107.1 So how’d we do with last week’s quiz? I’ve modified Chart 375 as Chart 375a below, giving your mother and father letters for ease of reference. We wanted to know how C and D are related.
107.2 The way to approach this is to notice that there is a direct line of descent between C and all 3 of Y, Z, and A. The same is true of D…so C and D are related 3 different ways…thru Y, thru Z, and thru A. We simply examine these relationships one at a time. Thru Z…C and D are half-1st cousins, since their fathers YOU and B are half-brothers…the sons of Z but with different mothers. Coefficient of Relationship = 1/16.
107.3 Now thru Y…YOU and C are half-brothers, having the same mother Y and different fathers, Z and B. D is your son, so C is D‘s half-uncle…CR = 1/8. This same line of reasoning applies on the other side of the tree: B and D are half-brothers, having the same mother A and different fathers, Z and YOU. And since C is B‘s son, D is C‘s half-uncle…total CR 1/16 + 1/8 + 1/8 = 5/16…slightly more related than half-brothers, which would be 4/16.
107.4 Yes, it’s certainly unusual, but completely correct: C and D are 2 individuals each of which is both half-uncle and half-nephew to the other…talk about tit for tat! And if this kinship arrangement sounds vaguely familiar, it’s the basic idea behind the song “I’m My Own Grampa.” It’s an idea that goes back centuries…as a legal riddle in India, it supposed a man marries a widow, then his father marries her daughter, and each couple has a son…how are the sons related? The traditional answer is, each is both uncle and nephew to the other…correct as far as it goes, considering descent as unilineal…thru one line…hence half-brothers are considered simply brothers. For our bilineal system, it would be half-uncles and half-nephews, since they’re based on half-brothers. I’ve sketched this out in Chart 376…YOU marry the widow B and have son C…your father A marries the widow’s daughter D and has son E.
107.5 And leaving YOU, your father and your half-brother where they are, but re-arranging the others, as on the right of Chart 377, we see that these 2 situations are indeed the same…only difference is on the left YOU and B and half-brothers…on the right YOU and D are not related…hence on the right E and C‘s CR would be 1/8 + 1/8 = 1/4….they don’t have the additional half-1st cousin relationship (1/16) that C and D have on the left.
107.6 But today’s title is “Smokin’ OPs, Part Duh”…referring back to #68…and OPs are Other People’s. I found a cousins chart that’s very swanky…fancier than mine anyway…and thought I’d share it with you. It comes from a site called “Cousins & Cousinhood: It’s All Strictly Relative.” Now after seeing so many web-pages simply copying whole chunks of text from Uncle Wiki, it’s nice to find one copying from someplace else. In this case, one Ted Cash has preserved a page explaining cousins created by one Frank Arduini “before the site disappeared.”
107.7 Ted’s right…no can find the original site…altho this cousin page appears to have been part of a larger site devoted to the Arduini and Pizzo families. And in the article, Frank refers to his own family tree several times, one reference we’ll get to in a bit. But I am sad to say that where he says “This is my feeble attempt at explaining…” he’s certainly right about that. While much of what he says is accurate, there are several big boo-boos, and at least one area that needs some clarification…and since that refers to the chart, I’ll get to that first. And BTW…I don’t mean to be overly critical…it’s just that these are interesting genealogical topics, and they deserve discussion.
107.8 The chart itself is essentially correct…mathematically, I prefer to give the extent of relatedness as a fraction, not a decimal percentage. Both are true of course…but can you really remember that 6.25% is 1/16…or that 1.563% is 1/64? The beauty of doing it with factions and powers of 2 is that you can easily compare different relationships. For example, in 107.3 suppose we had come up with a CR of 31.25%. Now what do you make of 31.25%? Well, it’s more than 25% or 1/4…beyond that it’s just a number. But expressed as a fraction, 31.25% becomes 5/16…which is 1/16 more than 4/16 or 1/4…telling you that this CR is probably some kind of combination of half-sibling (or equivalent, like uncle, nephew, grandparent) and half-2nd cousin (or 1st cousin once removed, great grand uncle, 2G grandparent.)
107.9 The real problem with this chart is that it combines the correct CR for each relationship with a number that stands for the degree of relationship…what he called “traditional”…and indeed, it’s what’s used by most legal entities and organized religions. And because these 2 sets of numbers are referring to different things, they don’t always match. For example, your CR to your sibling and to your parent is the same…but the degree number is different. As he says, “This way of measuring kinship was developed long before…Mendelian genetics, so it’s actually wrong in a couple of areas, but not enough to really matter to most of us.” Hmmm, selective truth…interesting concept. Suffice to say that some of the degree numbers (in the blue and silver boxes) refer to half-relations…and to that extent, you are related to your brother thru your father by 1/4, not ½…thus the different degree numbers. You are also related to your brother thru your mother by 1/4…hence the total CR of ½. Like I always say, a full sibling is mathematically a double half-sibling.
107.10 But if you actually read the entire article, you might catch 3 major mistakes, as I did. Now I am happy that in the chart, he uses the terms “grand uncle/aunt” instead of “great uncle/aunt.” I am not happy that he says the latter is “WRONG!!!” “Great uncle” isn’t wrong per se, it’s simply not preferred by most genealogists because it’s confusing. For example, doing it that way, your 3G grandfather and his brother would have a different number of “greats”…since they are of the same generation, it makes more sense that they have the same number of “greats.” But “great uncle” isn’t really a mistake, since it refers to one and only one relationship, and it’s the same relationship that’s referred to by “grand uncle.” Compare that with what would be a mistake: the ambiguous use of “2nd cousin”…meaning maybe your great grandfather’s great grandson (correct)…or maybe your great grandfather’s grandson, your father’s 1st cousin (incorrect.) There is no ambiguity like that with the use of “great uncle,” and so it’s simply a matter of style…choose prudently, sez me!
107.11 He also correctly notes that “from a genetic perspective, identical twins are really the same person.” True enough…but then: “First cousins descended through a pair of identical cousins are double 1st cousins, just as if their grandparents had been two pairs of siblings.” No, that’s not right…yes, such 1st cousins would have a CR of 1/4…twice that of normal 1st cousins, and the same as double 1st cousins. But they are NOT double 1st cousins…they are 1st cousins only thru one set of parents…i.e. the twins…not thru both sets. Just because the CR for 2 different relationships is the same, doesn’t mean those relationships are the same. Indeed, as he correctly points out, if your father is an identical twin, you’re just as closely related to him as to your uncle…but that doesn’t make them both your fathers, does it? Only one of them is your father…um, your father. Duh.
107.12 Finally, and probably less obviously, he makes a mistake talking about his own family tree…he says that he has great grandparents who were 2nd cousins once removed to each other…making him not only a son to his mother, but also her 4th cousin, 5th cousin, and 4th cousin once removed. Shall we diagram that out and see what’s what?
107.13 On the left side of Chart 378, he is C, his mother is B, his grandmother is A, and his great grandparents are noted as 2C 1R. Their ancestors are shown to prove how that could come about: as I have it, his great grandfather’s great grandfather was the brother of his great grandmother’s grandfather. Notice that whatever their actual ages, this was a cross-generational marriage, hence the removed. Now in the middle diagram, I do something tricky…I move A, B, and C under great grandmother Z, and suggest that great grandfather Y is a 3rd cousin to his own daughter A. Is this right? Yes…3rd cousins are the offspring of 2nd cousins…X and Z are 2nd cousins, so their respective offspring Y and A are 3rd cousins, besides being father and daughter. And finally, on the right we extend this idea down to C, and it turns out he is indeed his mother’s 5th cousin…so that claim checks out.
107.14 At this point it might occur to you that if we moved A, B, and C under great grandmother Z, we might just as well move them under great grandfather Y…and get another set of 5th cousins, ending up with a double 5th cousin relationship between C and this mom. So on the left of Chart 379 we try just that…but something very strange happens…working our way up, we discover that E is now a 1st cousin to his brother C‘s grandson X…he should be his grand uncle, not 1st cousin. What went wrong?
107.15 We are the victims of the ambiguity in the phrase “2nd cousins once removed.” Yes, it is true to say “If I am your 2C 1R, you are my 2C 1R”…but this is true only in the sense of “If I am your uncle, you are my nephew”…because a removed relationship links 2 generations, and those 2 positions on your family tree are not interchangeable…any more than you could be your uncle’s uncle…or your father’s father for that matter. Using the word “cousin” makes it seem like the 2 ends of that one relationship are interchangeable, since, after all, “If I am your 1st cousin, then you are my 1st cousin.” But we saw what nonsense results when you try interchanging removed cousins. What’s really going on is shown on the right side of Chart 379.
107.16 Since X and Z are 2nd cousins, X‘s son Y (who is coincidentally Z‘s husband) is Z‘s 2C 1R…and X‘s granddaughter A (who is also Z’s daughter) is Z‘s 2C 2R as well. That’s more like it…and working down, we find that C and his mother B are 4th cousins twice removed. And what did he say they were? 4th cousins once removed, so that’s wrong. The remaining claim is that mother and son are 4th cousins. We can check that by noting that 4th cousins have great great grandparents who are siblings.
107.17 Chart 380 shows one of C‘s great great grandfathers (blue box) and 2 of his mother B‘s great great grandfathers (pink boxes)…no siblings there. C‘s other great great grandfather is X, who is also his mother’s great grandfather…again, no siblings. So where “4th cousin” came from is anybody’s guess, unless it’s happening on the another side of the family. Barring that, I don’t see it…do you? Then let me know, darn ya! And we’ll reconvene here next week, deal?
Copyright © 2013 Mark John Astolfi, All Rights Reserved