(written from a Production point of view)
Spock finds himself marooned on the planet Delta Vega, a barren planet with many rocky spires. Despite his circumstances, he does not stress, as he has been trained to control his emotions and emotional state. This was done by learning techniques and puzzles that emphasized logic over emotion. While playing with a puzzle given to him by his father, Sarek, he reminisces about some of the other puzzles and crises he has faced.
When he was young, Sarek assigned a tutor to Spock in order to teach him how to play the Vulcan harp. He learned that the mathematics and logic behind the music would help him master his half-Human side inherited from his mother. This half-Human side also led him to being something of an outcast among his peers at the Vulcan Atheneum, but he learned to keep a calm focus. He also learned the Vulcan nerve pinch, something far more elegant than a brute shove or careless punch.
When adolescence arrived, he had to master the tal'oth test in Vulcan's Forge. He smelled the Sa-te kru beast before seeing it and realized that it was the embodiment of his roiling emotions. A simple nerve pinch allowed him to "pass through to a new state of consciousness" and become a mature adult.
Years later, he joined Starfleet and by this time was very proficient with the harp. He did notice that the harp's music affected the Human mind by triggering emotions, quite the opposite effect it had on Vulcans. One example was the way that it affected Lieutenant Uhura. On the USS Enterprise, he discovered the game of three-dimensional chess and found that "playing chess with Captain Kirk was a welcome respite from the perils we encountered." The lessons learned from this game also helped him suggest the means of defeating Khan Noonien Singh in the Battle of the Mutara Nebula by viewing things in a three-dimensional way rather than a simple two-dimensions.
He notes that Kirk never believed in unsolvable puzzles in no-win scenarios, but finds himself unsure. He knows that he is responsible for his circumstances, what has happened, and what will happen, but despite his efforts, he finds himself afraid. In the sky above, the Enterprise appears and he finds himself faced with a choice. "A choice that will change the course of history. But it is the galaxy's only hope... it is only logical."