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Proof you can do hard things

blog.nateliason.com

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Re: Proof you can do hard things

#61

Post by lcnPylGDnU4H9OF »

bigger_cheese wrote: post #38
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…

Rightly on Wrongly some areas of study have the reputation/stigma of being difficult attached to them. Back when I was a high school student math (not just calculus - but the entire subject of mathematics) had this reputation as being a "hard" subject as a result scores of my fellow students just decided math is to difficult I'm not going to engage with this. I suspect this is related to a fear of failure or kids bei…

> math (not just calculus - but the entire subject of mathematics) had this reputation as being a "hard" subject

To me it seems like a lot of the fault was with the curriculum: basically full steam ahead regardless of the class’ understanding. That’s especially bad in math when each chapter uses what the previous taught.

But the point about adult salaried professionals complaining that they supposedly can’t figure something out is disappointingly relatable. I generally believe that most people are "smart" and just don’t tend to bother using their brain as a muscle and that seems to make it doubly irritating to hear such complaints.

Re: Proof you can do hard things

#62

Post by jskherman »

lcnPylGDnU4H9OF wrote: post #43
jimmydddd wrote: post #42

Earlier quoted context omitted.

I saw an article where they asked a bunch of scientists and engineers if they actually used calculus in their professions. None of them did. They used Excel and the R programming language.

What did they do with Excel and R?

As a chemical engineering student, it's a whole lot of formulas cobbled together to spit out calculations that would otherwise be done on hand (especially empirical methods that compute estimates where a clean answer is not possible like $\int{\frac{\sin{x}}{x}}$).

The formulas usually come from what you study in school (e.g. the Redlich-Kwong equation in Physical Chemistry to estimate the properties of real/non-ideal gases).

What's neat is that before computers were popular in the early 20th century, these calculations (mostly empirical equations' iterations) had to be done by hand by engineers. So yeah... you can imagine how tedious it was (especially when you have tiny errors due to humans compounding) yet they were still able to build complex things (like factories!).

Re: Proof you can do hard things

#63

Post by kalid »

WesleyJohnson wrote: post #46

I lost interest in school around the 10th or 11th grade. I never took any math classes beyond what was required to graduate way back in '96 in Florida. I also didn't go to college. I've been a professional web developer since 2005 and a development manager (who still codes) since 2017. I don't understand the first thing about Calculus or even logarithms. I'm sure if I did, I'd probably be a better developer. I've had…

You probably understand logs intuitively. Don’t worry about notation, here’s the idea: sometimes we count digits, not values.

When we say someone has a 6 figure salary, we are counting how many 0’s (10s) to takes to get there.

For memory, we say something has 32 bits and can have 2^32 possible values. It’s more graspable to talk about the “address size” vs the “number of possible values”, especially for things that grow fast (like storage).

I’d suggest starting with your intuitions and slowly translating them to math.

(Without being a shill, I wrote about real world logs here, it may help: https://betterexplained.com/articles/using-logs-in-the-real-...)

Re: Proof you can do hard things

#64

Post by yCombLinks »

WesleyJohnson wrote: post #46

I lost interest in school around the 10th or 11th grade. I never took any math classes beyond what was required to graduate way back in '96 in Florida. I also didn't go to college. I've been a professional web developer since 2005 and a development manager (who still codes) since 2017. I don't understand the first thing about Calculus or even logarithms. I'm sure if I did, I'd probably be a better developer. I've had…

Khan Academy is great, but there are also an incredible number of great youtube videos. I would watch this 3blue1brown video to see if you like his style : https://www.youtube.com/watch?v=WUvTyaaNkzM

Re: Proof you can do hard things

#65

Post by ssivark »

jimmydddd wrote: post #42
wwarner wrote: post #31

I like the idea, but I’m gonna say that (a) calculus is more than a good challenge and (b) math is actually easy. To understand how things actually work, you need math, especially calculus. Deep learning? Calculus. Statistics? Calculus. Finance? Calculus. Physics? Calculus. Mech E, robotics, earth science, econ? Calculus. Second, calculus, like all math, is easy. Like that’s the point, it’s the science of simple thin…

I saw an article where they asked a bunch of scientists and engineers if they actually used calculus in their professions. None of them did. They used Excel and the R programming language.

If that were the case, I’d be extremely wary of their scientific output.

Re: Proof you can do hard things

#66

Post by yCombLinks »

hnthrowaway0315 wrote: post #39
stkai wrote: post #4

"My goal with our kids is to avoid lying to them as much as possible." ← Thank you. Why is that so difficult for parents to do?

Sometimes being absolutely honest is not the best option, I guess not only for kids but for all human interactions.

Yeah, but lots of parents lie far more often than would be useful for a child. But more importantly, absolutely honest is not the same as absolutely open. You can be absolutely truthful in the things you say without causing harm. If you think the truth would cause a child harm, then direct them away from a topic or tell them they aren't ready, etc.

Re: Proof you can do hard things

#67

Post by gmadsen »

roflyear wrote: post #49
wwarner wrote: post #45

Earlier quoted context omitted.

How you can use R without knowing calculus? Why would you even turn to R if you didn’t have a calculus problem to solve?

You don't use calc much when you use R, unless you're working on a problem that involves calculus, which isn't many problems, usually? R is usually used to do data stuffs in my experience. Like, "take in this data from this CSV, and do these manipulations" which may involve math but not often calculus.

using those "data stuffs" are usually based on calculus. Statistics and probability are both defined in terms of calculus.

calculus is the most basic of mathematical machinery, that it is essentially a requirement to do anything else.

Re: Proof you can do hard things

#69

Post by TexanFeller »

wwarner wrote: post #48
TexanFeller wrote: post #40

Earlier quoted context omitted.

It will be amusing if we find out that all the things come in discrete quanta, even space-time, which I hear hasn't been ruled out. Calculus and real numbers might not be sitting as pretty.

There isn’t that much difference btw an integral and a summation.

There are lots of corner cases where the difference matters, like when integrals with finite bounds can go to infinity where a finite sum cannot. Boundary cases and surprise infinities seem to be a common problem problem the theoretical physicists have battled in their theories for the last century.

Re: Proof you can do hard things

#70

Post by User23 »

jimmydddd wrote: post #42
wwarner wrote: post #31

I like the idea, but I’m gonna say that (a) calculus is more than a good challenge and (b) math is actually easy. To understand how things actually work, you need math, especially calculus. Deep learning? Calculus. Statistics? Calculus. Finance? Calculus. Physics? Calculus. Mech E, robotics, earth science, econ? Calculus. Second, calculus, like all math, is easy. Like that’s the point, it’s the science of simple thin…

I saw an article where they asked a bunch of scientists and engineers if they actually used calculus in their professions. None of them did. They used Excel and the R programming language.

R is a calculus. In fact all programming is reducible to first order predicate calculus. The Leibniz rule is pretty cool.
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