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November 2, 2004
Concept Maps and Visual Thinking
Yesterday, Chris Ruscio, following a lead from Hope Greenberg, draws the connection between Finite State Machines and HyperStory ... "a nondeterministic finite state automaton (NFA)…"
This leads to a riff on "visual thinking", "concept mapping", the "algebrification of the human mind," and the history of mathematical thought. When did algebra or geometry first become useful in non-mathematical thinking? Or, conversely, when did normal thinking first get turned into mathematics?
The Venn Diagram first comes to mind; related to the earlier Euler Circles, it is a popular example of geometry applied to thought[1]. It seems turns out that this was apparently in reaction to George Boole's use of algebra to systematize logic. Venn apparently was dissatisfied with the Boolean approach, and so documented his approach.[2]
[1] The Mathematical Universe, William Dunham, http://www.cut-the-knot.org/LewisCarroll/dunham.shtml. The link to Venn Diagrams explains the important (to the mathematician) difference between the Venn Diagram and the Euler Circles.
[2] http://www.andrews.edu/~calkins/math/biograph/biovenn.htm
[3] Today (2 November) is the birthday of George Boole (1815 - 1864).
Posted by sjc at November 2, 2004 1:26 PM
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