Your observation is a consequence of Kleene's recursion theorem, which I summarised briefly in http://vimeo.com/66863570#at=13m40s http://vimeo.com/66863570#at=

Your observation is a consequence of Kleene's recursion theorem, which I summarised briefly in http://vimeo.com/66863570#at=13m40s http://vimeo.com/66863570#at=13m40s (extracted from chapter 8 of http://computationbook.com/ http://computationbook.com/).