part 7 G4BB: World of Tinker-Toys

World of Tinker-Toys

7.1 Last week’s challenge was to make a Parental Tree diagramming Double Half 1st Cousins. Look at the left half of Chart 13. We start with the basic diagram for Half 1st Cousins, taken from Chart 8B. Abner and Zeke are Half Cousins on their Fathers’ side because their Fathers are Half Brothers…having the same Father and different Mothers. To make Abner and Zeke Double Half Cousins, they need to be Half Cousins on their Mothers’ side as well. We do this by making their Mothers Half Sisters…adding the Maternal Grandfather Abner and Zeke share, and the 2 Maternal Grandmothers they don’t…marked with a green X. The resulting diagram is a little messy…and here is where art meets science. Shifting things around, we get the diagram on the right.

7.2 At this point, it might be helpful to compare the Tinker-Toys for Double 1st Cousins (Chart 9) and Double Half 1st Cousins (Chart 13). As you can see, Abner and Zeke are Double 1C when their Fathers are Brothers and their Mothers are Sisters. They are Double Half 1C when their Parents’ relationship is Half Siblings instead of Full Siblings. This difference is clearly seen from the top to the middle generations…the “X” shape from Parents to Full Siblings…the “W” shape from Parents to Half Siblings.

7.3 And with these structures in mind, we can take the next step…Half 2nd Cousins. What might have appeared to be a dauntingly complex task is now seen to be simple…take the diagram for 2nd Cousins (from Chart 10-B, with the correct 2-line parental connections) and make the Grandfathers of Abner and Zeke Half Brothers instead of Full Brothers by replacing the X structure with the W structure. Bingo. How about Double Half 2nd Cousins? I won’t even bother, it’s so easy. Just take the Double 2nd Cousin Tinker-Toy and replace X with W.

7.4 Two important things to note: First, with respect to Cousin relationships, the words “Double” and “Second” have completely different meanings, altho they could easily be confused by the uninitiated. I think you’ve already absorbed that difference with the examples I’ve given. Second, we’ve been using the word “Double” in a very precise sense…that is, Abner and Zeke have the same relationships on both their Fathers’ and Mothers’ sides of the family, whether it was 1C, 2C, Half C, etc. In this sense their Double relationship is described as “regular.” But the term “Double” can also be used in a looser sense…they are related in 2 different ways that are not the same. There is no easy way to describe this, except to call it “irregular”: they are one thing on their Fathers’ side, and something else on their Mothers’ side. Chart 15 shows a typical Irregular Double Cousin relationship…Abner and Zeke are Full 1C on their Fathers’ side, Half 1C on their Mothers’ side. And once again, you can see the X and W structures associated with these relationships.

7.5 Thus, in this looser sense, there can be such a thing as “Triple Cousins,” and I have seen families describe themselves as such on the internet. Now in terms of CR (Coefficient of Relationship, which I’ll examine in more detail next week), we only deal in powers of 2, since everyone has 2 parents: 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, etc. Not coincidentally, these numbers are also associated with the way computers count, since they are also designed around the powers of 2: on or off, 0 or 1. Way back in the day, when they taught you about “Base 2” in math class (the nuns did it to us in 8th grade), I wonder if you realized how important it would be to future technology. But of course that’s why they were doing it…it was much more than just a theoretical curiosity. And recall that a kilo-byte, while technically defined as 1000 bytes, is in fact the power of 2 that is closest to 1000, namely 1024…one of those rare cases when you actually get more than advertised.

7.6 But can you really be “a third” of anything? I recall when Davey Lopes was named a coach for the Texas Rangers in 1988, he was announced as their “first black coach.” Reporters asked him if he really was black, and he replied that he was a third white, a third black, and a third Portuguese. I got the impression at the time that he was being completely serious. And of course, what he said is impossible. With a very complicated Family Tree, you can get a relationship that is close to a third, but never exact. For example, 5/16 is close to 5/15 = 1/3. In terms of decimals, 1/3 = .333 and 5/16 = .3125. But there are no real thirds…or any other fraction…1/5, 1/9, 1/10, 1/12…in genealogy except for the powers of 2.

7.7 Chart 16A shows a typical “Triple Cousin” relationship…Abner and Zeke are 2nd Cousins in 2 different ways, and 1st Cousins in 1 way, for a total of 3 relationships, as explained in the caption. (Notice I’ve simplified the Parent-Offspring relationship, from an “X” to an upside-down “V.”)

7.8 And to make these relationships a little easier to see, I’ll move Zeke and his Father below Zeke’s Paternal Grandfather, as seen in Chart 16B. I’ve based this “Triple Cousin” relationship on the Double 2C diagram since it was handy. But there are an almost infinite number of variations, especially give the prevalence of cousin marriages in the past. For example, in Chart 16B, if Abner and Zeke’s Paternal Grandfathers (their Fathers’ Fathers) were 1st Cousins instead of Brothers, Abner and Zeke would be 3rd Cousins, as well as 2nd Cousins and 1st Cousins!

7.9 Now last week, Charts 11 and 12 showed 2 different ways Double 2nd Cousins can be related…Bilineally, as 2C on Mothers’ side and 2C on Fathers’ side…and Unilineally, as Double 2C on Fathers’ side only. If you compare these 2 charts, you’ll notice the crucial difference…the occurrence of what I call the “Double Crossover.” For Bilineal, it occurs between the children’s (Abner and Zeke) and the parents’ generations. For Unilineal, it occurs between the parents’ and grandparents’ generation. And as is typical (and convenient!) in genealogy, this type of pattern repeats and expands. To illustrate this, I’ve diagramed 3 types of Double 3C relationships, and you can clearly see the downward “migration” of the Double Crossover. There are no simple terms for these different relationships…anybody wanna get Bi-Unilineal?…I didn’t think so. I have (big surprise!) devised my own compact system of describing them, which we’ll look at in a future edition of G4BB. For now, bear in mind that despite the different ways Abner and Zeke can be Double 3C, their CR is the same in all 3 cases, 1/64, which is why they are classified as Double 3C, and sensibly so.

UPDATE!!!  These 3 types of Double 3rd Cousins might be termed “regular”…because there are 3 other “irregular” types…see here: G4BB 71

7.10 BTW…a somewhat welcome term has come to my attention, and I intend to use it. The I-word (“incest’) is understandably unpleasant, and an imprecise term as well. For example, marriage between 1st Cousins is illegal, hence incestuous, in half the states in the US, but legal, hence non-incestuous, in the other half, altho obviously not completely accepted socially. Marriage between 2nd Cousins is legal everywhere, but not allowed by some religions. Thus, I shall be using the term “inbreeding” to describe the offspring of people who are blood relatives. It still has a negative connotation, granted…think of the movie Deliverance. But I think it is a useful and gentler way to describe relationships that may or may not be legal, moral, or socially acceptable…but nonetheless exist, and result in closer degrees of relationship than occurs otherwise.

7.11 And with that in mind, it might have occurred to you that there is a another way for Abner and Zeke to be Double 3C…and that is if their parents are the same 2 individuals…and 2nd Cousins. This is true in a sense…the children of 2C are always 3C…and if their parents are the same 2C, they are Siblings as well, and Double 3C to boot…since Abner’s Father is Zeke’s Mother’s 2C, and Abner’s Mother is Zeke’s Father’s 2C. The reason this type of relationship isn’t included in the 3 types of Double 3C is that those 3 types were meant to illustrate 2 individuals who were Double 3C only…with a corresponding CR of 1/64. But since CR is cumulative, the offspring that result when a 2C marries his own 2C have a CR of ½ + 1/64 = 33/64, not 1/64. Still, good catch.

7.12 Next week, we’ll look at the Relatives from U.N.C.L.E., and examine more closely the Coefficient of Relationship and how to figure it. But we’ll finish off this week with an email I received.

Dear Stolf: Your post about the Bee Super Sisters, who had a CR of 3/4 as compared to ½  for Full Siblings was interesting. But with people, isn’t there a thing called “Three-Quarter Siblings,” where the Parents that Half Siblings don’t share are themselves Siblings? from Stumpy, Cahulawassee River, Georgia.

Well, Stumpy, you’re right, and such a relationship is shown in Chart 18.  But the term “Three-Quarter Siblings” is a misnomer in that they do not have a CR of 3/4. The technical term for this is “Enhanced Half Siblings.” As you can see, Abner and Zeke are Half Brothers thru their shared Mother, and also 1st Cousins thru their Fathers…thus their CR is 1/4 + 1/8 = 3/8. This is half-way between the CR for Full Siblings ( ½) and Half Siblings (1/4), thus the term “Three-Quarter Siblings”…3/8 is half-way between Full (½ = 4/8) and Half (1/4 = 2/8). But they are not Super Siblings with a CR of 3/4 = 6/8, in the way the Bees are. Not even in Cahulawassee River, Georgia…but thanks for asking. Till next time, tell Aunt Bee Stolf says “Hey.”

Wicked Ballsy

I thought maybe you might like to see what Abner and Zeke actually look like…sadly, I’ve forgotten which is which, but there you go…

Copyright © 2011 Mark John Astolfi, All Rights Reserved

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