In a recent e-mail conversation with one of my "Friendly Mathematicians," who will hereafter be named "Professor B.," he reports that he has heard that "someone whom I respect told me that good mathematicians tend to think of math kinesthetically rather than visually. I think this might be true of physicists also."

I find this is true of my approach to math as well. I just didn't quite know the word for it (kinesthetically). That is, mathematical work and concepts relate to physical body movement and tactile experiences. Some of this is predictable: when I encounter an acute angle in geometry, I "feel" its sharpness (perhaps because my plastic drafting triangle actually does have sharp edges and points). But then angles are also paths traveled, as if I were driving my Electron car along the line-roads of geometry. An acute turn angle will cause more pressure on the driver than a gentler obtuse angle, and a sharp curve will exert more g-force on me than a wider curve. Just because I am not actually traveling these paths doesn't mean that I don't have some much more attenuated equivalent of it in my mind.

Similarly, when doing circle geometry or working with the trigonometric "unit circle," I literally feel as if I were going around in circles. I can even get dizzy if I stare at a circle for too long. The trigonometric "unit circle" also feels like a spinning wheel or an old-fashioned "tether ball" or a weight on a cord, which I am holding and spinning in a circle to demonstrate "centrifugal force."

And all this without leaving my chair!

As for color, I am mildly synesthetic, which means that I see numbers as colors. This peculiar perception is probably much more common than people think, and there are now some very good studies on the phenomenon, especially those of Richard Cytowic. Richard Cytowic's Website has a wealth of links to material on synesthesia.

I am certainly not as synesthetic as most of the people whom Cytowic has studied, but it is definitely noticeable for me. I know musicians who see different keys as colors, and another friend recently mentioned to me that she sees the different months of the year as colors.

My number colors are as follows: Zero: clear or transparent. One: white. Two: brown. Three: pale yellow, the color of the background of a New Jersey license plate. Four: rich orange. Five: dark blue, sometimes dark green. Six: pale blue, a color sometimes known as "periwinkle." Seven: Purple. Eight: golden yellow. Nine: black. For numbers with more than one digit, they are neither individual colors nor a mixture of the colors of each digit; they are a mosaic or a tiling of the different colors, except for number 11, which for some reason appears to me as beige. I can guarantee that your "number colors" will be quite different from mine; there seems to be no pattern to individual perceptions of synesthetic number colors.

In algebra, I perceive the variables a, b, and c as colors as well as x, y, and z. A is red, B is blue, and C is light blue (not yellow, as might be expected from primary colors). X is metallic gold, Y is bronze, and Z is black. These number and letter colors have been a distraction to me while working with math, and I've had to train myself not to see them when I am doing the work. Outside of mathwork, I enjoy seeing the mosaic of different combinations.

I am pleased to note that I am in good company; the famous physicist Richard Feynman was also synesthetic and saw numbers and other concepts as colors.

Posted at 8:02 pm | link