English speakers should learn math instead of a second language
leosstemhacks.wordpress.com
leosstemhacks.wordpress.com
You learn math because you want to be able to quantify scientific questions, or because you want to dig deep into quantitative logic for its own sake.
But what if you want to do something else? Such as getting to know your spouse, children or friends better. What if you simply want to make music?
I would say, then do that instead of learning math!
All this blog post highlights is that you should have a strong and clear learning goal, because if you’re learning Mandarin because it might seem useful on vacation to China, you might be spending your time inefficiently.
The idea of teaching children math as a language from day one is an interesting concept though. But even that still comes down to: start giving your kids amazing skills that you think will give them a fulfilling and good life from day one. Well yea, of course.
I'm not sure if you're saying you agree with this, but I certainly do not. What if you just wanted to learn a language because you find learning a new language enjoyable? I've spent the past year learning another language with absolutely no end goal in mind of what I would do with it - I just find it to be a fun challenge. It's just a hobby.
For my hobby, I don't do any of this analysis. I attend a class every week and outside of class, I practice daily. I don't ask myself if it is time and money well spent, I don't have an end goal in mind (aside from the vague goal of "learning another language") or any idea how this fits in to some bigger picture. I just do it because I enjoy it. If I did all the same sort of analysis that I do at work in the context of my broader life goals, my bet is that I probably would come to the conclusion that learning this language is a waste of my time. But, what is the point of living if you spend 100% of your time achieving goals and none of your time enjoying your life. Thus, I spend time on hobbies outside of work.
You mean like attending a class every week and practicing daily?
As another example, I also read fiction. I don't set goals like "I want to read X number of chapters this week" or "I want to read for X hours this week", nor do I track how much time I spend on it. It is purely for enjoyment, it doesn't matter.
I suspect that the same could be done with your idea of a strong and clear goal.
Yep, awesome but according to the post they shouldn’t. They should learn math because it is more useful. That is my issue with the post. Math is not more useful necessarily, because it depends on how you perceive life. One’s perspective on life tells how useful things are.
You'd think "well yea, of course" but man do I feel parents rarely do that. The majority, and I really do think the majority, seem to be content just doing nothing with the most valuable years of the childs life.
Perhaps I take that too seriously, but I don't think so. I feel that is one of our largest failings as a society. That and failing to encourage learning, lessons from past mistakes, self growth, etc etc.
I was pushed pretty hard as a kid and I’m not a very happy adult even though I excelled academically and have a lot of “skills”. All of that pushing made me constantly criticize myself and I still push myself way too hard and feel like I’m never good enough.
As a parent, sometimes I think it’s best to do “nothing” and let my kid enjoy her childhood and do childish things without an enormous amount of pressure to develop all of these skills and “get ahead”. Kids need time to have a carefree life for awhile without adults constantly dumping pressure on them to be prepared for adult life by the time they are five years old.
I tend to think that parents should present to their children as many different potential things to learn and excel at, but allow the children to drive themselves towards what interests them. Parents can then guide them accordingly. But the child should still feel themselves in control. Sort of like when Tibetan Buddhists find the next Lama- they have the candidate choose an item from the predecessor's possessions.
The devil is in the details now isn't it? I didn't mean to portray absolutes, I'm referring to parents who are either too uncaring or too uneducated to actually parent their children.
I'm sad that my desire for parents to parent was downvoted. I'm sure people (like your post) took my comment as a desire to push kids none stop, but I (as a person who grew up poor) am very frustrated by seeing, repeatedly, children (my friends and I mostly) who grew up without parents. It is not ideal.
How and how young?
I have a newborn I'm teaching numbers.
I really feel bad for the children of some of the people I see posting on HN regarding child dev.
Learning an instrument will help your brain in math. Learning any form of mindfulness will make you think more clearly and work efficiently. Learning languages will help you understand people and build connections and develop your brain in general.
> I disagree with this machine-like optimization of human life. We are not machines running OSes allocating time.
I doubt OP was offended. And I didn't say to change their mind. I said consider something that the tone of their comment indicated they hadn't seriously considered.
My brain fries when trying to figure it out. He shows me how to do it, and I get it, but man it's definitely a different part of the brain than I'm used to using.
Definitely going to apply this to my kids, and I wish my parents did this with me on a broader space. They sent me to english classes every saturday for a lot of years (from 7 to 15 or so), and even though I hated it at the time, I'm grateful that they did because it's definitely a plus in my life nowadays. (I'm from South America, most people don't speak english or have a below mid proficiency level).
I would call all these "big" languages, but I would not call Mandarin, Hindi or Arabic "global" languages. There may be over 700M speakers of Hindi/Urdu, but they live mostly on the Indian subcontinent and Hindi is not really a language of global business or education.
Spanish, and outside the above list, French, are more "global" languages in the sense that the language is a majority-dominant and/or significant language of business on several continents.
(FWIW I do know English as second language and understand a few words of French and Spanish, and can get along with everyday things in Mandarin, though I am more fluent in a couple of other small languages (Swedish and German). I am certainly not belittling the mentioned big languages, I just do not think they are truly "global".)
Having worked with Halliburton a while back it certainly seemed like Arabic was a global language to me. Many nations where you just have to speak it when interacting with people below the C level. There's also a lot of business you have to do in Arabic, and a lot of times when the expertise you may need is really only available from Arabic speakers. Like if you want a half way accurate estimate of how much oil Cuba likely has in the North Cuba Basin for instance. They have tools and techniques that others just haven't developed. (Or hadn't at the time.)
But I do think that when we are not so dependent on fossil fuels, Arabic will become a VERY unimportant language. I'm just not sure when that will be?
Oh, also, I'd imagine Mandarin is important too. A lot people who dealt with the Chinese on the "gotta get shit done" level used it all the time there. Also a lot of traders downtown were using that all the time when I lived in Houston. You kind of just had to when you were dealing with things in China because for many people in those sorts of positions, a lot of stuff is just moving way too fast to not be able to find the chase and cut to it faster than the next guy.
Or it was anyway? I don't know if business with China from the US is slowing because of the Trade War? Been out of that game for a while now.
Arabic also suffers from serious fragmentation: we would need help even between people Morroco, Tunisia, and Algeria even though they're basically neighbors. i think they are the same "language" in name only.
Mandarin and every other language is a no, even in the USA unless you live near a Chinatown. The only possible exception is Spanish. So there are just 2 global languages in my eyes.
A "global language" is by definition a language learned by significant numbers of people as a second language [1].
By most people's accounting, only English, French, and Spanish are global languages. "Minor" global languages on the rise include Mandarin, Arabic, and Hindi, but these do not have nearly the geographical distribution nor the populations of second language learners that the main global languages have.
That said, unless you have a partner or other significant connections to your target language community, consume a large amount of target language media, or are living in a country that speaks your target language, speaking to other people is not the main motivation to learn a language. You learn a foreign language because it's fun and because there are numerous studies indicating knowing a foreign language benefits your mental abilities and health.
Math courses have a much better track record of actually teaching their students something.
However, I think individual students should still take foreign languages in high school to fulfill college application requirements. On a societal level, though, those requirements are a massive waste of time and money.
All but 1 person had taken algebra, and with that I start into variables and functions.
So yes, people learn competent math skills in high school.
Yes, if you do not practice regularly (preferably daily), and with persistence, you will not reach a high level at a foreign language. Relatively speaking, maybe math is easier. But that's not much of an argument for math and against language learning, unless you have no actual interests and just want to check a box off a list.
To be fair, many (and maybe most) adults who claim to be interested in language learning also end up giving up because they are not willing to put in the effort. Too bad for them, and for you if you find it a "waste of time and money"; I find it far more rewarding than flaunting advanced math knowledge.
My guess is that this depends on the usefulness in somewhat common situations. English for non-native English speakers seems to work pretty well, especially in counties that don't dub movies and TV shows. I'm using my high school language skills right now.
Edit: admittedly, Latin didn't stick well with me though.
I went to "one of the best public schools" in America and have heard that college level language education isn't much better, so I think this is universally true of language learning classes in America.
The truth is that learning a foreign language is very "hard", where "hard" means requiring daily effort and willpower while often feeling confused and looking stupid while seeing little or no results for extended periods of time.
Generalizing this, I also thought I didn't like math until I went to university because all my math classes had been extremely boring and uninspiring. On a personal level, public school past the age of 14 was a massive waste of time and money.
Obviously I totally regret how absolutely inefficient I was at learning French because today I agree with what the article touches on: Learning a language is good for your brain, you not only discover structures and ways to express yourself in ways that weren't possible in your mother tongue. You find that some concept is really easy to express in that foreign language but not your own, or vice versa. Words that don't exist in your mother language etc. That is not to say learning other things (like math) doesn't have positive effects on your brain, but the article seems to limit the usefulness of learning a language directly to the utility value of speaking it.
From a personal perspective, knowing another language is enriching, but don’t do it purely for the earnings gain.
Again, don’t learn mandarin just for the money. English is much more important, even in a country like China, at the upper tech echelon.
China is really different: any foreigner managing a simple 你好 is praised for it, let alone a 大山 who has mastered Chinese tongue twister comedies.
Plus, there can be weird dynamics at work. Some people will actually look down on you as having somehow debased yourself for making too much effort to study the local language, both fellow foreigners and the locals themselves. As best as I can understand, they think it comes across as too eager to please, or an attempt to ingratiate, or that you obviously don't love your own culture enough, or that you evidently have too much time and thus can't be all that important... have heard some variation on all of them.
Especially in Asia, there's a kind of stereotype of the Big Important Foreigner who has been Appointed to this Developing Country to do Important Things. Suddenly breaking into fluent $LOCALDIALECT kind of shatters that illusion and raises all sorts of questions. Sounds strange, but it's a thing.
In China, it’s the reverse. They think foreigners aren’t smart enough to learn Chinese. That’s why they are always amazed when some expat can speak even the most basic phrases.
The scary thing is that’s it’s often these “expat bubble” executives that are making decisions. No wonder foreign companies in China get taken to the cleaners.
A senior Chinese manager in America is much more normalized than a senior western manager in China, (the former is an immigrant and has a green card, the latter is an expat and will go back next year after their assignment is done).
I don't regret it at all, but it's time and energy which might have been better spent learning other things instead. Especially when English is mainly the official language at work, and many people on the street can speak it for business or travel anyway. Career options here are much more limited unless you have a decent command of English. My bigger reason to want to learn it has been for social purposes.
> don’t learn mandarin just for the money
Did you reply to the wrong comment?
But also predicating all learning on its "objective usefulness" (however way you try to quantify this) seems short-sighted, what's the fun in learning something you know is useful but don't enjoy?
Somewhere there's a balance surely..
Otherwise what if someone said, don’t learn Math, learn Modula-2?
Because of opportunity cost
It's not naive to try and optimize learning to help maximize a fulfilling life. The available time in life to learn is finite and therefore choices have to be made.
Not every subject has equal importance. It would also be naive to think every subject or skill has equal relevance to a particular person's life and therefore one can just choose randomly.
(I learned that lesson very late in life. In my 20s, I was very careless and carefree about what I learned and I squandered away a lot of valuable years. I wasn't discriminating enough about the topics I spent time on.)
There's lots of enjoyment to be had in learning things that aren't immediately (or even remotely) useful, and there's often a lot of unanticipated utility in learning things that are pursued for pure enjoyment. There are entire fields in mathematics that were/are pursued for personal enjoyment and later proved to be incredibly useful (or might never be!).
> Not every subject has equal importance. It would also be naive to think every subject or skill has equal relevance to a particular person's life and therefore one can just choose randomly.
I'm not saying you need to choose your pursuits randomly or without account of the time they take, but I think making these choices only for monetary gain or purely on some basis of what utility you think they'll provide is a pretty joyless existence in either case, and w/ the latter consideration is a pretty naive accounting of your ability to meaningful assess an "opportunity cost". Leisure activity, learning for learning's sake, broadening your cultural horizons, etc. are all worthwhile things in my book.
If you're talking about opportunity cost in a fuzzy "there are other things I'd rather learn, or some particular thing seems more useful to me now" kind of way, that's a goofy metaphor and an unhelpful insight in the context of offering advice about what things to learn.
> (I learned that lesson very late in life. In my 20s, I was very careless and carefree about what I learned and I squandered away a lot of valuable years. I wasn't discriminating enough about the topics I spent time on.)
Without any context into what you think was squandered by learning other things, it's impossible for me to appreciate your POV on this, but it seems unlikely to me that you lost all that much.
I'm not sure what you're arguing against. Enjoyment is utility. But if I would enjoy learning two different things equally, I should pick the one that would also satisfy me in other ways, or the one that would deliver that enjoyment more efficiently, so I can also have time to do something else that I also enjoy.
There's a cost to spending time, that's why people call it spending time.
You don't need to be from Vulcan to understand you can't have it all simultaneously.
And it has nothing to do with microptimizing and minmaxing everything - which is a caricature.
Even just at the very high level view you know you have x time after work, and you could go study a foreign language, or you could study math, or learn to cook, or whatever. Some things you can fit together, most you need to prune...
Opportunity cost is an open-ended economic term, not some obscure math or physics arcana, and it's core is all about preferring one option over another after an assessment (of what you lose by not going with the other, etc).
Using it casually is totally compatible with the concept, it's not like using hard math (e.g. Godel's incompleteness theorem") in some pseudo-scientific fashion.
>To your point, everybody lives life this way, there's really no other way to live life than to make judgements, so why respond w/ that unless you're actually making some more targeted point about only learning things that provide you the highest utility.
Everybody uses O/C in some way or another in their lives (it's not some obscure idea of only academic interest), but not everybody uses it well.
Many waste efforts on multiple things ("jack of all trades"), others chose the thing that makes them worse off professionally or personally over better options open to them, etc.
So, that's the point I was making: choosing math over Chinese (as the author suggests) can work out well from a O/C perspective. Understanding math better is more approachable than learning a language like Chinese adequately to make anything of it, and can have a wide impact (especially to a programmer, but also in personal life, business decisions, etc).
lol I know its not arcana or hard math, but framing a decision people regularly make in life without any means of holistic assessment or accounting for the options like its a micro-econ problem if you just informally mean "make a judgement call", is the type of terminology abuse that's the hallmark of a pseud.
> but not everybody uses it well. Many waste efforts on multiple things ("jack of all trades"), others chose the thing that makes them worse off professionally or personally over better options open to them, etc.
And this is at the root of my objection to this, what could you possibly mean here by "not everybody uses it well"? To what or whose criteria can you possibly make such an assessment?
> So, that's the point I was making: choosing math over Chinese (as the author suggests) can work out well from a O/C perspective. Understanding math better is more approachable than learning a language like Chinese adequately to make anything of it, and can have a wide impact (especially to a programmer, but also in personal life, business decisions, etc).
You might fall in love with a Chinese national and want to learn your partner's native tongue. You might have your life wholly changed by a work of Chinese literature. This is why this whole framing is utterly insane, there's no way to account for all the ways your life might be bettered by both these pursuits. Why even make some facile pseudo-analytic attempt. It's just dumb STEM dick measuring to pretend like there's a way to assess this.
Well, I'm not an alien that just landed. So I have personal experience with life, an understanding of culture, an education, some historical knowledge, etc, and so I can make judgements (even without writing some full formal paper of citing stats) about people making the wrong choices in their lives.
Maybe not perfect judgments, but it's not like I'm some alien that has just landed on Earth from space, and one has to wonder how could I ever possibly "make such an assessment" for others.
But even if you ignore me as a non-authority on the matter, I can argue that people themselves frequently lament their own previous life choices and with they'd gotten with X or Y, or lament how their choice on Y brought them to the bottom, and so on.
So from that alone, we can safely assume that "not everybody uses [their assessments on what options to follow] well".
Rather, it's that you have only so much time to dedicate to things... if you're focusing very much on one, then you're not spending time with the other -- and overtime, you'll lose that other thing. If you can manage to spend a good amount of time on two things (let's say, learning a new instrument and learning a language) everyday, consistently, then you will get both.
You can create ungrounded abstractions all you you want, but as an older person who has commiserated with other older people, the common conception that it's harder to learn and retain things in older age is a real thing
- Homer Simpson
Or are you saying that non-Americans are less knowledgable because they learned one more language?
This is a pretty half-baked comparison. Math is great for describing things which can be defined precisely and their interactions. Numbers, physical systems, economics, etc.
Human language can be (and is) used for these purposes as well, but more broadly is useful for an entirely different purpose: expressing emotions, sussing out the meaning of things, developing relationships, providing a voice for the human condition. Mathematics is ill-suited at best for these purposes. Both language paradigms may be able to quantify how fast one has to run to get away from a lion. Only one of them can express why you’d want to, or the terror you’d feel trying to do so.
Agreed. I remember asking in high school what the material we studied was helpful for as I was struggling with motivation -- I was told to help shape my brain which is the blanket reasoning used from everything from Latin to music.
I think in addition to the important areas you highlighted, statistics is so fundamental to understanding the world around us and should be emphasized alongside.
Logic, so you can think straight, and epistemology, so you are able to recognize when your axioms are not actually hard facts, which is where a lot of complicated fuzzy-logic style disagreements (anything related to complex systems (weather, economics, government), culture, gender, sexuality, etc) break down even between two people who have highly advanced logical capabilities.
There have been several pushes for common languages. Latin once dominated at least the sciences and clergy. French was the literal lingua franca for a good while in various contexts. English has kind of taken over that role at the moment. But those languages are all a bit shitty when it comes to ease-of-learning. French with its complex grammar. English with its spelling oddities and its absolutely mind-bogglingly vast vocabulary. Latin, well, who even speaks Latin anymore.
Artificial languages like Esperanto are allegedly easier to learn, but they've never taken off.
I've long held the belief that the EU should make English a mandatory second language across all its member states. It's easily the most spoken second language in the EU already, but there are huge differences in proficiencies across countries/regions.
Well, every natural language that developed organically and was not artificially created will, by necessity, have its quirks. But if it is learned early enough in life and actually used on a daily basis, people will overcome these quirks.
Latin’s use as an international language of religion, scholarship and science occurred during the time when it was already all but dead. Only a tiny minority of the population knew it; and there was neither a universal system of education to teach it, nor mass media to provide continuous examples of its usage. When French and German were tried as international languages, the situation was somewhat better in the sense that they both were living languages; but still there was no infrastructure in place to teach it to large segments of the population. Now, I feel, the situation is very different. A huge proportion of population receives primary and secondary education, which offers a great opportunity to teach a common second language. A massive amount of films, books, or radio programs offer examples of oral and written English usage; and the Internet is connecting people at a previously unimaginable scale. Now, I feel, we have a fighting chance of finally getting a common language.
Of course, I understand that a language becomes international not only due to its linguistic merits, but in a large respect due to the political and economic power of the countries where it is spoken. And since China is on the rise and the West is somewhat in decline, I fear that English may lose its momentum, and we may lose our chance to have it as a truly universal language.
People may also resent being told that they have to learn a specific language for many different reasons related to their feelings about that language or the people who speak it. You can see pockets (or wide swaths) of resentment toward many widely-spoken languages.
I remember being shocked at the thought that people around the world wouldn't naturally get enthusiastic about Esperanto as a sort of Schelling point and just learn it. But if you think about the practical day-to-day communication dynamics that people confront, they usually have some particular regional or national language that would be especially useful to learn. That benefit is obvious and reliably foreseeable, whereas the benefit of joining in an inchoate humanity-wide auxiliary language project is speculative and at best delayed.
Or does it have to be YOUR language that everyone should be obligated to learn and communicate in?
Secondly, this kind of moral objection ("does it have to be YOUR language"), intended to shame the proponent of this idea for their presumptuousness, will never get us anywhere. Why don't we start this initiative by learning Mandarin, you say? Why not Arabic, someone replies. Why not French, another says. Why not Spanish, joins yet another. And Welsh, let’s not forget about Welsh, another cries.
Framing the question of why pick language X instead of language Y in moral terms is pointless. Sure, one can try to argue from a purely linguistic perspective, pointing out unwieldiness of Chinese characters as opposed to Latin-based alphabets; or the general rarity of tonal languages, such as Chinese; but that’s a crappy argument. A good argument, I think, is that we are at a point where English is already used as an international language in a number of spheres, and instead of discarding it and picking an entirely different language and re-training humanity to use it, it makes much more sense to continue pushing forward with it.
You have your qualms about Mandarin, but anyone can complain about a language they do not speak, and claim it is too difficult for this or that reason. Compared to English, Chinese grammar is very simple, the written language is compact, and there is little confusion about pronunciation. It seems as good as any (if not better than most) as an international language.
It seems you realize it as well, as it is hinted in your own posts; you will never convince everyone to pick your preferred language and convert to it. It is like trying to convert everyone to the same religion. You may think that your choice of [language/religion] is the best one, the one that makes the most sense, without realizing your own bias.
"Please respond to the strongest plausible interpretation of what someone says, not a weaker one that's easier to criticize. Assume good faith."
It is a funny thing to borrow English tricks and to make them with Russian. For example I love the idea of phrasal verb, especially when a preposition becomes a word the sentence ends with. It is so alien for Russian, but somehow it have meaning when done in Russian.
I mean, I like English but I'm not ready to throw Russian away. From other hand, using grammar of one language with other is a way to converge languages into one, but it mightn't work. Some people become nervous when their language borrows features of other languages, they see it as an expansion of that other language, they are afraid of losing their beloved language.
There is a vocal opposition in Russia to the borrowing words from other languages, especially from English, which is seen as a dominant language abusing its power to oppress weaker languages (a natural Russian reaction to any power: power exists to be abused, it is an axiom in the Russian culture). I know that French have an opposition like this, though maybe due to other reasons.
Maybe if English started to incorporate words and grammar from all languages around the world, it could become a language of languages, but I suspect that languages needs rules forbidding some constructs to be language that allow express things. Incorporating all possible rules probably would make any word combination to be allowed and language might lose its purpose.
English borrows words promiscuously from other languages. Many were borrowed from French after the Norman conquest. Many were borrowed from Latin and Greek by scholars. In fact there's a list of lists here:
https://en.wikipedia.org/wiki/Lists_of_English_words_by_coun...
All the loanwords in English is one reason why its orthography (spelling) is so difficult.
Chinese is rife with misinformation, alternative facts, sophistry and pure garbage, any thing scientific is either translated to English already or tranlated from English and other languages.
>and not-scientific content.
It's OK if you major in Asian studies or something, for an average guy the overall quality of Chinese content is just not worth you time. Not to mention modern Chinese only existed little more than a century.
I repeat what I said, I oppose spending too much time (more than dabbling) on Chinese by any average person or student, Chinese is a very messy language, for the people worth your time talking to they most likely already know basic English.
I like being able to talk to random other people speaking English as a foreign language. It's useful. It sure would be nice if English speakers would pick up some phrases or a basic understanding in a language of their choosing.
Also, languages aren't equal. Translating poetry is an art and most likely lossy. Emotions don't work the same across languages. I can tell my (ironically: Chinese) gf "I love you", but while that is true it is merely a crappy word by word translation of "Ich liebe dich". The latter is the sensation I feel, the former me describing as a 3rd party observer what's going on. Half-assed.
Don't learn Chinese because you read online articles claiming you should, don't stop learning Chinese because online articles call it useless and maybe do try to know more than one language..
Sorry, but you can't post slurs to Hacker News and we ban accounts that do it.
https://news.ycombinator.com/newsguidelines.html
(Sometimes people do this when they're of that background themselves and have some criticisms to make, so to speak, of the home team. That may be fine in person but it's not fine here. It has an overwhelmingly provocative effect whether you mean it that way or not.)
Language study and math are not mutually exclusive for me.
When I've learned math it's through focused effort, sitting down and doing math problems, thinking really hard, and talking to people with a whiteboard.
When I start study languages I'm mostly filling time, things like listening to podcasts in the language, going through Anki flashcards while waiting in line or on the subway, or reading things about the language.
Learning the foundations of a foreign language is closer to brushing my teeth or going to the gym than it is to learning math. You just do some mundane things every day for a long time and suddenly you wake up with new skills.
Once you have a solid foundation, then it's closer to having fun than studying. You just chat with people or read things you're interested in, the same as you probably already do for fun in your first languages.
Anyways, my point is that if you have even a little free time or some downtime (like a commute), you can probably fit in time to learn a new language and not take anything away from your other pursuits like actively studying.
That said, I don't think learning a new language is easy, but it's rewarding and the improved cultural understanding, of both your target language and culture and your first culture and languages, it brings makes it worth it to people who live in a globally connected society.
In the end, though, you're best off either studying something to reach a specific goal (learning the math that engineers need in order to become an engineer) or studying something that interests you.
In what specific everyday situations would most people find these useful? It's not like it's common for people run into situations where they say "if only I could calculate the predator prey systems" or "if only I could calculate radioactive decay." I've studied these, and I don't think I've ever run into some everyday situation where I've said "Man, I'm really glad I can apply my differential equations/vector calculus/etc. here." Even in the rare situation where I want to calculate compound interest I opt to just use a interest calculator since it's quicker and less error prone than doing it by hand.
The reason is, our society has a number of clear paths for people with highly developed M ability, but fewer viable paths for highly developed V ability. Basically just law school, and that isn't what it used to be. I think that's a problem for us as a society, but it's not going away soon. I'm advising my son to major in something quantitative.
That being said, the author's apparent advice not to take fl at all is insane. Especially for high school students. If you are not MIT/CalTech material, Ivies like to see foreign languages.
Not knowing what I don't know, I find it very difficult to gauge whether I'd benefit from learning more, if that makes sense.
I think the analogy between math and a language that you can learn as "native language" is quite far-fetched and flawed, but let's accept it for the sake of argument.
Then, I'd say that in most developed societies, we already learn math as a native language since birth. Many toys for babies are focused on counting (among other skills, like recognizing colors, shapes and basic words). Parents routinely ask their kids to count things, just as they help them learn the language. Then, once you go to preschool and then school, there are always math lessons alongside the language lessons.
So in my view, what they're advocating already happens, so I'm not sure what change they're proposing.
Just because I can read a math paper written in English or German I don't harbor any illusions I'll be able to understand one written in Mandarin.
On top of that there's that mathematical notation really isn't as standardized as one would hope. Neither is basic terminology (which already isn't consistent between different disciplines/schools within the same language).
So unless a Chinese mathematician deigns to translate the paper into a language I understand, I'll just be screwed.
The underlying concepts may be universal, but the language and notation of mathematics today just isn't.
Edit: For those who want to have a taste of what mathematics in a foreign language is like, have a look at this Chinese Wikipedia article on a very basic topic: https://zh.wikipedia.org/wiki/%E8%BF%9E%E7%BB%AD%E5%87%BD%E6...
https://github.com/melling/MathAndScienceNotes/blob/master/m...
https://github.com/melling/MathAndScienceNotes/tree/master/s...
https://github.com/melling/MathAndScienceNotes/blob/master/m...
This recent HN was interesting, for example:
Just make sure that you have native speakers to talk to, the benefit of learning a language is being able to talk to people!
If you don't know any maths there are things that are hard to describe or even conceptualise.
If you know only one language there are assumptions you make and things you don't know that you don't even know you don't know.
I'm European, speak 3 languages and use math every day, professionally. I've studied, lived and worked in the US for many years and am often shocked at some of my American friends' lack of perspective on international affairs.... keep-up with the math education but don't do it at the cost of languages... you can't afford to.
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In re: teaching math ASAP see Iconic Math http://iconicmath.com/ and (the general idea of) "Proofs without words" https://en.wikipedia.org/wiki/Proof_without_words
But I'd add that, for native English speakers writing to a broad audience, they should spend a little time learning how non-native speakers use and understand the language.
A few changes in word choice, sentences structure and idioms can make informal communication significantly clearer.
I don't like the idea of learning math INSTEAD of a foreign language, since both are meaningful and interesting for different reasons.
In writing math books I often had to come up with various analogies to try to motivate readers to invest the time---look, if you get through these hairy equations you'll have access to powerful math modelling skills and be able to read Wikipedia pages that have equations in them without going into panic. I'll add the "learn a new language for the culture/history" angle too, not sure which is more convincing...
So, if your choice is between calculus or Spanish, Spanish might be the better choice.
Strogatz writes, "It isn't necessary to learn how to do calculus to appreciate it, just as it isn't necessary to learn how to prepare fine cuisine to enjoy eating it." His book gives a broader view of calculus than any text--more like calculus appreciation.
> Most students who learn calculus will never, ever, integrate a function again in their life.
This is true. But will they never, ever use the concepts of slope or area under a curve? An appreciation for calculus (or mathematics in general) can enhance one's life in other ways. To know enough math to appreciate the mystery of unreasonable effectiveness of mathematics [0], is mind-expanding.
[0] https://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.htm...
Sometimes it just comes down to utility. If you live in Nevada and you’re wondering whether you should learn how to drive or how to sail, pick driving.
Seems to work for the rest of humanity.
I don't think learning Mandarin is such a bad idea, personally.