HR diagrams show in which of several sequences individual stars fall, each respecting the rough principle that hotter stars are of higher luminosity. (Sequences other than the main sequence may bend or be close to level, but let's put that aside.) Much about such diagrams takes some getting used to:
- We convey temperature on the $x$-axis and luminosity and the $y$-axis, and so might expect the main sequence to slope up. In practice it slopes down, because the $x$-axis is "running backwards": higher temperatures are on the left.
- Of course, the fact that the main sequence slopes down in this convention tells us the $y$-axis is "the right way up": the highest parts of the diagram have greater luminosity. But if you glance at the numbers on the $y$-axis, you might get the erroneous impression this isn't so, because the absolute magnitude $M_V$ falls toward the top. This is because it is a decreasing function of luminosity (a fact you'd never guess from the variable's name), specifically a negative logarithm of a nondimensionalised luminosity.
- Finally (this last concern is much lesser than the others), just in case the uninitiated's head isn't spinning enough, many values of $M_V$ are negative, which can confuse people trying to order the numbers too.
Needless to say, if we just put Kelvin on a logarithmic $x$-axis, increasing to the right, and wattage on a logarithmic $y$-axis (note that log-wattage will be positive even for very dim stars), increasing upwards, this would be a lot easier on everyone.
Now, part of the history behind this is that some decisions were made when we had a poorer understanding of what we were measuring. But this doesn't tell the whole story; as standards developed, one would expect rival diagram designs to be considered, and each option's pros and cons reviewed. How did astronomers settle on the status quo?