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Broggly comments on Existing Absurd Technologies - Less Wrong
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The whole idea of public key cryptography. Take a message, put it through a certain algorithm, but the algorithm doesn't work in reverse.
Rockets in space. A flying vehicle that seems to move forwards by pushing on nothing.
The absolute speed limit of special relativity. Not quite technology, but the experiments could be described.
Algorithms that are hard to reverse is pretty simple to understand. Every Schoolboy Knows that division is "harder" than multiplication, and I'm still not entirely sure how to find roots in my head.