The weight of history

When does it make sense to change an obsolete and unwieldy system?

Last week we mentioned the very sudden (in historical terms) replacement of the horse as a source of power and transport.  This week we turn to something that is arguably quite as obsolete, but has not been replaced.

If you look at a list of stars or other celestial objects, you’ll generally find their brightness given as a number, with the column headed “magnitude” (sometimes with other modifiers).  One peculiarity of this ranking, as we’ve noted before, is that brighter objects have smaller numbers.  This can be confusing to scientists and students, who expect bigger numbers to go with more of whatever you’re measuring.  Generally less confusing is the fact that it’s a logarithmic scale: to go from 3rd to 2nd magnitude you increase the brightness by a certain factor, instead of adding a certain amount.  That is, a 2nd-magnitude star is so many times brighter than a 3rd-magnitude star; the same factor by which a 4th-magnitude star is brighter than a 5th-magnitude star.

What is that factor?  Two would be convenient: each magnitude twice as bright as the next.  Well, no.  Ten, to fit in with our number system?  Not that, either.  The actual number is about 2.512.  It’s an historical artifact.

The first star catalogs we have, about two thousand years old, listed star brightnesses in six steps: the first-magnitude stars were the brightest, the second-magnitude stars the next, and so on to the sixth, which is about as faint as the human eye can see on a good night.  When telescopes came along and fainter stars could be seen the scale was extended to higher numbers.  However, since it depended on the observer’s judgement there was some disagreement among them.  When photography was invented and applied to stellar photometry there was finally an objective (I did not say easy) way to measure brightness.

Astronomers could have instituted a reformed system, with bigger numbers being brighter.  But that would have meant a break with something they were familiar with, and the inconvenience of having to translate between two systems whenever they combined earlier observations with new ones.  Instead, they refined and standardized the old system.  Since an average sixth-magnitude star was about a hundredth the brightness of an average first-magnitude star, and they wanted to keep the steps between them as ratios, the factor from one magnitude to the next is the fifth root of 100.  It’s an irrational number and awkward, but retains backward compatibility.

With the advent of electronic detectors, which were calibrated in good physicists’ units and measured energy in a positive direction, there was another opportunity to reform the system.  Instead, for the same reasons as before, the system was refined and more exactly standardized.

Our astronomer affirms that the system can be very clumsy to use.  For instance, he was once set to calculate the surface brightness of a set of objects.  He could measure the total brightness and the surface area, but the answer was not just one divided by the other; it’s pretty complicated to work out.  A reformed system would have made it easy.

Well, now it’s probably not as important as it was to change to a more straightforward system.  With digital computers ubiquitous, the arcane calculations involved with the stellar magnitude system can be pushed into a subroutine and forgotten. An obsolete, awkward system has survived by becoming less awkward.

And the fifth-root-of-100 system provides many practice problems for students just learning logarithms.