"Polish hand magic", and satisfying answers

A recent SMBC comic featured "Polish hand magic", a rather remarkable mathematical trick for multiplying on your fingers. I want to talk a bit about the trick, and maybe a little bit about the broader philosophical idea involved. So go read the comic, and then I'll babble a little.

( Read it? Okay then... )

The broader issue that this touches on is our scientific desire for a satisfying explanation of the workings of the universe. I've always hoped that once we really understand the foundations of physics, we'll know the reasons behind all of the seemingly random patterns in particle physics and astronomy and cosmology. ("Why are there four fundamental forces? Why are some of them so much stronger than others? Why are there three copies of the fundamental particle multiplet, with such different masses?" And so on.) It would seem almost cruel if there weren't some deeply satisfying structure beneath it all, and one big hope for string theory has been that it will provide those answers.

Or at least, it was. These days, people have come to realize that no matter how unique the basic structure of string theory may be, the connection between those immutable laws and the particle physics we actually observe depends on many details of how the universe happens to be shaped here where we live. I didn't want to accept that at first, but it wouldn't be the first time science turned out that way. Kepler's early attempts to explain the orbits of the planets in terms of nested Platonic solids seem almost laughable now that we know the true history of the solar system: at this point, asking for a fundamental reason why we have the planets we do doesn't even make sense. So while there's still some hope that string theory will pick out our particular universe as uniquely preferred, it doesn't have to be that way.

So there's the question: When is it reasonable to hope for a deeply satisfying answer, and when should we expect that much of even a beautiful pattern is just due to random chance? Is there any way to guess in advance?

Thoughts and guesses: Harry Potter and the Methods of Rationality

I've linked before to the fanfic Harry Potter and the Methods of Rationality: a sort of remake of the Harry Potter universe where Harry (and, it seems likely, Voldemort) has a strongly scientific mindset. I'm thoroughly enjoying it: the story itself is pretty good, and it's fun to see someone explore aspects of Harry's world (or a near copy) in the way I always wanted to.

Anyway, partly to make note of some current guesses and partly in case any of you folks are following the story and wanted to talk about it, I thought I'd say a bit here. Spoilers ahead up through chapter 25 or so. ( For those who are interested... )