TAIPEI ( TheStreet) -- You'd need a microscope to find these islands on most maps of Asia. No one lives there, unless you count short-tailed albatrosses.But boatload after boatload of activists cuts through choppy currents to reach them, turned away each time by Japan's wily coast guard. Most of the activists come from China, where the government claims the rocky protrusions as their own and wants Japan out. The unassuming islets, part of a huge constellation of others just like them, suddenly threaten to sink Japanese companies with business in China. Competing claims over what Japan calls the Senkakus and China the Diaoyudao have hatched waves of occasionally violent street protests across China plus boycotts against made-in-Japan products sold in the offended country. Taiwan makes yet another claim on the islands. Japanese people fearing for their safety have cancelled trips to China, while normally eager Chinese consumers avoid cars, electronics and shops that are emblematic of the world's No. 3 economy. (China ranks No. 2, so take that.) Like foreign firms from Europe or the U.S., the big names from Japan have expanded into China to take advantage of its fabled potential market and low-cost manufacturing bases. China is now Japan's largest trade partner. The number of Japanese subsidiaries has grown eight times since the 1990s, and they sold 11.4 trillion yen ($147 billion) worth of goods to China in the 2011 fiscal year. Another 13.4 trillion yen worth of stuff is shipped to China from Japan, London-based Capital Economics says in a Sept. 24 report on fallout from the turf strife. Compounding the dispute, China and Japan may never settle a series of problems that extend back to World War II. After Japan surrendered and left occupied China in 1945, it never adequately apologized and instead glorifies wartime acts, Beijing argues. It's astonished that Tokyo would now insist on controlling the disputed islets, plus claiming an undersea oilfield north of it. Japanese leaders accuse the Chinese government of bringing up these issues late in the game (Beijing said little until about 20 years ago) to stoke public nationalism while overlooking the renunciation of its World War II past with a 1947 peacetime constitution.