# A mathematical question about inbreeding **URL:** \ **Category:** Factual Questions\ **Created:** [June 16, 2009, 6:39pm UTC](https://boards.straightdope.com/t/a-mathematical-question-about-inbreeding/499971 "2009-06-16T18:39:14Z")\ **Posts on this page:** 13\ **Page:** 2
**Author:** ![Sampiro](https://avatars.discourse-cdn.com/v4/letter/s/2acd7d/32.png) [@Sampiro](https://boards.straightdope.com/u/Sampiro)\ **Post date:** [June 19, 2009, 3:40pm UTC](https://boards.straightdope.com/t/a-mathematical-question-about-inbreeding/499971/21 "2009-06-19T15:40:55Z")
So continuing the oddity of ancestry: Gilgamesh was said to be 2/3 divine. His father was Lugalbanda, a god king, and his mom was Ninsun, a goddess, so I’m not sure how this works, but let’s assume it’s this: Let’s assume Lugalbanda (or “Lou”) and Ninsun (or “Sunny”) were half siblings. Assume Lugalbanda’s father was a mortal and his mother was Ishtar. Let’s assume that Sunny’s father was a traveling sales god (but a god) and her mother was Ishtar. So Gilgamesh Has Three Grandparents (an early predecessor to the multicultural children’s tablet “Agamashandarakstiun Has Two Mommies” and it’s companion tablet “Vehandrahstanmishti’s Daddy’s New Bedchamber Slave”). Grandfather 1: a moral Grandfather 2: divine Grandmother: divine His mother is therefore divine, his father is 1/2 divine. Assuming all the gods involved had 2 parents, would Gilgamesh be 2/3 divine, or would he be 3/4 divine? ---
**Author:** ![Smeghead](https://avatars.discourse-cdn.com/v4/letter/s/f1d935/32.png) [@Smeghead](https://boards.straightdope.com/u/Smeghead)\ **Post date:** [June 19, 2009, 4:26pm UTC](https://boards.straightdope.com/t/a-mathematical-question-about-inbreeding/499971/22 "2009-06-19T16:26:32Z")
3/4 ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [June 19, 2009, 6:06pm UTC](https://boards.straightdope.com/t/a-mathematical-question-about-inbreeding/499971/23 "2009-06-19T18:06:08Z")
There’s no way to get exactly 2/3 ancestry of anything, with a finite number of generations of ancestors. Nor, for that matter, any other fraction whose denominator isn’t a power of 2. You could have someone who’s 3/4 something, or 5/8, or 11/16, or 683/1024, or so on, but never exactly 2/3. ---
**Author:** ![JonathanTheRed](https://avatars.discourse-cdn.com/v4/letter/j/8491ac/32.png) [@JonathanTheRed](https://boards.straightdope.com/u/JonathanTheRed)\ **Post date:** [June 19, 2009, 6:48pm UTC](https://boards.straightdope.com/t/a-mathematical-question-about-inbreeding/499971/24 "2009-06-19T18:48:02Z")
> [@Sampiro](#): > > So Gilgamesh Has Three Grandparents (an early predecessor to the multicultural children’s tablet “Agamashandarakstiun Has Two Mommies” and it’s companion tablet “Vehandrahstanmishti’s Daddy’s New Bedchamber Slave”). You gotta quit this focus on the number of distinct people in a generation, it’s not relevant. N generations ago, there will be 2[sup]N[/sup] “slots” for ancestors, and the occupant of each of those slots will contribute 1/(2[sup]N[/sup]) of the descendant’s genes. And it doesn’t matter whether each of these people is distinct. If the same person occupies multiple slots, he will contribute multiple shares of the descendant’s ancestry, and that’s all there is to it. Suppose Josephine is cloned 126 times, with half the clones having a Y chromosome inserted to replace one of the X chromosomes in the 23rd pair, making them male. The clones all mate with each other, producing a single offspring each, while Josephine herself mates with Rupert, again producing one offspring, leaving 64 individuals in the second generation. They repeat the process for five more generations, producing a single great-great-great-great-grandchild, Quentin. Would you really claim that since Quentin only has two great-great-great-great-grandparents, half of his descent comes from Rupert? Pish-posh. Rupert is a mere drop in the gene pool; Quentin shares nearly all of his genes with Josephine. And yeah, there’s no way to get a denominator that isn’t a power of 2. Having 1/3 or 2/3 descent is impossible. ---
**Author:** ![Sampiro](https://avatars.discourse-cdn.com/v4/letter/s/2acd7d/32.png) [@Sampiro](https://boards.straightdope.com/u/Sampiro)\ **Post date:** [June 19, 2009, 6:52pm UTC](https://boards.straightdope.com/t/a-mathematical-question-about-inbreeding/499971/25 "2009-06-19T18:52:33Z")
> [@JonathanTheRed](#): > > And yeah, there’s no way to get a denominator that isn’t a power of 2. What about a parthenogenetic frog? ---
**Author:** ![Yllaria](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/yllaria/32/3452_2.png) [@Yllaria](https://boards.straightdope.com/u/Yllaria)\ **Post date:** [June 19, 2009, 7:01pm UTC](https://boards.straightdope.com/t/a-mathematical-question-about-inbreeding/499971/26 "2009-06-19T19:01:42Z")
> [@Sampiro](#): > > What about a parthenogenetic frog? It makes an interesting band name. That aside, wouldn’t the offspring’s mother also be its father? Or are parthenogenetic offspring clones? For a clone, its grandfather and grandmother (maternal side) would be its father and mother, while its mother would be a place-holder. Still an even denominator. ---
**Author:** ![rivulus](https://avatars.discourse-cdn.com/v4/letter/r/839c29/32.png) [@rivulus](https://boards.straightdope.com/u/rivulus)\ **Post date:** [June 19, 2009, 9:40pm UTC](https://boards.straightdope.com/t/a-mathematical-question-about-inbreeding/499971/27 "2009-06-19T21:40:49Z")
> [@Sampiro](#): > > What about a parthenogenetic frog? Or if one of the ancestors is [Hephaestus](http://www.pantheon.org/articles/z/zeus.html)? > [@](#): > > According to legend, Metis, the goddess of prudence, was the first love of Zeus. At first she tried in vain to escape his advances, but in the end succumbed to his endeavor, and from their union Athena was conceived. Gaia warned Zeus that Metis would bear a daughter, whose son would overthrow him. On hearing this Zeus swallowed Metis, the reason for this was to continue to carry the child through to the birth himself. Hera (his wife and sister) was outraged and very jealous of her husband’s affair, also of his ability to give birth without female participation. To spite Zeus **she gave birth to Hephaestus parthenogenetically (without being fertilized)** and it was Hephaestus who, when the time came, split open the head of Zeus, from which Athena emerged fully armed. Bolding mine. ---
**Author:** ![JonathanTheRed](https://avatars.discourse-cdn.com/v4/letter/j/8491ac/32.png) [@JonathanTheRed](https://boards.straightdope.com/u/JonathanTheRed)\ **Post date:** [June 19, 2009, 10:21pm UTC](https://boards.straightdope.com/t/a-mathematical-question-about-inbreeding/499971/28 "2009-06-19T22:21:46Z")
> [@rivulus](#): > > Or if one of the ancestors is [Hephaestus](http://www.pantheon.org/articles/z/zeus.html)? > > Bolding mine. Those ol’ Greeks sure were inventive, I’ll give them that. It’s interesting that Zeus attempted to forestall a prophecy of his overthrow by swallowing a person… Zeus’s own father, Kronos, did the same to Zeus’s siblings, until his mother Rhea gave Kronos a rock in swaddling clothes rather than the newborn infant Zeus to swallow. Kronos, proof that immortality and deity do not necessarily confer wit, swallowed the stone without noticing any difference and eventually was overthrown and chained by Zeus and his undigested siblings. You’d think that such an experience would give Zeus some sense of the injustice involved in swallowing people, but no. (This is from memory and it’s been awhile, so I apologize for any inaccuracies.) As for Hephaestus, if the Greeks knew anything about genealogy, they’d have known that the parthenogenic offspring of a female are always female, and are genetic clones of their mother, which is why higher-order animals abandoned parthenogenesis long ago. Sex may be messy and inconvenient, but you can’t beat it for rapidly improving the gene pool. ---
**Author:** ![Smeghead](https://avatars.discourse-cdn.com/v4/letter/s/f1d935/32.png) [@Smeghead](https://boards.straightdope.com/u/Smeghead)\ **Post date:** [June 19, 2009, 11:39pm UTC](https://boards.straightdope.com/t/a-mathematical-question-about-inbreeding/499971/29 "2009-06-19T23:39:00Z")
> [@JonathanTheRed](#): > > As for Hephaestus, if the Greeks knew anything about genealogy, they’d have known that the parthenogenic offspring of a female are always female, and are genetic clones of their mother, They’re not actually clones. All of their genetic information comes from their mother, but the mother (depending on exactly how reproduction is accomplished) may have genetic information that the offspring don’t. They’re also not always female (turkeys, for instance, can hatch males parthenogenically, because in birds, it’s males that are XX and females that are XY). Other than that, you’re right on. 😃 ---
**Author:** ![Corner\_Case](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/corner_case/32/234_2.png) [@Corner\_Case](https://boards.straightdope.com/u/Corner_Case)\ **Post date:** [June 22, 2009, 5:41pm UTC](https://boards.straightdope.com/t/a-mathematical-question-about-inbreeding/499971/30 "2009-06-22T17:41:40Z")
You can get thirds from the mating of the aliens in Asmiov’s [_The Gods Themselves_](http://en.wikipedia.org/wiki/The_Gods_Themselves). ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [June 22, 2009, 5:46pm UTC](https://boards.straightdope.com/t/a-mathematical-question-about-inbreeding/499971/31 "2009-06-22T17:46:24Z")
Yes, I should have specified that I meant in species (like humans) which mate two at a time. But there’s no inherent reason why mating _must_ be two at a time, and one could certainly imagine other arrangements (which, knowing how crazy life can actually be, has probably come up with some species or another on this planet). ---
**Author:** ![Corner\_Case](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/corner_case/32/234_2.png) [@Corner\_Case](https://boards.straightdope.com/u/Corner_Case)\ **Post date:** [June 22, 2009, 5:51pm UTC](https://boards.straightdope.com/t/a-mathematical-question-about-inbreeding/499971/32 "2009-06-22T17:51:46Z")
> [@Chronos](#): > > …probably come up with some species or another on this planet). Oh, you mean like the Tenctonese in [_Alien Nation_](http://en.wikipedia.org/wiki/Alien_Nation:_The_Enemy_Within). 😉 ---
**Author:** ![stockton](https://avatars.discourse-cdn.com/v4/letter/s/b5a626/32.png) [@stockton](https://boards.straightdope.com/u/stockton)\ **Post date:** [June 23, 2009, 2:55am UTC](https://boards.straightdope.com/t/a-mathematical-question-about-inbreeding/499971/33 "2009-06-23T02:55:17Z")
> [@Smeghead](#): > > I don’t know what the hell is going on here, but I’d like to volunteer to head up the research program. Sounds great! Is your cousin really good-looking? [Previous page](https://boards.straightdope.com/t/a-mathematical-question-about-inbreeding/499971.md?page=1)