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 jester and slave to the other Platonians.
In 2268, the USS Enterprise arrived at Platonius. Enterprise chief medical officer Leonard McCoy determined that the others got their power from the food native to Platonius which contains Kironide, a substance that after being assimilated by the pituitary gland promotes psychokinesis. Unfortunately, since dwarfism stems from a malfunction in that gland that also regulates body growth, it is obvious that is why Alexander did not have the psionic ability.
When the Platonians refused to let the crew leave so that they could be used as slaves, and for amusement, Alexander helped the Enterprise crew escape. McCoy synthesized the kironide and injected himself, Kirk and Spock. They offered Alexander an injection, he however refused to get a dose out of disgust for his fellow Platonians' laziness and cruelty. Parmen, the leader of the Platoians, 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 approached Parmen with the knife. Alexander wanted to kill Parmen, Kirk dissuaded him.