The purest case of an ...

The purest case of an intelligence explosion would be an Artificial Intelligence rewriting its own source code. The key idea is that if you can improve intelligence even a little, the process accelerates. It's a tipping point. Like trying to balance a pen on one end - as soon as it tilts even a little, it quickly falls the rest of the way.
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 Eliezer Yudkowsky

Quotes from the same author

We underestimate the distance between ourselves and others. Not just inferential distance, but distances of temperament and ability, distances of situation and resource, distances of unspoken knowledge and unnoticed skills and luck, distances of interior landscape.
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 Eliezer Yudkowsky
Your strength as a rationalist is your ability to be more confused by fiction than by reality. If you are equally good at explaining any outcome, you have zero knowledge.
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 Eliezer Yudkowsky
You couldn't changed history. But you could get it right to start with. Do something differently the FIRST time around. This whole business with seeking Slytherin's secrets... seemed an awful lot like the sort of thing where, years later, you would look back and say, 'And THAT was where it all started to go wrong.' And he would wish desperately for the ability to fall back through time and make a different choice. Wish granted. Now what?
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 Eliezer Yudkowsky
The police officer who puts their life on the line with no superpowers, no X-Ray vision, no super-strength, no ability to fly, and above all no invulnerability to bullets, reveals far greater virtue than Superman - who is only a mere superhero.
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 Eliezer Yudkowsky
Maybe you just can't protect people from certain specialized types of folly with any sane amount of regulation, and the correct response is to give up on the high social costs of inadequately protecting people from themselves under certain circumstances.
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 Eliezer Yudkowsky