A mathematical method using swap distance in permutohedrons shows crosslinguistic gestures achieve at least 77% optimality, unlikely by chance, and unifies linguistic principles under optimal assignment.
(1−π 1)/2≤π 2 follows fromπ 3 = 1−π1−π2 ≤π 2.π 2 <min(π 1,1− π1) follows from combiningπ 2 ≤π 1 according to the definition ofπ i andπ 1 +π 2 <1
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How to measure the optimality of word or gesture order with respect to the principle of swap distance minimization
A mathematical method using swap distance in permutohedrons shows crosslinguistic gestures achieve at least 77% optimality, unlikely by chance, and unifies linguistic principles under optimal assignment.