Have you ever had one of those ideas that you thought were really cool, and inspired — and you were certain would never work? Maybe it’s the complexity, such that execution is never perfect. Maybe it’s the sheer number of things that could go wrong, or the consequences if they do. Or maybe it’s just that the idea is so simple, you worry there’s no way it could work. Oh – there’s also the fear of failure… that gets in the way too.
Sunday afternoon, my four-year-old daughter wanted to go outside and do some Kung Fu. Not the Spongebob Squarepants “kah-rah-TAY!” variety, but actually some of the Kung Fu she sees daddy teaching out the window on Tuesday nights. She is obviously too young to learn much of value, and I’ve already slipped in a couple of concepts that might help protect her. Still, I was waiting for her to get a little older before asking so determinedly, and has such had to rely on an old answer: logic.
When I used to do presentations for Junior High and elementary kids, I’d invariably get asked about my hobbies, or what I did for fun. In one case, I knew the teacher, who took it upon herself to let the class know that they needed to behave because I knew “Kung Fu.” The natural response for a middle-school student is “Show us some Kung Fu!” — which would lead to the whiteboard for a lesson in logic.
(No complaints from the peanut gallery – we actually study symbolic logic.) It does serve to make a point to those kids that there is more to self-improvement that learning how to punch and kick… it’s understanding the appropriate circumstances that make punching and kicking a correct response. And for that, we need a logical framework.
So here I am, about to spring a little joke on my four-year-old, when it occurred to me to find out how far I could go with the lesson. Either beyond her abstract-reasoning threshold, or past her patience and attention span. One would give.
I started by drawing three interlocking circles – the old familiar Venn diagram that we have so much fun with. The regions were red, blue, and green. I tried to limit the abstract just a little, by telling her the circles represented people who were wearing that color. Laura had a red top and blue jeans, and after a brief explanation of the diagram, immediately pointed to where she ought to be! I marked an “L” in that intersection of sets.
Too easy, I thought. Time to bring the curveball! I asked her where “I” would belong. As I was dressed in a black sweatsuit and black shoes, she was dealing with a null set. After a few seconds, I asked her if I belonged in the red region. She answered “No.” Same for the green region, and the blue. I asked here where I ought to be, and she pointed to the area above the circles. “You’re out there,” she said.
I didn’t underestimate the power of that moment. My daughter had been nearly effortless in making the biggest abstract leap of all: there is an area outside the domains. It is the spatial equivalent of the Arabs inventing the Zero.
I quickly described what other family members were wearing, and she nailed every one of the puzzles, telling me where to put an initial for each person. What happened next surprised even me. “Daddy, now let me show you some of my Kung Fu.”
She proceeded to pull three colors of chalk from the base of her little easel in the garage, and drew a pink circle, a yellow circle, and a purple one. Her first attempt didn’t come out quite the way she needed it to, as there was no zone of three-way overlap. I showed her how that was a little different than Daddy’s grid, and helped her re-draw it to fit.
The next thing I knew, she was telling me what my wife was wearing, and asked me to figure out where she fit on her board. I was stunned. Not only did my four-year-old pick up on some applied abstracts with geometry, she turned around and proved to me she knew it, by teaching it right back to me. (Please bear in mind, this is the child that is often hard-pressed to focus on what I am saying for more then four seconds at a time.)
Needless to say…
- I’ll not pull back any punches on what she might or might not be able to understand. Either she gets it or not, no harm done and no pressure. But no artificially holding her back because my expectations are lower.
- More time in the garage, just the two of us.
- More Kung Fu. Maybe a logic puzzle or two on the way to n actual syllogism.
What started as my wacky idea to entertain my child became a proof of concept. The method is sound. It is easily comprehensible, with absolutely no advance knowledge or fundamental necessary. Once learned, it is easy to apply. Had I given it just a moment of thought, I would have backed off and not started drawing circles on the whiteboard. For once, not thinking paid off.
Ike, the Arabs did not invent the zero nor the decimal system. They are called the Arabic numberals because the Arabs brought it to the West from India. Here is an excerpt from the entry on zero from the Wikipedia.
“In 498 AD, Indian mathematician and astronomer Aryabhata stated that “Sthanam sthanam dasa gunam” or place to place in ten times in value, which may be the origin of the modern decimal based place value notation.[8]
“The oldest known text to use zero is the Jain text from India entitled the Lokavibhaaga, dated 458 AD.[9] however, it was first introduced to the world by Al Khawarizmim, a Persian mathematician, astronomer and geographer[citation needed]. He was the founder of several branches and basic concepts of mathematics. In the words of Phillip Hitti, Al Khawarizmi’s contribution to mathematics influenced mathematical thought to a greater extent. His work on algebra initiated the subject in a systematic form and also developed it to the extent of giving analytical solutions of linear and quadratic equations, which established him as the founder of Algebra. The very name Algebra has been derived from his famous book Al-Jabr wa-al-Muqabilah.
“His arithmetic synthesized Greek and Hindu knowledge and also contained his own contribution of fundamental importance to mathematics and science. Thus, he explained the use of zero, a numeral of fundamental importance developed by the Indians. Similarly, he developed the decimal system so that the overall system of numerals, ‘algorithm’ or ‘algorizm’ is named after him.
“The first indubitable appearance of a symbol for zero appears in 876 in India on a stone tablet in Gwalior. Documents on copper plates, with the same small o in them, dated back as far as the sixth century AD, abound.”
good stuff, and this sentence is great, and i’d love to see a separate essay on it:
>>> It does serve to make a point to those kids that there is more to self-improvement that learning how to punch and kick… it’s understanding the appropriate circumstances that make punching and kicking a correct response. And for that, we need a logical framework.