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MinibearRex 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.
For me, the one-way functions weren't the impressive part of public-key crypto; it was the idea that you can stand in a crowded room full of people who desperately want to eavesdrop on you, hold a shouted conversation with someone you've never met before or spoken with privately, and keep everything secret. I mean, wow, y'know?
To bring Special Relativity into the realm of existing technology, one might emphasize the GPS system's reliance on it.
GPS itself is some pretty cool technology.
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.