I have discussed analogies here in the recent past, producing the writeup of a recent talk at a conference on the popularization of physics. I also singled out for an independent post a nice analogy to explain the problem of Naturalness (the "unnaturally low" mass of the Higgs boson and the resulting implications for new physics). Today a reader of this blog (signed "Ohwilleke") offered, in the comments thread of the writeup article, a much improved version of my "improvement". See below:
"Suppose that sum of the profits and losses of ten companies turn out to average out to be $10. If you only know this fact, and that a priori profits and losses in any given year appear to be more or less equally likely in the highly competitive market where these companies operate, what kinds of gross revenues do you expect the average company to have? Knowing only these facts, you might expect for a string of lemonade stands in a busy residential neighborhood. But you would be shocked if you learned that the companies had gross revenues that averaged tens of billions of dollars a year each, for the average profit to net out to $10 simply as a random average, even if profits and losses were equally likely. You would suspect that someone had carefully combed through tens of thousands of corporate reports to come up with a combination that was so equally balanced on purpose."
"Physicists, similarly, suspect based upon the unnaturalness of the near perfect balancing of the loop corrections in the absence of some unknown non-random principle that causes them to nearly balance out, when compared to the scale of the components, that the loop corrections probably actually balance due to some hidden structure that we haven't yet discovered."