User blog comment:Deedlit11/Is BEAF well-defined?/@comment-25418284-20121023211454/@comment-5529393-20121123001630

Hmmm, I'm not sure there is really a "why".? It just happens that each nesting layer on the right corresponds to 2 additional exponents on the left.? As a sanity check we could verify that there are indeed b^^(2n-1) "passengers" in the "airplane" of {b, p (...(1) 1)...) 2} and b^^(2n) passengers in the airplane of {b, p (...(0, 1) 1)...) 2} where the number of nestings is n.