January 29, 2008
I focus much of my time on philosophy of mind with an emphasis on consciousness, the experiences you have from the senses (vision, audition, tactile, etc.) and from thought. There is one large obstacle in the study of consciousness - there is no third person way to experience consciousness, you only have access to your own. Because of this, we are forced to rely on what people say they are experiencing, and people are notoriously prone to error in their introspective reports. It would be like studying how far people can jump by only looking at how far people say they jump when you know they are really bad at judging distance.
With that in mind, how do people experience numbers? I'm not sure what the answer is, but it certainly is not the norm to experience them as shapes. Take a look at this fascinating documentary on a savant who is able to perform complex mathematical calculations in seconds. According to him, he experiences numbers as unique shapes in his consciousness, and his method of multiplication is to place two of these shapes next to each other and look at the space in between. This space is a new shape which he then translates into an answer.
The end of part 5 and all of part 6 contain the most in-depth discussion of his experience of numbers. He is interviewed by a neural scientist at UC San Diego to see if he truly performs calculations in this way, or if he uses memorization (his memory is amazing, he recites pi to 22,500 decimal places early in the documentary). Although it is all only quasi-scientific, the idea that he is able to experience numbers as geometric shapes (or landscapes as he calls it at times) is cool.
If the way he experiences numbers enables him to perform calculations faster and more accurately, perhaps the way one experiences reading (as words, as a narration by an inner voice, or directly onto the ideas) can influence reading speed and comprehension. If this is the case, and the way one experiences reading is trainable, the effect on pedagogy would be huge. I didn't learn to read until I was in third grade because of poor teaching methodology (you can't learn to read like you learn to speak, through osmosis!), so I can attest to the deficiencies in our understanding here. I was in the dumb reading class. Boo hoo.
However, going back to the jumping analogy, how tough to study! Especially when everyone jumps different distances. So irritating when people experience the same thing in different ways! Where are the laws of consciousness? I'm a fan of laws. Sure am.