jbg

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?

Taken from this newsgroup message…

tags: invariance, symmetry, thinking

This entry was posted on Monday, April 2nd, 2007 at 3:40 pm and is filed under This'n'that, meta. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.