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Eleventh grade Max from England has a question for us, which references our Vortex Based Math pages:
"Hello prof! Lately I've been finding myself doodling little stars in the margins of my workbooks, seeing what patterns I can make with x number of points in a circle, a rule for arranging lines, making notation for different rules and so on. So far it's just been harmless messing around with patterns, but I saw your post on vortex maths and I'm concerned at the similarities I'm seeing with my own work. I don't think of myself as particularly 'mystic' but I do appreciate the patterns in mathematics, a la ViHart on YouTube and I'd rather not end up like Marko Rodin. My question is, should I keep on doodling and doing pseudo-mathematical patterns or move on and find something else? If so, what related things can I doodle that might bring me a bit closer to actual maths? Thanks for your time"
Well Max, I've got to tell you, this is one of the best questions I've seen in awhile. I like the way you're thinking. Before I answer your question, though I'm going to tell you a little story that your comment about doodling reminded me of.
When I was a kid, maybe in third or fourth grade, while all my classmates were learning addition and subtraction and the like, I was (I confess) a bit bored with math class.
So I started doodling. I doodled a tiny five-pointed star in the middle of my note paper. Then I drew a pentagon around it. Then I drew another star outside of that, and then another pentagon, and then another star, until my entire page was filled with stars within stars within stars.
And then I realized there was someone standing over my shoulder watching what I was doing.
It wasn't my teacher. Oh no, it was worse than that. It was the District Mathematics Curriculum Coordinator. And when you've been caught doodling by someone with such an impressive sounding title, it's a bit terrifying.
But Mr. Tame just asked me quietly, "What have you learned?"
I was a bit flustered (to say the least) but I had enough presence of mind to stumble out a response about how my first star wasn't perfectly drawn, and the more stars I drew, the more those errors got magnified.
He nodded thoughtfully and said, "That's a pretty important lesson," and then moved to look over the next student's shoulder.
I breathed a big sigh of relief and turned my attention back to addition and subtraction.
I appreciated Mr. Tame's willingness to let me get away with doodling. Because I did figure out something important about error and percent error (which I certainly could not have put into words at the time, but as Mr. Tame said, it was an important lesson).
So don't be afraid to doodle. Don't be afraid to explore. Don't be afraid of patterns. But don't stop just because you've found your pattern. Now ask the question, "Why?" That's where Marko and his buddies fell apart. They thought the pattern was the end of the quest. But the pattern was just the beginning. From there they should have gone on to ask questions like, "What is the cause of these patterns?"
I love that you referenced ViHart. Have you watched her video about the golden ratio and Fibonacci numbers? If you haven't you should. There are some amazing, astounding patterns related to the Fibonacci sequence and the golden ratio that show up in nature. But ViHart doesn't just say, "Have you noticed that the leaves of a plant spiral in patterns related to Fibonacci numbers?" She says, "These are astounding patterns, and let's see if we can figure out why a plant's leaves tend to grow in this way!"
That's the difference between a Rodin and a ViHart. One is satisfied to find a pattern, the other wants to know why the pattern exists. Some of the most interesting mathematics and science stems from people discovering patterns and then trying to figure out why they happen.
A wise old king (Solomon) once said, "It is the glory of God to conceal a thing: but the honour of kings is to search out a matter." The universe is filled with extraordinary and beautiful patterns. They're like a buried treasure hidden just below the surface. But don't just find them. Dig them up. Search them out. Understand them.
And if you can't answer the question "Why?" Don't get discouraged. Go find something else to explore, and maybe someday down the road your explorations will connect some dots, and you'll have an answer to the question that you couldn't answer today!
Thanks for writing, Max!