AlexMennen comments on Quickly passing through the great filter - Less Wrong
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This is isomorphic to the smoking lesion problem. EDT says it's a good idea to build the transmitter, but EDT is bonkers.
Excellent example, but I don't think it's 100% isomorphic because we don't understand the cause of the great filter and because thinking we are probably doomed might cause us to act in ways that increase the chances of us destroying ourselves.
Or everyone might think that way, causing them to blow themselves up with this "transmitter".