I don't know where all you zombies came from.
We've all heard the song 'I'm my own grandfather.' This theme has presented itself a few times, such as "All You Zombies-" by R.A. Heinlein; the writers of Futurama, over qualified for their jobs, wrote an episode where a time traveller accidentally slept with his own grandmother (Thus becoming his own grandfather).
This got me wondering whether you can have a situation like one of these stories without getting stuck in a causal loop of information? By information, I'll only consider genetic information. Obviously, "All You Zombies-" is right out, as the main character (In fact, almost all the main characters) are the same person. There's no inlet for novel genetic information, as all the protagonist's genetic information stems from exactly himself. The Futurama story presents a more interesting case. And potentially useful if you ever find yourself contemplating doing "The Nasty in the Pasty" in your future (or Past) time-travel adventures.
Inheritance isn't 100%. In fact, you're only half related to a given parent. Let's call Alex our time traveller. Alex goes back in time and mates with B. C grows up, and mates with D, producing Alex. Now, all C has to do, to avoid creating information, is pass on only B's genes. Easily done, right?
Now the odds of any one chromosome transmitting is, all things being equal, 1/2. There are three important exceptions to this rule I'll touch on in a moment. Given a typical human has 24 pairs of chromosomes, all C has to do is have the transmit the 24 that don't derive from A. The odds of this is .5*.5*.5.... etc for a total of .5^24. That's roughly 5.96046448×10^-8 I might be off by an order of magnitude, but that's either one in six billion, or one in 600 million. Either way, given the population of the world, that can happen. (EDIT: That'll teach me to do math at a late hour. It's actually one in 16,777,216. Very improbable, but still within the realm of possible, I think. With judicious rounding, a single person currently living on earth has a 1/3 chance of being this condition.) And to avoid problems, it would have had to have happened, else there would be a sort of paradox, and it would have never happened (Via anthropic principle-If it's observed, someone had to roll the dice and get lucky, or else it wouldn't /be/ observed.)
In the story, Fry sleeps with his Grandmother, thinking she /can't/ be his grandmother, since he just accidentally killed who he thought his grandfather was. She, however, is, and gives birth to his father, who then sires him.
The first problem stems from that pesky 24th chromosome, better known as a gonosome, or sex chromosome. They also have a .5 chance of being transmitted, but if a resulting offspring is of a given gender, then that chromosome /must/ have been the one that transmitted. Fry, in the TV story, had a genealogy that looked like this:
C transmits the y chromosome to A. A transmits the y chromosome to C. Woops. We have a loop. The y chromosome doesn't originate anywhere. That's a bit of informational causality problem. Well, maybe one could be their own grandmother?
You still run into a problem. There's something else that's transmitted in a sex specific way, and that's a bit of DNA in the mitochondria called MtDNA. It's transmitted maternally. So A got it from C got it from A... problem again. And you can't just solve it by making C male.
Again, we have a problem. This time, A gives C an X. C is XY (male) and must give that X to A to be the proper gender to mate with B. So the X chromosome flows from A to C to A. Loop again. The best women can hope for, sadly, is to be their own great grandmothers. Sorry, gals. I know you're crushed.
Lets make it work, shall we?
C gets her mtDNA from B, and gives it to A. A fails to give it to C. We're safe. C gets an X from both A and B, and can pass on B's X to A without violating informational causality. So the X flows from B to C to A, to C. Yes, C has two copies of the same X, and is inbred at that point. However, and here's the important bit, the X has a historic origin, and didn't just plunk down out of thin air. No information was created.Postscribed:
I'd like to consider a lesser problem, other than the glaring paradox of informational causality.
So from an arbitrary origin, A has the base number of mutations. Let's call that 0, for simplicity. There are ~200 novel mutations per generation in humans. Let's assume it's spread out evenly among the chromosomes, and lets employ some judicious rounding - 4 mutations per chromosome. If you track a chromosome stuck in one of these loops, it's going to start gathering mutations like crazy, making it degrade over its 'timeline' as the information is shuttled back and forth through time. It's going to have 8*n mutations, where n= the number of cycles since the arbitrary start. So you have information poofing into existence out of nowhere, and rapidly degrading down to nothing.
I'm not at all sure how that would work, because it seems the whole system would crash at the end - at some point, C wouldn't be able to pass on the information to A, which means C would have never got the information, which means C wouldn't have existed because A was never born to give rise to C...
The logical flow quickly goes to hell in a handbasket. So I don't think that could happen, if only for that reason. With the 'solution' genealogy, none of the genes are getting recycled, meaning none of them can degrade beyond what they normally would have after that many generations.Postscribed after my postscription: This also assumes there's no selfish genes mucking up the random inheritance bit. That's an important bit too.
This got me wondering whether you can have a situation like one of these stories without getting stuck in a causal loop of information? By information, I'll only consider genetic information. Obviously, "All You Zombies-" is right out, as the main character (In fact, almost all the main characters) are the same person. There's no inlet for novel genetic information, as all the protagonist's genetic information stems from exactly himself. The Futurama story presents a more interesting case. And potentially useful if you ever find yourself contemplating doing "The Nasty in the Pasty" in your future (or Past) time-travel adventures.
Inheritance isn't 100%. In fact, you're only half related to a given parent. Let's call Alex our time traveller. Alex goes back in time and mates with B. C grows up, and mates with D, producing Alex. Now, all C has to do, to avoid creating information, is pass on only B's genes. Easily done, right?
Now the odds of any one chromosome transmitting is, all things being equal, 1/2. There are three important exceptions to this rule I'll touch on in a moment. Given a typical human has 24 pairs of chromosomes, all C has to do is have the transmit the 24 that don't derive from A. The odds of this is .5*.5*.5.... etc for a total of .5^24. That's roughly 5.96046448×10^-8 I might be off by an order of magnitude, but that's either one in six billion, or one in 600 million. Either way, given the population of the world, that can happen. (EDIT: That'll teach me to do math at a late hour. It's actually one in 16,777,216. Very improbable, but still within the realm of possible, I think. With judicious rounding, a single person currently living on earth has a 1/3 chance of being this condition.) And to avoid problems, it would have had to have happened, else there would be a sort of paradox, and it would have never happened (Via anthropic principle-If it's observed, someone had to roll the dice and get lucky, or else it wouldn't /be/ observed.)
In the story, Fry sleeps with his Grandmother, thinking she /can't/ be his grandmother, since he just accidentally killed who he thought his grandfather was. She, however, is, and gives birth to his father, who then sires him.
The first problem stems from that pesky 24th chromosome, better known as a gonosome, or sex chromosome. They also have a .5 chance of being transmitted, but if a resulting offspring is of a given gender, then that chromosome /must/ have been the one that transmitted. Fry, in the TV story, had a genealogy that looked like this:
C transmits the y chromosome to A. A transmits the y chromosome to C. Woops. We have a loop. The y chromosome doesn't originate anywhere. That's a bit of informational causality problem. Well, maybe one could be their own grandmother?
You still run into a problem. There's something else that's transmitted in a sex specific way, and that's a bit of DNA in the mitochondria called MtDNA. It's transmitted maternally. So A got it from C got it from A... problem again. And you can't just solve it by making C male.
Again, we have a problem. This time, A gives C an X. C is XY (male) and must give that X to A to be the proper gender to mate with B. So the X chromosome flows from A to C to A. Loop again. The best women can hope for, sadly, is to be their own great grandmothers. Sorry, gals. I know you're crushed.
Lets make it work, shall we?
C gets her mtDNA from B, and gives it to A. A fails to give it to C. We're safe. C gets an X from both A and B, and can pass on B's X to A without violating informational causality. So the X flows from B to C to A, to C. Yes, C has two copies of the same X, and is inbred at that point. However, and here's the important bit, the X has a historic origin, and didn't just plunk down out of thin air. No information was created.Postscribed:
I'd like to consider a lesser problem, other than the glaring paradox of informational causality.
So from an arbitrary origin, A has the base number of mutations. Let's call that 0, for simplicity. There are ~200 novel mutations per generation in humans. Let's assume it's spread out evenly among the chromosomes, and lets employ some judicious rounding - 4 mutations per chromosome. If you track a chromosome stuck in one of these loops, it's going to start gathering mutations like crazy, making it degrade over its 'timeline' as the information is shuttled back and forth through time. It's going to have 8*n mutations, where n= the number of cycles since the arbitrary start. So you have information poofing into existence out of nowhere, and rapidly degrading down to nothing.
I'm not at all sure how that would work, because it seems the whole system would crash at the end - at some point, C wouldn't be able to pass on the information to A, which means C would have never got the information, which means C wouldn't have existed because A was never born to give rise to C...
The logical flow quickly goes to hell in a handbasket. So I don't think that could happen, if only for that reason. With the 'solution' genealogy, none of the genes are getting recycled, meaning none of them can degrade beyond what they normally would have after that many generations.Postscribed after my postscription: This also assumes there's no selfish genes mucking up the random inheritance bit. That's an important bit too.