On Jun 27, 11:49=A0pm, m...@[EMAIL PROTECTED]
(Mark Brader) wrote:
> James Allen writes:
> > The famous abolitionist martyr John Brown
> > =A0http://fabpedigree.com/s032/f250617.htm
> > was my 1st cousin 6 times removed.
>
> Congratulations or commiserations, as applicable.
When I first heard of this American "hero" he
seemed like a madman, but since I've read an
excellent biography of him. He may have been
a madman, but he was a very righteous and
influential person.
> > About how many 1st cousins 6x removed does
> > an average person have?
>
> A 1C6R is your great^5-grandparent's (G6P) sibling's child or
> your parent's sibling's great^5-grandchild (G6C). =A0If the present
> tense implies living cousins, then the answer is 0.
I've wondered about such usage too. I think
he *was* a martyr, but *is* my relative.
> Or did you mean to ask about all cousins who have been born?
I meant puzzlist to recognize the two types of 1C6R
and to determine that (if, e.g. we deal with
people sufficiently far back in time that people
not yet born don't become an issue) the two types
will be **very* roughly* equal in number.
> Most people still won't have parents' siblings with G6Cs yet,
> but dead children of G6Ps' siblings are another matter. =A0Okay,
> everyone had had 2^n G(n-1)Ps: that's 128 G6Ps. =A0These are not
> necessarily all distinct people, but I'll guess that lines of
> descent mostly don't overlap over that time period, and stay
> with 128.
>
> Now, families were bigger back then, but people also died younger.
> I'll guesstimate that one's G6Ps typically had 2.5 siblings who reached
> childbearing age and that these averaged 5 children each -- for a
> total of 1,600 dead 1C6Rs.
This seems quite accurate! One can't quibble with your
guesstimates which will vary widely by culture, economy,
etc.
> > How does this compare with the number of 6th cousins 1x removed?
>
> guess that a person will eventually have on the
> average 2^n G(n-1)C's.
Slight inconsistency: as you noted above, the very last
generation (where further procreation is unneeded)
might assume 5 children instead of 2.
> So for the first type of 6C1R, that gives 20,480 of them, although
> some will not have been born yet; and for the second type, about the
> same, in in this case many of them will not have been born yet.
Again, I think your estimates are very close.
Restricting to just one of the two types of "removal",
my crude estimate would be 5*2^(2N+M) for
Nth cousins M times removed "to the past", yielding
a (crude) 1280 answer for 1st-cousin 6x removed.
John Brown is my father's father's mother's mother's
mother's mother's mother's brother's son. I'll
claim that each link represents a doubling (except
the final child for which I'll use Mark's 5 estimate).
The "gotcha" is number of productive siblings.
(By "productive" I mean having at least one child.)
Since we're assuming a productive person has,
on average, 2 productive children, my 5-g grandparent
might be deduced to average one productive sibling.
The flaw is that 2 was just an average; statistically
my ancestor was likely to be part of a more productive
family. IIRC, 2 is a fair estimate of average number
of productive siblings.
> > I don't expect an exact answer -- just a "back of
> > envelope" estimate. =A0There is an interesting little
> > "gotcha" in the calculation.
>
> Did I overestimate badly due to not allowing for related people
> having children together? =A0I did consider it, as you see.
The doubling associated with each level of "parent's" may
seem to be the most reliable part of the above formula, but
even it is severely flawed. For example, the number of new
ancestors introduced at each level as King George I's pedigree
goes back is not 2^k as predicted, but rather
2, 4, 8, 16, 28, 50, 84, 129, 207, 346
(The number of his distinct 8-g grandparents isn't 346, as
implied, but 476. The discrepancy arises because 130 of these
ancestors are also his 7-g grandparents, and their descendants
would thus not be described by the cousin relation****p
associated with 8-g grandparents.)
I did *not* hunt for a particularly peculiar pedigree, choosing
the Founder of Britain's House of Hanover as an obvious
historical figure with a known pedigree going back several
generations (and with no relation to the Bourbon or Hapsburg
families supposedly notorious for *****). Yes, German nobles
marry within their own milieu so marriage partners will often
have a (distant) cousin relation****p, but the same is true
of commoners in most societies, at least until highly mobile
modern times.
If the number of one's unique new (K+1)-great grandparents
is p times the number of one's unique new (K)-great grandparents,
what is a good estimate for p? p =3D 2 may work well for most
American's 19th century ancestors, but George I's 15th century
ancestors are closer to p =3D 1.6. Reflection shows that eventually
p will become less than 1 -- after all, early H. sapiens started
as a small tribe. What is very surprising is that one doesn't
need to go deep into the past to find p < 1; for moderns it
seems to be enough to go back just to the 13th century!
James Dow Allen
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