For example, you might take an extensive set of observed values (from some 
sensor or generator) and then discuss strings that did not occur as being 
random.  From that you might use statistical methods to determine the relative 
likelihood of substrings and use them to talk about relative randomness using 
formal methods (forms that use abstractions and so on). That might be 
interesting to some people.
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Artificial General Intelligence List: AGI
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