Dear Stolf: I was helping my daughter with her homework on fractions and we were applying it to kinship. She noticed something that I couldn’t explain: half-siblings, with a CR of 1/4, are twice as closely related as 1st cousins (1/8), but only half as close as full siblings (½), correct? Yet half-siblings aren’t halfway between 1st cousins and full siblings…that would be 2 people with a CR of 5/16. Can you explain? …from Sam in Sausalitoburg
73.1 Dear Sam: But of course. The answer is this: what half-siblings are is half-way between full siblings and not being related at all. In that case, you’re measuring “half way” between 0 and ½. In the case of siblings and 1st cousins, you’re measuring “half way” between 1/8 and ½. What’s happening is, you’re getting caught up in something similar to the classic mistake of thinking 50% + 50% = 100%…it doesn’t work that way, because if you take 50% off, then take 50% off again, the second time you’re not taking 50% of the original total, but 50% of the amount that resulted after you took the first 50% off. It’s easier to explain with a blackboard… 😉 😉 But here at least is Chart 255, a “relationship ruler.” (The numbers get awfully small to see…if you left-click on the chart, you should be able to see it larger.)
73.2 When you say 2 people who are half-siblings are half as related as would be full siblings, that means as compared to 2 people who aren’t related at all. So in this sense, half-siblings (1/4) are “halfway” between siblings (1/2) and non-related (0). But that means half-siblings obviously can’t be half-way between 1st cousins and siblings…because 1st cousins are at 1/8, not at 0.
73.3 With kinship, the hierarchy of collateral relationships…moving out horizontally along the family tree… is full siblings, half siblings, 1st cousins, half-first cousins, 2nd cousins, half-second cousins, 3rd cousins, etc. Each describes a relationship that is twice as close as the next one over…siblings share twice as many genes as half-siblings, etc. But that’s not the same as saying any one of these relationships is “half-way” between 2 of the others…because in fact, none of them are half-way between any of the others, despite the use of the world “half” in half-siblings, half-1st cousins, etc. And again, that’s because you’re determining “half-way” between one relationship and the other relationship, not between one relationship and no relationship.
73.4 At the top of Chart 256, I have marked the relations that are half-way between siblings and all the other “standard” collateral relations out to 3rd cousin. And as you and your daughter correctly determined, the CR of half-siblings…despite the name…is not halfway between that of siblings and 1st cousins. Halfway between siblings and 1st cousins would be, as you said, 5/16. But you will see on Chart 256 that the hallway point between siblings and half-1st cousins, 2nd cousins, half-2nd cousins, 3rd cousins does get closer and closer to half-siblings at 1/4. That’s because with half-1st cousins at 1/16…2nd-cousins at 1/32…half-2nd cousins at 1/64…3rd cousins at 1/128…each of these is getting closer to 0, the base point that places half-siblings halfway to siblings.
73.5 And by way of contrast, on Chart 256 I have also marked the relationship that is halfway between 1st and 2nd cousins…5/64…just a bit closer to 1st cousins than half-1st cousins at 4/64 are. Ditto for halfway between 2nd cousins and 3rd cousins…5/256…just a bit closer to 2nd cousins than half-2nd cousins at 4/256 are. Could there be a pattern emerging here?
73.6 Look at Chart 257…here I have marked in orange the relationships that are halfway between each collateral relation and the next, from siblings out to 3rd cousins…notice that the top number in each fraction…the numerator…is always a 3! So if you were to figure the CR between 2 individuals, and it came out to 3-over-anything…in math, you’d say 3/x…that relationship would be exactly halfway between 2 “standard” collateral relations. But now recall, halfway between 1st and 2nd cousins…as well as halfway between 2nd and 3rd cousins…was 5-over-something…5/64 and 5/256 respectively.
73.7 And between 1st and 2nd cousins, you are skipping a collateral relation in between, namely half-1st cousins…same with between 2nd and 3rd cousins, you’re jumping over half-2nd cousins. Could this mean that a CR with a 5 as the numerator is a relationship that is halfway between 2 collateral relations but skipping one? Let’s test this hypothesis…between half-siblings and half-1st cousins, you are indeed skipping over 1st cousins…could the relationship that is halfway between them have a 5 in the numerator? Well, half-siblings is 8/32…half-1st cousins is 2/32…added together that’s 10/32, divided by 2 is 5/32…bingo! Let your daughter follow this line of reasoning out a littler further, and she’s in line for a scholarship to MIT, my friend…
73.8 In summary, I understand that to say on the one hand that siblings are twice as closely related as half-siblings, and half-siblings are twice as close as 1st cousins, makes it sound like half-siblings are half-way between siblings and 1st cousins…but as the charts show, that simply isn’t how it works. Such phrases as “twice as closely related” and “half as closely related” are reckoning the degree of relationship compared to 0 or no relation. On the other hand, “halfway between” reckons how related 2 people with one type of relationship are, as compared to people with another type of relationship…and the mathematical truth is, the “standard” collateral relations don’t fall on any of these half-way points…and that’s because the baseline is no longer 0. And in fact, the key to “getting” mathematics is to realize that some of our intuitive or “everyday” notions are simply wrong…as for example the idea that you can “add” successive %’s, as I mentioned back in 73.1.
Dear Stolf: Perhaps this is a little far afield, but I read somewhere that of the classic Disney cartoon characters, the only one who has offspring, in this case a son, is Goofy? Could this really be true? …from Huck in Yogiville
73.9 Dear Huck: Hey, kinship is kinship…it’s all good! But actually, you seem to be asking 2 questions in one…is Goofy the only one with a kid, and if so, how can it be Goofy, for gorsh sakes? Now that suggests a wedding night tableau I’d just as soon not contemplate…you can if you like, but I’d advise against it 😉 😉
73.10 But to answer both those questions…alas, the world is complicated, and the world of Disney cartoons is especially complicated. I would say, in a rather narrow sense, that what you read is correct. And the reason it’s Goofy that has biological issue…as opposed to Mickey or Donald with their putative “nephews”…is this: in the 1940s, Disney came out with a series of shorts (“cartoons”) called “How to…” demonstrating the pitfalls of skiing, riding a horse, etc. Lanky, goofy Goofy seemed the perfect candidate to endure the inevitable calamities. This series evolved into the “Everyman” series of the 1950s, with comedic takes on the trials and tribulations of modern life…again, Goofy was the perfect victim…even to the extent of having a son, who first appeared in Fathers are People Too in 1951.
73.11 And there he is on the left, most of the time referred to as Goofy Jr. or simply Junior…but he appeared in several shorts, and sometimes he is George Jr. since Goofy in this series is confusingly named George Geef. His mother, Goofy’s wife, is around…after all, Everyman has to be married…but remains nameless and faceless. Now jump ahead to TV and the early 1990s show Goof Troop…Goofy now has what can only be described as a “different” son, Max…and BTW he is a widow…Max’s mother, in an early episode, is said to be “up there amongst the stars.” So far so good.
73.12 Now to say only Goofy has a son is to limit it to the characters that I call “human animals”…while ostensively animals, they never-the-less talk, walk upright, wear clothing, have hands, and do typical human things like live in a house, drive a car, read the newspaper, etc. We’re talking, oh, Donald Duck, Mickey and Minnie, Horace Horsecollar, Gladstone Gander, heck even Oswald the Lucky Rabbit way back at the beginning. And it’s interesting you referred to the “classic” characters…that obviously would mean different things to different people…for this just-turned-61 Baby Boomer, the cut-off point is Ludwig Von Drake, introduced in 1961…to my mind the last significant “stand-alone” Disney cartoon character. The days of the theatrical “short feature” were ending, and from here on in, it was full-length feature films and their ensemble casts…and you must forgive me if I’m not up on the intimate life stories of characters from The Jungle Book, The Aristocats, The Rescuers, et al. I’m just not, and its my blog…ditto the TV characters that came much later…whether Darkwing Duck has a son…or Webigail has parents…I simply do not know, and frankly can’t rouse myself to find out.
73.13 But in the world of “human animals,” the place of normal humans is taken by what might be called “human dogs”…except for their flap ears and black button noses, they look like cartoon humans…the Beagle boys are the prime example, as are the non-duck members of the Donald’s nephews’ Junior Woodchuck troop, altho there you will occasionally glimpse a lad who can only be described as a “pig boy.” And Goofy…originally called Dippy Dawg…is a of course the ultimate “human dog,” simply more exagerated than most. But the point is, beyond “human animals,” there is a mad jumble of, for want of a better term, could be called “animal animals”…displaying a broad range of human and non-human characteristics…for example, compare Lady and Tramp as dogs with Pluto as a dog…the former talk…the latter, not so much, except for a Scooby Do-like mumble.
73.14 And indeed, plenty of Disney’s “animal animals” have offspring…Bambi’s parents, Dumbo’s parents, Dalmatians Pongo and Perdita…and of course Lady and Tramp: Scamp and his sisters (below, top right)….but even Pluto (top left) from the 1937 short Pluto’s Quin-puplets. So there’s your complete answer: yes, no, maybe, sort of…
73.15 But while I’m thinking of it, there has been much debate over the years…over and above which is hotter, Wilma or Betty…about why the Big 4, Mickey, Minnie, Donald, and Daisy each had nieces and nephews, but not sons and daughters. My personal opinion is that people inevitably over-think this: Disney simply didn’t choose to have these characters be married…hence they have no children, simple as that. Best known of course are Donald’s nephews, Huey, Dewey, Louie, and the mysterious 4th nephew, Phooie…see here, under Wicked Ballsy. Mickey’s nephews Morty and Ferdie didn’t catch on nearly as well (above, bottom right) altho they weren’t exactly strangers. Less seldom seen were Daisy Duck’s cleverly named nieces, April, May, and June (bottom, left).
73.16 And believe it or not, Minnie Mouse actually had nieces, altho they were employed so infrequently that their names are not consistent…most of the time they were Millie and Melody (above) but sometimes they were Tammy and Pammy…Millie and Tillie…and for a time in the 1960s, there was just one, again Melody, whose sole mission in life was to harass Morty and Ferdie. There was even an early story-book with triplets…Dolly, Polly, and Molly…and Mickey himself had a niece named Maisie in a 1934 short…well, you know how mice…um…oh, never mind…see you next time…
P.S. Holy cow…and I don’t mean Clarabelle, did I speak too soon? Thankfully, no…this is not Horace Horsecollar’s son, but in fact him as a Disney baby…from that “younger versions” fad of 20 years ago…still, can you imagine how rich you’d be if you were the cat who sold these guys their white gloves in bulk? 😉 😉
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