Duplicate Dunham

In Poul Anderson's "Symmetry," Dunham's problem is that he and his duplicate, or the two duplicates, respond identically to every stimulus. They cannot escape from their enclosed space because, when both try to open the door, each prevents the other from opening it. Over time, divergent experiences will differentiate them as individuals but that is not possible so soon after duplication and in their featureless environment.

However, my intuition is that random neuronic interactions will begin to differentiate them from the moment of duplication, thus that they will not continue to think, speak and act identically after the first few moments of separate existence.

Anderson creates a problem, then finds a solution, but I question the existence of the problem.