The fictional science of the sophons was also bad.
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The book author thought that protons were fundamental particles. Protons are made up of quarks. So the idea of unfolding a proton when it's made up of 3 quarks doesn't make sense. Put 3 marbles next to each other. Label the 3 marbles a proton. Unfold it. ???
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Quantum teleportation doesn't allow for FTL communication.