We can compare the argument for introducing an ‘oracle’ – that hides the names of the edge/color labels used by one binary tree from the other…

with the intuition given for how the zig-zag product creates rotation algebras that quickly mix a vector into the uniform distribution:

http://www.math.ias.edu/~avi/PUBLICATIONS/ReingoldVaWi2000.pdf

The latter paper goes to describe how to construct the large graph and why it works – to redistribute concentrations of probability:

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Computer Programmer who often does network administration with focus on security servers. Very strong in Microsoft Azure cloud!