The problem with being your own father

is not really a moral one. In the typical time travel story you were abandoned as a child, so after you travel back in time you don’t even know who is supposed to be your mother. Now what can you do: refrain from sex completely in order to avoid possibly having sex with your mother? If you were successful you’d just erase your own existence, which is widely considered undesirable, and is anyway impossible, as it would be a grandfather paradox. Or just a father paradox, in this case. This would just make your trip in time a miserable affair. You might as well accept your inexorable destiny and enjoy your time in the past.

No, the problem is, what the hell is your DNA? It needs to respect the consistency condition that the DNA of you-father is exactly the same as the DNA of you-child. But the DNA of you-child is determined by the recombination of the DNA of you-father with the DNA of your mother. For instance, the pair of homologous chromosomes 1 of you-father, F1 and F2, recombine with the your mother’s pair, M1 and M2, giving the possible pairs of you-child as F1M1, F1M2, F2M1, and F2M2 (ignoring crossover). Now F1F2 must be equal to one of these four pairs, which means that at least one of your chromosomes must be equal to your mother’s! That’s nothing surprising if you don’t time-travel, but if you do, it means that at some point you share a chromosome with this girl you just met.

Let’s say then that F1 = M1. Then the possible pairs of you-child are M1M1, M1M2, F2M1, and F2M2. The first possibility is bound to give you some horrible genetic disease, so let’s exclude that1. The second possibility would make you an identical twin of your mother, which is fine for chromosome 1, but cannot be the case for the sex chromosomes, unless you are one of the exceedingly rare true hermaphrodites and possibly also your own mother.

This leaves us with the most prosaic alternatives F2M1 or F2M2. Which are apparently unproblematic, until you ask where does F2 come from. It doesn’t depend on anything from the past, even probabilistic. It’s completely arbitrary, its genes don’t even need to be human, apart from the constraint that they shouldn’t make reproduction with humans impossible.

If that doesn’t disturb you, consider Everett and Roman’s undeserved Fields medal paradox: one day you wake up to find on your desk a paper, signed by you, with a proof of the Riemann hypothesis. You read the paper, check that the proof is in fact correct, and publish it. You become famous for the result and eventually receive the Fields medal. You then find a time machine, and use it to deposit the paper on your desk just before you found it. Now, who wrote this proof? Who deserves the Fields medal?

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