Corrected entry: When Prot is taken to the planetarium, he is told to map out the orbital path of K-PAX. When Prot is shown mapping on the board, the sounds and movements of the pen do not match up with what Spacey is doing on this board.
K-Pax (2001)
1 corrected entry
Directed by: Iain Softley
Starring: Jeff Bridges, Kevin Spacey, Alfre Woodard, Mary McCormack
Continuity mistake: The taxi ride to the planetarium begins in a Ford Crown Victoria but ends in a Chevy Caprice. (00:36:02)
Trivia: Kevin Spacey had to record the scene where Prot eats a whole banana (skin and all) 27 times.
Question: Despite Dr. Mark Powell's certainty that "Prot" is a delusional man named Robert Porter who lost his mind and attempted suicide years earlier, no explanation is ever given for Prot's extraordinary resistance to powerful psychiatric drugs, his superhuman vision (into the Ultraviolet range), and his knowledge of deep-space astrophysics, which not only rivals but exceeds the knowledge of Earthly astrophysicists. Prot's enigmatic abilities are tested by experts, and the experts are left scratching their heads. The probability that Prot actually is an alien entity occupying a deeply-damaged and "discarded" human body seems confirmed on many levels, above and beyond the rantings of a mere mental patient. So, why does Dr. Powell consistently reject the hard evidence before his eyes?
Answer: He rejects it for two main reasons. First, each of the items you mention have possible, even if unlikely, explanations. Some people have strange or no reaction to certain drugs (for example I have almost no response to any painkillers). People who have had their corneas replaced with artificial lens can see near ultraviolet (though nowhere near 300-400 angstroms). The sheriff described Porter as being very bright, and he was in to astronomy, so while a great stretch, not impossible he somehow formulated the information he presented. The second reason, building upon these, is Occam's razor. As a person in the sciences, Dr. Powell is driven to believe things have a reasonable explanation, even if we don't currently know what it is, and thinking Prot is just a bright and unusual human is a more reasonable belief to him than believing Prot is an alien possessing a human's body.
Just remarking, there's no comparison of painkillers and psychiatric drugs. Thorazine and Haloperidol (Haldol) are both powerful anti-psychotic drugs with numerous side effects. Prot is immune to Thorazine and Haloperidol (as well as alcohol), which is more than extraordinary, it's otherworldly.
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Correction: There is nothing that indicates that what is written will immediately show up on the screen. Perhaps there is a delay between the time the image is drawn to the time that it appears on the overhead.