Most ways of counting and measuring things work logically. When the thing that you're measuring increases, the number gets bigger. When you gain weight, after all, the scale doesn't tell you a smaller number of pounds or kilograms. But things are not so sensible in astronomy — at least not when it comes to the brightnesses of stars.

Ancient Origins

Star magnitudes do count backward, the result of an ancient fluke that seemed like a good idea at the time. The story begins around 129 B.C., when the Greek astronomer Hipparchus produced the first well-known star catalog. Hipparchus ranked his stars in a simple way. He called the brightest ones "of the first magnitude," simply meaning "the biggest." Stars not so bright he called "of the second magnitude," or second biggest. The faintest stars he could see he called "of the sixth magnitude." Around A.D. 140 Claudius Ptolemy copied this system in his own star list. Sometimes Ptolemy added the words "greater" or "smaller" to distinguish between stars within a magnitude class. Ptolemy's works remained the basic astronomy texts for the next 1,400 years, so everyone used the system of first to sixth magnitudes. It worked just fine.

Galileo forced the first change. On turning his newly made telescopes to the sky, Galileo discovered that stars existed that were fainter than Ptolemy's sixth magnitude. "Indeed, with the glass you will detect below stars of the sixth magnitude such a crowd of others that escape natural sight that it is hardly believable," he exulted in his 1610 tract Sidereus Nuncius. "The largest of these . . . we may designate as of the seventh magnitude." Thus did a new term enter the astronomical language, and the magnitude scale became open-ended. There could be no turning back.

As telescopes got bigger and better, astronomers kept adding more magnitudes to the bottom of the scale. Today a pair of 50-millimeter binoculars will show stars of about 9th magnitude, a 6-inch amateur telescope will reach to 13th magnitude, and the Hubble Space Telescope has seen objects as faint as 31st magnitude.

By the middle of the 19th century, astronomers realized there was a pressing need to define the entire magnitude scale more precisely than by eyeball judgment. They had already determined that a 1st-magnitude star shines with about 100 times the light of a 6th-magnitude star. Accordingly, in 1856 the Oxford astronomer Norman R. Pogson proposed that a difference of five magnitudes be exactly defined as a brightness ratio of 100 to 1. This convenient rule was quickly adopted. One magnitude thus corresponds to a brightness difference of exactly the fifth root of 100, or very close to 2.512 — a value known as the Pogson ratio.

The Meaning of Magnitudes
This difference in magnitude...	...means this ratio in brightness
0	1 to 1
0.1	1.1 to 1
0.2	1.2 to 1
0.3	1.3 to 1
0.4	1.4 to 1
0.5	1.6 to 1
1.0	2.5 to 1
2	6.3 to 1
3	16 to 1
4	40 to 1
5	100 to 1
10	10,000 to 1
20	100,000,000 to 1

The resulting magnitude scale is logarithmic, in neat agreement with the 1850s belief that all human senses are logarithmic in their response to stimuli. The decibel scale for rating loudness was likewise made logarithmic.

Alas, it's not quite so, not for brightness, sound, or anything else. Our perceptions of the world follow power-law curves, not logarithmic ones. Thus a star of magnitude 3.0 does not in fact look exactly halfway in brightness between 2.0 and 4.0. It looks a little fainter than that. The star that looks halfway between 2.0 and 4.0 will be about magnitude 2.8. The wider the magnitude gap, the greater this discrepancy. Accordingly, Sky & Telescope's computer-drawn sky maps use star dots that are sized according to a power-law relation.

But the scientific world in the 1850s was gaga for logarithms, so now they are locked into the magnitude system as firmly as Hipparchus's backward numbering.

Now that star magnitudes were ranked on a precise mathematical scale, however ill-fitting, another problem became unavoidable. Some "1st-magnitude" stars were a whole lot brighter than others. Astronomers had no choice but to extend the scale out to brighter values as well as faint ones. Thus Rigel, Capella, Arcturus, and Vega are magnitude 0, an awkward statement that sounds like they have no brightness at all! But it was too late to start over. The magnitude scale extends farther into negative numbers: Sirius shines at magnitude –1.5, Venus reaches –4.4, the full Moon is about –12.5, and the Sun blazes at magnitude –26.7.