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The Enterprise has become infected with Rigellian fever, which is a fast-acting, lethal disease. The only cure needs substantial quantities of the mineral ryetalyn. The come upon the uninhabited planet Holberg 917-G as a source of the mineral, and they only have four hours to retrieve the mineral and process it into the cure.
When Kirk, Spock, and McCoy beam down, they are attacked by a floating robot, which can deactivate their phasers. They are saved by the appearance of a man named Flint. Flint says they are trespassing on his planet and demands that they leave. Kirk explains the situation and says they will buy or trade for the ryetalyn, and if necessary take it by force, but they must have it. Flint claims to have powerful technology to counter them; the situation seems to be a stand-off until McCoy describes Rigellian fever as being like the bubonic plague. Flint has an odd monologue about the bubonic plague, and then he becomes somewhat more accommodating. He invites them to his house to wait while the robot gathers the ryetalyn.
Flint's house is impressive, with large numbers of Earth antiques. Although Flint said he was alone on the planet, we see him and a young woman named Rayna monitoring the Starfleet men from another room. Rayna begs Flint to let her meet them. It's not clear what their relationship is, because she looks young enough to be his daughter, but he tries to kiss her.
Flint's attitude changes completely when he agrees to let Rayna meet the men. He offers to have his robot process the ryetalyn under McCoy's oversight, and then he introduces Rayna. Kirk's face positively lights up when he sees her. Flint explains that when Rayna was an infant, her parents were killed while employed by him, so he became her guardian. He has educated her extensively in the sciences and arts, but she has apparently never met another human besides him.
While McCoy is working, the others play a little billiards and have a classic discussion about humanity. Flint says that he left Earth and the company of humanity because people are savages. Kirk tries to make the point that humans have improved much beyond savagery, but that everyone has to deal with a little ugliness in themselves. (I wonder if this was a comment based on Kirk's experience in season one in "The Enemy Within".)
Spock finds a Brahms waltz on the piano, and Flint encourages him to play so Kirk and Rayna can dance. Rayna is an excellent billiards player and dancer, but she is extremely uncertain when interacting with the other men, especially Kirk. But she seems to be developing a liking for him, and he returns the feeling.
McCoy returns and says that the ryetalyn is contaminated with an impurity that makes it useless. Flint promises to have his robot get more, and he will personally oversee the process along with McCoy to make sure the mineral is pure. When they leave, Spock comments on the unusual nature of Flint's artistic possessions: Da Vinci paintings that are absolutely authentic based on technique, but that are unknown and with modern materials; an unknown Brahms waltz written in manuscript in Brahms' hand; Pollock paintings that are again unknown, authentic, and made from modern materials. In addition, Spock's tricorder scan of Flint shows that Flint is some 6000 years old. Kirk brushes this off and goes to Flint's lab.
While in the lab, Kirk encounters Rayna. Rayna is troubled, and Kirk takes the chance to comfort her. Flint's robot shows up and approaches Kirk to attack; fortunately Spock arrives just in time to shoot it with his phaser. Later, Flint explains that the robot thought Kirk was attacking Rayna. Flint begins to show some signs of jealousy about Kirk's developing relationship with Rayna. In turn, Kirk is starting to get upset at what he perceives as Flint's overly controlling nature with regard to Rayna.
The ryetalyn is ready, but for some reason Flint hides it in a locked area of his lab. Kirk, Spock, and McCoy track it down. Spock has put the pieces together and suspects what else is hidden in the lab; he tries to get Kirk not to go in. Kirk knows something is up and insists. Inside, they find the processed ryetalyn. They also find previous models of Rayna, who is an android. Kirk and McCoy are astounded. Apparently Flint wanted Kirk to know in order to encourage Kirk to leave.
Flint arrives, and Spock asks him if he really was Da Vinci, Brahms, Pollock, and others. Flint confirms it and says that he was born prior to 3000 BC, and discovered that he couldn't die and healed incredibly fast when injured. Since then, he has been married countless times and gotten tired of having mates that would eventually get old and die. He built Rayna to be his perfect mate. However, he had trouble getting Rayna's emotions to develop, so he purposely pushed her and Kirk together. Now that she is starting to love, he wants to take over for Kirk.
Now that Flint knows that they know his past identities, he doesn't want to let them go for fear that once the Federation knows about him they won't leave him alone. He somehow instantly puts the Enterprise into miniaturized stasis and is going to do the same to the three of them.
Rayna arrives and condemns his actions; she also sees the evidence and realizes she isn't truly human. Flint and Kirk begin arguing over Rayna's fate, which leads to a fist fight. Rayna can't handle the violence on her behalf and tells them she will choose. Flint and Kirk each ask her to go with them; Rayna can't decide and falls over "dead". Spock declares that she couldn't handle her new, overwhelming emotions.
The Starfleet men take the ryetalyn back to the Enterprise and stop the plague on the ship. When Spock reports to Kirk in his quarters, he finds Kirk lamenting the fate of Rayna and comments that he wishes he could just forget. He goes to sleep after Spock's report. McCoy arrives to tell Kirk that Flint is dying; apparently his longevity was somehow related to living on Earth. Then he remarks that he's glad that Kirk is finally sleeping; he goes on a classic McCoy speech about how Spock probably can't understand the ups and downs of love. Even so, he also comments that he wishes Kirk could forget. Once he leaves, Spock goes to the sleeping Kirk and touches his forehead while intoning, "forget"; obviously he is employing some telepathic technique to change Kirk's memories.
I would have rated this episode more highly, because it has many positive aspects to it, but there's one major character problem: in order for the final confrontation to work, Kirk has to fall madly in love with Rayna in less than four hours. This is patently absurd. We know that Kirk is quite a ladies' man, and I believe that he has genuine affection for each of the women he romances. Actually, this is why his many affairs don't really bother me: I feel like he is "equal opportunity" and finds qualities to truly appreciate and love in all women, and he's not just having random flings.
Despite his many romantic relationships, we've never seen him ask a woman to run away with him, like he does with Rayna. He's never even considered leaving his command, and we don't have any precedent to show that he could take a wife with him on the Enterprise. Is he really going to take Rayna away from the only place she's ever known just to set her up in a little house somewhere while he's away on missions? He's not so foolish to think that such a situation would be workable. Thus, this part of the episode requires Kirk to act completely out of character. The end of the episode tries to patch this up a bit by having Kirk regret his loneliness, but this is a side of Kirk's character that we haven't seen at all since season one's "The Naked Time". From other episodes, I wouldn't have thought he was that lonely.
Beyond this major problem, there were a lot of good aspects of the show, especially in the presentation of the characters. This makes the problem of Kirk's instant love of Rayna even more apparent. Why not set up a situation where the Enterprise had to be at Flint's planet for longer? For example, perhaps there was some damage to the ship's engines and they needed some kind of specific metal to fix them. It could be set up such that it would take weeks to mine and refine the metal, then fix the engines. Kirk falling in love with Rayna over this time period would make sense. But instead we have the arbitrary four-hour time limit because of the Rigellian fever among the crew. (This absolute time limit is laughable, as well. The fever would not follow such a strict schedule in how it affected the crew.)
The character of Flint was fascinating; the idea of one person somehow being immortal and accumulating vast knowledge, skills, and money was very interesting and seemed logical. It's too bad that we only got a few glimpses into his past: his flashback about the bubonic plague in Constantinople and his discussion of his past wives. What other historic events did Flint witness? His search for an immortal mate was also quite poignant. His situation overall reminded me of the movie Highlander, although this episode certainly came before the movie; I don't know where the idea originated.
The episode displayed very nicely the friendship between Kirk and Spock. Putting aside the silliness of Kirk's instant love, we see how Spock recognizes the signs of Kirk's increasing affection for Rayna and does his best to keep Kirk focused on the mission only. Later, when he realizes that Rayna's android nature is going to be revealed, he does his best to keep Kirk from finding that out. He knows that Kirk will be crushed to find out that Rayna is a "fake". He does this strictly to protect Kirk's feelings, because the mission would likely be helped if Kirk knew Rayna was an android and therefore stopped loving her. That was Flint's intent, after all.
At the end of the episode, Spock again shows his friendship for Kirk by trying to alleviate some of Kirk's suffering by making him forget. It's nice irony that Spock does this without fanfare just after McCoy has accused him of not knowing anything about love.
While Spock's gesture with the act of making Kirk forget is significant and appreciated, I have to question strongly the morality and practicality of his actions. First, on the practical side: just what is he making Kirk forget? Obviously Kirk needs to know about the mission and others will discuss the mission with him, so he can't forget the whole mission. Even erasing the memory of Rayna would cause problems, should McCoy (for example) mention her. I can only surmise that Spock somehow caused Kirk to forget the pain he felt at Rayna's death.
Is it right for Spock to do this? He does it without asking Kirk's permission, which seems incontrovertibly wrong. However, friends sometimes do things to protect each other, and possibly this is the kind of action Kirk would be OK with. However, should Spock make Kirk forget the pain? After all, one of the ways that humans learn and develop, even emotionally, is through experience. Kirk's painful experience here might lead him to make a better choice in the future. Plus, it's part of his overall experience in life. I think Kirk said in a past episode that pain is part of being human (although I can't recall the episode at the moment). I definitely do not think Kirk would have approved of Spock's action. But will he know that it happened? Will he realize that he suddenly doesn't feel so bad that Rayna's dead? We never find out.
There's one other interesting issue that the episode partially addresses: what exactly is sentience? At the end of the episode, when Rayna says that she will choose between the men, she is obviously dealing with many emotions. Kirk is triumphant, declaring that she is "human". He doesn't literally mean human, but that she's a sentient being, with intelligence, consciousness, emotions, and self-awareness. How should the boundary between sentient and non-sentient constructed beings be decided?
As far as I can recall, no other TOS episode had a sentient computer or android. Nomad (in season two's "The Changeling") showed some signs of sentience, specifically being able to mind-meld with Spock. The androids in season two's "I, Mudd" are definitely not considered to be sentient; it's strongly implied that Harry Mudd used some of the female androids as sex slaves, and no one cared. The androids in season one's "What Are Little Girls Made Of?" are copies of humans, but since they are killed without qualms, they are apparently not considered sentient on their own. The rest of the androids and computers encountered in the series are clearly artificial intelligences closely following programming without much original thought, let alone consciousness and emotions. The episode here doesn't address the criteria for sentience - Kirk just declares it, and then since Rayna dies, there is no follow up to it. As far as I know, this issue isn't settled until the Star Trek: The Next Generation episode "The Measure of a Man" when Data is ruled to be sentient.
A final comment: obviously Flint is and should be upset at Rayna's "death". However, since she was constructed, can't he make another one? He has lost the time spent instructing her, but otherwise there doesn't seem to be a problem. Of course, now that he is dying he probably won't have enough time to do this. Along these lines, I also wonder how long Rayna was "alive" for. Some time, clearly, since she received an extensive "education", but probably not for the 20-some years that her age appeared to be. After all, she couldn't "grow". I wonder how Flint faked her childhood memories so she thinks she's a normal human.