The presence of the painter Johannes Vermeer in the title of Timothy Brook’s new book, “Vermeer’s Hat” (Bloomsbury, 288 pages, $27.95) is a bit of a red herring. There is nothing very wrong with trying to capitalize on the public’s love of Vermeer’s paintings, or on the success of Tracy Chevalier’s novel “Girl With a Pearl Earring.” (More objectionable is the title formula, invented by Julian Barnes with “Flaubert’s Parrot.”) But the reader who turns to “Vermeer’s Hat” for information about the 17th-century Dutch painter and his mysteriously luminous canvases will be disappointed. What Mr. Brook is interested in is not the way Vermeer painted hats — for instance, the gallant, broad-brimmed hat worn by the soldier in “Officer and Laughing Girl,” whose black swoop balances the white cowl that frames the girl’s sunlit face. His concern, rather, is for the hat itself — what materials were used to make it, where they came from, and who paid for them.

“The hat,” as Mr. Brook writes, “will be the door inside this painting that we will open.” The surprise of “Vermeer’s Hat” is just how broad a vista lies behind that door. It stretches from Delft, the provincial Dutch city where the painter lived and worked, to the Great Lakes of North America, the silver mines of Potosi, the porcelain factories of Jingdezhen in China, the spice islands of the East Indies, and beyond. In each chapter, Mr. Brook seizes an inconspicuous item in a Dutch artwork — a hat, a dish, a pipe of tobacco, a silver coin — and traces the long journeys that brought it to Holland from the ends of the earth.

What emerges from this technique is a vivid portrait of the 17th century as the first great age of globalization. To use Mr. Brook’s idiosyncratic metaphor, the world in Vermeer’s day was becoming Indra’s net — a Buddhist image for the interconnectedness of all things. “When Indra fashioned the world,” Mr. Brook explains, “he made it as a web, and at every knot in that web he tied a pearl. … Everything that exists in Indra’s web implies all else that exists.”

In the same way, each item in Vermeer’s studio implies a whole world of commerce. Take that hat, with its fine felt made from beaver fur treated with copper acetate and mercury. The grandfather of Vermeer’s officer could not have obtained such a hat at any price. By the 16th century, the indigenous beaver of northern Europe was extinct, the result of centuries of voracious trapping. European hat-makers were forced to turn instead to sheep’s wool, which produced a shapeless, colorless felt.

But in the late 1500s, European explorers in North America discovered that Canada boasted a vast supply of beaver pelts, and French traders spread through the St. Lawrence River valley to obtain them from native peoples. The trade was unimaginably lucrative: “Trade goods valued at one livre when they left Paris,” Mr. Brook writes, “bought beaver skins that were worth 200 livres when they arrived back there.” Soon the beaver hat became an essential status symbol for Europeans such as Vermeer’s officer, who would naturally wear his best hat when he went courting. The demand for beaver hats was so intense that the second-hand hat trade boomed — though it was closely regulated, Mr. Brook writes, “out of a reasonable fear of lice-borne diseases.”

Before that pelt could end up on a Dutchman’s head, however, it had to cross thousands of miles of land and ocean. Behind every commodity, in these early days of global commerce, lay a genuine adventure. Thus Mr. Brook’s chapter on the hat begins on a battlefield on the shores of the Great Lakes, where one July morning in 1609, the French explorer Samuel de Champlain and his native allies confronted dozens of hostile Mohawk warriors. The Mohawks were determined to break into the beaver trade, which was monopolized by the tribes of the Huron Confederacy. Champlain, however, had a secret weapon on his side: the harquebus, a primitive firearm whose loud report “astonished” the Mohawks. After his first shot brought down three warriors, the Mohawks fled. As Mr. Brook makes clear, trade and warfare were often hard to distinguish in Europe’s expanding commercial empire. Just as we seldom pause to think about the sweatshop workers who make our clothes, so Vermeer’s officer probably never reckoned the cost of his hat in American Indian lives.

North America is one of the pearls in the Indra’s net of Mr. Brook’s story. But the major strands in “Vermeer’s Hat” lead even farther away from Holland — all the way to China, on the other side of the world. Perhaps it is because he is a professor of Chinese Studies at Oxford that Mr. Brook sees China as the real center of gravity in the 17th-century global economy. But he makes a convincing case that, from Columbus on, the dream of China and its wealth was the major engine that propelled European explorers and merchants around the world.

Even Champlain’s voyage up the St. Lawrence was meant to discover a new, more direct route to China, by way of the fabled Northwest Passage. As Mr. Brook shows, it was hard for Europeans to let go of the fantasy that the Great Lakes might open out, on their western shore, onto the coast of Asia. As late as 1634, one mapmaker marked the empty space next to the Lakes with the legend, “It is believed that there is a passage from there to Japan.” One vestige of that error remains on the map even today: The Canadian city of Lachine was so named because Champlain hoped it would serve as a customs depot for merchandise headed to China.

Later chapters of “Vermeer’s Hat” draw on Mr. Brook’s intimate knowledge of China to show exactly what happened when European curiosity and lust for profit collided with Chinese conservatism and xenophobia. Vermeer’s paintings offer another “door” onto this story, in the shape of the porcelain dish full of fruit in “Young Woman Reading a Letter at an Open Window.” The china dish, Mr. Brook points out, is a subtle echo of the painting’s main theme, for the absent lover whose letter the woman reads might well be on a ship in the Indian Ocean, heading home from Batavia with a cargo of Chinese porcelain.

The first specimens of china that arrived in Holland were spoils of war, captured by Dutch pirates from Spanish and Portuguese vessels. Immediately it became another must-have consumer item. As Mr. Brook writes, “the first Chinese porcelain to reach Europe amazed all who saw or handled it. Europeans could think only of crystal when pressed to describe the stuff.” (The Dutch called it kraakporselein, “carrack porcelain,” after the Portuguese ships.) By 1608, the Dutch East India Company was placing huge orders. In the first half of the 17th century, over 3 million pieces of china made the long trip back to Amsterdam. Potters in Vermeer’s own city began to produce delftware in imitation of real china, helping to satisfy the limitless demand.

On the Chinese side, however, this flourishing new trade provoked more suspicion than satisfaction. The government of China tried to keep overseas trade under strict control: The Portuguese were allowed to do business out of Macao, and Chinese junks sailed regularly to the Spanish port of Manila, but any attempt by the Europeans to overstep these concessions was punished. Mr. Brook illustrates the point with the story of the Nostra Sehora da Guia, a Portuguese ship that wrecked on the Chinese coast. When the local authorities discovered hundreds of foreigners on the beach, including “Dwarf Pirates,” “Red Hairs,” and “Black Ghosts” (as the Chinese called the Japanese, Dutch, and Africans), they immediately confiscated their goods — killing and decapitating those who resisted — and sent them to jail. It took more than a year before the imperial bureaucracy freed them.

To the Chinese government, embroiled in a losing war against the Manchus to the north, all foreigners were mistrusted as potential pirates, missionaries, or spies. As Mr. Brook puts it, the “wider world was a source of threat, not of promise or wealth, and still less of delight or inspiration.” But as “Vermeer’s Hat” shows, in the 17th century as in the 21st century, there is no way out of Indra’s net. To those who protest globalization, this is a cause for despair. But as Mr. Brook concludes, “If we can see that the history of any one place ultimately links to the history of the entire world, then there is no part of the past — no holocaust and no achievement — that is not our collective heritage.”

akirsch@nysun.com