> > > 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.)
---David
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