The background hum of Discovery resonates as the screen goes to black leaving a cliffhanger for the audience to ponder. They'll have time too as the film goes to intermission. As mentioned in The Film Begins, Stanley Kubrick maintained the general format of a typical MGM movie. Here, he gave us the intermission. Usually, intermission comes a bit past the midway point of the film where all the characters and plot lines are firmly set. This is the case here. Now the audience gets a breather and can take a bathroom break or take the opportunity to get more popcorn. There is also opportunity to digest the events that led up to this point and think about where this is going. For first-time viewers of 2001, very few will make the connections of how the Cold War and concern for security and secrecy are contributing to the drama at hand. However, many may think about what Hal is really up to and how Frank and Dave, having such limited capabilities against such a seemingly omniscient computer, can handle the situation.
An anxious audience waits for the film to continue and reveal how the drama will be played out. The curtains open and again, we get a blank screen. Again, a piece of Ligeti's Atmospheres plays. The drama will have to wait.
Kubrick has a little fun at the expense of the audience here. The conflict between computer and the two humans is by far, the most palpable drama in the entire film and the intermission and return of the black screen and eerie music prolongs the anticipation of the resolution of the drama.
The intermission also reminds us that what we've been emotionally wrapped up in is just a small piece of the big picture. There are many themes at work here involving Man's place in the universe, Man's odyssey through evolution, God and the Intelligence that is driving humans to explore space. Ligeti's Atmospheres and the black screen remind us of the journey - inside and out that we are taking.
This part of the film provides many of the most memorable and quotable scenes since, unlike other parts of the film, it has a conventional narrative. The whole Mission to Jupiter chapter of 2001 is actually a self-contained story. In this regard, it is also the most understandable and easiest part of the film to relate to. Some people fail to connect this with the man-apes, the trip to the Moon, and the part of the story afterwards. This is why some seem to think of 2001 as a collection of stories rather than one large one. Often, people who find the film "boring", actually like this part and hated the rest.