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Proof you can do hard things

blog.nateliason.com

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Re: Proof you can do hard things

#261

Post by blueyes »

This comment is not for or against calculus.

Doing random hard things in order to get into college or get a white-collar job is really no different than pointless test preparation that shows you can follow instructions, and it has produced strange hierarchies such as Qing-era mandarins.

Much better to find something that intrinsically motivates you to do hard things that feel less hard to you. It'll take you further. Or you can prove to the world that you are capable of a yearlong mindless grind...

Re: Proof you can do hard things

#262

Post by foofoo4u »

TheAceOfHearts wrote: post #18

I hate the framing of problems or domains as hard, since it kept me from pursuing them further for many years. And the years later when I tried my hand at those problems, I found that it wasn't nearly as hard as it was being made out to be. Historically many problems have also been hard until people figure them out, and then they stop being considered hard problems. In recent years this has been mostly true of AI-rel…

I've seen the enthusiasm for any subject wither away when a child or teen is told a particular subject is hard, whether that be math, a programming language, or learning a musical instrument. I was this way. In their totality, yes, the subject is hard. But what they aren't taught about any difficult subject matter is that they are achievable by breaking them up into a series of small, easier to understand concepts. Their practical utility grows as the number of these small steps are achieved. And as they are achieved, mini demonstrations of their use should be performed so the student understands the importance and gets exited to continue.

Example 1: "I learned five notes in shape 1 of the minor pentatonic scale. That took a bit of practice, but now I'm able to play a bunch of cool licks. Neat! If I continue this path, who knows what other cool licks I can pull off!".

Example 2: "I learned how to import libraries. My lesson had me register a twillio account. I imported the twillio library into my python script. And I copied some code that'll instruct the library to send me a text message. I don't quite understand these python concepts, but wow, this is really cool; I just got a text message from my computer program. The fact that libraries can give me abilities like these is neat. I can already imagine how I can build some basic automation to leverage them. Who knows what else I can accomplish if I discover more libraries and understand python better to actually build something automated!"

Re: Proof you can do hard things

#263

Post by constantcrying »

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…

The language is the least relevant thing about learning mathematics. It is arbitrary and rooted in historical circumstance.

Saying math is about the language is like saying programming is about learning syntax. It is entirely irrelevant, the meaning is what is important.

Re: Proof you can do hard things

#264

Post by BiteCode_dev »

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.

Just using the extremum to show there is a difference.

The difference is not limited to the extremes. Why would it be?

Hence spectrum.

And math meet people early in the spectrum.

EDIT: thread limit reached, so I can't answer down there.

But in short, it's a HN comment, not a study. But I've been in 11 schools in my life. Some private ones with their own church inside, some for special kids, some for poor kids with a higher degree of violence.

I saw it again and again. The average math teacher is not worse than any other teachers. But the first field kids have a hard time is more often math than other fields. In fact, kids that are good at math usually can do ok in any other, even if not great. The reverse is not necessarily true.

At this point I'm just repeating the argument in the other comments.

Re: Proof you can do hard things

#265

Post by constantcrying »

lolinder wrote: post #256
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…

There's a major chicken and egg problem here—is math hard and therefore it has to justify itself, or is it hard because people don't think it's relevant and so they care less to try?

Why would something being hard mean it has to justify itself?

Re: Proof you can do hard things

#266

Post by projectazorian »

trinovantes wrote: post #220
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…

Math as a field of study might be hard but in my experience math pre grad-school is just memorization as much as any other subject. I studied for my exams by simply doing countless exercises and memorizing every problem pattern to the point where I'm just plugging numbers into a series of formulas, even if I don't fully know why I'm doing so.

Sounds like great preparation for Leetcode interviews ;)

Re: Proof you can do hard things

#267

Post by BiteCode_dev »

jameshart wrote: post #254
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…

Nobody is claiming that 100% of people can be trained to run a 100m in 9.58s. But there is some number of seconds which 90% of people can be trained to run 100m below. And it wouldn’t surprise me if it’s a much lower number than you think. Likewise not 100% of people can develop the mathematical horsepower of Von Neumann. But 90% of people can attain some level of proficiency in higher mathematical concepts… how high…

I don't disagree with any of this, I'm just stating math is a topic that shows the limits of people quicker in the curriculum than other fields.

Re: Proof you can do hard things

#268

Post by lolinder »

constantcrying wrote: post #265
lolinder wrote: post #256

Earlier quoted context omitted.

There's a major chicken and egg problem here—is math hard and therefore it has to justify itself, or is it hard because people don't think it's relevant and so they care less to try?

Why would something being hard mean it has to justify itself?

Because why put in the effort if it isn't going to bring any benefit? An easy subject can be swallowed even if you don't see the purpose because it doesn't cost you much.

That said, I lean towards the other option: it's considered a waste of time, so no one puts in the effort, so it seems harder than it really should be.

Re: Proof you can do hard things

#269

Post by projectazorian »

paulcole wrote: post #200
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…

> The question is never asked about any other school subject Are you kidding? Every tech-bro on the planet makes their disdain for literature, philosophy, etc. extremely well known.

Now now, let’s not be unfair, a bit of room is permitted for surface level study of classical philosophy, maybe some Nietzsche.

Re: Proof you can do hard things

#270

Post by greatwave1 »

BiteCode_dev wrote: post #264
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.

Just using the extremum to show there is a difference. The difference is not limited to the extremes. Why would it be? Hence spectrum. And math meet people early in the spectrum. EDIT: thread limit reached, so I can't answer down there. But in short, it's a HN comment, not a study. But I've been in 11 schools in my life. Some private ones with their own church inside, some for special kids, some for poor kids with a…

What evidence do you have that the biological limitations for mathematical ability meets people early in the spectrum?

I can think of several anecdotal counter-examples... students who seemed to have been falling behind, but with the right teacher were able to make significant improvements and become a top performer.

You can also take a look at many of the studies done on the educational gap, to see that better schooling can have a massive impact on secondary and post-secondary educational outcomes. Surely this wouldn't be the case if poor performers had some "biological limit" that prevented them from succeeding in high school math.

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