Sunday, February 28, 2010
I am a very visual person. I was raised by an artist and a computer programmer. This gave me access to artistic and flow-charting techniques. My dad used give my siblings and I flow chart templates to make art when we were young. When I became older, he explained what some of the shapes meant and then made a game for me. He'd give me a simple task and I would diagram the steps to do it, using those shapes properly.
As a family, we made almost weekly trips to the public library, bringing home art and music in addition to a multitude of books. Our home library sometimes had better references than my school's library. Arguments between myself and the sister just younger than me were usually solved by encyclopedias at ten paces. My mother made sure we had art classes. My dad made sure we had science lab kits. As a family, we made candles, leather and other crafts. Dad would also print out wall-size mazes which we kids and my mother would solved together. When I learned how to process information, it was not only through the verbal and mathematical means, but also visual and kinetic means.
I'm right handed, left eyed, and I have no dominant foot preference. I have taken math courses up to and including partial differential equations and I have about the same amount of credit hours in studio art as I do math. It probably follows without saying that my favorite math class was analytical geometry. I feel that this makes me qualified to make the follow statement:
Calculations can be done visually as well as mathematically.
Anecdotal evidence: When I was in high school, my mother took one of my classmates and I to an UIL science competition. Between the tests, the contestant schools could work on brain teasers. One of them was a word problem about how much material a sculptor would need if they made a bust twice as large in every dimension. While my extremely intelligent classmate began to do the mathematical calculations, my mother read the problem and immediately gave the correct answer. After verifying it with math, my shocked classmate asked my mother how she did the calculation. She used pictures and hand gestures to explain her thought process. He was totally lost by her explanation, so I gave him an interpretation he could understand. For the rest of the problems, my classmate and mother answered them with their own methods, while I translated between the two of them. In every case, both methods gave the same answers.
Historical evidence: All those wonderful geometry and trignometry relationships started out as a function of the relationships between visual elements such as lines, points, angles, planes and solids. M. C. Escher discovered several crystallography relationships years before the mathematical models, through purely graphical means. While many mathematicians hold Escher in the highest regard and consider him to have had an exceptional mathematical mind, he actually did very poorly with math in school and struggled to understand the mathematical treatises sent to him when he was older.
So, having made put that pet peeve to rest, I will share with you a diagram I made a few months ago showing visual processing as part of the problem solving process. While I do not detail how to do math visually (perhaps I will do that in another post), the diagram does show some of the ways visual processing has brought about solutions -> http://cosmicsiren.blogspot.com/p/diagram-of-visual-processing.html
O’Connor, J. J. & Robertson, E. F. (2000). Maurits Cornelius Escher. MacTutor History of Mathematicians. Retrieved February 28, 2010, from http://www.gap-system.org/~history/Printonly/Escher.html