Just as you will never know what you might have discovered if you used the time you spent learning calculus learning something else instead, of course. There is no magic formula to life.
> you shouldn't learn anything until you need it
Impossible. Simply existing as a functioning human means you are going to be constantly learning something. Not everything you learn will be useful, but that's also true of calculus. Not everyone finds it useful in the end either. You never know what will end up being useful, but you also can't learn everything.
The great thing about the curious mind is that you tend to be naturally drawn towards the things that are most useful for you. Those born most likely to do something with calculus already voluntarily choose to learn about it. You don't have to make them. The stereotypical druggy who has no interest in anything but getting high, who suddenly has his life turned around because you force him to learn calculus, is little more than Hollywood fantasy.
I know few adults that were forced to learn something as kids that regret learning it. Conversely I know tons of adults that, as a kid talked their parents out of being forced to learn something and as an adult seriously regret it.
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.
Yes but arithmetic is actually not intuitive at all, and you can certainly grow up to not know it. There's a lot of people who once grew up not knowing how to read, because they didn't go to school.
Children are still children, they very famously make poor decisions. Yes, not all children, but most. We have to mold and steer them, because for humans we come into this world as basically blank slates. We're not like other animals, ready to roll. We require decades of careful curation.
If you are in a situation where you don't need it, sure, but if you don't need it then who cares? I get the nebulous "but what about the discoveries you are missing out on", but the type of people who wouldn't learn something like arithmetic for fun also never find discoveries anyway, and never would even if you could force feed them all the knowledge of the world. That argument really doesn't apply to most people.
> Children are still children, they very famously make poor decisions.
Not quite. What children are most famous for is that they won't learn until they want to. Poor decisions, implying that they could have made good decisions if only they would have listened, are the outcome of them not learning even when you tried.
> We have to mold and steer them
There are deadbeats in the world, sure, but for the most part that just naturally happens at least up until they hit the rebellious teen years. Kids want to be by your side, watching, learning. We wouldn't have made it as a species if this didn't occur automatically. Like I said before, you cannot exist without learning things constantly.
Can you source this? I thought we were pretty much expressions of our particular genetics and the biological human substrate we all inhabit. This is very much not a 'blank slate'. Every time I've tried to look into or steelman the blank-slate I can never come across hard science that backs up the assertion that we are all 'blank slates'.
Blank-slate seems to be more of a liberal idea then a scientific one.
We also have case studies that if humans are not taught language then they won’t, and can’t, speak. Genie comes to mind.
If you speak math problems to your child you are… wait for it… teaching them arithmetic. That’s what teaching is.
Arithmetic is not something that just naturally exists in the world, it’s a purely human construct. It does have to be taught in one way or another, otherwise people won’t know it. And, unlike language, I seriously doubt parents are just speaking arithmetic randomly in conversation that often. Your kid most definitely will not just “pick up” arithmetic.
In fact, I doubt a kid would even pick up language if you never spoke to them directly, and instead they just heard bits in passing between adults.
Exposure to something and being taught something are usually recognized as being quite different, but it is clear now that you just want to play a game of semantics, so we can put and end to that.
> I doubt a kid would even pick up language if you never spoke to them directly, and instead they just heard bits in passing between adults.
Kids not being able pick up on language by listening to a recording of adults speaking about some random thing is supported by the research so there is likely some validity to the latter half of your claim, with some assumptions about what you mean about "heard in passing", but the research also strongly suggests that kids can pick up on language if those adults are surrounded by additional context. For example, if adults in the same room were talking about a visible object in front of them then the research suggests that the child would be able to pick up the language even when not directly spoken to.
Why do you doubt the research?
Most kids would never go to school if not forced. They'd play video games or watch youtube.
There are 0.7 billion adults that can't read. 40% of adults in 1st world countries can't do arithmetic.
https://theconversation.com/high-number-of-adults-unable-to-...
So, no, there is no evidence people will not learn without being made to learn. There are only anecdotes that some children get lucky and learn things on their own. That's not the norm and there is ample data to back that up.
Including whomever wrote the article.
"Suppose, a litre of cola costs US$3.15. If you buy one third of a litre of cola, how much would you pay?"
As cola has a large size-indpedenent cost, I would reasonably expect to need to pay more than the claimed $1.05 if 1 L is $3.15. Moreover, the marginal utility of 1 L isn't 3x more than the smaller container. There is no need to have that much soda when an appropriately scaled option is available. Based on real-world prices I could find (YMMV), 1 L of cola sells for $1.99, while a can (355 mL; about as close to 1/3 of 1 L as we find for actual sale) sells for $1.69, echoing that $1.05 is not a realistic price to pay on the open market. Most importantly, in actual practice I'd pay nothing for cola and order water instead.
And he is supposedly a lecturer in Economics and Social Statistics at a fairly well respected school. Goes to show, again, that the kids won't learn unless they want to. Forcing teaching upon someone plain doesn't work. Never has, never will. Incentivizing one to want to learn can work, but that's something else entirely and not at all what we're talking about.