Europeans and Chinese share a common image of the Mongols as mounted warriors thundering across the steppe, sweeping all before them. The image is a memory of defeat, partial for Europeans, who stopped the forces of Genghis Khan outside Vienna; total for the Chinese, who could not fend off his grandson Khubilai. The Japanese remember the Mongols differently. For them, Mongols are men in boats, which is how they arrived in Japan in 1274, against all expectations, all odds, and all common sense. That invasion failed, but once was not enough. As many as 100,000 men tried again seven years later in a stunning armada of 4,000 ships. Even if we use reason to re-evaluate the numbers, we cannot whittle them down enough to obscure the fact that Khubilai’s two campaigns were the largest flotillas of warships any state had yet put to sea. Their scale makes their defeat all the more remarkable. And this is yet another way in which the Japanese memory differs from ours: they recall the Mongols as losers.