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Proof you can do hard things

blog.nateliason.com

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Re: Proof you can do hard things

#151

Post by jokethrowaway »

szundi wrote: post #108
bruce511 wrote: post #102

This resonates a lot with me. At school I coasted, ignored all home work, never studied, and was a consistent C. I was continually told I could fo better by putting in some work (an objective viewpoint I agreed with.) But i had better things to do. I started programming in grade 7, from a book, with a Apple 2 (circa 1982). There were no forums, no Internet just me and a thin booket that came with the computer, plus l…

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.

Re: Proof you can do hard things

#152

Post by throwbadubadu »

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…

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 everyone's life and also one of the basic physics thing: The relationship between location, speed and acceleration. I find this very essential, vs category theory at least..

Re: Proof you can do hard things

#153

Post by l__l »

raincole wrote: post #145
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 think you need calculus to calculate right amount of fence for your garden. > Since math modeling is everywhere in "modeling" industries like engineerings, financial-ish jobs and othet In other words, certain career choices, as the OP says.

This makes the same mistake being called out in the comment you're replying to. The point isn't about the mechanics of solving a differential equation, it's about gathering the intuition about a way of approaching problems.

(Also, while it might not be the tools needed for the average homeowner, there are plenty of optimisation problems similar to "how much fence do I need" which are most easily solved by solving the Euler-Lagrange equations)

Re: Proof you can do hard things

#154

Post by hardware2win »

raincole wrote: post #145
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 think you need calculus to calculate right amount of fence for your garden. > Since math modeling is everywhere in "modeling" industries like engineerings, financial-ish jobs and othet In other words, certain career choices, as the OP says.

No, it is side effect while the goal is modeling which can be applied in your whole life, not just job.

Re: Proof you can do hard things

#155

Post by l__l »

throwbadubadu wrote: post #152
jokethrowaway wrote: post #150

Earlier quoted context omitted.

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…

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 this perspective, is pretty clear.

As for the general working person? I think it's just an exercise in learning to do abstractions correctly, which is valuable in any line of work.

There are actually people who advocate that we should base maths education on category theory much earlier (much as New Math was interested in teaching set theory early on, as a foundational topic). CT is an unreasonably effective tool in a large section of pure maths, so this doesn't sound unreasonable to me; it wouldn't be nearly so scary if it were introduced gently much earlier on (in the same way we start to learn about things like induction in the UK in secondary school, long before formalities like ordinals are introduced at uni). Currently only a very specific, highly-specialised section of the population learn CT, but if something like this were to happen, I'm sure we'd see lots of benefits which are hard to identify at the moment.

Re: Proof you can do hard things

#156

Post by _v7gu »

throwbadubadu wrote: post #152
jokethrowaway wrote: post #150

Earlier quoted context omitted.

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…

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…

Analogies are akin to morphisms, and I'm pretty sure everyone has used at least one analogy in their life.

Re: Proof you can do hard things

#157

Post by bbbobbb »

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…

I think that it is a US specific obsession.

I don't even know what "calculus" is really.

I have had plenty of math classes both in high school and later at university but I don't recall any significant distinction that would leave me with some concrete idea of "algebra" vs. "calculus" vs. "whatever" years later.

Re: Proof you can do hard things

#158

Post by beeforpork »

This is similarly true for finishing a degree. Luckily, that occurred to me before finishing a degree, because that did feel futile. But finishing a degree proves that you can finish stuff. That's valuable proof for yourself and when you need to give an impression.

The topic itself really doesn't matter that much -- which is also good, because then you can freely choose it to your liking, if possible.

TL;DR: I think this is very helpful advice to people who question stuff.

Re: Proof you can do hard things

#159

Post by Etherlord87 »

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'm using math(s) a lot, trigonometry, matrices, algebra… But most of my friend, family, I couldn't convince to learn math just based on the argumentation they can use it in practice.

Yes, calculating the right amount of fence is useful, but not only (as someone pointed out) you don't need a lot of math for that, people just take take a ruler on the plan, or count steps in field, going across the entire length, then estimate, and it works.

> estimation of 500km route arrival time while taking traffic statistics into the account

Who does this? How would you convince a friend to learn math in order to do this? What people do is they remember how long a 200 km route took and so they estimate the 2.5× longer path will take 2.5× more time.

We need examples of real world math applications, because such examples are scarce across the Internet.

Re: Proof you can do hard things

#160

Post by DrScientist »

l__l wrote: post #153
raincole wrote: post #145

Earlier quoted context omitted.

I don't think you need calculus to calculate right amount of fence for your garden. > Since math modeling is everywhere in "modeling" industries like engineerings, financial-ish jobs and othet In other words, certain career choices, as the OP says.

This makes the same mistake being called out in the comment you're replying to. The point isn't about the mechanics of solving a differential equation, it's about gathering the intuition about a way of approaching problems. (Also, while it might not be the tools needed for the average homeowner, there are plenty of optimisation problems similar to "how much fence do I need" which are most easily solved by solving the…

Interesting I've seen the opposite in highly trained mathematicians - they can really struggle with taking an intuitive leap without the safety net of the working out the numbers.

While it's always better to work out the numbers if possible, sometimes it isn't possible and people get trapped trying.

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