I'm still having a huge problem with this one. I agree genetically if you swapped out my great-grant-grandmother with another woman, and could still force all the same people to meet and conceive at the exact same moment otherwise, that the resulting person would likely be very genetically similar to me, but I don't see that as the problem at all.
Depending on the ancestor that gets removed, the "resulting person" could be genetically
identical to you. You don't get genes from every single ancestor you ever had. There's only a finite number of packets of information that get shuffled in reproduction, and eventually you get to the point where the number of ancestors you have in a given generation is larger than the number of packets, so there are some ancestors that you get
zero genetic information from. And the further back the generations go, the larger the number of genealogical ancestors that are not your biological ancestors, because none of their genes survived the reshuffling process through enough generations to reach you.
Look at it from the other direction -- you pass on 1/2 of your genes to your offspring, who pass on maybe 1/4 of your genes to their offspring (possibly more or less depending on how their own genes get shuffled), then the next generation gets 1/8 of your genes, the next 1/16, etc. So less and less of your genome is passed on to each successive generation, and eventually the fraction of your genes that survives is small enough that it could end up getting shuffled out of the lineup altogether, outcompeted for the finite number of slots in the chromosomes. And once you get to 15 or 16 generations after your own, that becomes virtually inevitable. Genetic inheritance is finite.
Or at least direct inheritance is. If you go back far enough, everyone's a descendant of everyone. The genes get reshuffled back and forth so widely through the population that we're all far more closely genetically related to each other than we are genealogically related to each other. So even if a given genetic ancestor is removed from your past, it's possible that whoever took their place in your ancestry (whoever their spouse married instead) would have a lot of the same genes, and would've passed the same fragments on to you. So there are at least some cases where even swapping out a genetic ancestor could make no difference in your genome, or an inconsequential difference (since a lot of DNA is non-coding, not all genes are expressed, and a given trait is determined by the interaction of multiple genes, not just one).
Kill my 2x Great Grandmother. Does my Grandfather just meet and marry someone else on the exact same schedule?
Well, that's only 4 generations back. As I said, a given set of genes would typically take twice as many generations before there's a good chance that it would drop out of the lineage altogether. At 4 generations back, you only have 16 direct ancestors. At 8 generations, you have 256, and at 12 generations you have 4096. So the odds that any single one of them would be indispensable to your ancestry get smaller and smaller the further back you go. All the changes you mention
could occur, but eventually they'd be outweighed by the hundreds or thousands of other ancestors whose lives played out without change.
Sure, there
could be cases where one ancestor makes all the difference. Go back to 1634 to the
Hercules of Sandwich en route from Kent to New England, toss Nathaniel Tilden's servant James Bennett into the Atlantic, and it would mean my paternal family never came to the New World. That could've had a radical impact on my family history from then on. At the very least, I might have a different surname now. But other ancestors might not have made such a critical difference to the overall family history.
So easy to make changes that affect the timeline in big ways eventually. Buy Hitler's mother a couple drinks at the bar, is she too hung over to conceive Adolph that night, and instead of WWII, you get to see Adolph Hitler's crappy watercolors instead? Genetically very similar guy, and maybe only conceived a couple days off schedule, but it's a different roll of the dice.
Hitler was not the only person responsible for WWII. He was just an effective catalyst for the forces that already existed in his culture. There were countless others in that place and time who were raised in the same cultural context -- a culture that encouraged childrearing techniques we now recognize as abusive and likely to produce sociopathy, a long-standing anti-Semitism in the society, a generation of economic hardship and resentment due to the harsh punitive measures imposed on Germany after WWI. A genetically alternate Hitler conceived a few days later would still have been raised in the same context, and might well have been born with whatever genetic predisposition toward psychopathy the "real" Hitler had. Even if you killed baby Hitler altogether, someone else might well have taken his place and done much the same things. The details would've been different, but the war and the genocide might well have happened anyway.
And of course it was a
world war, not just about Germany. Japan's war of conquest in Asia began a decade before Pearl Harbor, and Mussolini invaded Ethiopia four years before the Nazis invaded Poland.
So yes to genetics if the result is to just take random tissue samples at the end, but no in that there's a massive butterfly effect being ignored, and the further back you go, the bigger the hurricane in the present...
Sometimes, but not always. The butterfly effect is not an absolute guarantee. Yes, depending on the specific conditions, the atmospheric effect of the flap of a butterfly's wings in the Pacific
could be amplified enough to cause a hurricane in the Atlantic a month later -- but in different conditions, that flap would be damped out by other factors instead of amplified. It depends on the specific context. The butterfly effect is an illustration of chaos theory, after all, and the point of chaos theory is that the interacting factors are so complex that the result is not deterministically predictable. At best, you can determine a range of possibilities that
could result from the starting conditions, and say that some are more likely than others.