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Proof you can do hard things

blog.nateliason.com

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Re: Proof you can do hard things

#181

Post by throwbadubadu »

l__l wrote: post #155
throwbadubadu wrote: post #152

Earlier quoted context omitted.

But what is the general application of category theory, outside computer science.. and even there the average programmer who hasn't some type theory experience will stare at you with huge eyes when you mention it.. I love the wikipedia intro: Calculus is the mathematical study of continous change, the same way geometry is the study of shape and algebra... that's it perfectly. And the most basic application is in ever…

This is my field :) Category theory is about connecting the dots between different areas of maths. The "general application" is to allow you to reason over the structure of a problem you're interested in, while throwing away all the superfluous details. It arose when geometers and topologists realised they were working on the same problems, dressed up in different ways. I think the utility for technical people, from…

Don't need to convince me ;), but I mean this is for the very average person who argues like "why do I need more math than adding two numbers"... and even just "allow you to reason over the structure of a problem you're interested in, while throwing away all the superfluous details" and "learning to do abstractions correctly" would not seem more approachable to them than the calculus description I gave above? imo. Is there a simple real-life problem or model everyone should know or has touched in school this can relate to? I'd be curious, because as you frame it I may even need to revisit my faded memory, hm.

Re: Proof you can do hard things

#182

Post by rmbyrro »

jokethrowaway wrote: post #151
szundi wrote: post #108

Earlier quoted context omitted.

True when you happened to find just one of the soon best paying new activities. Catching butterflies would have worked out less awesome probably.

If you escape the employee mentality you can turn almost anything into a small business which provides value to the world. I really wish the world economy would be structured like this, with smaller entities taking more risk and responsibilities and less enormous corporations filled with people hating their lives.

Selling is the hard part of this world view. Most people don't have a well-suited psychological framework and it's hard to develop one. It's difficult to tell if it's even possible for so many people to become minimally good at selling to support themselves financially through a small venture.

Re: Proof you can do hard things

#184

Post by throwawybb1 »

phforms wrote: post #166

It’s really interesting how we shy away from some “hard” things, even though there is literally nothing at stake that could prevent us from doing them. Nothing life-threatening, no (or minimal) risk of physical or psychological damage, no social exclusion, no irreversable decisions about the future to make. Why can’t we just try/do it – what are we so afraid of? Many people (especially those in a lucky environment) c…

> It’s really interesting how we shy away from some “hard” things, even though there is literally nothing at stake that could prevent us from doing them. Nothing life-threatening, no (or minimal) risk of physical or psychological damage, no social exclusion, no irreversable decisions about the future to make. Why can’t we just try/do it – what are we so afraid of?

Heh, I don't know about that.

I got into motorcycles because of how dangerous they are. When I was just learning dirt riding I specifically picked out an old barely used logging road to do so. It's 2 hours from the nearest town, about 40 miles long winding road with a sheer drop on either side.

Getting there is tiring in of itself. Every time I started it, I was already fatigued from the ride out and I just go straight in without a break. But there's very little room of error. There's no cellular service, traffic is almost non existent. I don't tell my family when I got out there or where I am exactly. If I overcook a corner, loose focus for more then a second, fail to spot where the road's been eroded out, make just one little fatigued induced mistake... that's it. There's no getting out. There's no help coming. They won't even have my body to bury.

Finding the strength to crank the throttle wide open and hold it open right until the last millisecond before disaster is hard as hell when every instinct is screaming to slow down.

But in many ways, it's easier then trying to make friends or ask a someone out on a date. If and when I do make that fatal mistake, I don't have live with the knowledge that I screwed up a relationship or have to live with the regret what may or may not have not have been. Or worse; disappointing those who's opinion has weight.

Dying is easy. Living with the consequences is hard.

Re: Proof you can do hard things

#185

Post by uwagar »

jokethrowaway wrote: post #150
hardware2win wrote: post #141

>You know they will never use it in adulthood, outside of certain career choices. If somebody says stuff like this, then they do not understand math, imo. Im a little bit sad whenever somebody argues for math by using "no phone available at the moment" argument. Math is insanely powerful world modeling tool. Starting from calculating right amount of fence for your garden, to estimation of 500km route arrival time whi…

I don't get why calculus is always brought as an example. It wasn't particularly hard, the entire class had to learn it in high school. We all had it (in a slightly harder shape) in every university course (no matter how detached from what we actually needed) I forgot all my calculus after high school, had to relearn it in uni and then I promptly forgot again. Exactly as the article says, it was more about proving we…

calculus wasnt memorable to you?

Re: Proof you can do hard things

#186

Post by BiteCode_dev »

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 complicated.

But you can break down a math problem as much as you want, some of them are beyond what you can do comfortably. And a lot of students reach this limit early in their life.

I see this when I play board games with people: there is a threshold of rules and calculation power above which I lose 90% of the players. They just can't enjoy it, because it requires too much effort to play.

It's similar for me and sport. I've been doing exercise all my life, but my brother will always do more, and harder, because there is a barrier after which it's just too painful for me.

Math and athleticism can be trained, but there is a hard ceiling. And even before you reach that ceiling, closing the gap gets more and more expensive for some people, so much the ROI is difficult to justify.

Re: Proof you can do hard things

#187

Post by HellDunkel »

gjadi wrote: post #133
HellDunkel wrote: post #131

I am not convinced „doing hard things“ should be a top priority for kids. For my own kids -or actually everyone- i hope they find a passion big enough to make a living. This takes time and lots of experimenting and cannot be forced into existance. Grinding through „hard things“ can leave you with a great deal of confusion. It is so much easier to do „hard things“ if you love doing them. The problem with math is: it i…

I recommend reading So Good They Can’t Ignore You: Why Skills Trump Passion in the Quest for Work You Love from Cal Newport for a different perspective on this.

Thanks. I am sure there are some valid points to be found in this book but my own experience is enough for me at this point. I have worked in jobs where i was doing great and received positiv feedback- even earned more than today. Still hated it and moved on- best decision i could have made.

Re: Proof you can do hard things

#188

Post by aleph_minus_one »

jebarker wrote: post #17
kickaha wrote: post #8

Am I just hopelessly old fashioned? Or is this not most of the justification for bachelors degrees?

I suspect it's the justification for many PhDs. If you don't go into academia then chances are the content isn't that relevant, but the experience of having to problem solve in uncharted territory is a great confidence booster and skill to have.

> but the experience of having to problem solve in uncharted territory is a great [...] skill to have.

While I do love to solve such problems, in many business areas there are hardly any hard problems to solve as part of your job: either because they don't exist, or because hardly any boss would be willing to let you work focusedly for years to potentially solve one the hard problems that do exist (which is what a PhD in mathematics or physics is about).

Re: Proof you can do hard things

#189

Post by constantcrying »

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…

What I specifically dislike is the question "what am I ever going to use this for" or versions of it. Which I only ever hear about mathematics, but which can be asked about every other subject as well.

Yes, math is hard and definitely not for everyone, which I think is perfectly fine. But arguing that something has no use to you, because the first time in your life you actually have to engage in complex logical thinking is just lazy. The value of mathematics is independent of how hard it is.

Re: Proof you can do hard things

#190

Post by aleph_minus_one »

BWStearns wrote: post #94
codeisawesome wrote: post #81

Feels like many other comments here are trivial objections for the sake of sounding contrarian. Or even, humble bragging about how easy math was to the commenter. I found the article to be a great, new (to me), and widely applicable perspective on the matter.

It's almost like no one finished reading the post (emphasis added). > I don’t particularly care what grades my kids get once they start school. But I do care that they consistently prove to themselves they can do hard things. If Calculus is how they want to do it, fine, but there are many, many more options. Separately, as someone just recently learning calculus as an adult now I'm digging the obliviousness of the "m…

> I get where y'all are coming from but there's a deep lack of empathy there. Go teach some people something (anything) and learn that other people's brains don't necessarily contain your knowledge.

Concerning the empathy point: I do believe that to become good in mathematics, you seriously have to believe that everything in mathematics is actually easy, and you either don't work hard enough (so you fail understanding it; solution: work harder) or you are too stupid to understand the material (which means that you should better work even harder to understand the material to compensate for this weakness).

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