Inbook,
Radiation and network breaking in Polynesian Language Evolution.
(2005)
Abstract
The exploration and settlement of Polynesia was surely one of the greatest navigational
feats in all human history. At a time when Europeans were tentatively edging out
into the Mediterranean, Austronesians had colonised half the globe 7. Even more
extraordinary is that, at least according to Sharp 11, all of this exploration was carried
out in primitive sailing vessels capable only of coastal navigation. Sharp claimed that
the Polynesians had neither the technology nor the skills required for intentional voyages
of longer than 200 miles from a coastline. Hawaii, Easter Island and New Zealand were
discovered by accident, perhaps when the early sea-farers were blown off course in a storm.
(i) Exchange affecting this slot between islands a and b. An exchange from island a to
island b or from b to a affecting this slot occurs with probability (Aab + Aba )h +
o(h). If such a transfer occurs, the probability of Cab (t + h) equals one.
(ii) Exchange affecting this slot from another settled island x to a or b. For each
settled island x S (i) there is an exchange from x to a affecting this slot with
probability Axa h + o(h). If this transfer occurs the probability of Cab (t + h) is
Cbx (t). The formula for a transfer to b is the same with a and b reversed. Note
that we need to sum these probabilities over all x S (i) such that x = a, b.
(iii) Innovation for this slot on island a or b. A word innovation in this slot occurs
on a or b with probability 2µh + o(h). If there is a word innovation then the
probability cab (t + h) of a and b having cognate words at time t + h is 0.
