Q said that 99% of people would be in the hospital if they knew the truth. Hospital capacity won’t hold even a small fraction of 7+ Billion Homo sapiens.
Reconcile.
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Q knows about the miniaturization technology that can be deployed at the gates of every hospital globally
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Most humans in this circumstance will actually be incinerated and the hospitals will serve as a kind of morgue and soul transmission facility to the alien spaceships
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Hospitals exist on spaceships, in the oceans, or underground, to hold the 99% of people
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Q forgot to consider the limited capacity of hospitals globally