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I’ve spent the last week or so reworking the first draft of my universality article for Mathematics Awareness Month, in view of the useful comments and feedback received on that draft here on this blog, as well as elsewhere. In fact, I ended up rewriting the article from scratch, and expanding it substantially, in order to focus on a more engaging and less technical narrative. I found that I had to use a substantially different mindset than the one I am used to having for technical expository writing; indeed, the exercise reminded me more of my high school English assignments than of my professional work. (This is perhaps a bad sign: English was not exactly my strongest subject as a student.)
The piece now has title: “E pluribus unum: from complexity, universality”. This is a somewhat US-centric piece of wordplay, but Mathematics Awareness Month is, after all, a US-based initiative, even though awareness of mathematics certainly transcends national boundaries. Still, it is a trivial matter to modify the title later if a better proposal arises, and I am sure that if I send this text to be published, that the editors may have some suggestions in this regard.
By coincidence, I moved up and expanded the other US-centric item – the discussion of the 2008 US presidential elections – to the front of the paper to play the role of the hook. I’ll try to keep the Commonwealth spelling conventions, though. :-)
I decided to cut out the discussion of the N-body problem for various values of N, in part due to the confusion over the notion of a “solution”; there is a nice mathematical story there, but perhaps one that gets in the way of the main story of universality.
I have added a fair number of relevant images, though some of them will have to be changed in the final version for copyright reasons. The narrow column format of this blog means that the image placement is not optimal, but I am sure that this can be rectified if this article is published professionally.