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Top left: A photographer snaps some pictures of the monolith at TMA-1 on the moon. Top right: Between the taking of each snapshot, the photographer advances the camera, resulting in its being flipped and rotated ninety degrees clockwise (as viewed from his own perspective). Above left: A view of Poole reclining. If we rotate the image ninety degrees clockwise (from our own perspective), Poole will appear upright. The point is that the camera rotation at TMA-1 is a hint to each member of the audience to 'mentally rotate' (in his or her mind's eye) certain images presented on the movie screen. Above center: Heywood Floyd's daughter as she appears to Floyd on his video telephone screen, when he calls home from the space station on her birthday. Above right: The image of the daughter rotated clockwise by ninety degrees. Note that the two long, light gray objects behind the daughter now appear similar to legs, as if someone's feet are planted near the girl.
There are, in reality, no one's legs or feet near Floyd's daughter, as becomes obvious when she stands up near the end of the phone conversation (as shown at left), and her body's true orientation with respect to the surroundings of the room she's in becomes evident. The long gray objects (indicated by the two arrows in the screencap) are parts of a piece of furniture, not someone's legs. Nevertheless, Kubrick has here given us a hint as to something in his film that is 'hidden' from plain view: What's being suggested, by the image rotated ninety degrees clockwise as shown above, is that there could be an alien standing over the girl, in specific, an alien from the race that planted the monoliths, and it has effectively kidnapped her. Floyd's daughter wouldn't know she's been kidnapped, however, because the alien has fooled her by taking on human form (i.e., it normally appears to her to be a human; but see below). The reason we see the 'suggested alien' on the monitor appearing as it does to Floyd (i.e., like an alien instead of a human), is because we are here looking through Floyd's eyes, and Floyd himself is one of the aliens; or more accurately, an alien life force is 'occupying' his body.
Since our 'suggested alien' is standing right next to the daughter, it seems that she's lying about no one being around (she says that her mother isn't home, and that her caretaker, Rachel, is in the bathroom). What's ultimately being suggested, however, is not that the Floyd's daughter is lying, but instead, that the aliens can influence the minds of humans - they are able to get the girl to believe what they want her to believe, i.e., that no one is in the immediate area. This serves, in part, as a kind of security precaution, in case Floyd's phone conversation is overheard by someone else in the space station. If his daughter was to scream over the phone something like, "Help!! I've been kidnapped by aliens!", anyone who might overhear the conversation would no doubt get suspicious.
The fact that Floyd's body is occupied by an alien life force, explains his artificial, 'mechanical'-sounding manner of speaking, such as at the meeting at Clavius (shown at left): Even though the alien is able to occupy a human body, it's unable to fully mimic a human manner of speaking. However, Floyd is able to get through voice print identification security at the space station (as shown in the below left screencap), since the tone of his voice is the same as that of the 'original' Floyd (since Floyd's own vocal chords are being used to speak). Also, the alien is able to recognize people who Floyd knows, remember his home phone number, etc., because it has all of the knowledge and basic memory contents that the human Floyd had - the alien is effectively occupying not only Floyd's body, but his mind as well (and is therefore controlling his actions). Another hint we're given that Floyd's mind has been taken over by that of an alien, is that Floyd is shown having to read the instructions for the zero gravity toilet on the lunar lander (as shown at below right). Certainly the 'real' Floyd wouldn't need to read them, since, as suggested in his earlier conversation in the space station waiting area, with Elena, Dr. Smyslov, and the others, he has traveled in the lander before (i.e., he has made past trips from the space station to the moon). The point is that the alien must sometimes 'refresh' its memory about certain details - the retention of Floyd's memory by the alien isn't perfect.
Above left: Floyd has no trouble getting through voice print identification at the space station. Above right: Floyd needs to read the instructions for the zero gravity toilet on the lunar lander.
The rotating space station (shown at left) looks physically similar to a giant rotating film reel, and the rectangular slot in the hub in the middle could be imagined as being a key-hole: One 'key' to unlocking the meaning of the movie is image rotation, as described above.
Another rotation hint in 2001 is that the stargate transitions from a vertical orientation (above left) to a horizontal orientation (above right) while Bowman is moving through it, as if it has been rotated by ninety degrees.