After being un-nerved by the loud blast of TMA-1, we are treated to the gentle-sounding Gayane Ballet Suite. We are greeted with the title "Jupiter Mission 18 Months Later". We see a large spaceship with a spherical front, a long, spine-like middle, and 6 large exhausts in the rear. There is an antenna complex on top about halfway between the front and the back. There are three round openings in the front and a long slit of windows above them. After a good look at the exterior, we are shown the living area of the interior. It consists of a cylindrical room with a walkway going all the way around. We see a lone man jogging completely around the cylinder. The room is a sort of centrifuge - continuously rotating, thus, creating a simulated gravity along the walkway. This is the same principle the space station used.
There are two men. The first one is the one jogging and shadowboxing around the centrifuge. The second comes out of the center hub carefully "down" a ladder. In a centrifuge, there would be no gravity at the hub so as the man goes "down" the ladder, the gravity increases. Eventually, we find the two men eating and watching a BBC show. It is here where we learn a lot more.
From the TV interview, we learn the two men are Dr. Frank Poole and Mission Commander Dr. David Bowman. There are three other men in hibernation and will be awoken when the spaceship Discovery reaches Jupiter. We also learn about the 9000 series computer that runs all the systems of the ship. He is referred to as HAL and is considered to be the sixth member. After a question concerning the reasons for hibernation - which of course, are for the conservation of food and air, the remaining questions concern HAL. Here we learn that HAL is responsible for just about everything on the ship and how the 9000 series of computers have perfect operation records and have never made a mistake or distorted information. HAL even goes on to say that he is foolproof and incapable of error.
At this point, no explanation is given as to why there is a manned mission to Jupiter. It is a key to later events in the film.
Previously, we had seen ships that resembled parts of human anatomy. The Discovery resembles an entire living creature. It has a head (the centrifuge), three eyes (the windows), three mouths (the pod bay doors), three arms (the three pods that we haven't seen yet), three ears (the antenna complex), three legs (the exhaust ports). This suggests that Discovery, in having appendages in threes as opposed to a human's two, is superior to a human being. Discovery's brain (HAL) is superior to Man's.
Discovery is a tool. We already know from earlier that the more advanced and useful a tool, the more potentially dangerous it is as well. We already know that it essentially displaces the men on the ship, making them unnecessary and expendable.
Author Leonard Wheat suggests that Kubrick plays a subtle joke. Remember when the Orion "docked" with the space station. That scene suggests copulation. If you think of the Aries that exited the space station and went to the Moon as a sperm cell, you have ejaculation. When the Aries or sperm enters the Moon (Luna is a mythological mother), you have fertilization. Eighteen months later (twice the human gestation period), you have Discovery.
The manner in which Poole, Bowman, and HAL are introduced and the way we learn about the other astronauts and the mission itself - via a BBC show shows a lot of cleverness by Director Stanley Kubrick. Most directors would have used narration or clumsy dialogue to pull this off. The fact that Poole and Bowman are watching themselves on TV indicates narcissism on their parts. They've been in isolation for a month at this point and that could be affecting their behavior.
In the novel, it is pointed out that HAL stands for Heuristic ALgorithmic computer. Heuristics and algorithms are the two methods of problem solving. Heuristics involve spotting patterns and using previous experience and is generally something humans traditionally can do much better than a computer. Algorithms involves breaking up a problem into simpler, smaller problems and is a strength of computers. If HAL is as adept heuristically as he is algorithmically, then he is powerful indeed.
It was discovered after the film came out that if you took each of the letters of HAL and went one letter higher, you'd get IBM. This would suggest that HAL is one step ahead of IBM. Author Arthur C. Clarke emphatically denied that this was anything other than a coincidence.
James Horner, the film scorer for numerous films, was impressed with the way the Gayane Ballet Suite was used in the Discovery, primarily to suggest isolation and loneliness. He uses the piece in the opening sequence of Aliens in a similar way with the hibernating Ripley and cat, isolated in a spaceship.
This is one of the only films ever made that takes into account the fact that radio transmissions travel at the speed of light. This means no real-time conversations are possible between Discovery and Earth.