Alexander was a resident of Platonius who, unlike the other Platonians, did not have the power of psychokinesis. He was a person of extraordinarily short stature who served as court buffoon and slave to the other Platonians.
In 2268, the USS Enterprise arrived at Platonius after receiving a call for medical assistance for the planet's leader Parmen, who was suffering from a fever due to a leg wound that became infected. Enterprise chief medical officer Leonard McCoy later determined that the others got their power from the food native to Platonius which contained kironide, a substance that after being assimilated by the pituitary gland promoted psychokinesis. Unfortunately, since dwarfism stemmed from a malfunction in that gland that also regulated body growth, Alexander did not have the psionic ability.
When Parmen wanted McCoy to remain on Platonius after curing him of the fever, he also refused to let the crew leave so that they could be used as slaves, and for his amusement. Alexander agreed to help the Enterprise crew escape. McCoy synthesized the kironide and injected himself, Kirk, and Spock. They offered Alexander an injection, but he refused to get a dose out of disgust for his fellow Platonians' laziness and cruelty. Later, when the Platonians forced Kirk, Spock, Lieutenant Uhura, and Christine Chapel, the latter two forced to beam down, to each wear Greek garb and to entertain them, Alexander, disgusted to see the Enterprise crew subjected to the Platonians' cruel humiliation, grabs a knife and tried to stab Parmen with it but was stopped. Parmen then tries to force Alexander to stab himself but Kirk, observing, prevented it when the kironide shot McCoy gave him earlier had finally started to take effect. Parmen tried to use Alexander to kill Kirk. He forced him to try and stab Kirk, but Kirk, whose powers were now stronger, turned Alexander around and he again approaches Parmen with the knife. Alexander wanted to kill Parmen, but Kirk dissuaded him.