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For nearly three centuries, unless you knew a Mason, you probably never set foot inside a lodge, where members are inducted in ancient initiation rituals and vow to keep secret the metaphors of the world’s oldest fraternity. But Saturday, following a much more modern tradition, the Masonic lodges around the state will throw open their doors to anyone who wants to learn more about the group. The group, whose numbers are dwindling, is hoping to make the organization more accessible in an era when people move around so often that they may not know the Masons in their community. The Masons in Massachusetts began holding open houses eight years ago.