The Story
"During the past few weeks, I've wondered if you might be having some second thoughts about the mission." Hal informs this to Dave Bowman. Hal goes on to point out there are some "extremely odd things about this mission". Hal gives specific references to rumors about something being dug up on the Moon, the tight security during training, how the other astronauts (Hunter, Kimble, and Kaminski) were trained separately, and how they were placed aboard Discovery already in hibernation. Dave appears thoughtful during all this and concludes that Hal had opened the conversation in order to work on the crew psychology report. Hal admits that was what he was doing. Before he can say much more, he reports to Dave that he detects a fault in the AE-35 unit.
The conversation is forgotten as a faulty AE-35 unit is serious. From the computer displays, we can see it has something to do with the antenna complex that allows communication with Earth. Since the complex is on the exterior of the ship, an EVA (extra-vehicular activity) would have to be performed. Both Frank and Dave go through the preparatory steps for the EVA which includes a brief message from mission control confirming the need for the EVA. The preparation also means leaving the artificial gravity of the centrifuge and working in the weightless parts of the ship including the front control area and the pod bay.
In the pod bay, which also functions as an airlock, a red-space suited Dave has Hal prepare one of the 3 pods. The pod slowly extends away from the Discovery on a platform before Dave takes off making the pod an independent spacecraft. We see two asteroids whiz by - indicating that the Discovery is most likely in the asteroid belt between Mars and Jupiter. During all of this, all we hear is Dave breathing and a hissing sound - presumably from an air hose in Dave's suit. The pod slowly approaches the antenna and stops. The rest of the EVA will be a spacewalk as Dave pushes himself outward and floats toward the antenna.
Once at the antenna, Dave retrieves a small black box - the replacement AE-35 unit. He then opens a small hatch and pulls out the defective unit. No more of the EVA is shown but it can be assumed that it went successfully.
Meanings
Note the meticulousness of the entire EVA, everything is done so carefully. Even a routine repair such as this is taken very seriously. Every procedure must be checked and re-checked.
In Hal's conversation with David Bowman, we learn that the Discovery mission has something to do with the monolith found on the Moon.
When the group of primitive men defeated the rival group at the water hole, it can be assumed that the defeated group quickly figured out the use of the bone-club. Over the millennia, humans learned to keep their secrets and prevent their rivals from obtaining their technology. In the midst of the Cold War, Heywood Floyd makes a solo trip all the way to the Moon with the primary purpose of ensuring a potentially powerful discovery remains a secret. A conference of scientists is held, not to discuss a scientific discovery, but to discuss why its important not to disclose it. To fearful humans, security is that important since no one was sure what the monolith was or what it was capable of doing.
Since the Discovery mission is related to the Moon discovery, the security concerning the mission must have been extreme. Hal mentions how the three other astronauts were trained separately from Dave and Frank. Not only that, the other three astronauts were placed aboard the Discovery already in hibernation. They must have known more about the true nature of the mission than Frank and Dave. Because they are in hibernation, the information could not be leaked - intentionally or accidentally to Frank and Dave. This is important since Frank and Dave are public figures.
This security continues with Hal. Since Hal is in control of all operations on the ship. It was necessary to inform Hal of the purpose of the mission in case the human crew became incapacitated. Hal possesses this information but Frank and Dave do not.
This scenario presents Hal with a paradox. Hal earlier had said "No 9000 computer has ever made a mistake or distorted information. We are all, by any practical definition of the words, foolproof and incapable of error." Hal, by concealing information is in a way, distorting information. The security that he had been told is so vital to the mission is endangering his perfect track record. The longer he continues this deception, the more the risk of his breaking his most sacred priority.
Hal must do something to correct this, but how? If he disclosed the information, that in itself would be an error so he can't go that route. From the earlier chess game, we know that Hal is capable of thinking ahead and is able to predict the behavior of human beings. Hal makes the first move. He probes David Bowman to find out what he knows. Hal attempts to provoke a response by giving him clues. Perhaps Bowman has already guessed the mission's true purpose. If that's true, then Hal can be at ease that he isn't hiding anything.
Notice how Dave reacts when Hal mentions the something dug up on the Moon and the security precautions. We don't know much about Dave yet but as the film proceeds, we will learn that Dave is very careful and shrewd. Dave probably has deduced why he is on a mission to Jupiter. When Hal poses questions about his second thoughts about the mission, Dave is questioning to himself why Hal is asking this. Unfortunately, Dave remains discreet because he wrongfully concludes that Hal is working on the crew psychology report. That being the case, Dave mistakenly believes that Hal is testing him and it would be proper not to reveal anything.
Had Dave said something to the effect of "Hal, I know what you are getting at and Frank and I know what's going on." Everything would have been fine. However, Dave's non-response forces Hal to go to the next step. Hal fudges up a report of a faulty AE-35 unit - the hardware that keeps the antenna complex pointed to Earth.
Hal, in lying, is obviously committing an error. In Hal's mind, it is an error to fix another error and thus, cancels them both out. Hal may have a superior brain but his reasoning is more that of a child.
Why did Hal make up the fault of the AE-35 unit? The answer is in the following chapters.
Other Notes
This is one part of the film where different fans make very different interpretations. Let me go over some of them here.
Many 2001 fans say that David Bowman was too bored or brain-numb to understand what Hal is getting at. I simply don't accept this. Dave (and for that matter, Frank) is too intelligent to not have heard the rumors and not at least considered that it may have something to do with the mission. Dave, in not confirming Hal's suggestions, was being discreet, not stupid.
Many fans argue that Hal made a mistake in predicting the fault in the AE-35 unit. I strongly disagree. Future events support my belief that Hal called it faulty while knowing that it wasn't.
Many also question why David Bowman was able to walk in the pod bay that contains no gravity. They apparently did not notice the velcro walkways. Notice how carefully Dave walks.