# In a world with time travel, would it be possible to be your own mother's mother?

Given that you can travel back in time and have a baby there, or alternatively, send your baby back in time, would it be possible that this baby one day becomes your own mother (gives birth to you)? In other words, you would be your own grandmother.

This is intended to be a purely biological/genetic question. My main concern is that under normal circumstances you inherit about 25% of each of your grandparents' genes. Here however, you are one of your grandparents, so you would have to inherit 100% of this grandparent's genes and 0% of the other three grandparents. However, I have only limited biological knowledge, so I'm not sure if these assumptions are accurate. Another concern is incest. As you are your own grandmother, the one you have sex with will be your grandfather. (Again, note that for the scope of this question I'm only interested in the biological concerns of incest, not the social/cultural ones)

I have two ideas of a solution that I'd like to share, but I'm not sure if they are biologically possible:

1. Your egg that is about to become your daughter (and also mother) contains the exact same portion of DNA as your mother's egg that became you. From what I know, eggs (and also sperms) contain a random sample of ~50% of your mother's genes. So, could it be possible (though unlikely) that this random sample contains exactly those 50% that you previously inherited from your mother? This way, you and your mother/daughter only differ by the 50% of genes that the two fathers contributed to each of you. Genetically, you are half siblings.

2. Denote the two fathers F1 and F2. Also, denote yourself M1 and your daughter/mother M2. Via some bootstrap paradox mechanism (see below), it just so happens that your genetic fingerprint contains 1/3 of F1's genes and 2/3 of F2's genes, or in other words M1 = 1/3 F1 + 2/3 F2. If now M1 has a child with F1, it will be

1/2 M1 + 1/2 F1 = 1/6 F1 + 1/3 F2 + 1/2 F1 = 2/3 F1 + 1/3 F2 =: M2

and if this M2 has a child with F2, it will be

1/2 M2 + 1/2 F2 = 1/3 F1 + 1/6 F2 + 1/2 F2 = 1/3 F1 + 2/3 F2 = M1

My concern with this is that, even though the ratios of genes match, it's still unlikely that the randomly sampled egg of your daughter happens to contain exactly those genes that are needed to create you, and not a sibling of yours.

Please feel free to uncover any flaws in these two solutions. You may also use them as starting point for your own solution. Or, you may come up with something entirely different. But maybe, I'm missing something fundamental about how genetics/inheritance works. In that case please provide an explanation of why this absolutely never ever could work, no matter how obscure and incestuous the scenario might be.

In case it's relevant to answer the question, here is how time travel is supposed to work:

• Time is deterministic. Time travelers can of course try to change something, but they are doomed to fail. Everything will happen as it has always happened. Maybe this fact will resolve my concerns regarding unlikely events that I raised above, because they, well, just happen.

• The bootstrap paradox (or causal loop: https://en.wikipedia.org/wiki/Causal_loop) is a thing. There are several examples of items and information that don't have an origin, they just exist. For example a time traveler takes some book back in time and hands it over to the young author before he has written it or even thought about it. And only because he reads his own book from the future he knows how to write it. The mother-daughter-paradox I'm asking for would be just another example of a bootstrap paradox, where in that case the genes (or some portion thereof) would have no origin.

• Heinlein's short story All You Zombies (1958) goes a step farther - the same person loops several times, and is father, mother, child, and a supporting character. – user535733 Mar 4 at 13:36
• @L.Dutch-ReinstateMonica, well, I wouldn't want to spoil it for the author. He put a lot of work into that story. – user535733 Mar 4 at 14:01
• Time travel is (at least for now, at least as far as we know) purely science fiction. So you make your own rules. Pick the SF story you like best and follow their rules. Or make your own rules. – puppetsock Mar 4 at 14:33
• @puppetsock This is what I'm trying to do. The rules shall be: everything as we know it from reality, plus (deterministic) time travel. And I'm trying to figure out if this mother-daughter-paradox is plausible in this context. – sebrockm Mar 4 at 16:20
• @user535733 I was going to say the same thing about the movie Predestination, but I see it's based on the short story you mentioned. – JoL Mar 5 at 1:20

In terms of the biological mechanisms, you have two major mechanisms that come into play:

The first is the random segregation of chromosomes during meiosis, the generation of the egg cell. The egg cell will contain only one of each chromosome, and you need it to be the "maternal" chromosome each time. This is unlikely (1/2^23 for each generation) but unlikely is not a problem.

The second is the crossover mechanism that occurs during meiosis. The parental chromosomes are not directly passed on, they mix with each other and this means you get genetic recombination. So chromosome 1 in an egg cell isn't the same as the maternal chromosome 1 of the individual, or the paternal chromosome 1. It's a shuffled mix of both maternal and paternal chromosomes.

The exceptions to this rule are chromosome Y which is passed on directly from father to son and the mitochondrial chromosome which is passed on directly from mother to daughter.

It's estimated that crossover occurs around 75 times for human females (55 for human males), but there is nothing biologically that seems force the crossover event, aside from overwhelmingly high random chance. While there doesn't appear to be any mechanism that would check that a crossover has occured in order to determine if the meiosis is allowed to occur, it's extremely likely that it is physically impossible for the chromosomes to all be present during meiosis without enduring crossover events. Not everything is known about how crossover events are regulated but the systems seems to be rigged to always have crossover events occur during meiosis.

This makes it a little trickier to argue that it happened despite being unlikely because it might really defy fundamental physical forces. That being said, ignoring the crossover problem and suggesting that it is simply forced random chance seems reasonable enough because there are no known "checks" that crossover has in fact occurred that would stop a cell from completing meiosis if it hasn't.

If you want a stronger case, I would suggest explaining that the mother passes on 1/2 of her genes and her entire mitochondrial DNA to M2, F1 passes on 1/2 of his genes to M2. Now M2 has half of your genes and half of F1's genes.

Thinking about it a little deeper, I think that the problem you try to solve is not the one you outlined. You're asking if it's possible to "replace" your own grandmother, but you frame the problem as needing to provide 100% of your own genes.

M2 and F2 each pass on half of their genes to you. So you regain 1/4 of your original genes from M2. But you also have 1/2 of F2's genes and 1/4 of F1's genes.

Why can't the 1/4 of F1's genes happen to correspond to exactly 1/4 of your genes, and the 1/2 of F2's genes happen to correspond to exactly 1/2 of your genes?

To think about it a different way, you already know that your maternal grandparents, together, had 1/2 of your genes. You also know that your father has the other half. By going back in time and becoming your own grandmother you're only changing the maternal 1/4, but you know that this 1/4 already existed.

The case in which you need to provide 100% of your own genes is if you go back in time and, instead of replacing your own grandmother by having a child with your grandfather, you try to become your own grandmother by having a child with someone who is not genetically related to you in the original timeline.

The interesting thing about your question, though, is that it's only possible if a girl replaces her maternal grandmother. Replacing your paternal grandmother breaks the direct heritage of the mitochondrial genome. Conversely, a boy cannot become his maternal grandfather.

• This is precisely the kind of answer I was hoping for! +1 I was especially unsure of the meiosis process, so thanks for explaining that. The scenario you describe in the second half of your answer sounds similar to my 2nd proposal where the two fathers provide the "missing" DNA you need to be your grandmother, if I understand you correctly? Because that part you cannot have gotten from your mother because of 1/2*1/2 = 1/4. – sebrockm Mar 4 at 14:39
• @sebrockm I think so, to be honest I'm having trouble following your math, I don't see how you get 1/3 anywhere. But yes, the father provides 1/2 and the maternal grandfather provides the last 1/4, as they have in the original timeline. You provide 1/4 as a grandmother which you definitely would have. It's unlikely for all the meiosis events to line up perfectly, but your world takes care of pesky probability so it's all good and doesn't violate any biological mechanisms that I know of. – Thymine Mar 4 at 14:45
• Well, the 1/3 comes out of nowhere. The mother and daughter (or rather their genes) are a bootstrap paradox. Maybe with the exception of the mitochondrial DNA, they just happen to be identical by 1/3 and 2/3 with the two fathers. Why? Because then the math works out. By "mixing in" 50% of the genes of the "1/3-father" your daughter will again have that 1/3 2/3 ratio, just vice versa. And by having that ratio, when she has a child with the other father, that child can genetically be you, because that will switch the ratio again. I hope what I'm saying makes any sense :-D – sebrockm Mar 4 at 14:55
• @sebrockm If this time traveling escapade can only produce the exact same set of genetic information each time, then breeding (in- or otherwise) is a non-factor. By pre-defining the outcome as "exactly the same in every way", none of the factors which impact breeding will apply-- there fundamentally cannot be any changes. – Upper_Case Mar 4 at 17:29
• Your last paragraph is wrong. It assumes the time traveler must be the source for the mitochondrial genome or that they must be the source for the Y chromosome; neither is actually required. Those can be supplied by any other identical source of that specific genetic material, just like every other part of the traveler's DNA which isn't directly provided by the traveler. In theory, the time traveler could replace any of their ancestors, because what the ancestor contributes to the time traveler is always a subset of the time traveler's DNA, which the traveler can always provide. – Makyen Mar 5 at 6:24

"Unlikely" doesn't come into play with time travel. It happened that way, it must have happened that way, so probability is 1.

• why should it be impossible, you can always have a spontaneous mutation at least. – ths Mar 4 at 13:43
• for the flying pigs, the difficulty would be to justify the closed loop which makes them exist. – ths Mar 4 at 14:14
• @ths there's an awesome freak of nature of unknown origin in the archive. It's been decayed beyond recognition but we can remake it from the DNA -> ooh, we have to share this with our friends on a vacation to 21c -> this is a beautiful creature, we can't just kill it. I believe Alice the Librarian loves weird pets, let's give it to her – John Dvorak Mar 4 at 14:18
• @sebrockm You're complaining about the answer being tautological, but your scenario is tautological. I think what's interesting to you is that you imagine something interesting occurred with the genetics (something got cancelled out somewhere!) but that definitionally didn't happen. Depending on the rules of your time travel, either present-day you came first naturally, replaced the original gams, and subsequently adjusted her own genome (this occurs once, not iteratively) OR reality is outside time and whatever happened btwn you and your grandfather and mom and dad ended up (cont.) – lly Mar 5 at 6:23
• (cont.) duplicating gramma's genome in you. You're curious about what the odds of that occurring naturally are? 0. Can't happen, except by genetic engineering or by you/dad/grandpa having also replaced other members of your family as well and you just not knowing it yet. There are environmental, nutritional, etc. influences on genetic expression that just make it utterly, utterly impossible. But in your contrived scenario, it must happen with absolute certainly. – lly Mar 5 at 6:25

It sounds like you're looking for a single timeline. The only way that works is that you always were your own grandmother and just weren't aware of it. The genes you inherited from your other three grandparents happened to replace the identical genes you inherited from them and then took with you into the past. This is, of course, extremely unlikely, but it must have happened that way because otherwise there would be a paradox.

The only other way to avoid a paradox is for you going back to create a new timeline that branches from the old one at the point where you replaced your grandmother, and in the new timeline, your granddaughter would not have the same genes as you, i.e. would be a different person.

• Incidentally, the billiard ball equations describing single-timeline with wormholes say information comes from nowhere and is nondeterministic. – Joshua Mar 4 at 22:34

You are overlooking Case 3 (which is the inverse of Case 1)

In the (extremely unlikely, but still valid) scenario that your mother passes down to you exactly the genes that her father passed to her, then you can could inherit 0% from yourself.

Statistically, this situation (the "inheriting 0% of DNA from one grandparent", not the time-travel) isn't unlikely to have happened at least once - there's less than a 1-in-8,388,608 chance of it happening, but even with 10-million-sided dice, rolling 100-billion times gives decent odds on getting at least 1 to land on 10-million. It's not impossible, just highly improbable.

Oversimplified, assume that your DNA is merely 2 pairs of chromosomes, AB:CD, instead of 23 pairs.

Your Paternal Grandparents are AS:TU and VW:XD, and pass on the half-pairs A:T and W:D to your Father, AW:TD. You inherit sequence A:D from him.

Your Maternal Grandparents are YB:CZ - who passes on B:C - and yourself (AB:CD) - passing on any pair ?:? - leading to Mother ?B:C?1. You inherit B:C, for AB:CD without any (non-mitochondrial) DNA appearing spontaneously (i.e. being inherited from yourself, in a bootstrap paradox)

Of course, as alluded to in that last sentence (and covered in more detail in Thymine's answer), the bit that scuppers you there is the Mitochondrial DNA, which is passed down the Maternal line2 - much as the Y chromosome is passed down the Paternal line...

What this actually means is you can't be your mother's mother, and you can't be your father's father, but you can be your mother's father! (But not your father's mother, because you would then inherit your own X chromosome from your father3)

1: Your Mother could be any of AB:CD, AB:CC, BB:CD or BB:CC. It doesn't actually matter, since we will be discarding those chromosomes

2: There are exceptions, such as heteroplasmy (where mitochondrial DNA is inherited from both parents), which could lead to inheriting mitochondrial DNA from your maternal grandfather instead of yourself

3: Unless your father was XXY instead of XY, and inherited the extra X chromosome from his father. This generally leads to infertility, but there are medical workarounds for that

• Nice answer! But I believe my father and one of my paternal grandparents needs a D instead of a C, otherwise I don't see how I get my D back :-D – sebrockm Mar 4 at 17:52
• "rolling 100-billion times gives decent odds" is only true if you call a near 100% certainty decent. A 1-in-10-million chance is likely to have happened around 10,000 times in a sample set of 100 billion. It's significantly less than a one in a googol chance that it has never happened. – Rob Watts Mar 4 at 22:06
• If you are your mother's father, then your mother is her father's mother. So,these are either both possible or both impossible. – Stig Hemmer Mar 5 at 8:26
• Don't forget about genetic recombination during meiosis though! – Thymine Mar 5 at 9:23

This is of course a variation of the grandfather paradox. Here is an interesting video about it.

My take on this is:

# No.

Even when omitting the obvious paradoxes and creating the situation where you replace your grandmother, you are not just the sum of your grandparents' genes. You are also the result of (however minute) random mutation. You could obviously go back and get pregnant from your grandfather, but the grandchild you produce would not be you. Therefore you and your grandchild could not exist on the same time line.

• So, if I understand you correctly, you are saying that because there are always random mutations, it's impossible that my grandchild could have the exact same DNA as I have? So what if by some chance no such mutation occurs? Or what if two mutations occur that cancel each other out? I do see that it's unlikely (do you happen to know how unlikely?), but I don't see how your argument leads to a 100% certain No. – sebrockm Mar 4 at 15:27
• This assumes that the random mutations are in some way cumulative and different each time. That’s not necessarily true. In fact it might be a random mutation that brings otherwise divergent DNA back in line. Of course that all requires that this time traveler is and always will be and always was their own grandmother, which makes this a bootstrap paradox (girl/grandmother has/have always been) rather than a grandfather one (I replace my grandmother, so where did I come from?). – Joe Bloggs Mar 4 at 17:17
• @JoeBloggs agreed, but as stated, this answer omits all paradoxes. However even if the mutations didn't happen, (this is near impossible, as they aren't just random, but external factors play a role as well, so you'd have to live your grandma's life 1:1) and you'd produce a girl who is 100% identical to you, it still wouldn't be you, because it is a product of you. But that borders more on morality than probability. – Plutian Mar 4 at 18:30
• Of course you'd have to live your grandmother's life--you couldn't help but live your grandmother's life, because you are your grandmother. .What would you do, live someone else's life instead of your own? – David K Mar 5 at 13:24
• @DavidK this is yet another paradox. If you weren't your own grandmother to begin with, but replace her, you would have to effectively replace her for the rest of her life exactly. No hopping in your time machine back home after giving birth. Otherwise you will have a bootstrap paradox like Joe Bloggs mentioned – Plutian Mar 5 at 13:34

You don't need to inherit 100% of your own genes. You inherit 25% of genes from yourself (grandparent 1), the rest is coming from your other grandparents. It is irrelevant that the remaining 75% of genes from grandparent 1 is the same as yours, as they are discarded. They just happen to coincide with the parts you inherit from your other grandparents.

You didn't "become" your own grandparent, you have always been your own grandparent, you just didn't know.

### Maybe.

Time travel introduces all kinds of bizarre elements which don't necessarily interact well with one another. If your only constraint here is that one individual replace their own grandmother in a single instance, and that reality itself will bend to accommodate that while maintaining continuity, it is perhaps not literally impossible for this to happen through natural-esque mechanisms.

But the overarching issue is that, if people are free to travel into the past and do whatever they want but cannot change outcomes, then you've fully defined the system. It's that assertion that describes what's possible, not real mechanisms interacting with a fantasy mechanism with immutable properties. Because you've already fully specified the outcome, and that outcome has no particular basis in reality, then the word possible doesn't operate here in the same way it does in everyday English.

Some problems:

A view which begins with a metric of genes-in-common is too simplistic to describe this situation. Key events in human reproduction include mutations, crossing over, and environmental factors, including epigenetic factors, all of which exist independently of genes-in-common. Further, it's trivially possible to have the same proportion of genes in common while not actually having the same, specific genes in common, and for continuity you really would need the latter.

Let's define A as the "original" grandmother, B as the mother (who is to be borne to her own time-travelling daughter), and C as the time traveler. These introduce several (million) points of failure into the scheme beyond simple availability of specific genes.

In the broadest case, which you've considered, it's entirely possible that C will lack genetic information which B inherited from A, and therefore C cannot pass them to B. That situation would mean that B cannot be generated from C.

The other issues I mentioned include an extreme degree of randomness-- during crossing over the same chromosomes being replicated by the same process under the same circumstances may see alleles reorganized in new ways-- it's the same gene, more or less, but it may not work in quite the same way as the original did.

Mutations also matter, in a similar broader way. The molecules which make up DNA may be altered by a variety of factors, literally changing the blueprint which defines the organism. A similar issue is introduced by epigenetic factors-- environmental effects which influence which genes are expressed, and how often.

There are many, many other factors which would matter here (this is a poor summary of a miniscule subset of relevant information). But the underlying mechanisms you're hoping to rely on are far more complex than what was presented in the question, and so a solution that delves into that level of detail would automatically require more detail in order to be even naively valid.

The solutions

Of course, time travel itself is a totally undefined activity in real-world terms, and so you can introduce any properties or constraints that you want onto it. This would be enough to overcome any conceivable problem with the scheme, as the "rules" of time travel can simply override them by fiat.

Most of the first-order problems with this sort of loop are a result of randomness: which genes are available, and which specific events occur during cellular reproduction and organism development. If time travel inherently enforces continuity, you can hand-wave all of that away. C simply would have the correct genetic information, present in the correct configurations, in the correct structures, at the correct times to replace A silently.

In short, because you've already asserted that the outcomes of events which have "already" occurred cannot be changed, then all possible problems simply fix themselves or are conveniently elided. You don't need any mechanism to do this, because it's all time magic in the first place.

The only question is how "the timeline" enforces continuity in the face of behaviors which would, left to themselves, alter the course of events. If C went back in time and tried to murder her grandfather prior to B's conception by putting a loaded, working gun to his head and pulling the trigger, what specifically would cause that effort to fail, given that your time travel rules demand that it must fail?

I would posit that the bigger problem is that, because A gave birth to B, there is no way to change events such that C would give birth to B. If time is fully deterministic, as indicated in the question, then it's questionable (at best) for that change to take place-- what would A be doing instead of being pregnant and delivering B?

This is intended to be a purely biological/genetic question. My main concern is that under normal circumstances you inherit about 25% of each of your grandparents' genes. Here however, you are one of your grandparents, so you would have to inherit 100% of this grandparent's genes and 0% of the other three grandparents.

You are overthinking it. The situation is the same as if one of your grandparents had identical genes to you by pure chance, without time travel involved at all.

You inherit 25% of each of your grandparents' genes. You have 25% of Alice's genes, 25% of Bob's genes, 25% of Carol's genes, and 25% of Dave's genes. It just so happens that 75% of Alice's genes are identical to the ones that Bob, Carol and David have as well. Does this cause any paradox? No, not really.

Since you inherit 25% of your genes from yourself, those genes are stuck in a causal loop. As with any causal loop in science-fiction, those genes can be anything you want - you could be anything from a normal human to a quarter-demon that's still able to mate with humans. (Just please don't go into detail about the mating mechanics of quarter-demons, okay?)