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The Enterprise receives a call for help from a previously unknown civilization. Kirk, Spock, and McCoy beam down to discover a small, self-proclaimed utopia. The leader of the community, Parmen, got a scratch, which got infected, and is now on the verge of death. McCoy treats Parmen, and in the process we discover that Parmen and the other members of the utopia have telekinetic powers. Parmen's powers are the strongest, which has made him the leader.
One member of the community, Alexander, is a midget and does not have the "power". He tells the Starfleet men that they are the survivors of a civilization whose sun died; they traveled to Earth and lived there during the peak of the ancient Greek civilization. When the Greek civilization fell, they left Earth, taking with them their version of Plato's philosophy. Thus, they call themselves Platonians. After they arrived on their current planet, they developed the power. They live for thousands of years, and since they can do everything with their minds, they have lost their immune systems, making them vulnerable to simple injuries.
Despite Parmen's claims that the Platonians are peaceful and devoted to pursuits of the mind, we quickly see that they are not so high-minded. They have no problem using their powers to manipulate Alexander and move him around to do errands for them or entertain them. Parmen has used his power to lock the Enterprise into orbit; when Kirk demands its release, Parmen forces Kirk to beat himself up.
Later, Parmen and his wife Philana try to patch things up with the three Starfleet men. They give them gifts and Parmen says they are free to leave... except McCoy. They have realized they need a doctor, so they want McCoy to stay. Of course, McCoy refuses. Parmen does not like to be refused, so he begins using his power to force Kirk and Spock to sing and dance and do other humiliating acts. Spock is forced to laugh and cry. For some reason, Parmen thinks that witnessing their humiliation will force McCoy to capitulate; apparently the Platonians value dignity more than freedom.
The Starfleet men are finally allowed to retire to their quarters, where they begin to commiserate. Kirk is extremely angry with Parmen, but he is able to look past his humiliation. Spock is especially enraged by Parmen's treatment of them, particularly because he was forced to do things that could have injured Kirk. He forces himself to "master" his anger. This scene was nice demonstration of how the characters understand and support each other, even in very hard times.
They also begin to talk more with Alexander about the Platonians. Alexander is completely enthralled by them because they treat him nicely and they don't have the power. When he finds out that no one else in the Federation has the power, he becomes their staunch ally so he can go with them when they leave. From Alexander's information, Spock and McCoy deduce that the Platonian's telekinetic power developed from the ingestion the substance kironide in the local vegetation. Alexander did not develop the same power for the same reason he did not grow to full size. McCoy prepares an injection of kironide for Kirk and Spock that contains enough to give them telekinetic powers twice as strong as Parmen's; the catch is that they don't know how long it will take for the power to develop.
Parmen and Philana apparently are not amused by just Kirk and Spock anymore, so they have forced Lt. Uhura and Nurse Chapel to beam down. They and Kirk and Spock are clothed in Greek tunics and put into a small arena; when the audience of Platonians is revealed we find out that this is a stage. Parmen is going to conduct a show for the amusement of the other Platonians and to try again to convince McCoy to stay.
First Spock is made to sing. Then Spock and Chapel are paired up, as are Kirk and Uhura. Each couple is forced to kiss. There is some nice irony, as Chapel even mentions, that she's always wanted to be close to Spock, but not like this. After the romantic interlude, Kirk and Spock are led to a table of torture implements, with Kirk being forced to select a whip and Spock a hot poker.
Alexander can't stand watching his new friends be tortured, so he grabs a knife and tries to sneak up on Parmen. Philana sees him and "freezes" him until Parmen can take over and make him get ready to stab himself. Suddenly, the knife is knocked off-target, to Parmen's shock. Kirk reveals that he did it, which Parmen doubts. They play a mental tug-of-war with Alexander and his knife, until Kirk succeeds in putting Alexander with his knife at Parmen's throat. To Alexander's disappointment, Kirk doesn't kill Parmen.
Now that Kirk has shown his power to be stronger than Parmen's, Parmen is very happy to be as accommodating as possible. Kirk simply demands that there is no more interference with them leaving, and they take Alexander with them.
This episode has some interesting ideas and social commentary, but a lot of it is also slow and/or painful. First, the good points. Kirk did a pretty good job in this episode of demonstrating the high-minded moral principles the Federation espouses. He treated Alexander like an equal, asking his opinion, and thinking of his welfare as he would for a crewmember. What impressed me more, though, was the fact that Kirk and the others did not once think of resorting to force as a means of resolving their situation. Kirk talked Alexander out of murder twice, in fact, and once he got the "power" for himself, he did not use it at all violently.
I found the premise of the power of telekinesis causing the corruption of morals to be very believable. In such a small, closed society, it would be easy for many moral principles to be corrupted, let alone when the people have almost god-like abilities. In addition, the fact that the people were extremely long-lived meant that they had plenty of time to get bored. After all, they apparently don't believe in doing much physical activity, so how much contemplation can you do over 2000 years? They clearly reveled in the petty cruelty they could cause Alexander, and when the Enterprise crewmen arrived, they were an obvious new source of amusement.
The corrupt character of the Platonians became obvious during the torture sequences. First, of course, is Parmen's willingness to torture and humiliate others. But then the type of torture is illuminating. Parmen seemed relatively content to go for plain humiliation, but we could observe that Philana preferred her entertainment to be cruel and painful. She was the one, after all, who urged Parmen to get past the romantic "scene" in the final scenario and continue on to the whips and pokers.
Why Parmen and Philana thought that McCoy would ever agree to their demands when they demonstrated such cruelty is a mystery to me. Why would McCoy ever believe they would keep their word on any issue?
There were bad points to the episode, however. First, the previously-discussed torture scenes were painful to watch precisely because they were so humiliating; I felt bad for the actors, even. These scenes were also way too long.
There were some issues of logic with the Platonians. I can suspend my disbelief for the idea that they had visited the ancient Greeks on Earth. So why do they now speak English? Why aren't they speaking Greek? And how does Parmen know French phrases? (He used the term "piece de resistance".)
At least some of the Platonians with the power must have realized that it came from the local plants. Consequently, I have to think Parmen realized that if any of the Starfleet men remained they would eventually develop the power themselves. What did Parmen plan to do if he forced McCoy to stay, and then McCoy developed the power? I suppose that he didn't think McCoy would be stronger than him. I would also have to think that Parmen had no intention of allowing any of the other Starfleet men to remain for much longer, otherwise they would also develop the power. I feel like some of Parmen's actions did not make much sense in the episode, given these facts.
The ramifications of this episode were not addressed at all. First, how long will Kirk and Spock retain their telekinetic abilities? (Interestingly, we never actually saw Spock use them.) Second, now that the Federation knows that a person can acquire telekinetic abilities simply by pumping up on kironide, what will they do with that knowledge? This is a huge discovery that we never hear about again, which is typical of the series.