It's a standard concept in high school math, at last when I went to school.

In my experience back at school, the best math teachers would be those who explained mathematical concepts so that they could be readily understood and didn't sound like just mumbo-jumbo.

They don't offend me in the least in principle -- I am attracted to girls, you know. Even 3-year-olds.

I believe the idea of acting on them, and therefore breaking the established paradigms and the preferred power hierarchy between older and younger people currently pervading society, is what offends you. Not the attraction base in and of itself.

But my judgment about how girls (at least 99% of them) operate and think and develop leads me to oppose it for their sake.

How 99% of them operate is how society allows them to with its combination of legal and cultural controls, and your arguing that this represents the "natural" state of girls is beyond delusional. Which is why I do not think you seriously believe that, but simply have to promote it to justify your stance. Since it's well known that different groups of people have always behaved differently in situations where they lacked their freedom of choice and expression as opposed to environments where they did, you are playing another major case of dirty pool here that I doubt any objective reader is failing to notice.

There's a law against it, right? Everyone knows the law, right?

And that automatically determines whether or not the action in question is actually inherently harmful or not? You are being willfully ignorant of the very concept of "vice" laws, which are all about moralism and actually cause more forms of demonstrable harm than they prevent. Which is why the War on Drugs is finally being heavily challenged and it's now harder for LEAs that benefited from such laws to justify them any longer.

Even if the law is unjust I don't see any reason for outrage on behalf of those who break it.

There is the major of outraging on the unjust law itself. That is not the same thing as encouraging someone to break it (since breaking laws carry consequences of their own), but it does suggest sympathy for those who are hurt by unjust laws.

I think the social security tax on wages is unfair and should be replaced by a slightly higher rate on the progressive income tax. Will I be outraged at legal penalties leveled against those who (somehow) manage to avoid paying it? No, I work to change the law.

Which is precisely what pro-choicers are doing, Ethan! And which you routinely disparage us for doing.

Until then, it's understood you've got to follow it.

And...who is doing or suggesting otherwise here? However, you also do not see me showing a lack of sympathy for people who are arrested for smoking marijuana or or willingly engaged in sex work, as if those who do break unjust laws deserve contempt, even though we shouldn't be encouraging the breaking of laws. Unjust laws will be broken at times, and that is to be expected.

Underlying a lot of these disagreements is the frequency distribution -- how many girls actually want these relationships?

This is one of your most pervasive dirty pool arguments that go against both recent studies and deliberately ignoring the political and legal situation that anyone who is underaged currently finds themselves in.

The attraction base of mesophilia, recently officially designated as such by an important 2016 paper by Dr. Michael Seto, makes it clear that not only is this attraction base real, but a significant minority of younger people may have it.

And with the values of democracy, even one person having certain desires or a certain opinion should be allowed to express either.

In this little pond you mostly say it's substantial, everywhere else in society people think it's extremely low.

Because like you, most people can afford to believe that since younger people know they will be severely punished if they express that desire, since they have no civil rights and that particular type of desire is particularly volatile, that they can simply pretend we are seeing kids in their "natural" state. In fact, their parents would likely be heavily censured if they allowed them to express such feelings. The "everywhere else in society" you mention is euphemism for the adults who have legal control, and you know it, but you always appeal to the dictates of the consensus.

Of course, that "everywhere else" does not include various objective researchers, but you have also always conveniently ignored research conclusions you do not agree with as if they do not exist. Hence, when you repeat this line over and over again, as you always have, you are not only showing contempt for democracy and willful ignorance of recent scientific studies, but you are denying a very obvious legal, political, and cultural reality you are playing every reader for a fool.

I've raised this before,

Yes, ad nauseum, been effectively refuted every single time, and then went back to parroting it over and over yet again since that is how propaganda works.

but I'm going to do it again, with commentary: Some adults feel a profound desire to have a limb removed to make themselves in line with their self-image (it's in line with our support of trans people transitioning). Society lets them do this.

As Hadjuk recently observed in a straight to the point fashion, you make some of the most god-awful and desperate analogies one could possibly imagine. But please do keep saying them over and over again, because they definitely do have an effect on readers. Not the one you want, of course, but definitely an effect.

Now, presumably some children would also like this -- they feel profoundly wrong with that extra leg when they only want one. Yet society will not permit this. What an outrage! Denying children the right to self-determination! The main reason I oppose this is that I think the baseline rate of genuine desire for this is extremely low, and the chance that something else is involved (depression, a desire to be a rebel, etc.) in such a request is much higher.

So, because your ideology demands pigeon-holing every single mesophile out there as having ulterior motives for expressing those feelings--another common use of assumptions to justify a certain type of legal or psychological censuring--you believe the laws should be based on making such assumptions, and therefore making decisions for other people based on what you think instead of taking each one on a case-by-case basis.

Just like it's often presumed that the reason I date much younger women of legal age instead of middle-aged women is because I'm allegedly looking for an "easy conquest", or because I am "unable to get" older women, blah blah blah, assumption assumption assumption; or that younger women who have chosen to be with me are automatically suffering from "daddy issues," or felt "compelled" by my "superior worldly older man authority," blah blah blah assumption assumption assumption. All of which is utter nonsense, and not just in my case alone.

This prejudiced, presumptive attitude has even reached the point that the administration of legal dating sites like Match.com actually disallows older men who pay for an account there to contact any of the younger women of legal age who are more than ten years younger, and refuses to allow younger women with accounts the option to designate who they are willing to accept contacts from so they can opt in or out of appearing in searches by the men there. Instead, the administration decided there is "no good reason" for older men to seek out relationships with younger women on the site, and have decided for the younger women as to who they can receive messages from.

You are doing the same thing here, and setting policies based on popular prejudices (not the feelings themselves necessarily, but the right to act on them) sets the precedent where it is eventually applied to people who are considered legal adults in various ways. By not allowing people in a certain demographic to prove their feelings are natural feelings and not due to some ulterior motive, you create a type of deliberate self-fulfilling prophecy that you think creates the illusion of "proving" you are right. Which is like putting bars on a dog house to keep the dog in there and then claiming the reason the dog doesn't leave is because she clearly doesn't want to.

In the past, the GC reaction has been, "How dare you compare a desire for limb removal with consensual sex!"

Because many people on GC tend to think logically, and expect logical analogies that can be readily applicable to the world we live in. Then again, outrageous assumptions tend to result in outrageous analogies.

That's an example of an appeal to emotion rather than reasoning if anything is (what I get unfairly accused of).

It's actually an appeal to logic and common sense. But worry not, you are not likely to ever get accused of that too.

So maybe you're profoundly prejudiced against those who want a limb removed and it's showing.

Your awful analogies are becoming hilarious. Please continue them!

If not, then why? What makes it relevant in my mind is the role of extremely low probability as trumping self-determination as a principle that overrides everything else.

Which can equally be applied to disallowing opinions that are so unpopular and thus so marginalized due to heavy corporate and/or state censorship that it can be argued there is no need to actually allow it or consider it at all. You know, do to the illusion that so few people harbor it. Coincidence, Ethan? I doubt it, since that is how your anti-democratic justifications work and where their historical ancecedents always seem to lead.

I can achieve a better understanding with anyone who concedes this point

In other words, anyone who comes to agree with you that assumptions and anti-democratic policies can often serve the greater good. Or, at least to appeasing the greater consensus. No thank you, Ethan, I do not care to reach an understanding with you if the price for it is every principle that democracy and the notion of civil liberties are supposed to be based on.

and we know our difference has to do with that estimation of how often girls really do badly want sex with older men.

Putting your crude and emotionally loaded way of saying it aside: I think it's clear younger people prefer freedom of choice over all. And I think there are many mesophiles out there, based on sound research and much personal experience with mesophiles of legal age--both romantically and those who have visited this community--who would readily desire to form romantic relationships with older men (and women). And they would not always take the form of "having sex," meaning intercourse, which you are so quick to imply by wording it that way. Particularly in the case of children, they would likely take the form on a physical level of nothing more than cuddling, kissing, and simple touching.

As for perfectibility, "people naturally gravitate towards tasks that they have a natural aptitude for" may work for many,

I think it works for everyone who has ever enjoyed doing a certain task, and happens to be good at it and take pride in their work performance as a result.

but thinking it will work for everyone (or almost everyone) requires a rosy view of human nature.

Once again, the demonization of human nature that underlies your entire alarmist, anti-democratic, misanthropic policy system, which is solely based on how people behave in a very specific type of environment that is not exactly conducive towards encouraging good and fair behavior. This is comparable to the argument that because you observe people born and raised in a society where cannibalism is heavily practiced, that proves humans naturally gravitate towards cannibalism regardless of the environment they live in. The pattern is quite clear, as it underlies the bulk of most of your arguments.

Experiments with collective agriculture have generally been miserable failures.

Because such tiny communities were unable to access the resources that were controlled by a larger society surrounding them which controlled the technology and methods of exchange. A tiny community cut off from the rest of the world and still dependent upon interaction with it on its own terms for many things cannot provide freedom from want, and lacks the means to provide everyone with work opportunities in an area of endeavor in which they excel. It would require a few very specific skill sets that would have little use for many who had skill sets outside of producing crops and animal husbandry.

Benefits are shared equally between those who work hard and those who don't,

Actually, as noted, such tiny and relatively insular communities cannot provide work for people outside of a few specific required skill areas that relate to agriculture, simple construction, and working with animals. Hence, you get people who are good at the few required tasks working hard and those who lack one of those few skills sets only doing what they have to do and nothing more. Such mini-communities are also unable to provide work opportunities for those who are not able-bodied but could still contribute intellectual work and would work very hard indeed if afforded such opportunities because it was what they excelled at. Thus, such mini-communities separated from yet still dependent upon acquiring the resources of a greater society around them were logically destined to fail.

and as a result few people work hard and it collapses.

Because such a mini-community was extremely ill-suited for individuals who did not have a few very specific set of skills; because they were unable to actually provide freedom from want for everyone who worked hard, since they were materially incapable of an abundance for all; and because they lacked access to the productive technology of the greater society and were thus still required to barter with it via currency for much of what they needed. That was not human nature at fault, but an example of material-based reality and restrictions such tiny communities had to work under. That is why they invariably collapsed. Blaming "human nature" is a way to try to convince the 99% on the planet not to strive to create a better system based on such values, which would indeed be viable if practiced on a global scale with all available technological and virtual resources behind it. In the latter case, fulfilling jobs could be provided for everyone based on their skill set and individual temperaments, and human behavior overall would improve dramatically.