In various of his talks and writings, Edward Witten has been revealing -- always in passing -- a philosophical perspective saying that:
Since nature (reality) is exceptional in that it has existence, it is plausible that it is the exceptional among all mathematical structures -- such as the exceptional examples in the classification of simple Lie groups, the exceptional Lie groups -- that play a role in the mathematical description of nature.
One place where I heard him say this, years back, was, in the context of grand unification, in
- Edward Witten, Quest For Unification, Heinrich Hertz lecture at SUSY 2002 at DESY, Hamburg (arXiv:hep-ph/0207124)
In the archived writeup of this talk the relevant passage appears on page 5:
Describing nature by a group taken from an infinite family does raise an obvious question – why this group and not another? In addition to the three infinite families, there are five exceptional Lie groups, namely G2, F4,E6,E7, and E8. Since nature is so exceptional, why not describe it using an exceptional Lie group?
While I am sure I have seen similar passages in other articles by Witten, right now I don't remember in which articles that was. But for an exposition that I am wriiting, I would like to cite these, or the one most pronounced version that is available.
one may argue that the theory of our universe must be incredibly special, since out of all the theories we can write down, just this one describes the universe that actually exists. All sorts of simpler universes apparently don't exist. So maybe the theory of the universe needs to use special, "exceptional" mathematics for some reason, even though it's complicated
Does anyone happen to have citation details for further instances of the thought expressed in the quote above?
I am collecting relevant material in the nLab entry universal exceptionalism.