Dear Dr. Crowther,
I really enjoyed your essay. I found it to be a very insightful examination of current physical theory and the aspects that make them fundamental or not.
I wonder about some of the requirements, such as being non-perturbative, since some things simply cannot be computed mathematically in a direct fashion. Could such requirements imply that there might never be a fundamental theory?
My group has been working on an attempt at a foundational theory called Influence Theory,
Knuth, K.H., *Bahreyni, N. 2014. A potential foundation for emergent space-time, Journal of Mathematical Physics, 55, 112501. doi:10.1063/1.4899081, arXiv:1209.0881 [math-ph]
Knuth, K.H. 2014. Information-based physics: an observer-centric foundation. Contemporary Physics, 55(1), 12-32. doi:10.1080/00107514.2013.853426. arXiv:1310.1667 [quant-ph]
and you now have me thinking about to what degree what we have achieved so far is fundamental.
Thank you for your excellent essay!
Kevin Knuth