167.1 Always picking on Uncle Wiki why? Maybe because they deserve it…now there’s a novel approach! Because anybody, whether they know what they’re talking about or not, can put something in…and just as quickly, somebody else can take it back out. Above, we see that happened within the space of 2 months. Details of changes can be perused by clicking the “view history” tab.
167.2 And indeed, it was wrong for 2nd cousins…half the relationship of 1st cousins gives you half-1st cousins…half again gives you 2nd cousins…1/8…1/16…1/32 respectively. They got tripped up by using the concept of “degrees.” There are several distinct meanings for the word “degree” in genealogy…one applies to cousins only, others to all relatives…and since they’re different they obviously don’t agree. You’re better off not talking about degrees unless you indicate exactly what you mean.
167.3 But beyond that flagrant fail, it’s worth examining just how sloppy these 2 opening paragraphs really are, bearing in mind that anything can be changed at any time…
A cousin is a relative with whom a person shares one or more common ancestors. Completely wrong. A person shares ancestors with all their blood relatives…so your uncle, your grandmother, your son, your half-sister, they are all your “cousins.” Not!
In the general sense, cousins are two or more generations away from any common ancestor, thus distinguishing a cousin from an ancestor, descendant, sibling, aunt, uncle, niece, or nephew.
And since that first sentence was wrong, they have to immediately take it back…bumbling, stumbling. Also I object to the phrase “in the general sense”…which means there is some specific sense in which what follows does not hold true. I’d love to hear about numbered cousins who are less than 2 generations removed from a common ancestor…unless you mean “0th” (zero-th) cousins, i.e. siblings, in which case OK…and were you math major?
However in common parlance, “cousin” normally specifically means “first cousin”.
Fair enough, I suppose…I’d be tempted to say “cousin” by itself always means 1st cousin…be it normally, specifically, or both. It’s true you could refer to a 2nd cousin as “your cousin”…trouble is, everyone would assume you meant your 1st cousin…then again, some people don’t mind being misunderstood as long as they’re technicality correct, God bless ’em.
Systems of “degrees” and “removals” are used in the English-speaking world to describe the exact relationship between two cousins (in the broad sense) and the ancestor they have in common.
That parenthetical “in the broad sense” tells me whoever wrote this knows, or at least suspects, a fundamental truth of our kinship system, but doesn’t want to come right out and admit it…and that truth is that 1st, 2nd, 3rd etc. cousins (what I call “numbered cousins”) are of your generation. A removed cousin is of a different generation, and thus is not your cousin but somebody else’s cousin! In other words, cousins “in the narrow sense” are the only cousins you can have. You’ll also notice they use the word “degree” to mean 1st, 2nd, 3rd, etc. This is something different from the “degree” you’ll see stated in civil law and and various church rules, which applies to all relatives, not just cousins.
Various governmental entities have established systems for legal use that can more precisely specify kinships with common ancestors existing any number of generations in the past, though common usage often eliminates the degrees and removals and refers to people with common ancestry as simply “distant cousins” or “relatives”.
All cousins are relatives…not all relatives are cousins…IT’S THE LAW! “Distant cousins” tends to mean 2nd or beyond, but there is no generally agreed upon definition.
167.4 But fine…you get the feel of it…the rest of their “cousins” article teeters back and forth between sense and nonsense, clarity and confusion. It’s typical of the flailing and failing that is Uncle Wiki’s hallmark…you’d think they’d have the common decency to be at least slightly embarrassed by it, but they seem not to be…the Age of Mediocrity in full bloom.
167.5 TBT, the only definition of “cousins” you’ll ever need is this: Cousins are descended by an equal number of generations from a pair of siblings. That’s it…nothing more than that.
167.6 But as hinky as Wiki can get with the facts (and what qualifies in their minds as a “fact” to begin with) it is still only a matter of degree…there’s that word again! They’re hardly the only offender…and to their credit, they don’t charge for any of it…unlike….
167.7 …WolframAlpha, aka Wolfram|Alpha…yeah, I did think about calling this blog Related|How|Again? but I was embarrassed that I didn’t know what a “|” is called…a line? Uncle Wiki does a decent job describing what this subscription service is about (left) so I decided not to rewrite it. It was created by physicist Steve Wolfram…his book “A New Kind of A Science” is, well, interesting….a bit over-ambitious perhaps. It’s too complicated to get into here, except to say his theory is that all of reality, at its fundamental level, is not analog but digital…based on “cellular automata” algorithms, which are easily modeled on a computer. I was fiddling around with these 25 years ago on my prehistoric Commodore 64…only I didn’t write a book about them…d’oh! The Game of Life is typical…see here…
167.8 This program lets you query kinship relationships gratis…perhaps as a kind of free sample. I saw it recommended on another genealogy website and figured I’d give it a try. Much to my dismay, for 1st cousins I got a degree of relationship equal to 1/16…it should be 1/8 (below left). To further check this, I tried brother, and sure enough, again incorrect…1/4 instead of ½…crazy.
167.9 Well, you hardy need an advanced degree in Intergalactic Environmental Psychology from Silo State Teacher’s Aide Junior College at Dr. Smithsville to see what’s going on. I suspected it right away, and confirmed it by trying “grandson”…it came out correct at 1/4. To be absolutely sure, I did grandfather and mother…both also correct. See what’s happening? For direct ancestors and descendants it works fine…for collateral relatives they are too small by a factor of 2…see my corrections below.
167.10 So what’s a “brother” who’s related to you by 1/4, not the correct ½? Your half-brother of course. They are figuring degree of relationship based on just one line of descent, father’s or mother’s, when it should be both…thus they are wrong for all collaterals, starting with full siblings. Yes, despite the fact that they picture both father and mother in their diagrams, they are still only counting relationship thru one of these parents, not both. And it shouldn’t surprise you to learn that if you try asking them “half-brother” or “half-first cousin,” you get no answer at all…they don’t think such things exist.
167.11 Could I resist pointing all this out? No chance…A and B are a couple of messages I left at various related websites…turns out a lady named Ann Turner C had beaten me to it by 4 years. Good for her. Ultimately, these morons replied to me D and they’re not budging…they insist that they’re correct. Amazing but true…caveat emptor big time, sez me. How confident can you realistically be of anything else Wolfram|Alpha tells you if they can’t get simple kinship calculations right?
167.12 Now last week I promised you some “deep thoughts.” I will not deny that Chart 593 below is complicated…but study it, because once you have it, you understand the principle of sexual reproduction…and the mathematics of kinship follows directly and logically. But let’s dive in…
167.13 Genes make you the organism you are…they control everything. The innovation of sexual reproduction is that you have 2 complete sets of genes…call them Column A and Column B…one from your father, one from your mother. With asexual reproduction, there is only one set of genes…and that is what an organism’s offspring gets…it’s in effect a clone. The problem is that if the parent has a “bad” gene, the offspring gets it automatically…and depending on how bad it is, the offspring may not last long enough to reproduce, as the parent was fortunate enough to do.
167.14 With sexual reproduction, the existence of 2 sets of genes gives you a “second chance”…if a bad gene is present in Column A, it might not be in Column B…and since the offspring gets a random combination of A’s and B’s, the chance that you get the bad gene is reduced to 50%…with asexual, the chance is 100%. And even if you get a bad gene from one parent, you may get a good one from the other parent, and if the good one is dominant, it takes over and the bad gene is inactive, or recessive. Again, you have the chance to side-step that bad gene.
167.15 Needless to say, this innovation has been a whopping success. As a consequence, organisms that reproduce sexually can change or mutate more quickly than asexual…they can adapt to changing environmental conditions, and bottom line, survive. I’ll go out on a limb and suggest that this adaptability was an added bonus…the basic idea was to bypass bad or detrimental genes. At any rate, let’s see how sexual reproduction creates the degree to which kin are related. You have between 20,00 and 30,00 genes…in Chart 593, I have simplified that to just 8…4 in Column A, 4 in Column B.
167.16 You get only one set…here it’s Column A, in blue…from your father, and that’s a random mix of your father’s A’s and B’s. We can simulate this by flipping a penny…heads you get Column A, tails you get Column B. For your brother, we flip a dime…and top left of Chart 593 shows the 4 possible outcomes…you both get A…you both get B…you get A, he gets B…you get B, he gets A. Over thousands of genes each will occur about 25% of the time. Also notice that as a result, your father’s genes form 4 categories…those you both get, those neither of you get, those you get but your brother doesn’t, and those he gets but you don’t…and again, each category is 25% of the total of your father’s genes.
167.17 If you now look at the bottom of Chart 593, you’ll see that of the 4 genes you and your brother get from your father, you will share 2 of them…in this case, dark blue 1 and light blue 2. That’s 2 out of 4. Same identical thing happens with your mother…total, 4 shared out of 8…a relationship between you and your brother of ½. And since half your genes come from your father, you and he are automatically related by ½…it’s just that the ½ with your brother and ½ with your father come about in different ways. Contrast this with the case of half-brothers, Chart 594.
167.18 Here, since the mothers are different, no genes are shared there…only the 2 of 4 from the father…total, 2 shared out of 8…a relationship of 1/4. And that’s it…I defy the knuckle|heads at Wolfram|Alpha or anyone else to dispute it…because they can’t…it’s cold hard scientific and mathematical fact. Should I now draw a similar chart for 1st cousins? I could…but there’s no need to…because as I said, all of kinship flows from these 2 fundamental results…½ genes shared between father and son, ½ between brothers.
167.19 And as a quick example of how that would work…consider your father’s brother…as, brothers, they are related by ½. Now if you had the identical genetic makeup as your father, you too would share half your genes with his brother, your uncle. But you don’t…you only have half of your father’s genes…so you share 1/4 with your uncle…it’s just that simple.
167.20 Further, if your father shared all his genes with your uncle, your father would be related to your uncle’s son, your 1st cousin, by ½…but he doesn’t, he only has half his brother’s genes, so your father’s relationship to your 1st cousin, his nephew, is 1/4. Now just as before, put yourself in your father’s place…to your 1st cousin, your father is 1/4…so you are half of that, 1/8. And so it goes, up, down, and sideways along the family tree…rock solid mathematical relationships that no cellular automata can alter. As for Wolfram|Alpha, I’m reminded of something my Dad would say: You may be smart, but not smart enough to admit when you’re wrong. See you in 7, for another round of Famous Relativity…
Copyright © 2014 Mark John Astolfi, All Rights Reserved