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In many episodes with the Q, they seem to place themselves as omnipotent and ultra-intelligent, superior beings - but at the same time, they do such a poor job at portraying themselves as omnipotent, that I'm asking myself how that fits with their "selfproclaimed" superior intelligence.

First of all, a really omnipotent being should be omniscient. Why? Because as an omnipotent creature, you'ld be able to make yourself omniscient.

But they are obviously not omniscient, proven by the many "surprises" they face. This also makes it a bit weird when time travel plots come into play... how can a species that is not bound by time, be surprised by the future? (example: when Q is punished and turned into a human). The result of that is that one can guess: No, the Q are not omnipotent.

Now, why do such incredibly "intelligent" beings do such a poor job at making others believe they are omnipotent, as they seem to imply? If they really are so incredibly intelligent and superior to humans, shouldn't they have a much easier time to manipulate them than just doing some "magic tricks"?

The reasons for this out of universe are obvious (after all, there is still a need to create characters that are entertaining) - but what would be an explanation in-universe? Is it as obvious to other species, that the Q are basically lying? Do the Q, in reality, possess human intelligence just with more knowledge?

And yes, they can access a huge amount of knowledge in a very short time - but that's not intelligence. A computer can do that too.

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    Just because you have access to all information doesn't necessarily mean you've noticed everything. The Q likely see branching realities of possibility, and thus may not be certain what will actually come to pass. – Nerrolken Aug 17 '15 at 14:08
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    Have the Q ever really claimed to be omnipotent? The very concept is classically paradoxical. I've never read them as claiming to be omnipotent and omniscient (ie Gods), just very very close. They've stated that humanity could one day surpass them, after all. Also, you seem to list intelligence as binary - human intelligence and then omniscience. There are states between! – DavidS Aug 17 '15 at 14:08
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    Also worth mentioning: when Q is made into a human, he mentions his IQ as being 2,005. Even if this was sarcastic (which is likely), it likely means that an IQ of 2,005 would be high even by Q standards (otherwise he'd have picked an even higher number). This gives us a rough estimate of his possible intelligence, and more importantly, a probable confirmation that his IQ can be measured, and thus isn't infinite. – Nerrolken Aug 17 '15 at 14:10
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    @Katai My point is that calling them omnipotent is misleading - omnipotence is paradoxical. Could a Q create a stone so heavy they couldn't lift it? – DavidS Aug 17 '15 at 14:22
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    Perspective may be the issue -- to the Amoeba in the petri dish, the researcher is clearly both omnipotent and omniscient, but not from the researcher's perspective, nor that of his/her peers. But, if the researcher could communicate with the amoeba, it would probably be simpler to claim both than to try to explain something far beyond the amoeba's understanding. A bit of condescension might be understandable, too. Then again, despite all his/her power, if the amoeba is Naegleria fowleri, it could well be able to kill the researcher if handled improperly. – K-H-W Aug 18 '15 at 7:03
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This conversation between an ascended-type being (the Pollisand) and a more-or-less "normal" woman (Oar) comes from a different fictional verse (James Alan Gardner's Ascending, book 5 of his League of Peoples series), but it gives one possible answer:

    “Ah,” the Pollisand said, “but perhaps my facade is an act. A truly advanced being might realize it’s best to approach lesser species in a non-threatening way—as a ridiculous-looking creature who comes across as a pompous jerk barely able to keep his foot out of his mouth. It puts you at ease, doesn’t it, when you say, This Pollisand guy isn’t so scary; he’s not the swaggering staggering super-genius the rest of the universe thinks he is. You catch me making a few goofs, you throw my words back in my face, and after a while, you relax cuz you think I’m not smart enough to pull the wool over your eyes.”
    If this was an attempt to disconcert me, it nearly worked. A vastly intelligent beast who controlled what I saw and heard might indeed present himself as a silly buffoon so as not to be taken too seriously, On the other hand, a silly buffoon might boast of himself as a vastly intelligent beast who was merely play-acting. Which was more likely?
    “The most important point,” I said, “is that I wish to know the direction of your plan. What is your goal? What is your purpose?”
    The Pollisand shuffled his feet, “All right. The part of the plan that concerns you—the immediate part of the plan—is related to the race you call the Shaddill.”
    “Are you for them or against them?” I asked.
    “I fervently want,” the Pollisand said, “to wipe them off the face of this galaxy. And your part in the plan will help accomplish that.”
    “Why did you not say so?” I reached out and laid my arm across the alien’s back in a comradely manner. “Of course I shall help you defeat the Shaddill… especially if you fix my Tired Brain too. You should have known I would say yes if you put it like that.”
    “I did know,” the Pollisand said in a soft voice totally unlike his previous obnoxious tone.

Later, in the same book:

    “Hey,” he [the Pollisand] said, “I keep telling you: I’m a fucking alien mastermind.”
    “Or,” said Festina, “a complete fraud who takes credit for being a lot more omniscient than he really is. You took damned good care to keep your leathery white ass out of sight till the Shaddill were gone. Could it be you were afraid to tangle with them directly?”
    “Ah, yes,” said the Pollisand in an even more nasal voice than usual. “A god or a fraud? Am I or ain’t I?” He lifted his forefoot and patted Festina fondly on the cheek. “You don’t know, my little chickadee, how hard I work to keep the answer ambiguous.”

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    I think it'd only appropriate that you cite the source for this conversation. – Tango Aug 17 '15 at 16:30
  • That's actually a point I was thinking about as well, that would explain some inconsistencies (but then again, the inconsistencies would offer the problem of being too obvious). When Q was a human... he didn't know what sleep was. But he still mentioned having his knowledge about the universe. The only way this would make sense would be "acting dumb". But then again, that mistake would be so obvious that one would suspect he's "acting" - since he should know the concept of sleep. I was actually surprised that the crew didn't find that strange. – Katai Aug 18 '15 at 12:00
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    Knowing about a concept and experiencing it is.not.the.same. – flq Aug 18 '15 at 21:18
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If we accept that it's just "near omnipotence" instead of true omnipotence it does not change anything. He already demonstrated enough of his power to prove that he is way beyond everyone else, and technicalities do not influence that judgement nor the behaviour presented in response.

Intelligence itself is also worth looking at. While there are many definitions to choose from, they mostly converge on the idea of understanding the world and making plans in order to steer the future in alignement with their plans. The true measure of intelligence is how well an actor does in achieving it's goals. We do not know his True Goal - however, if we follow Star Treks route of "all the races are in principle similar"... His own amusement, helping people he likes and steering humanity towards an unspecified but glorious future seem to be of interest to him, and are achieved each time he makes an appearance.

And as a side note - computers are (currently) not intelligent and can't do anything with the pure knowledge available. However, the goal-achieving part of intelligence benefits greatly from having knowledge, so there is a good case to be made, that more knowledge does in fact increase intelligence

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There probably are Q who are omniscient but the ones we see havent chosen to give themselves that ability if they had they would cease to interact in any physical capacity

the Q we see like to play games and playing a game isnt much fun if you know the outcome already

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Omnipotence is a complex concept, perhaps best defined by its inverse: how many things are there that a being cannot do? This becomes more complex if there are multiple comparable beings. What limits are there on Q's power? Other Q.

So perhaps the question is appropriately asked, what limits are there on Q's foreknowledge? Other Q. They can not with 100% surety predict each other's actions. Thus Q can be surprised, but only by Q.

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