I usually tend to find ENTPs the most influential (with INTPs and INTJs coming in second). The reason is probably that ENTPs are an external projection of everything INTP's often want to be: outgoing, verbally eloquent, charismatic, highly inventive, socially enjoyed and almost naturally popular. Many people I have often admired are ENTPs (such as Bertrand Russell, George Carlin, Nikola Tesla, Thomas Edison, and Socrates -- a great xNTP). I've even enjoyed many fictional ENTPs (such as Jack Sparrow, Mark Twain -- as he was depicted during the Star Trek Enterprise series -- and perhaps Dr. House).
ENTP; I don't think I've ever known one personally. But I can't help but be thrilled with such characters when I find them in fiction. (I'm thinking of an exemplar omnipotent entity from a certain continuum...)
I personally think "Q" can be quite annoying at times, as he always seems to be harassing the Enterprise crew by abusing his omnipotence (which actually got him in trouble a few times throughout the series). But despite that, I do find his mocking of others/insults to be downright hilarious (just like Dr. House). At one point, in fact, he tells Worf to "go eat a book." It's also slightly comical how Q tends to playfully piss off Picard often with seemingly childish antics, like a real-life troll on the loose. But I wouldn't call Q influential, personally. I just tend to relate to some of his behavior, while also disliking some of it. Perhaps the most relatable aspect of Q, for me, is that he seems to have a superiority complex (so that he talks down to others constantly). That's always entertaining. But personally, when it comes to the Enterprise, I prefer Data, Barclay, and Picard (two INTPs and an xNTJ).
Maybe also an INTJ, which is another character outlook I enjoy when I encounter it in fiction. I had one INTJ friend when I was younger, and our conversations were always this dynamic of her bringing up topics (usually) and us having challenging discussion-debates on them which could go on for hours. I admired her for her vast knowledge of topics which I never delved into, and I sometimes didn't know what she talked to me for
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I might have been the only person who could handle it, and I guess we both found it fun.
Agreed. Besides INTPs and ENTPs, I tend to really find INTJs fascinating (from a sort of perplexed, ignorant point of view, as I do not entirely understand how they operate). Although, INTJ/INTP relationships can lead to disaster, if both have extremely large egos. I used to know a guy who was slightly INTJ (but strongly balanced with INTP), with an extremely large ego; half the time we just argued about who was right and who was wrong, rather than actually discussing anything. But again, that depends on the size of the egos involved. My wife is an INTJ (balanced with INFJ), which of course leads to a very small ego, so that we can usually discuss things for hours. She'll usually take an empirical approach, while I'll often take a theoretical approach.
At any rate, when it comes to INTJ style thinking, I would say Captain Picard embodies it quite well, and he's extremely fascinating. Perhaps another is Sherlock Holme's arch nemesis Professor Moriarty (who seems to be an INTJ as he was depicted in many Enterprise episodes).