Saturday, August 22, 2015

ancestors - a digression

by cindy jane walker

illustrations by palomine studios

to begin at the beginning, click here

for previous chapter, click here


everybody has ancestors. lots of them.

some people are more interested in them than others.

dad was kind of interested, interested enough to talk about them sometimes.

so i got kind of interested.

but what interested me was not the recent ancestors, the walkers who founded walkerville and all that.

it was how many ancestors i had, how many the average person has, and how i compared to the average person.

i was just curious.

i went to the library but i didn’t find much to help me out.

so i tried to figure it out myself.

the math is easy but not helpful.

everybody has 2 parents, 4 grandparents, 8 great-grandparents, etc.

lets say four generations per century - average age of parents 25 - that is about 80 generations back to the time of christ.

that is 2 to the 80th power, which is about 1.2 septillion - 1,200,000,000,000,000,000,000,000.

but there were only about 300,000,000 people at the time of christ.

the books i got from the library mostly went in one of two directions - pointing out that being “directly descended” from jesus christ or mary magdalen or whoever did not amount to much. or pointing out that there are really no “races” and that racism was wrong.

in one book the author mentioned on almost every page that racism was bad. i already knew racism was bad - can we move on please?

one thing i noticed - this is just in the books i read - there seemed to be no terminology to describe what i was interested in.

call yourself g0. your parents are g1, your grandparents g2… thirty generations back is g30, 200 generations back is g200… and so forth.

every g has units of descent - g1 has 2 units, g2 four units etc. when you get back to 80 generations, you don’t have 1.2 septillion individual ancestors but you have 1.2 septillion units of ancestry. call the percentage of units in any g pgx. so if jesus christ was one of your ancestors in g80 his pg80 (percentage of units of ancestry in g80) might be 1 in 1.2 septillion (very unlikely if you are descended from him at all) - or it would be something much higher.

back to “units of ancestry” as opposed to numbers of ancestors . everybody has a father and a mother - each would have a pg1 of 50 percent. if they are not brother and sister then you have four grandparents who each have a pg2 pf 25 percent. suppose your mother and father were half-siblings - had the same father but separate mothers. you would have three grandparents but still have four “units of ancestry" - the one grandfather would have a pg2 of 50 and the two grandmothers a pg2 of 25 each.

go back ten generations - to g10 - you have 1,024 units of ancestry but it is unlikely that you actually have 1024 different ancestors in that generation. you might have about 400 (?) but their pg10 would vary widely. some would actually have a pg10 of 1/1024 - .097. others would be much higher.

my question is - as you go further back, how high might any individual’s gpx be? in theory it could be very high - suppose 1500 years ago, one man and one woman establish themselves in a little valley and they multiply through 50 generations, with no outsiders entering the valley. inhabitants of the valley today would have 2 ancestors in g50 with pg50 each. an unlikely scenario. but how high might one individual’s gpx - in relation to yourself - be, 60 or 80 or 100 generations be?

one recurring idea in the books and articles i read - “if a person lived 2000 years ago, either they have no descendants or virtually everybody on the planet is probably descended from them”. this makes sense, but does not take into account the way the percentage of ancestry would vary.

note that i am only talking about descent itself - not genes or acquired characteristics or “race”. these things can be subject to considerable uncertainty, but it is a fact that you have ancestors. of course in practice it quickly becomes impossible to actually determine who they were.

dear reader (if any) i am sorry f i am boring you - or not making any sense. i just find this stuff interesting.

here is something else to consider and then i am done.

every person has direct male ancestors and direct female ancestors going back into the “mists of time”… this is a fact, even if you can never ascertain the details. call these direct ancestors f1, f2, f3… and m1,m2, m3… your father is f1, your paternal grandfather is f2, your mother is m1, her mother is m2…

somewhere in the world , probably around the time of plato or king david, your f100 existed… and somewhere else, probably quite some distance away was your m100 or maybe your m95 or m105… go back even further and your f2000 and your m2000 were walking the earth. somewhere.

you do not know who they were, but they really existed. maybe robin hood or king arthur never existed, but they did.

and even further back than that, climbing a tree or cracking clams at the waters edge…

i just think that is kind of interesting.


next: the clown