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Invariant Thinking...

Arguably the most fruitful principle in physics has been the notion of
symmetry. Covariance and gauge invariance - two simply stated symmetry
conditions - are at the heart of general relativity and the standard model
(of particle physics).

This is not only aesthetically pleasing it also illustrates a basic fact:
in coding reality into a formal system, we should only allow the most
minimal reference to be made to this formal system. I.e. reality likes
to be translated into a language that doesn't explicitly depend on its
own peculiarities (coordinates, number bases, units, ...). This is a
pretty obvious idea and allows for physical laws to be universal.

But what happens if we take this idea to the logical extreme? Will the
ultimate theory of reality demand: I will only allow myself to be
coded into a formal framework that makes no reference to itself
whatsoever. Obviously a mind twister. But the question remains: what
is the ultimate symmetry idea? Or: what is the ultimate invariant?

Does this imply "invariance" even with respect to our thinking? How
do we construct a system that supports itself out of itself, without
relying on anything external? Can such a magical feat be performed by
our thinking?

 

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