Your quote explains the exact opposite of entropy... That grimoire basically says the darkness wants to resist entropy as effectively as possible, which means having the universe take on a "shape" that's perfectly adapted to resist falling into chaos. It takes energy to resist entropy, that's why the darkness is exterminating things that aren't fit to resist it because they're wasting the necessary energy to resist it.
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Well, think about it this way: the goal of the Darkness is to exterminate life, to exterminate civilization. It does nothing but destroy - the Collapse, the whirlwind. Therefore, it is Entropy. The Traveler builds up worlds (our Golden age, for example) making it the opposite Entropy - Energy. But that's a discussion for another time. The Hive seem to have a similar function to the darkness - they seek to take energy from those who have it, and take it for their own, thus growing more powerful. They seek to be the only things left in this universe. And the more they take, the more powerful the worms within them (the worms are the things that give the Hive their power) grow. However, this raises a peculiar point; one day, there will be nothing left to take, and then their worms will devour them, as per the bargain that Oryx and his sisters struck with the Worm-Gods. So, one day, the worms (which may be even closer to the Darkness than the Hive) will kill their Hive hosts. And then, truly nothing will be left. In other words, Oryx was being played. The Darkness wins, and the universe descends into nothingness. Entropy.
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That is not true. The goal of the darkness is to act as a force that weeds out all but the fittest for survival. That's pretty much the bullet point of all of Oryx's grimoire.
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Destroying civilizations and killing living things increases entropy though
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On a fine scale, yes, but not on a universal scale if you're replacing them with a civilization designed to sustain existence. That's what the hive/taken have been doing. Weeding out things that wouldn't ultimately resist entropy in order to replace them with something that will continue existence. That is the final perfect shape Oryx sought.