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> 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 wh

> 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.

godelski 2y ago
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?

godelski 2y ago

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?