I have come to believe the theory that people have profoundly different styles of cognition :) Alternate representations are incredibly useful to get as many s

I have come to believe the theory that people have profoundly different styles of cognition :) Alternate representations are incredibly useful to get as many styles of cognition on board as possible. I found I could grasp the equation immediately with help of the diagrams, and translate that to an internal abstraction representing the world. For me the equations themselves are a much more inert thing to approach and take much more effort to untangle. We all think differently. Especially so the more abstract the thought is it seems. As we approach each individual's limit of abstraction. Then we start to diverge further and further in how we think. I personally am a very visual thinker, and find Einstein's descriptions of thoughts to match my experience of cognition: “Words or the language, as they are written or spoken, do not seem to play any role in my mechanism of thought. The psychical entities which seem to serve as elements in thought are certain signs and more or less clear images which can be “voluntarily” reproduced and combined…but taken from a psychological viewpoint, this combinatory play seems to be the essential feature in productive thought — before there is any connection with logical construction in words or other kinds of signs which can be communicated to others.” Einstein was smarter than me though. I'm a computer scientist. I know some mathematicians, and was talking about matters of cognition with them. One of the mathematicians – a mathematician's mathematician who is easily able to learn math from maths books – told me that his style of thinking is effectively the same as is printed the books. My mind was blown. For me, reading the same books involved "translating" into half-abstract visual/sensory elements. Once translated into my native representation of cognition the acquisition is complete and I can think in the new visual-sensory-abstract symbols. My friend on the other hand basically thinks in the words and math symbols found in the books.