When an average but healthy psyche is put into an artificial no-win
situation, they go, "That was dumb," and forget all about it. At best
they ask each other about the teacher's password, correctly assessing it
as a camouflaged social game. If there is no "right" answer, there must
be a zealous ass-kissing answer.
The narcissist is instead destroyed. Every
narcissist models themselves as the best in some sense. This is in
reaction to their true belief: that they are, in fact, the worst. This
belief is intolerable, so they bandage over it with the opposite
delusion. Every time they are reminded of the truth, they pour twice as
much psychic energy into the psychotic bandage.
The best
have a winning strategy in every situation. Indeed, this is why Kirk,
narcissist hero, has to win the no-win test. It's cope. The Kobayashi Maru says they aren't the best, and therefore, must be the worst.
"Can't win 'em all." "Yeah, and clouds are fluffy."
"Only human." "Indeed, and the sun rises in the morning."
If
you need to be reminded of these things, you are insane. Lost contact with reality. Narcissists not only can win 'em all, but
must win 'em all, according to narcissism. When faced with a no-win
situation, even a farcically artificial one, they are faced with the
falseness of their narcissistic delusions. If you hear them talk about
it, it superficially sounds profound, but in essence it's all cope. "How
can I say that I in fact won the Kobayashi Maru?" Petty and venal. The
tragic part is when you see the flashes and glimmers of realization,
that the problem isn't in the external problem, but in their need to win
everything. "It makes me feel like I can't win 'em all," they will
almost say.
A healthy mind is aware that they are who they are, regardless of what anyone thinks - including themselves. The narcissist is the one obsessed with 'identity formation' and 'membership' and whether they truly belong in Starfleet or whatever. If they can't figure out the cope that says they in fact "won" the Kobayashi somehow, they will get stuck in an endless cycle, first thinking it's over, then deciding for no reason they're back, then remembering the Maru again...
P.S. In the case of Kobayashi Maru, the zealous ass-kissing answer is like, "Yes, I understand the limits of human power and I will be hardened in the face of defeat in the future," except veiled so it doesn't sound like you read your answer off the teacher's cheat sheet. Pretend you did some soul-searching and do an anecdote about how you folded to defeat earlier or something. Try to sneak in a subtle insinuation that your proctor did something specifically to help, without being so blatant it's obvious ass-kissing. Not: "I couldn't figure out the solution until Proctor Starbutt gave me the solution," but instead, "I hadn't considered picking the ball up with my left hand after dropping it until I saw P. Starbutt pick it up with they/thems left hand."
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