We already know from TOS that Mutlitronic computers are able to develop sapience, with the M-5 computer being specifically designed to “think and reason” like a person, and built around Dr Daystrom’s neural engrams.
However, we also know from Voyager that the holomatrix of their Mk 1 EMH also incorporates Multitronic technology, and from DS9 that it’s also used in mind-reading devices.
Assuming that the EMH is designed to more or less be a standard hologram with some medical knowledge added in, it shouldn’t have come as a surprise that holograms were either sapient themselves, or were capable of developing sapience. It would only be a logical possibility if technology that allowed human-like thought and reasoning into a hologram.
If anything, it is more of a surprise that sapient holograms like the Doctor or Moriarty hadn’t happened earlier.
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In this case, ‘sapience’ is correct. However, I don’t recall them ever making a distinction, in-universe, between the two.
The main difference between sentience and sapience is self-awareness. A sentient being has consciousness, the capacity for sensation, and a subjective experience. Many animals can be described as sentient, although it’s hard to know for sure what’s going on inside a fish’s head. Sapience, on the other hand, is marked by a higher level of cognition and intelligence. Human beings are sapient creatures.
Not as far as I’m aware. TOS did seem to make more of a distinction between the two, but TNG treated them as one and the same, with most other series following suit.
No, sapience would be the right word in this case. Sentience is more for general self-awareness, whereas Sapience is more for human-like intelligence, which the Doctor (and Moriarty) express.