Earlier quoted context omitted.
I think your initial premise is flawed - that males and females form neat clusters with perfect Gaussian distributions, on any reasonable number of dimensions. Yes, on the axis for attraction to men, gay men are shifted towards the female group. On the majority of dimensions, males and female are probably hard to distinguish. On some dimensions, gay men may indeed cluster away from women.
You're overstating my premise. I was not saying very much, and you're implying I was saying a lot. Who said the clusters were neat? Or that characteristic distributions were Gaussian? "Women" and "Men" are words that we associate with observable characteristics. They are extremely messy, so much so that there isn't even one characteristic in all of the many dimensions that we would all agree evenly cleaves the "Men"…
I do agree with the very narrow premise of your original claim:
> Isn’t “being attracted to males” a predominantly female characteristic in animals that reproduce sexually? On the “sexuality” dimension, do not gay men fall closer to the female cluster than the male cluster?
I don't, however, agree with your later claim:
> By default, let’s assume that homosexual men have the same distribution of all other traits as heterosexual men. In N-dimensional space, they are biased slightly away from dead center of the male cluster towards the female cluster because of the female bias of the attracted-to-men trait.
I would hold that this isn't true, because I would suggest that N here is extremely large, and in many of those dimensions, homosexual men are skewed away from women, even more so than heterosexual men. I do not know what those dimensions could be - perhaps something as esoteric as "Testosterone Levels", "Median Household Income", "Toxic Fathers", "Suicidal Ideation", "Substance Abuse", or "Gut Microbial Diversity". In some dimensions, homosexual men are probably hypermasculine. In N-dimensional space, humans as a whole are probably indistinguishable, let alone homosexual or heterosexual men.
I do not agree either with the claim:
> The point I was trying to make is that the only thing you can say about homosexual men without invoking stereotypes is that they are attracted to men. And in a statistical sense, that is a feminine characteristic.
[...]
> To restate: Male homosexuality can be described as a trait that male homosexuals share with women. If we assume the default about all other characteristics, i.e. that they are distributed in the same manner as they are in other males, then that would mean homosexual men are ever so slightly skewed female in distribution. That's it. Note that the "if" clause isn't a claim I am making, it is simply a proposition on which the argument is predicated. If it is false, the argument no longer stands. I am not making any judgement about that claim, I am only building on it in the hypothetical universe where it is true.
Yes, the only thing we can say about gay men with certainty that distinguishes them from straight men without invoking sterotypes is that they are attracted to men. It does not follow, however, that they are alike in every other way. On this singular dimension, yes, male homosexuals are shifted towards females. However, the original top level comment that we're responding to had used terminology suggesting gay men == effeminate men. Your initial premise is right, but only if we regard attraction as the defining characteristic and discard everything else. If we expand that definition to N-dimensional space as you did, then no, it's very likely not true, because of all the many ways in which gay men are probably shifted away from women.