Taking the approach in: http://www.msri.org/realvideo/ln/msri/1999/vonneumann/schneps/1/
I view the Grothendieck-Teichmuller conjecture as saying that $Gal(\mathbb{Q})$ is isomorphic to a well understood object. That is, it is isomorphic to $Out^*$ of the fundamental group of the Teichmuller lego.
This seems to indeed be informative about $Gal(\mathbb{Q})$! My question is whether the Grothendieck-Teichmuller philosophy has predictions about how $Gal(\mathbb{Q})$ acts on varieties defined over $\mathbb{Q}$ (for example $\mathbb{P}^1_{\mathbb{Q}}\smallsetminus ${$0,1,\infty$}). From the way that I formulated the conjecture, it is not obvious to me that it does; but I think I am missing the greater picture.