Actually, the exponentiation of ancestry proves that Salazar is the ancestor of everyone in Great Britain by the pigeonhole principle, except in your case where each of his descendants only has one child. That is an extreme outlier and not likely to happen, all things considered.
A recent paper shows that everyone who lived in Europe 1000 years ago is an ancestor of everyone living in Europe today (barring immigration of course):
We can furthermore conclude that pairs of individuals across Europe are reasonably likely to share common genetic ancestors within the last 1,000 years, and are certain to share many within the last 2,500 years. From our numerical results, the average number of genetic common ancestors from the last 1,000 years shared by individuals living at least 2,000 km apart is about 1/32 (and at least 1/80); between 1,000 and 2,000ya they share about one; and between 2,000 and 3,000 ya they share above 10. Since the chance is small that any genetic material has been transmitted along a particular genealogical path from ancestor to descendent more than eight generations deep [8]—about .008 at 240 ya, and 2.5×10−7 at 480 ya—this implies, conservatively, thousands of shared genealogical ancestors in only the last 1,000 years even between pairs of individuals separated by large geographic distances. At first sight this result seems counterintuitive. However, as 1,000 years is about 33 generations, and 2^33≈10^10 is far larger than the size of the European population, so long as populations have mixed sufficiently, by 1,000 years ago everyone (who left descendants) would be an ancestor of every present-day European.
Great Britain is a lot smaller than Europe as a whole, so it probably takes even less than 1000 years for this effect to work.
The pigeonhole principle doesn't say what you want it to. It guarantees that some ancestors will show up multiple times on everyone's trees; it does not guarantee or even suggest that every ancestor present on anyone's tree is present on everyone's trees.
That aside, it's not clear that the descendants of Salazar Slytherin would mix sufficiently with the rest of magical Britain in 1000 years of wizard generations (possibly longer than Muggle generations, given differing lifespans) for the paper's findings to apply. Running with general experimental assumptions is not effective for specific and extraordinary cases.
Two new short chapters! Since the next one is coming tomorrow and we know it'll be short, let's use one thread for both.
This is a new thread to discuss Eliezer Yudkowsky’s Harry Potter and the Methods of Rationality and anything related to it. This thread is intended for discussing chapter 105 (and chapter 106, once it comes out tomorrow). EDIT: based on Alsadius' comment about thread creation for MOR chapters, let's also use this thread for chapter 107 (and future chapters until this nears 500 comments) unless someone objects to doing so. Given that this is the final arc we're talking about, thread titles should be updated to indicate chapters covered.
There is a site dedicated to the story at hpmor.com, which is now the place to go to find the authors notes and all sorts of other goodies. AdeleneDawner has kept an archive of Author’s Notes. (This goes up to the notes for chapter 76, and is now not updating. The authors notes from chapter 77 onwards are on hpmor.com.)
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically: