#6: World of Tinker-Toys

tinker toy6.1 The challenge in #4  was to make a Parental Tree outlining double half-1st cousins. On the left of Chart 13, we’ve started with the basic diagram for half-1st cousins , outlined in Yellow from Chart 8b. Abner and Zeke are half-cousins on their fathers’ side because their fathers are half-brothers. 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 a maternal grandfather Abner and Zeke share, and 2 maternal grandmothers they don’t share…marked on Chart 13 with a green X. The resulting diagram is a little messy…a bit of judicious shifting around yields the diagram on the right, the added grandparents still marked with a green X so you can verify where they were.

chart 13

6.2   Below we 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 1st cousins when their fathers are brothers and their mothers are sisters. They are double half-1cousins when their parents’ relationship is half-siblings instead of full siblings. This difference is clearly illustrated by the double X and double W connections between the grandparents’ and parents’ generations.

chart 13A

6.3  With these patterns in mind, we move on to half-2nd cousins…simply change the grandfathers in Chart 10-B  from full brothers X to half-brothers W and we’re done. For half-3rd, half-4th, half-5th cousins just shift the W back a generation.

chart 14

6.4  Now in this context, the word “double” has described a relationship that Abner and Zeke share twice, once on their fathers’ side, once on their mothers’ side. But it was the same relationship…1st cousins, half-2nd cousins, whatever it may be. Do the relationships on either side have to be the same? The answer is no…as seen in Chart 15. We call this double cousin relationship irregular, since the 2 sides are different…regular would be if they’re the same. And now, the word “cousin” is being used in a looser sense…it means some type of cousin…in this case 1st and half-1st.

chart 15

6.5  Thus, there can be such a thing as triple cousins, and some families describe themselves as such. A typical example of triple cousins is shown in Chart 16A…Abner and Zeke are double 2nd cousins on their fathers’ side and single 1st cousins on their mothers’ side. There is no relationship per se of which they are “triple”…which is to say, there is no relationship they share 3 times…triple 1st cousins is impossible, since we only have 2 sides to our family, not 3. Abner and Zeke can be 1st cousins thru their fathers and 1st cousins thru their mothers…there are no relations left for that third 1st cousin relationship.

chart 16 A

6.6  On the other hand, since 2nd cousins are descended from the siblings of grandparents, and everybody has 4 grandparents, there can be triple 2nd cousins…in Chart 16A, Abner and Zeke’s mothers are sisters…simply make them 1st cousins, and the boys are now 2nd cousins 3 ways. Make the mothers double 1st cousins…like the fathers are…and now Abner and Zeke are quadruple 2nd cousins….quadruple because there are 4 grandparents. And if you’re thinking, well heck, there are also 8 great grandparents for 3rd cousins…yup, you’re on the right track, my friend!

6.7  Of course these multiple cousin relationships I’ve described are regular…each is the same degree of cousin. In Chart 16A, the triple cousins are irregular since they are not all the same…2nd cousins twice and 1st cousins once. Yes, it must be obvious by now that I do not now nor have I ever suffered from math-o-phobia…quite the contrary! And it is my firm belief that if things are simply explained, and built up from the basic to the more complicated, one step at at time, you needn’t suffer either…

chart 16 B

6.8  To make the relationships in Chart 16A easier to see, we can move Zeke and his father below Zeke’s paternal grandfather, as seen in Chart 16B. It should by now have dawned on you that the possible combinations are practically endless…for example, in Chart 16B, if the boys’ paternal grandfathers were 1st cousins instead of brothers, Abner and Zeke would be a different combination of irregular triple cousins: 3rd, 2nd, and 1st!

6.9  And owing to the fact that our family trees grow “wider” as we go back thru past generations, variations start to appear. We have seen that there is only one way you can get 1st cousins cousins or 2nd cousins. This is true for all of what I call numbered cousins…3rd, 4th, 5th, etc. If Abner and Zeke are any degree of numbered cousin…and “single” or just once…there is only one way that can happen: each has a direct ancestor who is a brother to the other’s direct ancestor…how far back determines the degree. There is only one way to be double 1st cousins as well…but when we move on to double 2nd cousins, things begin to split off…

chart 11

6.10  …which is what we saw with Charts 11 and 122 different ways Abner and Zeke can be double 2nd cousins. Bilineal and Unilineal are terms that crop up in many genealogical contexts…bi means 2…uni mean 1…and lineal refers to a line of direct ancestors…all connected by a series of parent/child relationships. In Chart 11, Abner and Zeke have fathers who are 1st cousins, hence they are 2nd cousins…they also have mothers who are 1st cousins, so they are again 2nd cousins…double 2nd cousins, 2nd cousins 2 ways, thru 2 lines of descent…bilineal.

chart 12

6.11  In Chart 12, Abner and Zeke have fathers who themselves are double 1st cousins…thus Abner and Zeke are double 2nd cousins thru only one line, their fathers’…unilineal. Now you might wonder if there 2 types of double 2nd cousins really amount to the same thing…are the Coefficients of Relationship equal? They are…1/16 in either case…that’s twice the CR of single 2nd cousins, 1/32.

6.12  But to confirm these 2 different forms of double 2nd cousins amount to the same genetic relationship, we simply check for grandparents who are siblings…that is where 2nd cousins come from after all. In the bilineal case, Abner’s paternal grandfather is the brother of Zeke’s paternal grandfather…that’s 2nd cousins. But also, Abner’s maternal grandfather the brother of Zeke’s maternal grandfather…that’s 2nd cousins again…double 2nd cousins…check! And notice were the bi of bilineal comes in…we went to their father’s fathers and their mother’s fathers…2 lines, father’s and mothers.

6.13  With unilineal…we again find 2 sets of grandparents, shared by Abner and Zeke, who are siblings…in this case, their paternal grandfathers are brothers…and their paternal grandmothers are sisters. But notice, we did this thru Abner and Zeke’s paternal lines only…they have no relation thru their mothers..hence unilineal. The bottom line: to be 2nd cousins, you must share a pair of grandparents…and Abner and Zeke do this twice, whether bilineally or unilineally.

6.14 The key thing to understand is this: in both these cases, there is what I call a “crossover” between 2 family lines…represented by the big wide X in both Charts 11 and 12. The difference is, this crossover comes at different generations…from Abner and Zeke’s parents’ generation for bilineal…from their grandparents’ generation for unilineal. And as is the case for all of genealogy, this “movable” crossover occurs with all degrees of cousins…and Chart 17 show 3 different types of double 3rd cousins…amazing, huh?

chart 17

6.15  And if you’re really sharp-eyed, you might have noticed a seeming discrepancy…in the middle diagram, it says that Abner and Zeke’s fathers are double 2nd cousins…but aren’t they also double 2nd cousins in the diagram on the left? Yes, they are…the difference is, in the middle diagram, no grandparents are double 1st cousins, as they are on the left…instead, there are 2 pairs of single 1st cousin grandparents.

6.16  But getting back to double 2nd cousins, I must leave you with a “revolting development,” as they used to say on The Life of Riley…there is yet a 3rd type of double 2nd cousins, over and above bilineal and unilineal… Wha–? Yup…tune in again next week…

wicked ballsy

abner zeke

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


Copyright © 2011 Mark John, All Rights Reserved


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