An unnecessary problem

Scientists sometimes set themselves problems just to learn.

For the last couple of weeks our astronomer has been working on a problem in Special Relativity.  It’s not one that came up in a textbook problem set, or in the course of research, but was suggested by something he read in a book on the subject, one published almost a century ago.

(Most scientists have old books like this in their libraries.  The older authors sometimes have clearer explanations of things, or insights that are worth reviewing now and then, or at any rate a different way of looking at the subject.  Often progress comes simply from looking at things in a different way.)

The problem itself (a sort of combination of the Twin Paradox with a spinning disk) is not terribly important.  Nor was there any doubt that there is a solution within Special Relativity; that theory has been well-tested for over a century, always working out fine within its area of application.  But our astronomer had not seen the problem solved, and (something to his surprise) realized he didn’t know how to do it.  So he set himself the problem in order to understand SR better.  This is common practice among scientists.  It may not lead to a publishable paper, it may not further the work of science as a whole, but it is a useful learning tool for those no longer in class.

He’s just about done with it.  He’s checking certain cross-connections, making sure it all hangs together (as you may recall, something our autistic student does as a matter of course), but it works so far.  It has a pleasing simplicity, as well as an implicit transcendental equation that can’t be solved in closed form.  These are good signs.

How he went about solving it reveals something more about the workings of scientists.  He pulled out several SR textbooks, reminding himself the techniques one uses, and finding the limits of what had been done before in this direction.  Then he went for a walk.  (Well, he used commuting time and other periods away from computers and desks, which comes to the same thing.)  He’s found that often the breakthrough in a problem comes while traveling on foot.  Perhaps it’s that there’s only room in one’s mind for the essentials of a problem.  At any rate, he worked out the way to approach the problem in transit, and only sat down to go through the algebra when he knew the direction he wanted to take.

(It doesn’t always happen this way.  He’s had ideas that, once put into equations, only showed that 0 = 0.  Nothing in research science is guaranteed.)

It’s possible, even probable, that not all scientists work this way.  But many do.  You’ll see it in the libraries of old books on their office shelves, as well as the very walkable gardens and quadrangles of many universities.  These could be the most cost-effective pieces of equipment in science.