Thomas Fleming is a prize-winning historian and bestselling author and expert on the American Revolution.

(CNN) Few people understand that Alexander Hamilton, betting that Aaron Burr's first shot would miss, planned to fire in the air. Called a "delope," it was a duelist's way of humiliating an opponent by suggesting he wasn't worth shooting. Hamilton had messed up his attempt to dump sitting president John Adams. He needed a great leap forward to regain his status as the leader of the Federalists, forerunners of today's Republicans.

Meanwhile, President Thomas Jefferson was ham-handling his second term in spectacular fashion. When British and French navies began seizing American merchant ships, Jefferson banned all his nation's vessels from the high seas. Soon 40,000 sailors rioted in our ports. Businesses collapsed and New England talked treason. A newspaper described it as "cutting a man's throat to cure a nosebleed."

"What if" -- or counterfactual history -- offers a unique way to explore the motives and potential actions of a major historical figure such as Alexander Hamilton. What if he hadn't died after that duel in 1804? We can't know for sure, obviously.

But here are some ideas:

The Hamilton who survived the duel would have run for president against Jefferson's handpicked successor, brilliant but colorless James Madison -- and won going away. He would have taken the country in a new direction, creating a trained army to win the War of 1812, absorbing Canada and changing the nation's name to The United States of North America.

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