Cascades, cycles, and insight are three ways in which the development of intelligence appears discontinuous. Cascades are when one development makes more developments possible. Cycles are when completing a process causes that process to be completed more. And insight is when we acquire a chunk of information that makes solving a lot of other problems easier.
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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 "Evicting" brain emulations, and you can use the sequence_reruns tag or rss feed to follow the rest of the series.
Sequence reruns are a community-driven effort. You can participate by re-reading the sequence post, discussing it here, posting the next day's sequence reruns post, or summarizing forthcoming articles on the wiki. Go here for more details, or to have meta discussions about the Rerunning the Sequences series.