Using words instead of math

Here on the 100th birthday of General Relativity our science consultants were pondering why Relativity and Quantum Mechanics were so easy for them to accept but so hard for people a century ago.  Certainly it’s not because we’re more insightful or brighter scientists–quite the opposite.  Nor is it that we’re better at math; again the opposite is true, and these are highly mathematical subjects.  We finally concluded that we’re comfortable with the theories because we were told the stories, word-descriptions of what the math means, from an early stage and so the theories never seemed impossibly strange.  The stories are important.  But it’s also important for both scientists and laymen to understand their limitations.

Long before we could do any of the mathematics we were familiar with much of the strangeness of Relativity.  For someone brought up only in Newtonian physics, in which time is absolute everywhere and space is an unobtrusive stage on which everything happens, it was much harder to conceive of space-time as an inextricably mixed object that could curve and even vibrate.  In this case, as in others, the hard part of learning is unlearning what you already know.  For us it was already familiarly strange.

So the stories are important in helping scientists understand the science.  And they are very useful also for communicating what’s happening to the public, the people who cannot follow the rather intimidating equations.  But it’s also important to be aware of the limitations of stories:

• They take time to write, and aren’t unique.  The concept of energy, overwhelmingly useful and implicit in Newton’s formulation, wasn’t introduced until almost two centuries after Newton.  And the Copenhagen interpretation of quantum mechanics (Schoedinger’s cat and all that) is still disputed by some physicists, even though everyone works the math the same way.
• They don’t always give answers themselves.  Stars have different masses; stars convert hydrogen to helium as a power source; stars with more mass are hotter at the center, converting hydrogen more rapidly.  So a big star has more fuel, but burns it faster.  Which lasts longer?  You have to do the math to find out (small stars are much longer-lived).
• They may be oversimplified.  The Bohr atom has an electron circling a proton like a planet around the Sun.  The picture is easy to grasp, gives one good answer–and many, many wrong ones.
• They may give a false impression of understanding.  This is easiest to see in popular accounts of mathematics itself.  An account of the human struggle to prove, say, Fermat’s Last Theorem can be entertaining and insightful on many levels, definitely worthwhile.  But at the end the reader won’t be able to prove anything.

It’s up to the scientists to interpret their work and come up with the stories.  Writing good ones is an art form and not easy.  Their most important tasks are to make them as accurate as possible, and to be clear about how far they’re simplified.

For non-scientists, beware of reasoning by analogy, and of substituting the story for the science.