If you took the same measurements from another galaxy, would they still point to Earth as the center?
A viewer who saw The Principle asks whether, if one arbitrarily selected another galaxy and performed the same measurements from there, those measurements would still point to Earth, and whether this could be modeled from existing data.
Answer
No, they would not see the same thing. There is only one place that you can see the so-called axis of evil running right through our ecliptic plane from one end of the universe to the other; if you went to another galaxy you would see it going between the Earth and the sun and off to the other side. Measurements taken toward the Milky Way, which is at about a 60-degree angle to the ecliptic, do not line up; it only lines up with the sun-earth ecliptic. Someone made a similar argument on X, that any place can be considered the center because you can only see out so far and that edge follows you, so you always look like the center. My answer is Edwin Hubble already refuted that in 1929: looking out with the 100-inch telescope at Mount Wilson, he saw that all the galaxies, wherever he looked, showed a redshift of their light. If you see redshift everywhere, the Earth has to be in the center of it all; otherwise you would see redshift in one direction and blueshift in another. That is how you determine whether you are actually in the center, and Hubble did not like that, so he and others got rid of the center by putting all the galaxies on an expanding balloon so that every galaxy sees redshift from every other. But the honest reading is that the redshift everywhere means we are in the center.