Scrubbing Calculator demonstrates a tool for exploring practical algebraic problems without symbolic variables. Instead of x's and y's, you connect concrete numbers and adjust them interactively.
Interactive Exploration of a Dynamical System demonstrates a tool for manipulating differential equations where every variable is shown as a plot, and every parameter has a knob that can be adjusted in realtime. This helps the user develop a sense for how the parameters of the system influence its behavior.
Up And Down the Ladder of Abstraction is an interactive essay about using visualization in a systematic way to design and understand systems.
Simulation As A Practical Tool is its early precursor, where I started working out the ideas behind this effort.
http://vimeo.com/23839605/
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