"Inside" v. "Outside" analysis of multiple stars/single stars, compared to...?

Miscellaneous and Personal Stuff I Must Share
1

Here is a list of the nearest stars/multiples nearest our Solar System:

(Sun)

Alpha Centauri A, B, C

Barnard’s

Wolf 359

Lalande 21185

Sirius A, B

(I’ve left off a couple of Brown Dwarfs.)

Now, let me define star-point as either a single star or a true binary, triple, etc.

Star-sun is any individual body.

Excluding our own Sun, Sol:

3 out of 5 star-points are single stars. Not so for 2, so its 2 out of 5 primary elements with companions. (A minority.)

But there are 8 individual star-suns. On this individual basis it’s 5 out of 8 with “company”. (A majority.)

We can get slightly different statistics if we include our own sun, but it shows essentially the same pattern.

I think of this as “inside” versus “outside” analysis.

The question I pose is whether this has any relationship to the perennial “paradox” here at SDMB of “At least one is a daughter” …

Compared to…

The Smiths had a daughter, and then one other child. What are the odds that it is a son?

Well???

(I mean, is it possible I’m just all wet with an inkling of a comparison here? Please think through carefully before you jump all over me, though.)

2

Isn’t it unknown if Alpha Proxima is actually gravitationally bound to the Alpha Centauri system? Making it either a triple star system or a binary + a single.

3

Proxima Centauri is indeed unique. Combining the unusual distance from A, B of 800 billion miles with the proximity of the entire system means that the angular separation to us is in DEGREES, rather than minutes or seconds.

But none of this affects the basic observation I started out with.

Including two brown dwarfs or starting out with Sol instead of leaving it out, or both has no real effect.

(It’s interesting that
the Wikipedia article I used for data is actually titled nearest stars to Solar System, or some such, and then lists Sol as if the title were nearest stars to Earth.)

The most surprising thing in the article is the many other terms for this one body under “Other Designations”.

4

I didn’t think to add that this thread really should not be about nearest stars per se.

It’s just the example I first noticed this non-paradox.

Let’s say that there is a local adventure game with young folks. Some kind of role playing game with physical outdoor activities. The planners give the participants the choice of asserting the desire to go solo, which would be honored. However, some participants would agree to team up in small groups of up to 3. The planners would describe advantages and disadvantages of each choice.

So some take the solo position (more mobile on short notice of changing conditions) while some lead or join a team (advantages of teamwork).

But every team has a designated leader.

The line-up:

1.) Sally

2.) Al, Betty, and Percy

3.) Barney

4.) “Wolfman Jack”

5.) Lalanna

6.) Sarah and “Beany”

“Majors” Al and Sarah have companions, so that’s 2 out of 6 majors for 1 in 3.

But if we consider each individual (total 9) only 4 are “single” so it’s 5 out of 9, a majority for companionship.

I keep thinking that there is some mathematical relevance to the non-paradox * as expressed here on Wikipedia and which seems to be a recurring argument here.

  • Non-paradox? To be more precise, there is a need to express the question with the right choice of words, that is, the right kind of scenario. Digging deep down in the Wikipedia article there is an analysis about possible ambiguity.