The story
Paris1789
Joseph-Ignace Guillotin was a physician, a professor of anatomy, and in 1789 one of the deputies for Paris in the new National Assembly. In October that year he put six articles before it. The same crime should carry the same punishment whatever the rank of the criminal. Where the punishment was death, it should be death by a simple mechanism, quick, and the same for a duke as for a thief. Until then a nobleman was beheaded with a sword and a commoner was hanged, or broken on the wheel.
He is reported to have told the Assembly that with his mechanism the head would fly off in the blink of an eye and the condemned would feel nothing but a slight coolness on the neck. The deputies laughed. A song about the doctor and his machine was in the streets within weeks.
The machine itself was not his. It was designed by Antoine Louis, secretary of the Academy of Surgery, and built by Tobias Schmidt, a German harpsichord maker with a workshop in Paris. It was tested on sheep and on corpses, and first used on 25 April 1792 on Nicolas Jacques Pelletier, a highwayman. The crowd, used to a spectacle, complained that it was over too fast. For a while people called it the louisette, after Louis. Then they called it after the doctor, and it stuck.
The king went under it in January 1793, the queen in October, Robespierre the following summer. Guillotin lived on, quietly, and died in his bed in 1814. After his death the family petitioned the government to give the machine another name. The government refused. So the family changed theirs.

The gap
The word means the blade, and in offices it means the cut: a guillotine on spending, a guillotine motion to end debate. The man behind it was arguing for mercy. His idea was that if the state must kill, it should do so without pain, without a show, and without one death for the rich and another for the poor. He got two of the three. The show turned out to be the point.
He did not die by his own machine, whatever the story says; that was a different doctor named Guillotin, in Lyon. He died of an infected shoulder, at seventy-five, a man whose name had become the one thing he had tried to make kinder.