In the current part of Hofstadters text, he explains his approaches to more complex sequences that may be easy to human cognition but are generally hard to crack by computer algorithms. Sequences for example where patterns or numbers move around in lawful manners (e.g. singlers or bouncing doublers) are generally easy to spot by the human eye, but make hardly any sense if deciphered by counting the occurrences of certain numbers or interchanging sequences.
It is their notion of figure and ground according to the Gestalt laws which make these features so salient to us, having to cope with similar effects in nature. Other such features like plateaus (strings of the same number "1111"), up- and down-runs (continuous up- or down-counting sequences, "2345", "98765") and palindromes (symmetrical sequences, "014410") are also salient to the eye, but had hardly any mathematical relevance in the existing sequence-seeking programs before.
Hofstadters suggests some kind of bottom-up approach for finding such 'islands' (as he calls them) first and making sense of them, by finding their connections in the next step. This approach is by far more natural than the previous methods, the author briefly touched in the first sub-chapters. In my opinion, the notion of similarity should also play an important role among the other mentioned features. Even though this criteria would be much harder to implement, due to its broad definition, similarities among islands or slightly deviating sub-sequences reveal most of the connections between them and therefore useful hints about the generation process itself.
After this part of the book, I am actually sorry Hofstadter does not let us in on the actual realization of Seek-Whence program, because I imagine some details of it even more useful than the mere description of problems it can deal with.
[This blog post has been edited after the assigned deadline, because the original post was embarrassingly short and general.]
Tuesday, September 15, 2009
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