Let's face it; it can be kind of hard to pin down Dr. Heywood Floyd in a character analysis. He spends most of his screen time in transit from the Earth to the moon, and while the imagery is spectacular and The Blue Danube Waltz is a lovely tune, there's only so much characterization one can get from a guy sleeping in his seat during a commercial fight. Still, he has an important role in the story.
Most obvious is that Floyd's character doles out a lot of exposition. After about a half hour of no dialogue whatsoever, the film had to start planting some narrative seeds somewhere, and the exposition we receive here serves to connect the other chapters.
For an example, let's consider this dialogue exchange:
MICHAEL: Here's what started the whole thing.
FLOYD: Oh, yeah.
HALVORSEN: When we first found it, we thought it might be an outcrop of magnetic rock, but all the geological evidence was against it. Not even a nickel-iron meteorite could produce a field as intense as this. So we decided to have a look.
MICHAEL: We thought it might be the upper part of some buried structure, so we excavated out on all sides, but unfortunately we didn't find anything else.
HALVORSEN: And what's more, the evidence seems pretty conclusive that it hasn't been covered up by natural erosion or other forces. It seems to have been deliberately buried.
FLOYD: Deliberately buried.
This dialogue sets up important details for later. First and foremost, it's telling us that this object isn't natural, and if it isn't natural, then someone, or something, must have created it and put it there.
Another example is when Floyd is giving his speech to the leaders of Clavius base. He notes:
FLOYD: I'm sure you're all aware of the extremely grave potential for cultural shock and social disorientation contained in this present situation if the facts were prematurely and suddenly made public without adequate preparation and conditioning.
Later, when HAL is sharing his misgivings about the mission with Bowman, we can infer that this concern about preventing "culture shock and social disorientation" is a part of the reason that the astronauts aren't told about the true purpose of the Jupiter Mission.
This is later confirmed by none other than the exposition guru himself, Floyd. After Bowman disconnects HAL's higher brain functions, a message appears. In it, Floyd informs the crew—what's left of it anyhow—that the monolith has been transmitting a radio signal to Jupiter.
This speech is the last bit of dialogue in the film, and through it, Floyd helps the audience connect the episodes in prehistoric Africa to the Jupiter mission, and helps propel Bowman toward Jupiter and the film's mysterious conclusion.
Pen and the Art of Space Maintenance
Floyd's story conveys information through its visual imagery as well as its expository dialogue. At first glance, space travel appears like a wondrous tomorrowland. Everything's sleek and streamlined, and the computer screens display a vast amount of information and technological wizardry. We're simply in awe of how little we understand what's happening on those screens. The impression is furthered by the use of The Blue Danube Waltz during these sections.
But the film starts to include imagery that subtly suggests the difficulties and dangers of space travel. For example, think about that floating pen.
Floyd's fallen asleep on his spaceflight to the space station, because for him space travel is no big deal. It's just another business trip. He's probably got Platinum Elite frequent flyer status on Virgin Galactic. As he's sleeping, his pen floats from his shirt pocket. The stewardess (that's what they called them back then) comes out and quietly returns the pen to his pocket.
But notice how she's dressed; she has Velcro shoes to prevent her from floating off the floor, and every step she takes is deliberate and difficult. She's even wearing a cushioned hat, like a bicycle helmet, to protect her from a bonk to the noggin.
All this simply to get a pen to stay inside a pocket. The imagery informs us how difficult living in space truly is. Other playful images in the same vein include the tray of packaged space food and the zero-gravity toilet that comes with ten (ten!) steps worth of instructions. So when we see Bowman and Poole doing a spacewalk later, we have a better understanding of the difficulties these men must undergo to travel and live in space.
Water Hole v2.0
Although seemingly very different, imagery from Floyd's chapter continues the story from the Dawn of Man chapter, and we see that a lot of the problems of our hominid ancestors have been resolved in the space age.
When the hominids tried to sleep earlier in the film, they were worried by the sounds of the predatory leopard in the distance. In contrast, Floyd sleeps like a baby despite the fact that he's flying in space. If anything goes wrong, he's a goner; the vacuum of space is a far more effective killer than any leopard. Yet he seems content and trusting, swaddled as he is in technology.
The scene between Floyd and the Russian scientists isn't all that different in its themes as the scenes of the hominids' group confrontations. When Floyd first meets Dr. Smyslov, he offers him a drink. Notice that the round table is full of drinks and the scientists surround it with Floyd facing the camera. Despite its clean white surface and some swanky modern furniture, this scene parallels the water hole.
Like that scene, we have two rival groups of hominids here, Americans and Soviets. This film was released in 1968, during the Cold War era, so the pairing of the USSR scientists and an American was likely a deliberate choice by the filmmakers. This confrontation is missing the bone clubs of our prehistoric ancestors and even the nuclear weapons of the superpowers, but it's played with a new weapon for the space age: information.
Smyslov pries Floyd for information about the mystery surrounding Clavius base: the lack of communication, gossip about an epidemic, and a major incident where an emergency landing was denied. A battle of wills ensues:
SMYSLOV: Quite frankly, we have had some very reliable intelligence reports that quite a serious epidemic has broken out at Clavius. Something, apparently, of an unknown origin. Is this, in fact, what has happened?
FLOYD: I'm sorry, Dr. Smyslov, but I'm really not at liberty to discuss this.
SMYSLOV: I understand. But this epidemic could quite easily spread to our base. We should be given all the facts.
FLOYD: Yes, I know. As I said, I'm not at liberty to discuss it.
Floyd's clearly the victor in this exchange; he's got the 411 and is not giving it out.