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Author Topic: Silly application of math
FlyingCow
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Math "proves" we're all related

quote:
“No matter the languages we speak or the color of our skin, we share ancestors who planted rice on the banks of the Yangtze, who first domesticated horses on the steppes of the Ukraine, who hunted giant sloths in the forests of North and South America, and who labored to build the Great Pyramid of Khufu,” Olson and his colleagues wrote in the journal Nature.
This claim is absurd, to me.

The basics are that each generation we look back, our number of ancestors double. We have 2 parents, 4 grandparents, 8 great grandparents, etc. Leaving the current population with trillions of ancestors.

The study then goes on to say that there were not that many people, so our ancestors must overlap.

It then goes on to say that, because they overlap, we mathematically must all share common ancestors.

However, it doesn't factor in things like geographic divisions and segregation of cultures and peoples. Some group just didn't comingle, and have their own subset of ancestors that may or may not have intermixed with other groups.

Anyone with a firmer grasp of science or math want to debunk this one?

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Dagonee
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*ahem*
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fugu13
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No need to debunk it, the math is very solid, its the article that's bad. The basic logic is roughly as communicated, but the approximations on time and likelihood are based on a complex simulation that has parameters for population sizes, inter-population travel, and the like, which even with very conservative estimates give remarkably recent results.
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FlyingCow
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Sorry, Dag. Didn't see the previous thread.

So, essentially, when the pyramids were being built in Egypt and Newgrange was being built in Ireland, those two peoples have intermixed to the point that every one of us is related to both sets of builders?

Seems far fetched to me, even if it is mathematically logical.

I mean, you could tell me the mean, median and mode of 2 trillion numbers is 6... but that doesn't prevent the number 6,546 from being in that list.

To say all people share a set of common ancestors only 5000 years old seems to ignore outliers to the data that surely must exist.

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fugu13
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Keep in mind that one single immigrant 'injects' all their ancestors into a population. Only one immigrant has to move between Egypt and Ireland (or more likely, one from egypt or ireland to some intermediate point, and then later one from that intermediate point to the other endpoint) for all or almost all the ancestors far enough back in Egypt (or Ireland) to become ancestors of future generations in Ireland (or Egypt).
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FlyingCow
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Only one immigrant has to move there, then procreate like a bunny rabbit, and have his progeny procreate like bunny rabbits at all social levels from peasant to royalty.

Add to this the difficulties of travel and the insular nature of many cultures at that time.

As probable as it is that ancestral lines cross paths with every other ancestral line between today and five thousand years ago, it is also possible that ancestral lines exist that escaped such crossover.

Proving that there aren't would require tracking the ancestry of every human being.

It's nice to say that in the game Six Degrees of Kevin Bacon you can always get to Kevin Bacon - but there are actors that have existed in the history of cinema that do not lead where you want them to go - at least not in six steps.

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fugu13
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The immigrant doesn't need to procreate like a bunny rabbit at all. In any regularly intermarrying population, it only takes a limited number of generations for everyone to have at least one common ancestor, and not many more for everyone to have the same set of ancestors going far enough back. This is a consequence of the whole geometric growth thing, and easily demonstrated in observable populations.

Also, most of that stuff about insular populations is poppycock. We've known about huge waves of immigration, colonies of ancient civilizations all over the world, and similar, for quite some time.

And as I pointed out, the creators of the simulations are well aware of these effects; that's why they used simulations, to see how much these effects actually mattered.

Regarding six degrees of kevin bacon, its worth nothing that the only actors not in 6 or 7 degrees of kevin bacon are ones who were the only or nearly the only actors in tiny films, usually far back in history. That is, the sorts of people whose lines would have 'died off' in the case of populations, leading to them not being anybodies' ancestors.

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FlyingCow
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quote:
And as I pointed out, the creators of the simulations are well aware of these effects; that's why they used simulations, to see how much these effects actually mattered.
I'd like to see the simulations, actually.

I don't trust scientists to be "well aware" of anything, quite frankly. There have been plenty of experiments and conclusions in the history of science that were based on faulty premises or unaccounted for variables. I'd like to see a report that shows exactly what factors they took into account, and what factors they deemed inconsequential. What parameters were used?

As you said, the article is bad - it doesn't give enough information and sensationalizes the result of a simulation. Saying that "all people alive today are descendents of the pharoahs" seems a bit much.

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fugu13
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Read the linked article in the other thread.
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fugu13
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(and I'd say its fairly certain we're all descendants of the pharaohs -- they often had many children, as well as being wealthy and well-traveled, not to mention being entangled in several events effective at spreading ancestry, such as Alexander's campaigns and the Roman empire)
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FlyingCow
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I missed the second page of the article, actually - though I'm still not entirely clear on the logic used.

I understand better the simulation and the parameters, but I still don't see the shared common ancestry except from behind a fog at the moment.

To take it on a microcosm:

Take my first cousin and myself.

His parents are not my ancestors, and my parents are not his ancestors. However, my father and his father are brothers.

So, the grandparents on my father's side are shared ancestors between the two of us.

However, the grandparents on my mother's side are not his ancestors, nor are the grandparents on his mother's side mine.

If you take my geneological ancestry as a big V, and his as a big V, they overlap with a smaller V - with sections on either side that do not overlap. While we have shared ancestry, we also have ancestry that is not shared.

Am I totally off base here?

The one link between the one set of grandparents (and all the preceding generations that led to that set of grandparents) connects us - but we have twice as many ancestors not in common. Take any random person who is in the larger set of "all people related to either him or me" and there's a 2 to 1 chance that they are not a shared ancestor.

At the grandparent level, we share two, but there are four grandparents who are not common. At the great grandparent level, we share four, with eight that are not common.

I think, talking through this, I'm beginning to understand a bit more.

Somewhere back along the great V of your ancestral geneology, you overlap the big V of everyone else, somewhere. It may only be one person, but there is some overlap.

I think I get that any given two people have at least one shared ancestor. So, Ramses and I share an ancestor somewhere, and Ramses and Charlemagne share an ancestor somewhere, and Charlemagne and I share an ancestor somewhere.

I don't get, however, how Ramses *himself* is my ancestor, though, any more than my cousin's maternal grandparents are my ancestors. Just because my big V and Ramses' big V overlap, doesn't mean that that particular individual overaps into my V, does it?

Talking this through is helping me understand more, but I'm still not quite there.

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fugu13
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You miss that there's also a big V going forward for each person. Perhaps Ramses had two children, then each of those children had two children, then each of those children had two children. Now we have eight great-grandchildren of Ramses, and any one of those (or their descendants, of course) could have been one of your ancestors, making Ramses your ancestor.

Also, you're missing that the V's going backwards start to overlap again. If there continued to be only that one couple of overlaps, then you'd quickly exhaust the past population of the earth, going back in time, as noted. At some point, some of your n * great grandparents were some of his m * great grandparents, and going further back the amount of overlap only increases.

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FlyingCow
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quote:
Now we have eight great-grandchildren of Ramses, and any one of those (or their descendants, of course) could have been one of your ancestors.
I totally agree with that, but that's not what the article seems to be saying. It's not that they "could have been" one of my ancestors, but that one of them "is" my ancestor. It's the definitive nature of the statement that is hanging me up, I think.

I think it's possible for two people to have descendants that go many many generations without intermarrying with the descendants of another two people. I don't know how far that could go, but I suppose if there was only one child per generation, it could go on quite a long ways. Could it go back 1000 years? Sure. 7000? I'm not so sure.

Those V's going forwards don't have to be true V's, either, as many lines die out here and there, leaving only one surviving member of a generation, or two. So, while we're guaranteed to have a true evenly balanced V going backwards, that is not the case going forward.

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fugu13
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The probability approaches 100% that anyone sufficiently far in the past is your ancestor, unless his line died out. The statements they've made don't include people whose lines die out.
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FlyingCow
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And there really is no way of knowing if a person's line died out or not. So we may or may not be related to Ramses - though with the amount of children he sired, it's probable. Still, it's not statistically impossible that any of the ancient pharoah's lines died out, or any ancient ruler for that matter.

I can agree with that statement, though, that anyone sufficiently far enough in the past whose line did not die out would be your ancestor. It's just a matter of what "sufficiently far" means. I can grasp the 7000 years ago conservative mark mentioned in the article, I think, but not the 2000 years ago mark mentioned.

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El JT de Spang
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Anyone who's line died out is now no one's ancestor, by definition.

But I see your point. It makes for good print, but it would be difficult to trace from any specific living person to any specific historical person, who's given lineage may have been discontinued X generations ago.

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fugu13
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2000 years is not the least conservative mark for anyone in the past (whose line has not died out) being your ancestor, but for everyone alive today to share at least one ancestor, a much easier target.

It is of course not impossible that someone we know with high confidence to have had many generations of descendants would have had his line die out, it is merely vanishingly improbable.

Not to mention there are lots of other pharaohs out there.

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Shawshank
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I've read that 2000 years ago any two people now shared a common ancestor within that time period. It's between 5,000-7,000 years ago that any of those people whose line didn't die would be our ancestors.
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