• The Key to Developing Mathematical Theories.

  To develop a strong conceptual theory grounded in mathematical statements,

  1. 1. Explicitly state your assumptions.
  2. 2. Construct a simple model based on these assumptions.
  3. 3. Show that your system must necessarily exhibit some phenomenon under your assumptions. 
  4. 4. Finally, build a strong argument that this system is a metaphor for some meaningful construct of reality. 

  The especially hard parts are:

  1. • in keeping the model simple enough that the message is as universal as it should be. Features of the message that are true only in special contexts should be removed, and distract from the core principle. 
  2. • in building a persuasive argument that this system is a reasonable proxy for the phenomenon in real life, and that this system captures the essential features of this instance of reality rather than the quirky details.
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