G4BB 70: Magic Tricks

Magic Tricks

70.1  One of the coolest things about blogging is how easy it is to correct mistakes. With a newspaper, the best you can do is issue a correction the next day, and hope somebody will see it. With a book, you have to wait for the 2nd edition, if there is one…which you can then, in the best BS tradition, label “completely revised!”  But with a blog…just zip, zip, done and done…like the boo-boo never existed.

70.2  Here’s what used to be in 65.12 of my Cousin Wiki critique…

“Children of double first cousins are double second cousins to each other. This could be taken to mean the children that double 1st cousins have with each other. Here at G4BB, we use the gentle euphemism “interbreeding.” But it actually means double 1st cousins having children with unrelated mates. Still, if your parents are double 1st cousins to each other, you will indeed be double 2nd cousins to your siblings.”

The last sentence now reads: “And after all, if your parents are double 1st cousins to each other, you will be quadruple 2nd cousins to your siblings, not double 2nd cousins.

70.3  You know, when somebody asks me “What were you thinking?”…I’ve found the best answer is simply to say: “I wasn’t thinking.” Certainly I wasn’t here. But oddly enough, this dovetails with the topic I wanted to cover today…end result: blog writes itself.

70.4   So is my correction correct? Let’s take a closer look at double cousins. There is only one way 2 people can be double 1st cousins: 2 siblings from the Jones family marry 2 siblings from the Smith family and each has a child. It could be 2 Jones brothers and 2 Smith sisters…2 Jones sisters and 2 Smith brothers…or a Smith brother marrying a Jones sister, and a Smith sister marrying a Jones brother…but it’s siblings marrying siblings, that’s it, no other way it can come about. For double 2nd cousins, there are 2 ways: bilineal and unilineal…

70.5  And the reason there are 2 ways is something I said a while back, talking about the basic definition of cousins…that is, start at the bottom and work your way up…for example, 4th cousins have parents that are 3rd cousins…3rd cousins have parents that are 2nd cousins, etc. As opposed to starting at the top, with grandparents, with whatever number of “greats”…and working your way down. The trouble with “top-down” is you get multiple paths…thus for example, 2 great grandchildren of a married great grandfather and great grandmother could be 2nd cousins, 1st cousins, or siblings to each other…because in this case, there are 3 different kinds of downward paths. So starting at the top, 2 individuals can be double 2nd cousins in 2 ways because there can be 2 different types of paths.

70.6  In Chart 234a, X and Y are 2nd cousins because their fathers A and B are 1st cousins…X and Y are also 2nd cousins because their mothers C and D are 1st cousins. Thus X and Y are double 2nd cousins, and this type is called “bilineal” because it thru 2 lines…the fathers’ line and the mothers’ line. The important thing to notice is that there is no double relationship until X and Y’s generation…it takes the 2 different lines of single 1st cousins A/B and C/D coming together to make the double 2nd cousins.

70.7  Contrast that with Chart 234b…here the fathers A and B are double 1st cousins to each other…therefore their children X and Y are double 2nd cousins. The “double” relationship is in a sense passed down to the next generation. This is called “unilineal” because it comes thru only one line, the fathers’…the mothers C and D are unrelated to each other, thus no cousin relationship derives from them.

70.8  Ah, but what if C and D in this case were 1st cousins? As we see in Chart 235, X and Y would be “triple 2nd cousins”…twice thru their fathers and once thru their mothers….and I suspect you see where this is going…!

70.9  If C and D could be single 1st cousins, they sure as shootin’ could be double 1st cousins, as in Chart 236…making X and Y quadruple 2nd cousins, or 2nd cousins 4 ways: twice thru their fathers and twice thru their mothers.

70.10  And now for today’s first “magic trick.” Swap the genders of Y’s parents B and D…next substitute B for C and A for D as in Chart 237…and finally consolidate or “collapse” the duplicate individuals as in Chart 238a

70.11  …and you get Chart 238b…A and B are double 1st cousins to each other, and their children X and Y are quadruple 2nd cousins to each other, just as they were in Chart 236 when they had different sets of parents…and Chart 237 is the connecting link that proves it. Of course X and Y are also siblings, but that’s kinship for you.

70.12  So with all that under our belt, here’s the point: For today’s blog, I was playing around with the idea of double 1st cousins once removed. I started with Chart 239…this is based on my mantra that cousins removed are the cousins of someone in your direct line, just not you. Here, X is not the double 1st cousin of A, but X’s father B is…thus X and A are double 1C1R. But is this bilineal or unilineal? It’s tricky, since A and B are double 1st cousins thru both their fathers and their mothers…thus their relationship is bilineal. There is in fact no such thing as unilineal double 1st cousins. But the trouble is, X is related to A thru his father B…in other words, thru his father’s line only…and thus thru only one line. X’s mother and her line isn’t even part of the diagram since they are irrelevant to this double 1C1R relationship. Thus A and X are unilineal 1C1R.

70.13  Now it might strike you, as indeed it struck me, that there could be a bilineal version…and sure enough, Chart 240. Here A is X’s 1st cousin on his father’s side…and B is X’s 1st cousin on his mother’s side. In this generation, there are no double 1st cousin relationships…simply a person X with 1st cousins on both sides of the family, as it would be with most of us, unless we have parents who are only children. But now, A and B get together…after all, they are not blood relatives in any way…and have a child Y.  X and Y are 1C1R since X is 1st cousin to Y’s father A…same on the other side: X and Y are 1C1R because X is 1st cousin to Y’s mother B. Thus X and Y are double 1C1R, and are so bilineally…thru Y’s mother B and also thru Y’s father A.

70.14  Yes…as you may have noticed, I drew Charts 239 and 240 after I encountered that correction to G4BB 65…so just for the sake of argument, I thought I’d redraw them in the style of Chart 234, the 2 kinds of double 2nd cousins.

70.15  As you can see, Chart 241a (Chart 239 redrawn) corresponds to Chart 234b…mothers C and D, as well as X, are not shown since they have no connection to the 1C1R relationship. Chart 234a doesn’t come into play since no one in the parents’ generation of A B C and D is a double 1st cousins to anyone else, hence none of them and the offspring of another can be double 1C1R. And Chart 240 is redrawn as Chart 241b…and I would hope that something very interesting springs out at you…

70.16   and that is: add Z, an offspring of X, and we have Chart 242, our 2nd magic trick: a 3rd way to have double 2nd cousins! But is it unilineal or bilineal? Well, sure looks like unilineal on Z’s side…thru just his father’s line…but bilineal on Y’s side, thru both his father’s and mother’s line. I thought of calling this 3rd way “semilineal”…implying half one way and half the other…but strictly speaking, there are relationships here thru 1 line and thru 2 lines, but not thru, literally, half a line.

70.17  The prefix we’re looking for is sesqui-, meaning one-and-a-half, or half as much again…from the Latin semi + as + que, most commonly seen in the name for a 150th anniversary, “sesquicentennial.”  Thus, sesquilineal…and to tell you the truth, I really wasn’t expecting this, just sort of stumbled upon it…how serendipitous, nez pah?

Wicked Ballsy

For my final magic trick…

70.18  With the double 1C1R, in both cases one individual was a double 1C1R ascending to the other…the other being a double 1C1R descending to the first…using Spanish kinship terminology, a double 2nd Uncle and a double 2nd Nephew. I wondered if it were possible to have a “mixed double”…2 individuals that were each both 2nd Uncle and 2nd Nephew to the other.

70.19  And I suspected the answer was yes, since I had analyzed the song “I’m My Own Grandpa”…the key there is that a man marries a window, then her grown daughter marries his father. This is in fact enough for pseudo-self-grandfatherhood, but to flesh out the song, each couple then has a son. An old riddle from India poses this scenario and asks the relationship of the 2 boys to each other…assuming only paternal (unilineal) descent is relevant, the answer is, each is both uncle and nephew to each other…with our bilineal descent thru both parents, we would call them half-uncles and half-nephews.

70.20  So Chart 243 shows a mixed pair of 1C1R…and let’s verify. Is X the 1st cousin of Y’s father B? Yes…since Y’s father B and X are the sons of brothers D and A. Is Y the 1st cousin of X’s father A? Yes again, since Y’s mother E and A’s father C are siblings. Check and double check…true, just about everybody in the world has a 1C1R…but few have a mother who marries her own grand nephew!

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Copyright © 2012 Mark John Astolfi, All Rights Reserved

shameless single plugs, that pack a double wallop…

Other  Blog at http://stolf.wordpress.com  (the legendary Stolf’s Blog)

Podcasts at http://stolfpod.podbean.com  and   http://thewholething.podbean.com

More bloggage at  http://travelingcyst.blogspot.com

Updated Resume at http://travelingcyst.blogspot.com/p/resume.html

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