This note presents an example roofs-and-boxes to refute the idea that sequence extrapolation is a paradigmatic problem for AI. The plausible idea was that intelligence predicted the sequence of future sensations from the past sequence of sensations. The roofs-and-boxes example illustrates that intelligence requires knowing about objects in the world and not just about one's history of sensations---even if one's goal is to predict future sensations.
Another justification for writing this up many years after I discussed it in lectures is that almost all machine learning research does not undertake to infer structures in the world and not just classify the data.
Opinions differ about how difficult roofs-and-boxes is. Most people think it is impossible starting from scratch. Donald Michie said he though a good cryptographer could do it. Maybe it would take a team of cryptographers with a war to win.
Appearance and Reality presents the problem of determining the reality behind appearance in the form of a puzzle much easier than roofs-and-boxes. Many people solve it.
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