In fact, the vast majority of my friends did, so my mental model is more useful to me than one that apportions a larger cut to the rest of the population. I also find it egregious that thirteen years of schooling doesn't get everyone to this level, so I want to hold the education system accountable by not loosening my standard.
> If [almost] no one actually learns it in high school then a phrase like "you only need high school knowledge" means nothing to most people.
I agree that this isn't as good at conveying information (unless the consensus changes), but that's not all I'm trying to do.
This is the point though. If you know your mental model is wrong, you should update your model rather that perpetuate the errors. It's okay to be wrong and no one is upset at you for being wrong (at least not me). But if you are knowingly wrong, don't try to justify it, use the signal to help you change your model. I know it isn't easy, but recognize that defending your bad model makes this harder. It is okay to admit fault and you'll often be surprised how this can turn a conversation around. (FWIW, I think a lot of people struggle with this, including me. This comment is even me trying to reinforce this behavior in myself. But I think you will also be receptive because I think your intent and words diverged; I hope I can be part of that feedback signal that so many provided to me.)
> so I want to hold the education system accountable
So hold them accountable, not the people in these. I think you intend to blame the system, but I think if you read your message carefully, you'll see a very reasonable interpretation is that you're blaming the person. It is because you're suggesting this is a level of math that everyone should know.
For a frame of reference the high school I went to is (currently) in the top 20% of CA and top 10% of the country. I checked their listings and while there's a 50% participation rate in AP (they also have IB), they do not offer Linear Algebra or anything past Calc I. So I think this should help you update your model to consider what opportunities people have. I think this is especially important because we should distinguish opportunity from potential and skill. I firmly believe metrics hinder the chance of any form of meritocracy in part due to the fact that opportunity is so disproportionate (more so due to to the fact that metrics are models. And you know what they say about all models ;).
If we want to actually make a better society and smarter population, we should not be diminutive to people for the lack of opportunities that are out of their control. Instead I think we should recognize this and make sure that we are not the ones denying opportunities. If we talk about education, (with exception at the extreme ends) I think we can recognize that the difference between a top tier high school student and a bit below average, is not that huge. Post undergrad it certainly grows, but I don't think it is that large either. So I'm just saying, a bit of compassion goes a long ways. Opportunity compounds, so the earlier the better. I'm fond of the phrase "the harder I work, the luckier I get" because your hard work does contribute to your success, but it isn't the only factor[0]. We know "advanced" math, so we know nothing in real life is univariate, right? You work hard so that you may take advantage of opportunities that come your way, but the cards you are dealt are out of your control. And personally, I think we should do our best to ensure that we the dominating factor that determines outcome is due to what someone can actually control. And more importantly, we recognize how things compound (also [0]).
I'm not mad or angry with you. But I think you should take a second to reevaluate your model. I'm sure it has utility, but I'm sure you're not always in a setting where it is useful (like now). If you are, at least recognize how extreme your bubble is.
> I think we should do our best to ensure that we the dominating factor that determines outcome is due to what someone can actually control.
I think this is where I'm coming from as well. When I got to university, I met tons of people who were just connected to the right resources, be they textbooks, summer camps, math tutors, or college counselors. My lucky break was a smart father and learning about AoPS in 4th grade, but I still wish I knew what else was out there.
It'd be great if people didn't need to get lucky to learn this stuff. There is a whole group of people paid to set standards and make people aware of what is out there. The standards filter down from the board of education to the teachers, and the teachers don't actually have much sway in what they teach (re: r/teachers). So, my ultimate goal for imposing my definition of "high school math" on everyone else is to make it common enough that the standards reflect that, rather than a slow trend of weakening standards that has happened in the past few decades[*].
But... now that I type this all out, it seems pretty far removed, and probably does more harm than good (except in my bubble). It'd be much more effective to send a few emails or get myself elected to one of these seats.
[*]: Note, standards have obviously risen since the early 1900s, but they've actually fallen in the last twenty years.
And I think you hit on a good point. It's harder to know what we don't know and easier to think we do.
Another thing I think about a lot is Hanlon's Razor. I think people misinterpret it because the term "stupidity" is often used harsher. Maybe because we don't want to admit that we're all stupid[0]. I also despise the phrase "good enough" because many times the details do matter. It's not that we shouldn't approximate things, but that we often use this phrase to dismiss nuance. It's an unfortunate consequence of weak feedback signals. In the same way as if you fix something before it is broken you will save a lot of time and money, but the signal isn't apparent because you don't have the counterfactual experience of running around like a chicken who's lost it's head when shit hits the fan (but you probably have somewhere else).
So, we're all wrong, right? It's not like there's anything objective we can actually hold onto. But there are things that are less wrong, and that is meaningful. But the environment moves and time marches, so it's important we ensure what was once less wrong doesn't become more wrong. If our beliefs are unmoving, we'll only become more wrong with time. And that doesn't seem to be any of our goals and this fact doesn't sit well with our ego that creates that unmoving force in us.
FWIW, I'm highly in favor of younger kids learning much more difficult math. I've seen studies of how kids as young as 5 can learn core concepts of calculus (hell Terrance Tao exists). I'll settle for Middle School lol.
[0] In one framing I think our stupidity is impressive. We're bumbling chimps who can barely communicate with one another. Yet look what we've accomplished! I find this quite motivating, but it does not allow me to forget how foolish I am. Besides, if there's nowhere to move up, what would be the fun in that?
> I know many people who did take...
In fact, the vast majority of my friends did, so my mental model is more useful to me than one that apportions a larger cut to the rest of the population. I also find it egregious that thirteen years of schooling doesn't get everyone to this level, so I want to hold the education system accountable by not loosening my standard.
> If [almost] no one actually learns it in high school then a phrase like "you only need high school knowledge" means nothing to most people.
I agree that this isn't as good at conveying information (unless the consensus changes), but that's not all I'm trying to do.