I am logging what I witnessed in different fields, the example and potential contributing factors for two – three crevice. Exploring the intractability boundary, I theorized two is guarded by dual whereas three is attacked by the absence of consistency certificate. Bilinearity (observed in (X/M)* = X/M*) may be how dual contribute to consistency.

  • F = ma is second order
  • matrix has two sides leading to all “dual” theorems such as f** = f
  • 1, i two complex analysis basis
  • “Two is a company, three is a crowd” (Churchill)
  • Three body problem does not have closed form solution
  • Heat equation is second order differential equation which is associated with brownian motion – a basis for a important class of stochastic process
  • Two matroid intersection is easy (polynomial solvable but near P-NP boundary as it is hardest within the easy) whereas three matroid intersection problem is Np-hard. So is 3 vs 2 satisfiability (note 2 Max-SAT is in NPC).
  • Normal distribution is the distribution with the highest entropy given two moment information (mean and variance) which stems from its self duality (same form of pdf and characteristic function).
  • Oxygen forming two, not three, degree bond (some other sigma and phi bond in orbital examples to be added)