Sure, the names CW/CCW don't matter. But I first have to determine an orientation for each star system, to look at it to see if it is spinning CW or CCW. If I don't, then we cannot decide which way it's spinning, since it's spinning CW from one view, but CCW from another.
E.g., let's say I orient each star system in the galaxy such that it appears to be spinning CW: then by definition, all star systems appear to spin CW. I could choose the other method, and now all star systems spin CCW, despite nothing in the universe changing. I could orient them randomly, and it'd be 50/50. But that tells us nothing: we're sampling how we orient the system to sample it, not any innate quality of the universe.
That is, the entire question, to me, is how do you pick a frame of reference, since there seems to be nothing upon which to pin a frame of reference to.
You are looking for some sort of absolute reference. A "frame" of reference is arbitrary and relative. It's something you just make up and the rules which you made up apply only relatively and within that frame.
When you look at a paper map, it says North on it, pointing to the "top" of the page. That north is not the real North. It points in whatever random direction the paper happens to be pointing. The paper is a frame of reference, and that "north" only applies relative to everything else on that paper.
If you turn the paper 90 degrees, North no longer points "up" relative to your eyes (although, now it may point "up" relative to my eyes since I am not you but standing next to you).
So that particular instance of "north" is arbitrary. There is no higher or more absolute reference that it is based on.
You pick any direction you want and call it "north", because you can lay that paper down on a table in any direction you want. And it doesn't matter what direction you picked. There is nothing special about "up relative to my eyes" because your eyes point in a random direction. Your eyes and the table and the paper are all somewhere on the surface of a sphere called Earth for one thing, your eyes and the paper might be pointing in any direction at all in 3d space simply by being anywhere on the surface of a sphere. Let alone that the sphere is rotating and travelling in an orbit which itself is in a larger orbit etc etc.
The distribution of celestial objects is full of uniqueness. It's one huge fingerprint. So it is possible to pick identifiers. You can pick objects and then recognize them later from their positions relative to other objects, like finding the north star by recognizing the big dipper.
You can pick any 3 stars and say "For the purposes of the next 5 minutes, let's call this star A and this star B and this star C. A is the north pole, B is the south pole, C is 12 o-clock or 0 degrees, and degrees count up clockwise when looking from north to south."
Congratulations. You just created a coordinate system that you can apply to the entire imagined universe. All other objects can be described in relation to this reference.
That is a frame of reference. There is no "north", you just picked a random direction and said "This is north. Now, relative to that, what directions do the axis of rotations of all other objects point?"
Probably for this question and really all others, it makes more sense to use a rule that "north" for any object is always described relative to it's own direction of rotation. IE rather than saying "this solar system rotates CCW", what you measure is the angle of each objects own local "north" relative to the universal north you made up. Each objects own local "north" would be pointing up from a clock face matching it's rotation.
It does not matter at all which objects you picked for A, B, and C. All that matters is that you use those same points and relationship rules for all subsequent measurements.
(Also since everything, including A, B, and C, are always moving, there is a 4th point of reference which is some arbitrary single point in time)
And for the purpose of the question about random distribution, it does not matter what direction you happened to pick to call north, because we don't care what the directions of all other objects are called, or what they refer to, only are they distributed randomly or is there a bell curve, or some other non-random plot?
> Are you telling me you don't know what the term "frame of reference" means
… I know what a frame of reference is.
> or how to establish one?
That's the entire question, here. For a given star system, how do you establish a frame of reference to then decide whether the system as a CW or CCW spin, without the determination being arbitrary, since we're asking to learn something about nature here.
> You can pick any 3 stars and say "For the purposes of the next 5 minutes, let's call this star A and this star B and this star C. A is the north pole, B is the south pole, C is 12 o-clock or 0 degrees, and degrees count up clockwise when looking from north to south."
We were trying to establish the spin of a star system. Short of it being a binary star system, there's one star.
We can't really consider multiple star systems simultaneously, as it wouldn't make any sense. Say you pick a star at random, A; you arbitrarily designate one of the two poles of the star as "north", and "up" as a vector straight up from the star's "north" pole. First, the CCW/CW rotation of star system A hasn't been decided by any fundamental law of the universe, it's been decided by our choice alone. Had we chosen the other pole to designate as north, then the rotation is reversed.
If we go to a second system, B, and maintain our definition of "up" as "up in the A system" … that makes no sense. This system could be edge-on the the up vector from A. For B's rotation, we need a vector perpendicular to the plane of system B.
(Whether a system is CCW or CW is going to be about the "up" vector, but the "up" vector for a system has to be from the system's center, and then perpendicular to the plane of rotation.)
Sure, the names CW/CCW don't matter. But I first have to determine an orientation for each star system, to look at it to see if it is spinning CW or CCW. If I don't, then we cannot decide which way it's spinning, since it's spinning CW from one view, but CCW from another.
E.g., let's say I orient each star system in the galaxy such that it appears to be spinning CW: then by definition, all star systems appear to spin CW. I could choose the other method, and now all star systems spin CCW, despite nothing in the universe changing. I could orient them randomly, and it'd be 50/50. But that tells us nothing: we're sampling how we orient the system to sample it, not any innate quality of the universe.
That is, the entire question, to me, is how do you pick a frame of reference, since there seems to be nothing upon which to pin a frame of reference to.