In the predawn hours of Dec. 31, 1775, American soldiers advanced through a blizzard toward the old stone walls of Quebec City. Their boots slipped on ice. Wet gunpowder jammed their muskets. The city’s defenders pushed them back with withering cannon fire. By the time the sun rose, hundreds of Americans were dead, wounded, or captured. The assault had collapsed, and Canada remained in British hands.A few months later, the Americans ended their invasion of Canada. The United States declared its independence in July with 13 states, not 14. Had the invasion succeeded, America’s map would look very different today. The country would have begun its life as a bilingual nation and soon become an Arctic power.On America’s 250th birthday, we remember a small republic that won its independence, spread west across a continent, and grew into a global power. But this is only one version of America that might have emerged. For two and a half centuries, the size and shape of the United States remained an open question. Americans debated, foreigners resisted, and key moments like that snowy battle led to outcomes that seem inevitable only in hindsight. Each change of the map was both driven by and helped create a different vision of America.