at minute 13.24 we see how susskinds application of padics to future and past branchings can also be related to Turings notion of connectedness.
If we view A as a quantum mechanic’s style hermitian operator and we view the expression form as the powers/numbers of generators (e.g. I and J) used to walk the multiple wheels’ wirings when moving from start to end state (when described from the middle), then we can see that if those 2 portions of the path are labelled as padics (positive for the future and negative powers for the past) then we have an operator A that can test for connected-path (that A != 0)
This would give us a calculation for Phi, in a concrete representation.
For the first time, we have a function that can actually justify giving us a probability of 0 in those paths that are not a sequence of generators.
Remember, for Turing either of the generators ( I or j) can be recast as that generator to the mth power – giving 1 – which is then the value of x, above. If the current path label (as a padic) can be conjugated then till one lands on the rod attached to the unit element of the group, then one has a algebraic way of stating connectedness. One can, on a spider, do some forward searching m rounds (testing closure).