I just call it “pi but for curves”

That definition also gives a nice introduction to e's taylor series!

A loan is subdivided and sold in different allotments each year at a different interests rate, principal, and terms. You want to sell the entire debt at some point in the future. How do you calculate the price such that you don’t sell at a loss?

Why does that formula work? ;)

I did not say "derivation of the formula" by accident: this is about why would this produce something that makes sense as "interest-as-percentage"?

That is the integral

You're assuming banks use that formula and not just YOLO it, "haha fuck you pay me more".

>it just seems good for your brain and interesting for how you think about the world.

I am fluent in 3 languages, and while it is convenient, I assume claims about it being "good for your brain" are just as pseudoscience-y as all the other claims about what is good for the brain.

One of the languages I know doesn't even use a Latin alphabet, and I spent many hours learning it when I was little. And it's basically useless (obviously just my experience) except for communicating with older family members. Once they pass away in ~3 decades, I doubt I use it again.

Actually, the biggest incentive for me to teach my kids that language is so that we have a secret way of communicating in public (in the US). But I have failed so far, because it's just a lot of work to teach kids another language when you and your spouse prefer to speak in another, and so the kids are not completely immersed in it.

Knowing English as a second language and Dutch as a first language is different than knowing, for example, Dutch as a second language and English as a first.

I know people in both camps. I have more respect for English speakers learning Dutch than for Dutch speakers learning English. Even though I respect both. But the simple truth is: there's a lot of incentive to learn English. There is not a lot of incentive to learn Dutch.

Why Norwegian? Why not Luxembourgish then?

I think it's hard to have the kind of meta-skills as a child, it's kind of hit and miss. (Ie discovery, learn what to learn, how to learn, make learning pleasant). As an example, music is one thing that works best if parents, siblings and friends are into it and you can do it together or if it's somehow ambiently present most of the time. But if it's something that you only go to lessons for, decided by someone else, that you don't enjoy etc - then it's often like pouring water into a dry well. Yet those mechanical even if less enthusiastic skills can then be useful later, if the inspiration comes, with a new social circle etc. Or similar with sports. In some families, it's more "present" in an ambient way. When waiting for something outside, the kids have some hockey sticks and a tennis ball lying around and just start playing, maybe with adults who also find it fun. Or talking with the family about the news in an analytical way: that person leads that party and they have these values, while that other person drives these other things. If you have these available then different kids are exposed to things and can pick up things they are more inclined to. I've read lots of mathematician and scientists' stories how Martin Gardner's problem books drew them in to the field. So parents exposed them but didn't force. And their exceptional inclination did a lot of work.

> Most kids, left to their own devices, would not learn arithmetic.

Unlikely. Too many things in life depend on arithmetic. Most people will learn things when they must.

What is more likely is that kids won't learn arithmetic before they need it and therefore may theoretically miss out on the aforementioned discoveries that are overlooked when one doesn't already have a foundation in arithmetic. However, most people never have such discoveries anyway. Those who do tend to be the type that would learn something like arithmetic just for fun.

> I know few adults that were forced to learn something as kids that regret learning it.

As a once child, if I didn't want to learn something, I didn't. Forcing someone to sit in a classroom where a subject is being taught, for example, is not the same as actually learning the material. So this is an obvious truism. Those who didn't want to learn something never did.

I loved learning about jerk, snap, crackle, and pop as higher-order derivatives of position wrt time in physics.

F=ma is slightly important for physics, no? And deriving the equations is kind of the point; it's the understanding of "why" something is true.

e.g. I can tell you things act like a spring near (stable) equilibrium, and you can believe me, but why on Earth would that be true? Well, Taylor expand the potential at equilibrium. Define V(0)=0, and equilibrium means V'(0)=0, so V(x) ~ V''(0)/2 x^2, so F = -dV/dx = -V''(0)x, which is a spring with spring constant k=V''(0).

That's all a very conceptual explanation; the point is near an equilibrium, zoom in and you have a parabolic potential! What is the potential for a spring? A parabola! This is basic Calc BC stuff, but it also justifies why we might care about about simple harmonic motion. Calculus is the whole business of "zooming in."

> I’m not sure there’s enough overlap between physics and calculus to justify calculus.

You need calculus to design a windmill or an auto engine or an electric motor beyond the "just sort of works" level. Most of analog electrical engineering is defined by calculus. Althogh, yes, you can get LTSPICE to do most of that for you.

I mean one example is like a dampened spring system or RLC circuits or something. You can simplify a lot of systems down to those types of simple physics systems you learn about in class.

A lot of it I think is just training people to adopt a "physics-like" or "math-like" way of thinking and giving them a general overview of how things work.

Just like all school problems of this nature I have ever seen, the question lacks precision.

How long does a production run take and how many units can you do in a single sun? Since this isn't mentioned, the answer is to produce everything at the last second of the year. But we are also missing information on why the factory needs to produce 12,000 components in a year and for whom and about the logistics involved in getting those components to the buyer.

I always hated these type of questions for their lack of precision. You haven't even mentioned how many units in a single production run will be faulty and need to be scrapped instead of delivered, how am I supposed to optimize anything?!

Can you do a single run on the last day of the year?

Music can do so much more than just paying rent. You can impress your future wife with your playing or singing. It's a form of therapy for many.

It's true it won't pay the bills, but knowing one instrument is a good skill that differentiates you from others.

> "Everyone alive in the developed world today grew up in a wondrous period of history where the middle class had many luxuries previously only afforded to those with inherited wealth. There are signs that period is ending."

People have been freaking out about this pending doom for as long as we've walked the earth. Most of it stems from either old age or political hyperventilating (both symptoms of perceived displacement). Humanity's still grinding forward ... faster than ever.

I think becoming proficient in some form of artistic expression is very helpful for achieving self-actualization.

My biggest frustration, currently, is a lack of time and energy to devote to my creative projects. I still give them some time, but between a full-time job, child care, and other day-to-day responsibilities, it is not as much as I would like.

My wildest hope for society in my lifetime is that we will experience dramaticly shorter work weeks. Keynes predicted 15 hour work weeks by 2030 or so. If I could afford a modest life on only 15 hours of labor, and devote other time to family, friends, and art, I would feel so amazing. I'm skeptical of the claims of AI, but a society where a shorter work week is the norm would turn me into its biggest fan.

Anyway, despite my frustration, the time I spend with my creative projects results in my greatest self-satisfaction, after the time I devote to raising my children. And the creative outlets I pursue today are directly related to the artistic skills I developed in my youth (including music). So yeah, it probably won't pay the bills, but there's much more important things in life than bills.

I'm not suggesting a career. I'm saying those three things are always valuable to learn.

On the one hand yea, but on the other hand, society is trying to create a situation where the biggest necessities are less of a burden. The big 4 IMO are: food, water, air, sleep. I get water out of the tap. It costs a lot less for me to get clean water than it is costing people 500 years ago (on average). At least that's my guess anyway.

The traditional career for people studying music theory is acquiring wealthy parents.

Your college major doesn't determine your career path, and the sooner people stop pretending that they are necessarily correlated, the better.

That’s called strawmanning.

I didn't have that but I instead did a lot of music production as a teenager, hand dragging midi notes. It turns out, I have perfect pitch. But I learned that at 27 where a musically trained person noticed it. I make melodies all the time in my head.

It was a funny moment where she was like "you have perfect pitch!" "What is perfect pitch?"

I guess it's a shame, I could've been a great musician if I was trained.

In any case, if you want to meet up online, my email is in my profile. You sound fun!

None of the wealthy people I know had wealthy parents. Most of them had parents who didn't even have shoes for significant periods of time.

‘Hey, Claude, make me a painting of a sunset.’ Voila, you know how to make art. ‘Hey, Chat, write me a sonnet.’ Voila, you know how to write poetry. But you don’t really though, don’t you. Text-to-speech didn’t come into existence with the advent of agentic AI, and yet you will have a hard time getting any job or being part of most communities if you are illiterate. It turns out technology did not make literacy obsolete. In any case, we already know that putting screens in front of children is harmful, so unless someone advocates harming children, using a modern computing device (touchscreen slate, keyboard and mouse, etc) as a replacement for basic education is highly suspect.

What a zero-brain statement.

Literacy is way more than deciphering text into the words they represent.

Have you tried lighting a fire without matches? It's deeply satisfying.

As much as they'd know how to bake bread by buying a loaf in the shops.

Hey Claude, can you have sex with my wife for me? Voila, your wife now has an actual lover. Having sex with your wife can be as obsolete as real intimacy, with the advent of technology.

I dunno. Inside most families seems to be almost a perfect socialism. From each according to his abilities...

Scaling it up is hard, though.

Well that's certainly engaging with the meat of his comment, instead of the HN equivalent spamming stupid X clapbacks for likes. Bravo.

I guess you needed some validation today.

Lmao. This comment combined with the one above are just a microcosm of the worst HN has to offer.

What sort of socialism was at play when the British forced Ireland into famine during the potato blight? What about the British role in India’s famine? What about the many famines brought about by civil wars and ethnic conflicts in Africa? The Great Depression, famously brought about by socialist policies and definitely not gilded age wealth inequality decadence?

If you’re looking for a common thread, it’s authoritarianism, not socialism.

I don’t disagree, but I’m not seeing many other options here.

Modern Western European socialism has probably suppressed wages and increased unemployment relative to the US, but hasn’t led to starvation.

Buying lots of stocks, owning my home, maxing out my Roth 401k and Roth IRA as opposed to funding more short term priorities, with the idea that my retirement account isn't just funding my retirement, but possibly buying my kids houses as well. Would like to start a lifestyle business when the kids are older. Looking after my health so that I have more time out of the hospital. When my kids are old enough I'll teach them the absolute necessity of making money and every way I can think of to do that, that whatever they do when they grow up they have to be willing and able to do the version of it that makes money. If they love dance, they better be prepared to be dance instructors and open a studio or savagely commit to going pro, or be prepared to do something else to pay the bills and keep it as a hobby.

We've been financially fortunate enough to be in the top 25% of US households, and even I'm living the reality where I can't afford what my dad could afford working effectively the same job at the same age. Looking out at the world I see little reason why that trend should reverse, it'll have to get a lot worse first.

If I'm right I have a good shot to keep my family on the better side of this shitty transition, and if I'm wrong then my kids will have even more freedom than average, at the cost of a slightly more humble present. Probably won't step on a plane much over the next 2-3 decades, and that's fine.

Who was it that said he'd never let his education interfere with his learning? I'm in favor of learning, but what we think of as education isn't particularly conducive towards that.

I feel the same way about education, but as someone who received an education, I'm biased. I like knowing things and understanding things.

Studies on education and well-being don't really validate us though. They generally find a positive correlation between education and happiness when you don't control for other factors. But better educated people are usually from a higher social class, have better income, are healthier, are less likely to have been abused, etc. When they control for these factors, the correlation often goes slightly negative.

(If ASI does all the labor, education would no longer cause better income or health, so we want to remove those confounders.)

There are a number of proposed explanations for this, and it doesn't prove causation. But the data isn't on my side.

Also, I think there are two kinds of learning, easy learning and hard learning, and most people will only do easy learning without extrinsic motivation.

Easy learning is fun. It's why there are so many edutainment videos on YouTube and TikTok. Learning cool facts, or reading an educational book (without doing exams or problems) fall into this category.

Hard learning requires more effort. An example would be learning Cal II. You have to study and practice, and you likely won't get it right away. People do hard learning all the time, but usually because they have to.

Before online courses were a thing, friends or family would sometimes tell me they wish they could go back to college and take some courses they were interested in. Now we can, for free, at our convenience. But they don't. We'll watch endless edutainment videos on YouTube, but we'll only enroll in Cal II if we think we may need it.

If future AI can do everything, the extrinsic motivation is going to disappear. People will naturally tend towards easy learning. Maybe that's good enough. Easy learning will help us get funny jokes, recognize references, and appreciate good movies. But you don't need school for this type of learning. It's everywhere, and people seek it out because it's fun.

> still, i think getting ASI to distribute itself properly is going to be harder than people give credit

I'm guessing you mean getting AI to allocate resources and distribute wealth fairly without employment? Assuming we don't get a doomsday scenario, I see two likely possibilities. If a democratic government has control, people will vote to give themselves wealth. We end up with something like UBI, and people vote with their wallets to decide what the market (controlled by AI) should produce.

The other option is we get a dictator. With ASI and robotic armies, the factors that normally protect us from dictatorships would be gone. Currently, if the president wanted to declare himself a dictator, he would need support from a lot of people. At the very least, the military would have to back him. And you need your citizenry to be productive. They make all your food and machines and services. But if the army is composed of deadly autonomous drones instead of people and one person has authority over the army, they basically have absolute power and they don't need other people for anything. The factories keep running. The drones gun down anyone who resists. We're left at their whim, and we better hope they aren't cruel.

The hell? Where did you get that from?

Yes, a little bit of intelligence would be necessary to follow directions, but not much education. We were discussing education.