Dear Jonathan (foolowing your comment ion my thread),
As far as dessins d'enfants are concerned, the members of the triple (0, 1, /infty) have well defined meaning. Sorry that I just copy my earlier post:
The Belyi theorem (see the step 3 in my Sec. 2 giving the definition of a child's drawing) and the property that the child's drawing D itself is the preimage of the segment [0,1], that is D=f^-1([0,1]), where the Belyi function f corresponding to D is a rational function. All black vertices of D are the roots of the equation f(x)=0, the multiplicity of each root being equal to the degree of the corresponding vertex. Similarly, all white vertices are the roots of the quation f(x)=1. Inside each face, there exits a single pole, that is a root of the equation f(x)=\infty. Besides 0, 1 and \infty, there are no other critical value of f.
In experiments you will have 0 or 1 as the result of the experiment (in the single or multiple qubit context) but the unobserved \infty is needed in the explanation. The way the black points (bit 0) and white points (bit 1) ly on the dessin (a graph on the oriented surface such as the sphere S2, or a Riemann surface with holes) is such that sigma(0)*sigma(1)*sigma(infty)=id, where
sigma (0) is the permutation group attached to the black points 0 (how the edges incident on the black points rotate) and sigma (1) is the permutation group attached to the white point 1 (how the edges incident on the white points rotate).
It is still binary logic but in a more clever way (may be this has to do with Grothendieck's topos, I have not thought about this aspect).
Thanks again for your interest.
I intend to write you again about the Hopf fibrations.
My kind regards.
Michel
