It's not news that tomatoes, chilies, potatoes, and corn are New World foods, or that the Spanish introduced European livestock and their dairy products to America. Here, Sokolov (How to Cook, 1988, etc.) goes well beyond these grade-school givens in tracing how Columbus's bumbling discovery began a process of transoceanic cross-fertilization that changed the world's cuisines. Most interesting is Sokolov's examination of a half-dozen distinctive New World cuisines--Mexican, the great example of a truly mixed and integrated melting pot; Peruvian, in which native and Spanish cuisine developed side by side; that of Cartagena, Colombia, a black city fed on African, local and Spanish ingredients prepared by Spanish methods, etc.--and how each evolved in its own way depending on the indigenous cuisine and agriculture and the social, political, and population makeup of the colonial societies. As for Europe, the distinctive national cuisines we know today (largely from their codification in cookbooks of the l960's and 70's) did not arise until well after Columbus's time and would be unrecognizable without their New World staples. Today we are experiencing a virtual global meltdown based on immigration (``colonization from below''), technological advances (jet travel and refrigeration), the rage for novelty, and the Americanization (in our case) of the French nouvelle cuisine, which Sokolov sees as a witty and ironic parody of that country's old haute cuisine. There is some wit to Sokolov's own take on this ``post- modern'' period, and much to chew on in his tracking down of the complexities of the earlier revolution.