Self-referential New Years Resolutions
December 31st, 2007
For some reason, I enjoy making self-referential New Year’s resolutions.
For example, let’s say that last year I resolved to keep the resolution which I would make the following year. A bit strange, but there seems to be no reason I can’t resolve to do something in the future. New Year’s resolutions in general are a statement about what you intend to do in the future.
Now, this year I resolve to break the resolution I made last year.
I’m not going to bother writing down the reasoning that follows this, but I’ll pause while you take a moment and work it out. If you want.
It essentially a form of the “The following sentence is true. The preceding sentence if false.” sort of thing, applied to New Year’s resolutions. The significance of this is difficult to convey, and I’d be the first to say that I’m not the person you want to go to if you’re looking for a complete explanation of Gödel’s theorem. But since it was Hofstadter’s excellent book on that subject that sparked my interest in computer science in the first place, I maintain a friendly attachment to this sort of thought experiment.
3 Responses to “Self-referential New Years Resolutions”
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December 31st, 2007 at 12:21 PM
*This author is in no danger of ever landing a job as a comedy writer." I've always summed up Gödel's theorem this way: he proved (almost?) that a system could not be complete ... if it was "complete" it included contradictions. Probably not doing it justice, but I like it because it helps me envionsion knowledge as fractal ... an infinite-regress sorta thing ... the more we know the more we become aware of what we don't know. If you enjoy Hofstader you really should get into Martin Gardner. He had a Scientific American column called "Computer Recreations"; the Aug85 edition launched Mandelbrot into the public eye, the real birth of fractals as entertainment. ^5 ben
December 31st, 2007 at 02:15 PM
I've read a little after Gardner, but I gravitated more toward Raymond Smullyan's math books. Not sure why; maybe because they were a little more deliberately silly, or just plain weird. This semester I'm taking Calculus II, so I don't think I'll be doing any recreational math other than homework & related problems.
December 31st, 2007 at 02:19 PM
...anyways, I suppose a more "purely" self-referential resolution would be "I resolve not to keep this resolution." The paradoxes-are-not-allowed school of thought would probably say that my first set of resolutions ought not be allowed, as both resolutions refer to an action outside of the present year, and a New Year's resolution is intuitively confined to the single year immediately following. Though, that school of thought would not like my new resolution, either, as it is a resolution about resolutions, and would therefore be... a meta-resolution?