If you have a system that gets better at making itself get better, it will appear to discontinuously advance. Add in the ability of intelligences to accomplish tasks which previous intelligences labeled impossible, and you have the potential for dramatic advancement.
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This post is part of the Rerunning the Sequences series, where we'll be going through Eliezer Yudkowsky's old posts in order so that people who are interested can (re-)read and discuss them. The previous post was When Life is Cheap, Death is Cheap, and you can use the sequence_reruns tag or rss feed to follow the rest of the series.
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