David Hobby wrote:
>
> > > > David Hobby wrote:
> > > >
> > > > > The above would have been easier to state if we had general kinship
> > > > > terms based on degrees of genetic relatedness. Sibling, parent and
> > > > > child are all "halves". Grandparent, grandchild, aunt, uncle, niece,
> > > > > nephew, half-sibling, and so on are "quarters". And you know you're
> > > > > really a redneck if you need fractions which aren't negative powers
> > > > > of two!
> > > >
> > > > Oh, like 17/2^N for some N? I think that number (not sure what N is)
> > > > describes my kinship relation to a particular someone. Details
> > > > available upon request. (Anyone wanting details to actually calculate
> > > > the mess, ask!)
> > > >
> > > > Julia
> >
> > > I'm not sure that I have the courage to ask for your details.
> > > This stuff can get messy fast. But I bet that your 17/2^N is
> > > of the form 1/2^k + 1/2^(k+4), since that seems easiest.
> >
> > OK, case 1, of the guy related to me where I believe it's 17/2^N: He is
> > my third cousin from one pair of ancestors; my fourth cousin from a
> > second pair of ancestors; my fourth cousin from a third pair of
> > ancestors; and my sixth cousin from a fourth pair of ancestors.
> >
> > My uncle calculated the degree of relation (all his children are related
> > to him through the same sets of ancestors), and he's slightly more
> > closely related to me than a second cousin would be. If we know what k
> > is for saying the second-cousin fraction is 1/2^k, then the relation
> > degree is as you give above. (1/2^k for 2nd cousin, 1/2^(k+4) for sixth
> > cousin. At least, that's what it ought to be, yes? Or am I off? If
> > so, please correct me!)
>
> That's what I was thinking. But then I get 1/2^7 for the 3rd
> cousins, 1/2^9 for each time it's 4th cousins, and 1/2^13 for the 6th
> cousins. Adding is not actually valid, but here it's a good
> approximation. So I get: (64 + 2*16 + 1)/2^13, which is doesn't
> really get close to 17/2^N for any N.
> I imagine that we are not communicating well. Let's take
> something as simple as 2nd cousins. These are individuals who share
> a set of great-grandparents, right? If they are at different
> "generational levels", then they can't be cousins?
> I do get that first cousins are 1/8th related, while second
> cousins are then 1/32 related, at least with my definition of
> "second cousins". Help?
>
> ...
> >
> > Julia
> >
> > who knows how many ancestors she has in common with that cousin at the
> > generation where you'd expect to have 128 ancestors; it's 34. (And she
> > herself only has 126 there.)
>
> There should be a formula for genetic relatedness from this
> fact. Although HOW she had only 126 might well matter... Ignoring
> that, and assuming that the generations aren't getting mixed up, I
> get:
> Each of your 128 ancestors is 1/128 with you, as are your
> cousin's to her. So to the extent that adding is valid, there are
> 34 different ways that you are 1/2^14 connected to your cousin,
> giving 34/2^14 = 17/2^13. (It seems that adding is valid when
> none of your 128 ancestors are themselves related to each other.)
Actually, it's "him", not "her", and the two that make my 126/128
instead of 128/128 are ancestors of his. Not quite sure what this does,
but if anyone is really trying to come up with a number, that might be
helpful. (Gender is just clarification, not having to do with any
mathematical relation. And he read almost no SF in college, but *did*
read _Snow Crash_. I sent a long list of recommends to him a few years
ago, though, to help him catch up some.)
Julia
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