I mean, the clusters ALWAYS correspond to something. Always. If we have one cluster for every single individual in the study, those clusters will correspond perfectly to the number of individuals in the dataset. It will be a 1:1 correspondence. Does that mean there are about 8 billion+ races? Yes. It does.

Yes, 8 billion+ races. " I mean, the clusters ALWAYS correspond to something."

You never adress the elephant in the room, that when we set the k to a low number we don't just get clusters that correspond to "something", but we get clusters that just HAPPENS out of pure luck, who would have even thought this to be the case: racial clusters

You're clearly smart enough to know the game you are playing there, and so you are smart enough to know you won't get away with it.

Ok, I will admit that I was doing that, and I should've clarified because I knew it might've come off as disingenous. Under the assumption that my position was true, you conceded that race was real and then you moved the goal post to say that race as a concept isn't meaningful (without ever proven that, you just claimed it to be the case)
"I should point out that I am providing you the courtesy of pretending that 'race' is a legitimate taxonomic category"
But then you didn't attack my claim that there is more than 1 human race. You moved the goal post to say that the k racial clusters aren't meaningful.
Forgive me?

If your question is, "Why is it possible to choose a k value that corresponds to one of the many available socially popular racial classification schemes?" Now there is a question we could talk about. But it is a specific question. The answer is not 'because race exists.' We would need to talk about why humans evolved to classify each other along ethnic boundaries, how we prioritize our distinctions, what selection pressures might have contributed. Lawrence Hirschfeld is currently the leading expert in this field.

I can't explain how much I admire this level of subversion. It is simply blows my mind every single time.

I would like you to answer that question though.

"We know that race is not real, so how come when we cluster human genetics, we get racial clusters? Well, since we know race is not real, the explanation must be something else. "

And this is exactly what Hirschfeld's work demonstrates. Indeed, we humans do have a naive race-assignment module. That is the true home of race, the closest place where race is real science. But that is a real feature of evolved human cognition, not a real feature of human populations. Scientifically, race is in the eye of the beholder.

I don't know that this is true. Self-identified race align 98-99% with estimated race. The outliers are just racial boundaries, biracials and so on.

There is a reason you keep bringing up the social classifications of race, even though I am staying glued to the science. It's because you know that you need to leave science to come up with a way to justify your k value. You need to find a way to legitimize your preferred race number, and you can't do it with science

No, as I've said before, race realists don't believe in a FIXED set of races. We don't mind an arbitrary k, in fact we would assume an arbitrary k.

"Jesus is white." A Jew, is white, apparently, and you feel the need to append that information to every single post you make, right at the top.

Its my flair. I don't want to go into a religious/political debate. I've seen a post of yours (yes, I stalked you a bit before deciding to engage you in a debate hehe) and it said that jews are the most pure whites. After we have finished this debate about race. I would like to delve into that subject if it interests you. However it will divert the attention too much away from the current subject thats already huge if we started on it now.

But without meaning to, you are showing your hand by mentioning textbooks at all.

You had a misunderstanding of kmeans algos that even 1st year students don't have because its in chapter1 of most textbooks on this subject. To my recollection 1st year undergraduates do use textbooks.

I know you aren't dumb. I already kind of apologized for being snarky, but I will actually apologize here. It's just that I already know you, I have met you and your arguments 100 times, and I can't help but feel as if we are already pals engaged in friendly and lightly abusive sparring. Truth be told, I learn more from altrighters than I have from many professers, who would never acknowledge something as straightforward as the warrior gene. I know you aren't dumb. You're wrong, and you're clearly not formally trained in this, but you are well-spoken and you've retained complex information well.

Its all good. I will reciprocate your mannerism and conduct. You're not wrong, but you've been misled, have some misguided misconceptions due to a lack of understanding of the fundamentals of the methods that you're using but these can be fixed and once thats done, then you can return the favor and school me, where my understanding reveals to be lacking.