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"The nature of this elementary particle is best expressed through these thirty equations."
"Ok, ok, but what do those actually mean in reality?"
"Reality?"
Most of those equations are full of things that can make sense, and then there is a fine structure constant.
It's all over particles, but we don't know what it is. It has no units. It's just a number that is needed for physics to work.
[The Fine-structure Constant] quantifies the strength of the electromagnetic interaction between elementary charged particles.
Why the constant should have this value is not understood, but there are a number of ways to measure its value.
Sounds like we know what it is, we just don't know the reason for its value. (Edit: Unless I'm misunderstanding what you mean)
The strangeness of the Fine Structure Constant isn't it's value, it's that we don't know what it is.
Other constants have units that explain what they are doing. Like converting miles to meters we multiply by meters/miles. But this is just a number that is needed. That's so strange I can't think of another example.
R, as in PV = nRT. Why is it R? It's just a number, no units.
There's tons of these things.
Meh, there's pi, it has no units because it's the ratio of one distance to another...
I feel like this might be another example of OPs meme. Feyman called it a magic number we have no understanding of. It's one of the great mysteries of modern physics.
Sounds a lot like what we used to call the "fudge factor".
We still need to develop the equations for reality whatever that means