December 18, 2009

Paradox genetics

Human genome, volume XIrregular Webcomic! #2518 brings up the "my own grampa" paradox - if you go back in the past and have a child, you can become your own grandparent.

There is an interesting genetic issue here. Around one fourth of your genome will be from yourself. So what genes will be there? At first look, clearly they could be *anything*, since they are not constrained by ancestry. They might be completely random. In fact, they are far more likely to be random or alien than human, since the number of human-like genomes is far, far smaller than the number of random genomes.

However, there are some boundary conditions. These genes must not only produce a viable time traveler, they must also produce a time traveler who can get a fertile child with (presumably) a human. This seems to introduce a rather powerful constraint: the arbitrary genome cannot deviate strongly from a typical human genome.

There is still room for plenty of arbitrariness there, though. One way of looking for time travelers would be to look for people with a very high concentration of unique SNPs - they are potentially descendants of self-related time travelers who introduced a large bunch of arbitrary differences into the genome [*].

This issue is related to the problem of computation with closed timelike curves: if computers are allowed to get information from the future, can you get information from "nothing"? After all, you could have a program receiving (say) a blueprint for a making transparent aluminum from the future, check that the blueprint is correct, and if so send it back into the past. This way you would get information you don't know how to produce yet can check the correctness of "for free". This computation scheme was originally proposed by Deutsch as causal consistency computing in 91 (another early version was by Hans Moravec), and he called the phenomenon the "knowledge creation paradox." Dave Bacon showed that causal consistency allows solution of NP complete problems and Scott Aaronson and John Watrous showed that both classical and quantum time-computers are equivalently powerful - both belong to the class PSPACE. See Aaronson's excellent lecture notes for more on this.

This suggests that putting the right selection constraints on your offspring/parent can produce any necessary mutation. Imagine that your offspring/parent catches an illness (before reproducing) that is normally 100% fatal. They will however have a mutation that will save them, since otherwise the situation would be inconsistent. Of course, quantum mechanics might also conspire to prevent them from encountering the illness, but immunity-producing random variations in the genome are likely to be more probable than avoiding a common virus (compare this to the problems in quantum suicide computing, where the likelihood of the machine breaking down needs to be held much lower than the likelihood of finding a solution). The above beneficial mutation case of course applies to poisons or anything that would prevent them from reproducing. So if you, devious grandparent-harassing time traveler as you are, put your parent/offspring into a deathtrap that can only be escaped by having some superpower, then the amazing power of causal consistency will have given them it! Not only that, the same is true for yourself - until the moment you reproduce.

[* Multiple parenthood a la Heinlein's "--All You Zombies--" has no constraints at all beyond the time travel loops. That produces a reference class problem, since there is no reason for the person to be even human (or an observer). Unless external events always kill off/remove time travelers that look alien. ]

Posted by Anders3 at December 18, 2009 12:00 PM