# Technical Article: The Derivation and Meaning of the CMB Anisotropy Vectors

## “The Derivation and Meaning of the CMB Anisotropy Vectors”

Two articles here on Geocentrism Debunked written in a more popular style lay out the fact that the CMB vectors, on which the new geocentrists have based so many of their claims, not only do not align exactly, but do not carry any positional information and by definition converge at the point of observation.  Therefore, contrary to the claims of the geocentrists, they don’t point at anything, they don’t describe the physical center of anything, and they don’t give us any information about the position of the Earth (see “Yes, the CMB Misalignments Are a Problem for Geocentrism” and “The CMB Alignment Challenge”)

Now, in the article, “The Derivation and Meaning of the CMB Anisotropy Vectors”, Dr. Alec MacAndrew lays out in a more technical fashion the mathematical demonstration of these facts.  Here are some salient excerpts:

Both [scientific] papers make it clear that the multipole vectors define only directions of CMB features on the spherical surface of last scattering and do not carry information about the position of the Earth (or any object in the Universe). Indeed, that is obvious from the fact that the entire analysis is carried out in spherical co-ordinates (θ, Φ) (and not in (r, θ, Φ)).   The vectors identify directions of CMB features and they are a function of (θ, Φ) and so are unable to define positions in R3. The vectors necessarily originate at the point of observation, and therefore it can be said that all the CMB vectors (including but not limited to the multipole vectors) “pass through” the Earth because that is where we are [9]. A hypothetical alien 100 million light years away doing these measurements and this analysis would acknowledge that all the multipole vectors originate at his location.

And:

Note that since the area vectors depend solely on the multipole vectors, then the area vectors also carry no position information, being determined purely by angular spherical co-ordinates. They, like the multipole vectors, originate at the point of observation by definition and they also are defined only up to a sign. They do not carry information about the position of the Earth (or any object in the Universe).