The Gayane Ballet Suite resumes as the film focuses on Frank Poole. Frank is lying on a table with protective shades, apparently trying to get a tan. Hal announces that a transmission from his parents has been received.
Frank's mother and father appear on the video screen. They briefly talk about finances and other personal stuff. They wish him a happy birthday and quickly sign off. Frank barely stirs through the whole message. He can't respond since, as mentioned before, transmissions take minutes to cross the gulf of space to reach the Discovery and of course, any reply would take just as long.
We next see the end of a chess game between Frank and Hal. After an exchange of moves, Hal points out to Frank that his next move will lead to a checkmate. Frank resigns the game.
We now focus upon Dave Bowman. He is drawing sketches of the three men in hibernation when Hal calls him. Hal wants to look at his drawings. Upon reviewing them, he wants to ask Dave a personal question.
Little does Dave know but another chess game has begun.
It is evident that both Frank and Dave have considerable amounts of free time. It is also apparent that the two men are awake at alternate times and are perhaps together only at the meal. Notice that Frank was wearing a robe while Dave was in uniform at the meal. This would add to the sense of isolation as each man spends most of his time alone. What effect does such isolation have? Note the oddity that Frank is trying to get a tan. What's the point of that?
The message from his parents seems to barely interest Frank. He is more interested in his own personal comfort. Both mother and father ramble on about mundane, earthbound stuff that Frank can't really relate to anymore. Isolation has distanced him from his loved ones beyond that of the physical distance.
The sad Gayane Ballet Suite echoes the sense of isolation.
Note that as in the case with Heywood Floyd, Frank is an American with a relative who speaks with a British accent (his father).
Note also, that as in the video conversation with Floyd, it is somebody's birthday.
There is a lot to the brief chess match. First of all, many of the Frank's pieces are still in their original place so it appears he is on the defensive. Secondly, notice that after Poole moves his rook away from his king, Hal is able to predict the outcome - a checkmate.
The chessboard configuration where Hal made his prediction that Frank would make the losing move of capturing his queen.
In being able to predict what Frank will do next, Hal is demonstrating the heuristics aspect of his brain. A purely algorithmic computer, as we know them, would not be able to use prior behavior to estimate future behavior. Hal obviously can.
If Hal is as adept heuristically as he obviously is algorithmically, his mind would seem to be clearly superior to that of Man's. Has man made a tool that is completely superior to him?
Hal can appraise Dave's artwork. This reveals more of his heuristic ability. One must have experience to judge the quality of art. Note how he remarks that Dave has "improved". How could a computer make this kind of judgment?
The chess game shown is from an actual chess game played in 1913. In How Hal Plays Chess, we learn that Stanley Kubrick, a very good chess player himself, chose this game particularly because it requires a clever sacrifice of the queen to win.