The insights on knowledge generators are inspiring, especially the paragraphs discussing on the development in mathematic symbols. Having studied math for over 16 years (since 1st grade in elementary school), I have never thought about the nature or the insights of the logical symbols or diagrams that I used every day almost. It is a new perspective for me to consider them as performers of reasoning other than representation of the logics. For example, the Venn diagram cannot describe the information precisely but it can display the interactions clearly.
Similarly, visualizations in other scenarios can act in the same way. Yet the most cases I have encountered are representing existing information, the function of visualization as an approach to create new information is more interesting and important to me. In the former situation, visualization is only a tool to facilitate the address of information; while in the latter circumstance, it becomes a method of exploration and research that brings more value and knowledge. The current adoption of visualization are largely limited to the use of display known information. Sometimes visualization generates new knowledge when they display some unsual features. However, there is seldom a static method of creating new information through visualization, which I believe worth more research and study. It is a more direct and powerful way of information generating due to the essense of its visual form and the large amount of information it could carry via shapes, outlines, colors and so forth.