Spain had maintained a colony on the island of Jamaica since the early 1500’s. In 1655, English soldiers took the island from a small number of Spanish troops. After several attempts by the Spanish to re-take the island, the governor and wealthy landowners concluded that they needed more protection than the Royal Navy was prepared to offer. In 1657, Governor Edward D’Oyley offered the buccaneers access to Port Royal and letters of marque against Spanish shipping, in exchange for their protection.
Oliver Cromwell rules England as “Lord Protector”. Philip IV of Spain has reigned over the Spanish Empire for nearly 40 years. On paper, the ruler of France is Louis XIV, but since he’s still in his early teens, the real power is in the hands of his mother, Anne of Austria, with considerable input from Cardinal Mazarin. Mazarin’s mentor was Cardinal Richelieu. (Yes, the same Cardinal Richelieu who was played by Tim Curry, who has not only played Long John Silver, but Captain James T. Hook, as well. Yes, the same one that had the problems with some Musketeers.) France and England are allied in a war against Spain. The Tokugawa shogunate is in charge of Japan, which is a closed country, allowing very limited relations with other countries.
Coffee first arrives in France in 1657, carried by a traveler returning from a visit to Constantinople, but won’t be generally available there until a couple of years later. Thanks to the East India Company, it has already become available in England. London has had a coffeehouse for a couple of years. The tables are turned, though, when it comes to chocolate. Hot chocolate had been a popular drink in Europe for some time, but in 1657, a Frenchman opened the first chocolate house in London.
The first pendulum clock is patented in 1657 by Christiaan Huygens, who also publishes the first book on probability theory. This means that the 3d6 bell curve that lies at the heart of GURPS is cutting-edge science.
While there are methods of determining one’s longitude, in 1657, none of them are effective for use on a ship at sea. Though the sextant lies decades in the future, navigators have equipment to determine latitude. The crew of a ship on a long voyage would know their location north or south of the equator, while having only a relatively vague notion of where they were, east to west.
The Salem witch trials are still 35 years in the future. Shakespeare has been dead for over 40 years, Miyamoto Musashi for 12. Fifteen years ago, Abel Janszoon Tasman’s expedition brought the first European contact to the Māori. (It didn’t go well.) The Great Plague of London hasn’t yet occurred; neither has the Great Fire.
Isaac Newton is a teenager living on his parent’s farm, with no training in mathematics. It’s still a few years until the Royal Society will be established. Science is only starting to question the idea that fleas just spring into existence from dust, and maggots from raw meat. It’ll be another six years before cells are discovered.
New York is still New Amsterdam, for a few more years. Harvard University has been established for nearly twenty years, and is training Puritan ministers in the Massachusetts Bay Colony.