Can progressives be convinced that genetics matters?

> I’m absolutely convinced that not all people can learn algebra or calculus. To me it is obvious this is so since the mentally disabled can’t.

Not all people can read, it's obvious since the mentally disabled can't. Yet with proper education, all non-disabled people can be taught reading.

But that doesn't mean everyone can read, if you're illiterate by your 20s, you're gonna have a hard time catching up. Same for mathematics: most people reaching even high school are too mathematically illiterate to catch up[1]. Is genetics a factor: definitely, but it's among many others.

The reason why it's a partisan issue is the following: if I say genetics is a decisive factor, then I can say «it's natural, there's nothing we can do so we don't need to spend all that government money trying to help those people». The left-sided point of view goes as «There's nothing we can do about genetics, but we can change everything else. Then we need to find what are all the other factors, because those are the actionable ones». The conservative focus on genetics is mainly a justification for doing nothing.

> There’s a level of “intelligence” that’s necessary to learn a given topic. Not everyone can learn all topics.

“intelligence” is conveniently pretty ill-defined, but I don't think I'm more intelligent than my doctor friends, yet they struggled a lot to grasp even the most basic concepts of algebra when I tried to help them during our studies. “Not everyone can learn all topic” but I have yet to find evidences that your ability to learn a random topic you're not interested into is correlated with the common acceptance of the word “intelligence”.

[1]: that doesn't mean it's impossible, just likely well beyond the amount of effort they can (or want to) afford.

My feeling with math is that moving on too soon is disastrous. If you move past a subject without having grasped it, you don't have a good base for the next subject. This compounds, and the explanations stop making sense.

At that point people are trying to help you but saying things to you as if you are stupid, but you still don't understand. That really sucks, so people get afraid of math. Avoiding it, and nodding when asked "do you understand" when really they do not. This is hard to fix because you need to go back to the point they did not understand, but the fear and pain makes even teaching that a lot harder to fix as well.

My feeling is that most people should be able to understand algebra. However, I think that requires a very deliberate and personalized approach for some people. Certainly with collective classes, if you go at the speed of the slowest student there will be slow progress and a lot of people who are bored and mentally check-out.

If any approach is going to work for people who have real difficulties, it needs to be small-scale personal teaching, and it needs to come with trust. Someone needs to feel like they can keep saying "no I do not understand" without disapproval, disappointment, or frustration from the tutor.

Yeah, but the whole debate is about how much is genetics responsible for intelligence vs the environment. There was a claim that genetics is responsible for ~70-80% of variance. Pick any intellectual ability and lack of environment can cause for an individual to not be able to achieve that, so how can genetics be responsible for that much variance?

The question is where and how does the 70-80% come? How is it meaningful and how is it measured?

I'll go one further and say that very few people in the entire human population would be competitive with Usain Bolt in the 100 meter when he was setting records, no matter what kind of training they had. There would be a few more beyond the world class sprinters Bolt was demolishing. Similarly, there would be very few people who could beat Nadal in 5 sets on a clay surface. Djokovic happens to be one of those few. But, those are extreme outliers.

Still though, we could ask how many people in the entire human population could run under a 4 minute mile with any amount of training, time and resources? Obviously more than have done it, but how many? Certainly not remotely close to everyone.

>Math notation is very consistent and it’s optimized for convenience.

Hard disagree. The most important thing I learned is that it is all made up on the spot to the point that the lecture material explicitly says that books have used 6 different forms of notation for the exact same concept. When you understand that you drop any pretense of "design" in the notation. That helps you abandon foolish ideas that it is "consistent" and that the only thing it is optimized for is the author. When you understand that then it's just a meaningless barrier to overcome but it also becomes easy to overcome precisely because it is that trivial. You just get used to it and e.g. learn the alphabets of the dozen languages (including klingon because the lecturer had to make that joke) from which the variable names where sourced from. Once you did the meaningless grind the barriers are gone.

> People who complain about notation usually actually have problem with the substance, and the complaints about notation is just a coping mechanism, to deny hurtful reality that one can’t understand something hard, blaming external factors instead.

No it is quite simple. You can't understand an easy or hard concept if you can't read it. I still remember how I understood nothing in the first semester. Then when I was preparing for the exam everything was extremely easy because the notation was understood by that point.

>If you have some concrete suggestions about mathematical notation, ways it could be improved in more than superficial manner, I (and the rest of mathematical community) is very much open to hear them.

As I already said that is meaningless because there is no universal notation. "The mathematical community" will adopt a fraction of proposals and further splinter into separate "factions".