Humanity seems to have an insatiable desire to assign numerical scales to just about anything relating to size, quality, beauty, distance–anything that can be measured. But at times we seem to have trouble knowing whether we’re going forward or backward. A first-degree murder is considered more heinous than a second-degree one, but a third-degree burn is considerably worse than a second-degree burn. You would not want to be around for a magnitude 8 earthquake, while you likely would not even feel a magnitude 3 tremor. With beauty, a rating of 10 is considered absolute perfection, whereas it is the worst you can imagine when it comes to pain.
Against this setting of numerical confusion, we have the system of “stellar magnitudes,” which assigns a number to how bright a star appears in the sky. Astronomers assign bigger numbers to fainter objects. Most folks blame Hipparchus of Nicaea for this oddity. Around 150 BCE, Hipparchus is supposed to have pronounced that the brightest stars in the sky were “of first magnitude;” those only half as bright were deemed “second magnitude stars;” and those only half as bright as that were “third magnitude”–and so on, until he got down to the number six, after which he ran out of stars.
Fast-forward to the year 1610, when Galileo Galilei pointed his telescope toward the sky. In his quite-readable essay Sidereus Nuncius, he describes how . . .
“. . . 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. For you may see more than six further gradations of magnitude. The largest of these, which we may designate as of the seventh magnitude . . .”
That pretty much set the measurement system in stone. But in 1856, an astronomer named Norman Pogson found a critical error in our thinking: While using newly developed instruments that enabled accurate quantitative measurement of the brightness of things, he found that our perception of a one-magnitude–meaning a factor-of-two–change in brightness was slightly off. In actuality, it was closer to a factor of two and a half. While seemingly not a big deal, that old five-magnitude difference between the brightest and dimmest visible stars implied a brightness ratio of 32:1, while in reality it was closer to 100:1. And so Pogson set the rule by which we live today: A magnitude difference of five is exactly equal to a brightness difference of 100. Or, if you are mathematically inclined, the brightness difference between one magnitude and the next is the fifth root of 100, or 2.51188643.
The good news is that now that we have a mathematical expression, we don’t have to stick with whole numbers. We can measure and denote brightness differences down to a small fraction of a digit. But that introduced new problems, such as the observation that not all traditional “first magnitude” stars shine equally bright; in fact some, like Sirius, were far brighter than others.
But where do you go if your standard for “biggest and brightest” isn’t actually biggest–or, in this case, smallest–enough? You go one step smaller, down to 0 magnitude. And when that isn’t enough, you venture into the weirdness of using negative numbers to indicate really, really bright stuff.
Still, a mathematical scale can only compare ratios of brightness rather than assign brightness values until a starting point is established. The scale was finally fixed in an absolute sense in the 1950s with the pronouncement that the bright summer star Vega was exactly of magnitude 0. It is the star against which all other stars are now compared.
So what is the brightest star in the sky? Most people would probably say it is Sirius, which, at a magnitude of -1.46, is 3.8 times brighter than Vega. But that would be overlooking the obvious: the Sun, which shines at a whopping -26.74 magnitude. That’s about 25 magnitudes brighter than Sirius, which means it appears ten billion times brighter!
I’m not sure if Hipparchus would be delighted or dismayed with what we’ve done with his idea. And while you, too, may think this counting system is backwards, it’s too late to change it now.