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.
Property B.1.If1≤i≤m, we have πi ≥ 1−(i−1)π 1 m−i+ 1 (A1) and π1 ≥ 1 m ≥ 1 N .(A2) Proof.We have T= NX i=1 πi = i−1X j=1 πj + mX j=i πj ≤(i−1)π 1 + (m−i+ 1)π i
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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.