Charting the distance from Rigel to Cassiopeia

I dreamed that one of my students, a girl of nine or ten, was sitting at a table with a large star chart in front of her. It appeared to be some sort of azimuthal projection of the celestial globe, and she was using a thread to measure the distance between two points on the chart. A woman (apparently one of her teachers; no one I know in real life) who was standing behind her, watching proudly, explained to me that the girl had figured out all by herself how to chart the distance from Rigel to Cassiopeia.

"Very impressive," I said, "but of course you can't actually do that."

"What do you mean?"

"Well, space is three-dimensional, and the chart doesn't show the third dimension. You can only measure degrees of arc, not light-years."

"Hey, that's true, isn't it? I'd never thought of that!" The woman looked at me as if I were about the cleverest person she had ever met.

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Upon waking, I realized that the girl's operation made even less sense than I had said in the dream. You use a thread to measure distances on the curved surface of a globe, but on a map you can just use a ruler; and the only sort of distance you can measure accurately on an azimuthal projection is distance from the central point. Also, Cassiopeia is not a single star but rather a sprawling constellation containing multiple galaxies, so "the distance from Rigel to Cassiopeia" is strictly meaningless.

My immediate reaction was that the dream was a symbol of the futility and stupidity of all human intellectual endeavor. The little girl was proud of her accomplishment, and my dreaming self was proud of having found something wrong with it, but in fact both of us were about as far from discovering anything true or meaningful as Rigel is from the most distant galaxy in Cassiopeia.

Why Rigel? Why Cassiopeia? I jotted down the names just after waking, thinking they must have been chosen for a reason.

Rigel, the bright blue star in Orion, has a name that comes from Arabic for "the foot of the great one." This made me think of Daniel's vision of a colossal statue with a head of gold, breast of silver, and so on, down to its feet of clay -- whence the proverbial expression "feet of clay" for a fundamental flaw or weakness in an respected person. The "foot of the great one" also calls to mind the heel of Achilles, with a similar proverbial meaning. (It is also interesting, but not particularly relevant, that Rigel is one of the proposed identities for Earendel, the bright star in the Old English poem that so famously inspired Tolkien.)

Cassiopeia, in mythology, was the queen of Aethiopia, punished for her vanity and boastfulness by being chained to a throne in the heavens -- a curious story, since immortalization as a star or constellation is generally seen as a reward rather than a punishment. One wonders if Cassiopeia even realized that her fate was indeed a punishment; perhaps in her vanity she thought of it as an apotheosis.

Both Cassiopeia, then, and the "feet of clay" suggested by Rigel represent the elevation to "greatness" of a fundamentally flawed person. This fits with the general theme of the dream, in which the girl and I were both praised for the "cleverness" of what was actually a reflection of our astronomical stupidity.