Today’s post is part of a special series here on Planet Pailly called Sciency Words. Each week, we take a closer look at an interesting science or science-related term to help us expand our scientific vocabularies together. Today’s term is:
DEGENERACIES
Okay, I have to be honest with you: I really don’t understand what this term means. It’s a statistics thing, and it gets really mathy. But since I came across this term in a paper about the TRAPPIST-1 planets, I felt I should try to get some sense of what a degeneracy is. What I learned, at least in relation to planets, was interesting enough that I thought it was worth sharing with you.
Imagine we’re playing a game of “Guess Who?” You know my person has red hair, but you still don’t know my person’s age or gender, you don’t know if my person is wearing glasses, or if my person has freckles. That one datapoint—my person has red hair—eliminates a lot of possibilities from the board, but there are still plenty of possibilities left over.
Those left over possibilities can be refered to as degeneracies (if I’m understanding the proper usage of this term). In that paper on the TRAPPIST-1 planets, it says: “The derivation of a planetary composition from only its mass and radius is a notoriously difficult exercise because of the many degeneracies that exist.”
In other words, if you’re playing “Guess Who?” with planets, knowing a planet’s mass and volume (and thus being able to calculate its density) still leaves you with a whole lot you don’t know about that planet.
This reminds me a lot of the Earth Similarity Index and the problems with using that system to identify Earth-like planets. Venus, for example, scores rather highly on the E.S.I. because its mass and volume are so similar to Earth’s, but Venus is not at all Earth-like in the sense that most people mean when they talk about Earth-like planets.
I’d say I plan to study this concept more, but I think I’m done for now. I tried to read this paper from 2010 which seems to have introduced the subject of degeneracies to planetary science and warned that they’d be a real problem in the study of exoplanets. But after attempting to slog my way through that paper, I think I’ve had enough mathy stuff for a while.
Planet Pailly 
I think you’ve got it right.
The best way to think about degeneracy is as equivalence. A system is degenerate if multiple possible configurations of the system correspond to its measured state. So in Guess Who, Eric and Joe both have blond hair, so knowing that the character has blond hair narrows the solution down to two degenerate states – Eric and Joe (there are other characters who also have blond hair, but I’m ignoring them for simplicity.) On the other hand, if Eric was the only character with blond hair, then knowing that the character’s hair was blond would lead to an exact solution (Eric) and the system would be non-degenerate.
Similarly, knowing a planet’s mass and radius, doesn’t pin down its exact composition – different compositions may have the same mass and radius. Degeneracy is a confusing mathematical way of saying something rather simple.
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Excellent! Glad to get your expertise on this. I felt 93% certain I understood the concept in relation to planets, which was really all I needed to know to get through that TRAPPIST-1 paper. But I couldn’t say if I understood how the idea related to anything else.
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