Black Hornbill, Greater Kruger Park, 2008
Hanging out with friends Jake Leachman and Kevin Vixie. While I was in the bathroom, these two — my fellow mechanical engineering prof, and Big Data mathematician, came up with a great discriminator — guiding principles can’t be proven or disproven. You can’t disprove calculus. It works for a range of estimation, and gives answers with a range of validity and reliability dependent on the problem.
Algorithms can be, of course, proven or disproven, and as such are a limited metacognitive set. Their reach is by necessity bounded. Guiding principles are metacognitively open systems. I’m sure this goes back to Godel’s Incompleteness Theorem. The other thing to ponder philosophically is how this meshes with the receptivity of given social organizations to either recognize knowledge boundaries or embrace wisdom.
So if you’re looking for a proof for Spiral Dynamics, or my own augmented version of Empathetic Evolution, well, good luck! They’re supposed to be open systems, and they just make things simpler. I’m also going to lean on Jake to write up the original Boltzmann/Ernst Mach conflict regarding the existence of atoms in the comments. It falls out along this lines.
It's About Empathy - Connection Ties Us Together 
As requested… Ludwig Boltzmann made two of the largest contributions in science history:
1) a statistical equation for entropy S=log (#ways),
2) statistical derivation. Of the ideal gas law: Pv=RT.
Both of these proofs relied on a belief Boltzmann had that gases, fluids, and solids were composed of small particles, what we now know as atoms.
The much more eloquent, and Nazi, Ernst Mach (yes the same Mach as the Mach number) derided and abused Boltzmann in public science debates continuing to go back to one statement, “I don’t believe that atoms exist!” All too classically, Mach could not find problems with HOW Boltzmann derived his proofs, or the new insights they provided, just the premise. This abuse tragically drove Boltzmann to commit suicide only months before Einstein’s Brownian motion paper that proved the existence of atoms.
Einstein himself fell into the same trap with quantum mechanics and Heisenberg’s uncertainty principle stating, “I don’t believe that God plays dice with the universe.” Fortunately for history, Einstein was not a hateful Nazi and nobody committed suicide over the remark.
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… yup, while you can prove things *with* calculus, and you can prove that some system (like calculus) is flawed (contradictory) or consistent, it really makes no sense to “prove calculus”.
So, you can’t prove calculus.
Where we get the pieces of the puzzle can be pretty mysterious — that study/conversation is on completely different plane/universe, so we most often content ourselves with fitting the puzzle pieces together.
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As we discussed earlier, it’s the open system thing vs. closed system thing. Godel’s Incompleteness Theory covers this ground, and is applicable.
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