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Proof you can do hard things

blog.nateliason.com

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Re: Proof you can do hard things

#271

Post by constantcrying »

greatwave1 wrote: post #257
BiteCode_dev wrote: post #248

Earlier quoted context omitted.

> I believe that any perceived immutable barriers or obstacles are almost entirely psychological. Laws of physics are laws of physics. And biology is applied physics. People in sport have known that for a long time. You can train as much as Usain Bolt, he still has a huge advantage. Thinking the other human characteristics are not affected by this is weird. You will never be Von Neumann, no matter how much you spend…

There's a big difference between edge cases like Usain Bolt and Von Neumann, and the barriers that most people actually run into. The vast majority of people are not biologically incapable of making it through high-school level math, or even becoming a very capable mathematician with enough high-quality teaching and dedication.

>The vast majority of people are not biologically incapable of making it through high-school level math, or even becoming a very capable mathematician with enough high-quality teaching and dedication.

It was hard for me to accept, but I know that after many years of University math education there are things I will never be able to understand. I have had very good grades in my Masters, but I realized that I will never be able to do research in pure mathematics.

Almost every person I know struggled with math far more than I did. How would they become research mathematicians if I couldn't after years of study? The belief that secretly almost all people are better at mathematics than me, despite me trying for many years, seems utterly absurd.

Do you think I really am in the bottom ~50% of the population in terms of mathematical ability? Because I know I will never be a pure mathematician.

Re: Proof you can do hard things

#272

Post by BiteCode_dev »

kamaal wrote: post #253
BiteCode_dev wrote: post #186

Earlier quoted context omitted.

That's because math is harder for most people. There is no difference between learning a name in history or in biology, or some workflow. But math reasoning really filters out people in a way nothing else does. All other topics just require memory and basic reasoning. Even physics mostly is hard because of math. And philosophy, mostly because of jargon and references. Otherwise, if you break it down, it's not that co…

>>But math reasoning really filters out people in a way nothing else does. Learning Math is just like learning a language, the issue is the script/alphabet/symbols used to communicate, its dictionary, its grammar are all complicated its hard for common people to get a grip on it. Almost all people can follow logical sequence of arguments provided they understand the language in which they are described. This language…

> Almost all people can follow logical sequence of arguments provided they understand the language in which they are described.

No.

I know people that have been explained repeatedly with absolute patience and love that correlation was not causality, with simple examples. They agree on the moment, but wait a week and they still mix it up again and again.

That's one of the smallest and easiest logical concept to grasp, and they never integrate it.

Practically, in day to day life, mixing correlation and causality served them very well. It's actually often true. But as soon as it's on the news or a graph on the internet, it's over. Because it's abstract.

And the persons are not dumb either: they are very competent in other fields.

Re: Proof you can do hard things

#274

Post by greatwave1 »

constantcrying wrote: post #271
greatwave1 wrote: post #257

Earlier quoted context omitted.

There's a big difference between edge cases like Usain Bolt and Von Neumann, and the barriers that most people actually run into. The vast majority of people are not biologically incapable of making it through high-school level math, or even becoming a very capable mathematician with enough high-quality teaching and dedication.

>The vast majority of people are not biologically incapable of making it through high-school level math, or even becoming a very capable mathematician with enough high-quality teaching and dedication. It was hard for me to accept, but I know that after many years of University math education there are things I will never be able to understand. I have had very good grades in my Masters, but I realized that I will neve…

> Do you think I really am in the ~50% of the population in terms of mathematical ability?

I don't know nearly enough about your personal background to make any sort of judgement on to what extent your success up through university came from innate "mathematical ability" versus other factors.

But I do know that making it through a Masters-level program makes you a very capable mathematician, even if were unable to start a career in pure mathematics.

You made it further along in your mathematical education than 99.9%+ of students, and I have a very hard time believing that "biological predisposition" is what's stopping many people from making it past high-school level math.

Re: Proof you can do hard things

#275

Post by greatwave1 »

blitz_skull wrote: post #241
DarkNova6 wrote: post #206

Earlier quoted context omitted.

> math reasoning really filter out people in a way nothing else does. Disagree. I say: Bad math teachers really filter out people in a way nothing else does. "Here is a list of rules which can be used in specific circumstances. I am not going to tell you why you would need them and the exam will feature several corner cases. Also, I will not provide any examples or detailed explanations because what would other peopl…

You didn't go to the high school I went to. Some people, fundamentally, just cannot do math.

Was it a good school in a wealthy area?

If not, what makes you confident that your peers were falling behind due to some sort of innate inability, instead of as a result of compounding poor teaching or other environmental factors?

Re: Proof you can do hard things

#276

Post by sublinear »

BiteCode_dev wrote: post #212
DarkNova6 wrote: post #206

Earlier quoted context omitted.

> math reasoning really filter out people in a way nothing else does. Disagree. I say: Bad math teachers really filter out people in a way nothing else does. "Here is a list of rules which can be used in specific circumstances. I am not going to tell you why you would need them and the exam will feature several corner cases. Also, I will not provide any examples or detailed explanations because what would other peopl…

True. But even with the best teachers for every field, math or sport will filter out people way more harshly, and sooner, than any other field. You can smooth things out with quality teaching, but there is a human hardware limit, and you reach it sooner with those two. Many people don't like to hear it because their ego is bruised or because it goes against the idea that "everybody can do anything". This is wrong. Bi…

I wasn't the best math student in school and there was a lot I didn't fully understand back then, but I eventually learned it all and more as I got older. I know I'm not the only one. It seems more like a function of time and effort than a "human hardware limit".

Re: Proof you can do hard things

#277

Post by bobwow396 »

andruc wrote: post #9

Everyone commenting so far seems to be missing the forest for the trees. Doing hard things, and the proof that comes with it, is empowering.

Exactly this. The article isn't really at all about calculus, but rather the benefit of challenging yourself more generally. Doing challenging things that push you out of your comfort zone better prepare you to do the things you actually want to do later in life.

Re: Proof you can do hard things

#278

Post by robertlagrant »

constantcrying wrote: post #259
robertlagrant wrote: post #243

Earlier quoted context omitted.

> What am I ever going to use my skills in analysing 20th century literature for. You can use the same skills to spot when a news article is trying to manipulate you. > What am I ever going to use my knowledge about Roman history for? You can see how empires fall, and vote against those things. > What am I ever going to use my knowledge about the structure of our government for? Understanding why things happen around…

You are completely missing the point here. If you know "why empires fall" (nobody does) then you could just teach that, the historical context would be almost irrelevant and even the premise of a cyclical history, which can be broken by voting, seems completely insane. >Thankfully you did all those things, so now you can write a well-written letter to the correct person in government, citing the parallel problems wit…

> If you know "why empires fall" (nobody does)

I said see how they fall. Not every way, and not necessarily why, but how.

> then you could just teach that, the historical context would be almost irrelevant

I don't think you can see how they fall without historical context. That is the how.

> even the premise of a cyclical history, which can be broken by voting, seems completely insane

I didn't mention a cyclical history. Some things repeat, but that doesn't mean in general history is cyclical.

I don't mean to comment in a way that's too much on the nose, but I've just broken out various statements of yours and shown how they didn't follow from what I said. Spending time studying literature in a controlled environment, can help train children to read what's being said, as opposed to what they guess is being said. It's not perfect, but it can help a lot.

Re: Proof you can do hard things

#279

Post by zer8k »

BiteCode_dev wrote: post #186
constantcrying wrote: post #179

I really despise all the "why you should care about math" takes. The question is never asked about any other school subject and only mathematics has to justify itself that way. I had to learn about categories of plants and animals, interpret 20th century literature, learn about events from a thousand years ago, I did presentations on the demographics of European countries, how certain chemicals react and much, much m…

That's because math is harder for most people. There is no difference between learning a name in history or in biology, or some workflow. But math reasoning really filters out people in a way nothing else does. All other topics just require memory and basic reasoning. Even physics mostly is hard because of math. And philosophy, mostly because of jargon and references. Otherwise, if you break it down, it's not that co…

I can second that. I was an pretty good programmer as a kid. I'd go home and write whatever I could imagine on the old 286 box my parents had. I spent time in "gifted" programs at school, etc.

However, I hated math. HATED it. Did so poorly in it through high school I ended up in college in basic algebra. It wasn't until college I found out I loved math and it was only because I got lucky and had a string of amazing professors.

I suspect this is true for other subjects as well. I also hated exercise until I discovered what I liked doing. PE teachers ruined it for me. Runs were terrible because there was no cadence. Push ups were terrible because no one checked form. The entire exercise of pre-college education is a box checking effort to get you ready for the factory. Perhaps we simply need to stop having the unmotivated teach the motivated. This goes true for research professors forced to teach as well.

Re: Proof you can do hard things

#280

Post by satokema »

You should do calculus because it translates to actual problem-solving. Not everything is nice and chunky in discrete - calculus allows you to model and calculate continuous kinds of problems. Even if its not the area under the curve or some infinite series thing, it's a really good intro to modeling things in terms of adding up many small steps.
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