G4BB 71: Doubling Down

Doubling Down

71.1  Today we’ll continue examining double cousins. Unless they have an instance of it in their own family, people are generally unfamiliar with the idea that 2 individuals can be simultaneously related to each other in more than one way. As we have seen, the term “double” and its successors (triple, quadruple, etc.) are typically used to label what’s technically called “regular double relations”…this simply means each of the individual relationships is of the same type…2nd cousins…half-first cousins…3rd cousins once removed…etc. When the the relationships are different…for example 1st cousins on fathers’ side, 2nd cousins on mothers’ side…this can also be described as a “double cousin” relationship…what genealogists would call an “irregular double relationship.”

71.2  As many have bemoaned, there is no easy way to describe such irregular multiple relationships…and given the large number of possibilities….let alone their increasingly complex nature…there seems there never will be…which doesn’t mean we won’t try…and very soon too!

71.3  We’ve been been examining the concept of multiple relationships in its most basic form…that is, from parents whom are not related to each other. But these concepts of double cousins will also apply to interbreeding, and indeed the resulting complications come fast and furious. I was reminded of this when I re-read G4BB 16: Royal Action! concerning ways that Queen Elizabeth II and Prince Philip are related to each other. Again, I made a mistake, which I have since corrected…

71.4   …and that is, owing to the Royal Couple each being a great great grandchild of Queen Victoria and Prince Albert, who themselves were 1st cousins, the 5th cousin relationship between QEII and Philip is doubled. This bumps their CR…based on the 5 relationships I cited, and which I believe are the 5 closest…up from 29/2048 to 30/2048…now a wee bit less distant than half-2nd cousins, 32/2048. But this is a good time to reiterate that in spite of an obvious goof, the resulting adjustment really is quite small, which is what you’d expect from relationships this distant.

71.5  But double cousins have popped up in another couple of instances. I’ve been lucky enough over the past few months to get a little ahead of myself writing blogs and making accompanying charts…and I had recently found this plaintive plea at a cite called RootsWeb concerning a Norwegian family, um, tree…

71.6  A vine indeed! But no need for all that paper, honestly…the connections can be diagrammed fairly routinely…just take it one step at a time, you know? And as shown in Chart 244, Ethel and W.E. are double 2nd cousins…since Ethel’s mother Ellen is 1st cousin to both W.E.’s parents….thru 2 sisters on W.E.’s mother side, and thru a sister and brother on W.E.’s father’s side. Mind you, I had mapped all this out while I still, mistakenly, thought there were only 2 types of double 2nd cousins, unilineal and bilineal. I subsequently discovered there is a 3rd kind, which I’ve dubbed sesquilineal (see G4BB 70)…and with Chart 244, that’s what I had right in front of me…but as they say, I literally didn’t know what I was looking at!

71.7  BTW, I first learned about the types of double cousins from an excellent, altho extensive and sometimes quite involved, website here: GENETIC AND QUANTITATIVE ASPECTS OF GENEALOGYI’m a little surprised he missed the 3rd kind, but he was thinking along different lines, giving a total of 6 kinds of double 2nd cousins…counting 2 types of full, 2 types of half-, and 2 types involving identical twins. But it just goes to show, this stuff is complicated enough to throw even a retired professor off 😉 😉 I still recommend this site quite highly…it is in fact the inspiration for much of what we do here at G4BB.

71.8  More double 2nd cousins cropped up at a website tracing a family tree back to Merry Olde England, and involving an ancestor who defeated a double 2nd cousin in a parliamentary election, as described here…

71.9  Having found this account, the researcher put together the portion of the tree below, but wondered if he was getting it right…the X’s thru the individuals shown indicates that they are dead…telling me this tree extends down to the present day, and some presumably un-X’d relatives. Those commenting confirmed that all looked kosher based on their own genealogical research, altho one poor soul asked: double 2nd cousin…is that the same as 2nd cousin twice removed? Which gave me a guilty chuckle, but tells me that despite relatively meager levels of readership, G4BB fills a need for sure!

71.10  At any rate, in Chart 245, I simplified the Newport/Bolton connection…first based literally on the original tree (left), then re-arranged to more clearly show the double 2nd cousin relationship (right)…which you will confirm is unilineal.

71.11  Still, I got to wondering if I was the only one who realized there were 3, not 2, distinct types of double 2nd cousins…seemed unlikely, but this isn’t something thrown around in casual conversation, nez pah? Sure enough, I found the charts below…

71.12  The offspring from the top generation are drawn in an odd way, but once you see how they’re doing it, it turns out to be right on the money, as you can see in Chart 246…unilineal top, bilineal middle, sesquilineal bottom…

71.13  So now, for the sake of argument, shall we take a peek at double 3rd cousins? (Did you guys have a pool on when I’d get to double 3rd cousins? Did you have 71.13? I expect you to split it with me…see PayPal link above…) Back in G4BB 7, I diagrammed  3 “regular” types of double 3rd cousins as Chart 17…the top row of Chart 247 replicates Chart 17, and the bottom row shows the other 3 types. As you can see, this was originally drawn using what I call the Parental Tree format…fathers and mothers are not connected to each other, only to their offspring…and in addition, for clarity of explanation, I kept siblings next to each other (as opposed to one pair separated to opposite side)…resulting in downward lines of decent that “crossed” other lines. Altho when you look at it, it is interesting and I think illuminating to see where those “crosses” come about in each case.

71.14  But in Chart 248, those 6 types of double 3rd cousins have each been translated into the format we’ve been currently using…and we address the issue of what to call them. Anybody in favor of semi-bi-unilineal? I didn’t think so. So beyond the 3 types of double 2nd cousins, we need something more flexible…and here’s where that goofy idea of calling siblings “0th (zero-th) cousins” comes in handy. 0 will refer to siblings, or specifically, a union in the siblings’ generation…1 means 1st cousins…2 means 2nd cousins. Thus the 6 types are 0-0-lineal, 1-1-lineal, 2-2-lineal, 0-1-lineal, 0-2-lineal, and 1-2-lineal. And if you check each term against its corresponding diagram, I think you’ll see this nomenclature is pretty straightforward. For example, 0-2-lineal double 3rd cousins are 3rd cousins owing to a union in the siblings’ (0) generation on one side, and in the 2nd cousins’ (2) generation on the other.

71.15  And of course, considering double 2nd cousins this way, unilineal would be 0-0-lineal…bilineal would be 1-1-lineal…and sesquilineal would be 0-1-lineal.

71.16  Complicated? Sure, but the beauty of this system is it can be extended indefinitely, out to double cousins of any degree. I once said that when it comes to the use of mathematics in genealogy, you can use a little or a lot or none at all, it’s up to you. But a little definitely goes a long way…for example, it answers the question of how many types of double 4th cousins…or 5th…or 6th…there are. And if you’re game, continue on…otherwise, see yez next week…

71.17  To take double 4th cousins as an example, the 6 types of double 3rd cousins still hold…just add another generation to the bottom of each of the 2 lines, and those 2 new additions are now the double 4th cousins. But the union that brings about the 4th cousin relationship can now also occur in the generation just before the 4th cousins, that of the 3rd cousins, designated 3…so we also have the “new” types 0-3, 1-3, 2-3, and 3-3…for a total of 6 + 4 = 10 types of double 4th cousins. And that’s how it will proceed…for Nth cousins, the number of types of double cousins will be N more than there were for the previous degree of cousins. What we’re doing is actually adding the numbers from 1 thru N, and that total gives you the number of types of double Nth cousins.

71.18  And if you’re not really in the mood to add 1+2+3+4+5+6+7+8+9+10…well, guess what? Nobody is! Which is why there’s a formula for it…the number of types of double Nth cousins is N x (N+1) / 2. Just multiple the degree of the cousins by the next number and divide by 2. Let’s try it with 10th cousins…10 x 11 = 110…divided by 2 = 55…or 55 different kinds of double 10th cousins. Done and done. Like I said, when it comes to math, a little goes a long way…


Copyright © 2012 Mark John Astolfi, All Rights Reserved

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One Response to G4BB 71: Doubling Down

  1. Loretta says:

    Its like you read my mind! You appear to know so
    much about this, like you wrote the book in it or something.

    I think that you could do with some pics to drive the message home a little bit,
    but instead of that, this is great blog. A great read.
    I will certainly be back.

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