The fellow who sailed with Cook was Tupaia.
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Tupaia's Chart map catalogued in the British Museum as a 'Chart of the Society Islands with Otaheite in the centre July-Aug 1769' was brought back from Cook’s voyages in the Pacific. By reading this chart traditional Pacific navigators conceived of their sea environment.
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Some info about him and his navigation prowess here
Quests of the Dragon and Bird Clan: Glossary: Tupaia's Map
So to try and relate this to the topic. is there any genetic evidence that amerindians came accross the Pacific? All very tenuous & late
I know.- The best evidence for Polynesian- Americas contact I have found so far is the humble chook.
Wiki says
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by about 700 AD, the Polynesians had settled the vast Polynesian triangle with its northern corner at Hawai'i, the eastern corner at Rapa Nui (Easter Island), and the southern corner in New Zealand. By comparison, Viking navigators first settled Iceland around 875 AD. The Polynesian voyagers reached the South American mainland and there are suggestions that they made contact with indigenous South Americans. Carbon-dating of chicken bones found by Chilean archaeologists on the Arauco Peninsula in south-central Chile date from between 1321 and 1407 AD. DNA analysis of the bones match those found in prehistoric samples from Tonga and American Samoa, and a near identical match from Rapa Nui (Easter Island). The sweet potato, known in Polynesian languages as kumara or kumala is widely grown around the Pacific but originated in the Andes. There are also linguistic similarities - sweet potato is kumar in Peru.
There is no conclusive evidence that Pacific peoples actually settled on the South American mainland or that South American peoples voyaged into the Pacific.
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Polynesian culture - Wikipedia, the free encyclopedia
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In 1803 Martinez de Zuniga published a history of the Philippines in which he asserted that the people of Polynesia and many other Pacific Islands, including the Philippines, spoke languages closely related to those of South America,
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From this homeland region, now called West Polynesia, the trail of artifacts leads to the archipelagos of central East Polynesia-the Cooks, Societies, Australs, Tuamotus and Marquesas, and then from there to the distant islands of Hawai'i, Rapa Nui and Aotearoa. In all the hundreds of excavations conducted throughout Polynesia, no prehistoric pottery or other ancient artifacts that can be directly traced to either North or South America have been uncovered. Although the pre-European cultivation by Polynesians of the sweet potato, a plant of South American origin, indicates that there must have been some communication between the Americas and Polynesia, the archaeological record demonstrates that Polynesians are descended from seafarers who moved eastward across the Pacific from the western edge of the ocean.
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Chickens came from SE Asia