"In high school he had not solved Euclidean geometry problems by tracking proofs through a logical sequence, step by step. He had manipulated the diagrams in his mind: he anchored some points and let others float, imagined some lines as stiff rodes and others as stretchable bands, and let the shapes slide until he could see what the result must be. These mental constructs flowed more freely than any real apparatus could. Now, having assimilated a corpus of physical knowledge and mathematical technique, Feynman worked the same way. The lines and vertices floating in the space of his mind now stood for complex symbols and operators. They had a recursive depth; he could focus on them and expand them in more complex expressions, made up of more complex expressions still. He could slide them and rearrange them, anchor fixed points and stretch the space in which they were embedded. Some mental operations required shifts in the frame of reference, reorientation in space and time. The perspective would change form motionlessness to steady motion to acceleration. It was said of Feynman that he had an extraordinary physical intuition, but that alone did not account for his analytic power. He melded together a sense of forces with his knowledge of the algebraic operations that represented them. The calculus, the symbols, the operators had for him almost as tangible a reality as the physical quantities on which they worked. Just as some people see numerals in color in their mind's eye, Feynman associated colors with the abstract variables of the formulas he understood so intimately. 'As I'm talking,' he once said, 'I see vague pictures of Bessel functions from Janke and Emde's book, with light tan j's, slightly violet-bluish n's, and dark brown x's flying around. And I wonder what the hell it must look like to the students.'"
At first my thought was to write a program that could do physics, allowing for as much abstraction as the user wanted. For example, one could model a roller coaster as one train, or as several cars, or as several cars with people in it, and so on. It has the same "recursive depth" that Gleick described, except it was for actual objects and not for equations. And if you think about it, we do this all the time: understand the whole, and only go into the details if necessary.
I only wrote a sparse amount of documentation then, and never wrote a single line of code for it. The idea slowly turned from physical modeling to mind mapping. My problem with mind maps is that, one you can't search them with computers, and two it gets really messy when you have lots of stuff on it. The latter is especially true if the lower branches have a lot of connections, so you have lines flying from this side to that side. And yet, mind maps are really all about these connections; without them the mind map would just be a spread out hierarchy tree.
One way to solve this ugly mess is to visualize the tree in 3D. You would only see a small part of the tree at a time, a cluster of branches at the same level. Links to other parts of the tree would be, well, links, and clicking on them would take you to another cluster of ideas, with the link highlight somehow. Each individual idea would perhaps be identified with a URI based on its location in the hierarchy. This way, any idea can be placed into the map, and be easily linked without making the map complicated. This would also embed the idea of recursive depth; one could keep pushing ideas down the tree, and again keep them linked without uglifying the map.
The only downside I see to this is the lack of complete picture, being unable to see everything at once. Perhaps on each level the size of the words would indicate how many nodes and links that branch has underneath it, giving the map the appearance of a tag cloud?
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