Yes, math has practical applications to topics like finance and construction, but it also has real applications to philosophy. We already know that kids are some of the best philosophers around, why wouldn’t they be interested and able to wonder about those aspects of math? (If you don’t already know that children are terrific philosophers, or you want to play with philosophy with your kids a bit, check out Jana Mohr Lone’s blog about philosophy for children..)
So, I introduced my son to Zeno’s dichotomy paradox. I mentioned that this was something he might find intriguing since he enjoys puzzles and wordplay. I showed him the TedEd video below. It was an interesting idea to him, but it was some time before he came back to me asking, “How is this possible??” (And to be truthful, I didn’t have an answer that satisfied me or him, so I had to brush up on my own understanding of Zeno’s dichotomy paradox and recall it’s connection to calculus. It’s not terribly convoluted – scroll down to Mathematically Speaking to see. Or just watch the video.)
After sharing the paradox with his friend, he came running back to me….”Mom! You have to explain this better to me! Johnny says it’s just my opinion and that it’s not true!”
And now I get to discuss with my son how to have a conversation with someone who doesn’t agree with you…
Mathematically speaking…Zeno’s dichotomy paradox is an entree into the topics of infinity and limits. These are subjects that are typically first addressed in Calculus, a class that your child will not likely be exposed to until late high school, if at all. Why wait until then to tantalize kids with the fascinating thinking that underpins these topics? This paradox says that motion is impossible! What kid wouldn’t want to argue with that? Zeno was a pre-Socratic Greek philosopher. He noted that if you are traveling from point A to point B, you first have to cover half the distance from point A to point B. Then, you’ll have to cover half the remaining distance. If you continue traveling half the distance that is left, you’ll never get to point B because you can always slice the remaining distance in half again. While that logical argument makes sense, we know there’s something wrong with it, because I CAN walk from point A to point B. The logical (and mathematical) key is in seeing that every smaller slice of distance toward point B is accompanied by a smaller slice of time needed to cover that distance. In fact, the slices are shrinking in a sequence such that when they are all added together, even though there are infinitely many terms to add, their sum is converging to a finite number. Does that make sense? It would probably help to see a visual…which the video above provides! Remember, too, that it’s not important for YOU to have this concept mastered. It’s only important that you are willing to expose your child to the idea, and then explore it together if it sticks. Have fun!
* I’m sure he didn’t say “may I”, but I’m using poetic license to make my kid sound more polite than he was. Always remind yourself to take social media with a grain of salt.
**Names have been changed to protect the nerdy.