I watched 2001 again last week. First time in years.
The primary visual representation of HAL, the computer, is the red-dot lens. It looks like a single eye (Masonic/Illuminati symbolism?)
Also, when HAL is being shut down, he sings the song that scientists used to help create his voice, "Daisy Bell (Bicycle Built for Two)":
Daisy, Daisy, give me your answer, do,
I'm half crazy all for the love of you.
It won't be a stylish marriage,
I can't afford a carriage,
But you'd look sweet upon the seat
Of a bicycle built for two.
Hearing the song made me wonder about the etymology of the word "daisy."
Old English dægesege, from dæges eage "day's eye," because the petals open at dawn and close at dusk.
Anyway, no telling what the meaning of the song is within the movie, but I'm sure it's there for a reason. Probably some commentary on the elite's transhumanism. My guess would be that Kubrick and Clarke didn't believe machines could be trusted. They may get us to the next step in evolution, but we should never attempt to merge with them.