I am desperately trying to pull together my first packet of work for this semester and I think I just found my theme. Sharing the beginning with you all:
“We don’t know one millionth of one percent about anything.”
- Thomas Edison
At the residency this autumn, up at Goddard, I sat in on a talk my advisor gave about GeoGebra and the Mandelbrot set. What I took away from the talk and demonstration was that mathematics is an art, and a study. Math is as much a puzzle maker an answerer to puzzles.
My understanding of it all is that the discovery of one plus one equaling two is a visual, universal observation as is subtraction, multiplication and division and the beginnings of Algebraic thought. Drop a handful of pebbles on the ground and you can easily see the results of addition, subtraction and create sets, subsets and venn diagrams galore. It is clear and precise and you can categorize it. It is tangible, can be manipulated.
As you work with bigger numbers and bigger ideas than simple sets, you have to still understand and be able to visualize the base you got there from. It isn’t about faith that a number you see is what you want it to be. When the Mandelbrot set was demonstrated and then displayed in a computer graphic I was amazed. I understood that somehow the building blocks of mathematics had been stacked one on top of another to arrive at the formula that created it. But I was also accepting on faith that the professor in the front of the room understood the math that created the formula the Mandelbrot graphic was built on. Because I had no clue and could not even begin to understand how it happened.
But I didn’t have to know it to see what I saw. I had to have faith in the math without understanding that the math caused what I saw.
Did it exist without the math to generate it?
