We are both wrong. I was thinking "Island south of Japan" and I said Taiwan, but I should have said Okinawa, which was conquered by Japan and part of the Japanese empire in the 1890s:

https://en.wikipedia.org/wiki/Ryukyu_Kingdom

https://en.wikipedia.org/wiki/Karate

Taiwan was also conquered by Japan and was part of the empire in the 1890s, which I think is why I confused it with Okinawa.