I'll start by mentioning that a bunch of telekinetic's would not be able to move a space-ship a distance relative to that of using an FTL-engine, in a practical way. (one telekinetic is generally capable of moving an object a distance relative to its size and mass, it also gets increasingly harder if the object moves out of sight.) The amount of telekinetic's necessary would be huge. It's more impractical than unacceptable though. Also, why would it be harder to charge the smaller ships (I'm guessing you meant the bigger ones.)
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doesn't really tell us anything regarding their amount of power
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As said, chose one category of powers, as far as I have understood, "something"-kinetic seems to fit for you.
sounds feasible
good
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from what you say, they just like to fight
their view of purity is stupid, not a problem, but stupid
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stupid code, but moderate system to uphold it
you didnt read what I said last time.
fair enough, though the metal would be possible to "unmake" if one knew what to do
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what exactly are you aiming for with "recreating DNA" ?
If you really insist on having no projectile weapons you are more or less worthless in a long distance battle. (and projectiles propelled through supernatural powers are still projectiles...)
Im still not entirely convinced of the need for the DNA part?
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strange story, really strange behavior, not a problem
seems like a good goal