Strangeness
The "strangeness" of a strange loop comes from our way of perception, because we categorize our input in a small number of 'symbols' (by which Hofstadter means groups of neurons standing for one thing in the outside world). So the difference between the video-feedback loop and our strange loops, our "I"s, is that while the former converts light to the same pattern on a screen, the latter categorizes a pattern and outputs its essence, so that as we get closer and closer to our essence, we get further down our strange loop (according to Hofstadter's book 'I am a Strange Loop').
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