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Parmen was the leader of the Platonians, a race of aliens who claimed to revere the works of Plato. They abandoned their homeworld when its star went nova and settled a new world. They had used a eugenics programme to pare their society down to a few dozen bred for physical perfection and longevity, with Parmen living for over 2000 years, much of it spent married to his wife Philana. The fruit on their new home contained a high amount of kironide which granted the Platonians telekinetic powers. Parmen had the strongest powers and claimed leadership as their philosopher-king, arguing that anyone could do whatever they wanted if their mind was strong enough. He and the other Platonians bullied Alexander, who lacked the telekinetic powers because an atypical growth hormone meant he was unable to absorb the kironide.
The Platonians had never had a doctor and their lifestyle left them with little resistance. As a result, when Parmen suffered a mild scratch, he developed a serious infection, prompting the Platonians to send out a call for help. The Enterprise responded and Kirk, Spock and McCoy beamed to the surface. Parmen's delirium caused violent telekinetic outbursts strong enough to affect the Enterprise but he was eventually sedated and cured. However, he kept the Enterprise locked in orbit. When Kirk confronted him about it, Parmen forced him to repeatedly slap himself.
Parmen did not intend to let the Enterprise leave and tell the Federation about them, and also planned to convince McCoy to stay as the Platonians' personal physician. When McCoy refused, Parmen used his abilities to threaten and degrade Kirk and Spock, forcing them to behave in a ridiculous fashion, such as laughing or crying hysterically, reciting rhymes and having Alexander ride Kirk like a horse, with the demonstration slipping into menace when Spock danced around Kirk in a way that threatened to crush his head.
After a brief respite, Parmen and the other Platonians forced Lieutenant Uhura and Nurse Chapel to beam down and continued the amusement with Kirk and Spock forced to play the role of courting them. However, McCoy had injected Kirk and Spock with a high dose of kironide. When it took affect, they gained the Platonians' powers and could no longer be controlled by them. Parmen tried to deny it and to force Alexander to kill Kirk, but Kirk overcame him, yet refused to use Alexander to kill him and talked Alexander out of doing it of his own accord.
Humiliated, Parmen submitted to regular starship visits to check on his people and conceded that uncontrolled power made people in savages. Kirk warned him not to forget the speech before he, Spock and McCoy left the planet, taking Alexander with them.
