[SomeStupidPoint]

But if you tuck in your knees and the other guy spins differently, that's a sign you're the one spinning, no?

[styrophone]

Yeah, the choice of a non-inertial reference frame for this example is a little confusing to me too. I also haven't been able to find an independent mention of the spinning astronaut experiment.

[dogma1138]

No because you technically performed an action which changes the system.

Relativity states that there isn't a measurement you can take if you change the system however it's a different story.