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English speakers should learn math instead of a second language

174 points by abrax3141 7y ago

chaosite 7y ago
Note that the Wikipedia claim about total speakers, the Wiki page notes that "Speaker totals are generally not reliable because they sum estimates from different dates and sources, usually uncited."
cromwellian 7y ago
Why not learn multiple? Why make a false dichotomy? Math, programming languages, and alternative spoken languages are distinct useful things you can learn. Otherwise what if someone said, don’t learn Math, learn Modula-2?
- coldtea 7y ago
  >Why not learn multiple? Why make a false dichotomy? Because of opportunity cost
  - buzhidao 7y ago
    not really. if you are waiting in a line, or taking public transportation, you can use you smartphone to practice some natural language, but not math which requires deep focus.
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  - almostdeadguy 7y ago
    Okay if you want to treat life like an RPG you need to minmax the right skills in, fine. That's a very strange, naively calculated, and from my perspective, totally unfulfilling way to live life.
    - antidesitter 7y ago
      That’s a very strange reading of the parent comment.
    - jasode 7y ago
      >you want to treat life like an RPG you need to minmax the right skills in, fine. That's a very strange, naively calculated, and from my perspective, totally unfulfilling way to live life. 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.)
      - almostdeadguy 7y ago
        > It's not naive to try and optimize learning to help maximize a fulfilling life. The time in life to learn is finite and therefore choices have to be made. 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.
  - malaxii 7y ago
    The opportunity cost of learning a language at school is very small.
- deleted 7y ago
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- mpoteat 7y ago
  I've always had a suspicion that one person can't be a master of all things due to the physical limitations of human memory. Isn't that why we specialize?
  - whatshisface 7y ago
    More like the physical limitations on lifespan.
    - coss 7y ago
      But probably memory as well. If I start specializing elsewhere I'll forget the intricate details of the thing I'm already specialized in.
      - pen2l 7y ago
        Don't think it works like that. 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.
        colordrops 7y ago
        It does work like that. As you get older your ability to retain information wanes.
        Apocryphon 7y ago
        That could be physical degradation from age, not necessarily the "running out of disk space".
        colordrops 7y ago
        Why does the cause matter?
- rolltiide 7y ago
  Eh read the article, there are more interesting points worth discussing or disagreeing with in it
mistermann 7y ago
I would argue that an individual (and in turn, the entire world) would be benefit more from learning the "languages" of, or getting a good grounding in, logic and epistemology. 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.
tzjmetron 7y ago
Plain retarded tripe.
finnjohnsen2 7y ago
«there are no studies that suggest that learning math as a “native speaker” does not have at least the same, and perhaps even more benefit», this reasoning is so flawed.
melling 7y ago
I collect math, machine learning, statistics, etc urls. The ones discussed on HN have the HN discussion below the article: https://github.com/melling/MathAndScienceNotes/blob/master/math.md https://github.com/melling/MathAndScienceNotes/blob/master/m... https://github.com/melling/MathAndScienceNotes/tree/master/statistics https://github.com/melling/MathAndScienceNotes/tree/master/s... https://github.com/melling/MathAndScienceNotes/blob/master/machine_learning.md https://github.com/melling/MathAndScienceNotes/blob/master/m... This recent HN was interesting, for example: https://news.ycombinator.com/item?id=19811715 https://news.ycombinator.com/item?id=19811715
siwatanejo 7y ago
That's like saying "learn to play an instrument, not cooking". Everyone has different tastes/needs.
Profan 7y ago
The article reads a bit like a rather long way for the author to excuse avoid learning a few of the natural languages of which it seems he would have much use. (Like French that they mention half their family speaking, or Mandarin with which they say they have a fascination..) 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..
Al-Khwarizmi 7y ago
I don't get the point they're trying to make. 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.
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js8 7y ago
Actually, math is not an universal language. There are several different languages within math, see http://math.ucr.edu/home/baez/rosetta.pdf http://math.ucr.edu/home/baez/rosetta.pdf
seanmcdirmid 7y ago
As someone who lived in China for 10 years, they aren’t wrong if we are just talking about earning potential. The number of bilinguals is pretty high, you would make more than a couple of thousand RMB a month if you knew English in addition to a native mandarin. On the other hand, a machine learning expert would easily start around 60k RMB/month. From a personal perspective, knowing another language is enriching, but don’t do it purely for the earnings gain.
- Kaveren 7y ago
  If you're living in a country where you don't speak the mainstream language, living there is more than reason enough by itself to learn it.
  - whfeiabsvdv 7y ago
    And it’s embarrassing how many people live in a country for years but still can’t be bothered to learn the language. Especially in East Asia.
    - seanmcdirmid 7y ago
      That really isn’t China. You won’t survive without some mandarin, so you learn a basic level pretty quickly.
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  - seanmcdirmid 7y ago
    A lot of foreigners working in China get by with only basic daily life mandarin. Mine was better than most, but no where useable for work. 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.
    - Kaveren 7y ago
      It's pretty embarrassing to live in a country for 10 years and not being able to use it for work.
malloryerik 7y ago
Maybe he should try studying math in Mandarin. It doesn't have to be so zero-sum...
- twelve40 7y ago
  haha that's very optimistic! I'm thinking about getting into gymnastics and also maybe skiing, a cork 720 backflip seems like a good first step!
xvilka 7y ago
There is a lot of unique content in Chinese already, and the number will grow substantially in the upcoming years. It includes scientific and not-scientific content. So I wouldn't call learning Mandarin a "waste of time".
- AFascistWorld 7y ago
  >It includes scientific 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.
  - darklajid 7y ago
    Meeting someone half way is nice. 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..
  - slaslasla 7y ago
    With that mentality I doubt that you speak a foreign language. If that's the case, of course you think that everything "important" is translated for you already - it's not going to show up on Google if you don't search it in its published language. Considering your tone I doubt I can convince you, so all I will say is that you don't know what you're missing.
draw_down 7y ago
Seems a bit silly. Americans typically learn enough math for the example problems he lists by the time they graduate high school. I don't think learning Mandarin is such a bad idea, personally.
mettamage 7y ago
You want to learn Mandarin to talk to people who cannot speak the languages you know, or because you’re interested in Chinese culture/history. 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.
- jm__87 7y ago
  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. 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.
  - khuey 7y ago
    "My hobby is X and I want to be better at it" seems like a pretty strong and clear goal to me.
    - jm__87 7y ago
      Not really, though. I build software for a living. If I told my boss "we should make X better" they would probably want to know in what way will X be better, how much better do I want it to be, what will we gain from these improvements and approximately how long will it take me to make the improvements. That is, there should be a clear goal in mind that fits in to the bigger picture with a rough estimate of cost associated to determine if this task is worth undertaking. 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.
unixbeard1337 7y ago
My read on this is pretty complex. On the one hand, my verbal ability is off the charts - I never scored lower than an 800 on a PSAT or SAT. My math ability is good but not great. For some time I've felt I'd have been better served by being the worst math or CS student at my college rather than one of the best foreign language students. 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.
- alexhutcheson 7y ago
  Yeah, even for state schools there is often a foreign language requirement. For example, University of Maryland requires applicants to have taken at least 2 years of foreign language courses[1]. If you decide not to check those boxes, you’re just making the college application process unnecessarily difficult for yourself. Take 4 years of Spanish or whatever else and move on. [1] https://admissions.umd.edu/apply/requirements/freshman https://admissions.umd.edu/apply/requirements/freshman
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dvduval 7y ago
Math + Mandarin = X; Math + English = Y; Mandarin = 1.11; English = 1.12; Article Usefulness = Math(X-Y)
- abrax3141 7y ago
  You need to factor in: “English is the de facto language of Business, Engineering, Science, and, most influentially, The Internet.”
  - dvduval 7y ago
    Ok, but spend a little time on the Chinese internet. Sure, they use "some" obligatory English, but the dependency is likely not what many imagine it to be.
throwaway072019 7y ago
Someone who's studying these as a hobby is likely going to run into more uses for Mandarin in their day to day life than, say, Calculus. You're more likely going to run into a situation where you're saying "I wish I could talk to that person" or "I wish I knew what that said" than you are going to run into a situation where you go "I wish I could calculate the second derivative of that formula." And though I doubt self-studying either of those is going to boost your career much, self-studying Mandarin is probably going to be more beneficial (it makes sense to stick "I speak Mandarin" on more resumes than "I know calculus"). 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.
- superkuh 7y ago
  Sure, you don't run into situations requiring math. Instead existing everyday situations are perceived in new ways because you understand calculus.
  - throwaway072019 7y ago
    Can you give an example? I can't think of any everyday situation that most people would run into where calculus comes in handy. It's definitely necessary for certain specific applications, but not ones I'd call everyday situations.
    - im3w1l 7y ago
      A lot of things are governed by differential equations, so understanding how they behave is helpful. Financial models, physics models, biology models commonly use them.
      - abrax3141 7y ago
        Epidemics, zombie invasions, zombie epidemics, vaccination, vaccination against zombie invasions.
      - 7y ago
azangru 7y ago
I am sad I am not seeing a strong cultural push towards everyone learning a single common language (which, for historical reasons, could well be English) at least as a well-acquired second language. Instead, the received present-day norm is to insist on cultural and linguistic diversity. Learn Spanish. Learn Mandarin. Learn German. Learn French. Oh, and while you are at it, learn Welsh or Irish too... It’s bewildering. And those enormous corps of translators seem like such a wasted effort!
- Tharkun 7y ago
  Y Gymraeg is a lovely language. Music to my ears. 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.
  - klodolph 7y ago
    “Literal lingua franca” might be a bit confusing, because Mediterranean Lingua Franca was a pidgin based on northern Italian dialects.
  - seszett 7y ago
    English is already a mandatory second language in pretty much all countries of the EU. Where it isn't mandatory, it is still the de facto second language in education.
  - azangru 7y ago
    > 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. 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.
ptaipale 7y ago
From article: "So, really, there are only five global languages: English, Mandarin, Hindi, Spanish, and Arabic." 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".)
- bilbo0s 7y ago
  I don't know man? 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.
  - Apocryphon 7y ago
    At some point it just seems like semantics, appropriately enough. There are some significant regional languages like Arabic - or Portuguese, which hasn't been brought up yet - that a lot of people speak and potentially can be relevant depending on the industry or field. It's just that not all of those people are as widely distributed as the other languages.
thinkpad20 7y ago
> Just as natural languages derive directly from our needs to do things with, and communicate about, things in, and state of in the real world, such as running away from lions, attracting mates, and (more recently) engaging in commerce, mathematics derives directly from our needs to do the exact same sorts of things: count chickens (or the number of lions you are running away from), mark time, distance, and rate (as you run from them) and their relationships, and so on. 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.
Tharkun 7y ago
I feel like it's much easier to start learning Mandarin than Maths. I can't really put into words why I feel this way, given that there are great resources like Khan Academy out there. Maybe it's easier to gauge fluency in a language than it is in maths? When do you stop learning? Maybe you're proficient enough when you can order from an all-Mandarin menu? As soon as you can't read a bit on a menu, you know what you need to work on next. But what about maths? I know how to add and divide. I'm fluent at trig and pretty good at some bits of algebra. Pretty rusty in calculus and OK at stats. I'm sure having this knowledge makes parts of my job easier. But maths is such a huge and diverse field. 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.
alexhutcheson 7y ago
Another compelling point is that high school foreign language students almost never gain meaningful competence in the language they study: https://www.econlib.org/archives/2012/08/the_marginal_pr.html https://www.econlib.org/archives/2012/08/the_marginal_pr.htm... 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.
- Kaveren 7y ago
  As far as the U.S. goes, I doubt students remember much of the math they learn, or gain much more competency in math than they would via a language course.
  - robertAngst 7y ago
    I teach a programming class and one of the 'easy' things I ask about is- "Have you taken algebra?" 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.
    - Kaveren 7y ago
      Knowing what functions and variables are is below high school level, and I'd say it'd be comparative to knowing basic greetings in a foreign language. I doubt that many students who don't go on to study math after high school remember what's taught in courses at or past the Algebra 2 level.
  - alexhutcheson 7y ago
    There are lots of standardized tests that evaluate students’ math proficiency, and lots of research examining specifically how much math proficiency students gain from each year of school. Learning and retention could definitely be improved, but I’ve never seen research that claims it’s as low as it apparently is for foreign languages.
mantap 7y ago
Learning other languages has absolutely improved my life and changed the way I think, just as much as learning mathematics. It has opened my eyes to the world that exists outside the anglosphere. Just make sure that you have native speakers to talk to, the benefit of learning a language is being able to talk to people!
cosmodisk 7y ago
Languages are overrated.I was born in a country with population of only 3M people,so I had no choice but to learn English.Later on in life I also learned Russian,because I ended up living with Russians for more than a year.Yes, it's great to go out there and be able to talk to people but that's about where it ends. That's why, unless one has some useful skills(IT, engineering, plumbing,etc.), knowing languages won't take you very far.In my previous company most people spoke at least 4 languages.And what? Everybody was on crappy salaries,even though most were very well educated but very few could do anything outside linguistics sector.In business, languages help, however I'm yet to see any jobs that'd pay more just because one can speak German and Italian...
chmod775 7y ago
The author's argument immediately fails at the fact that math papers are written in natural language and you'll have no chance of understanding the paper if you don't speak that language. 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%95%B0 https://zh.wikipedia.org/wiki/%E8%BF%9E%E7%BB%AD%E5%87%BD%E6...
maoeurk 7y ago
The author raises a good point that I agree with: math provides more direct value than learning a foreign language to native English speakers. The author talks about what children should be learning and I don't know enough about children's education to disagree, but if you're an adult, I think it's a good idea to learn at least one second language. 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.
carapace 7y ago
Fun fact: more people speak English in China than in North America. - - - - In re: teaching math ASAP see Iconic Math http://iconicmath.com/ http://iconicmath.com/ and (the general idea of) "Proofs without words" https://en.wikipedia.org/wiki/Proof_without_words https://en.wikipedia.org/wiki/Proof_without_words
- Apfel 7y ago
  Having lived in China for several years, it's very important to stress that the average English level of those "English speakers" is lower than that of your average American toddler.
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TomMckenny 7y ago
The author makes a good point of course. 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.
iamvik 7y ago
I like learning languages because I like learning. There doesn't need to be a reason. This is a very engineery perspective, I don't like it.
ivan_ah 7y ago
I like the comparison between learning the language of math and learning a foreign language. In both cases, learning the language gives you increased access to more culture, history, knowledge, and means to express yourself. This is a good way to answer "Why do need to learn math?" which people often ask me. As in "What am-I going to use this for?" 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...
heisenbit 7y ago
Before one has learned a foreign language one has not a deep understanding of their first language at all.
nneonneo 7y ago
Basic math is _really_ important, and not uniformly taught well. Stuff like understanding compound interest would help a _lot_ of people avoid poverty or financial hardship. What's surprising to me is that mathematics education (in many places) emphasizes things that are rarely useful _in daily life_ while ignoring things that are actually critical in many situations.
- marcolussetti 7y ago
  > Basic math is _really_ important, and not uniformly taught well. Stuff like understanding compound interest would help a _lot_ of people avoid poverty or financial hardship. What's surprising to me is that mathematics education (in many places) emphasizes things that are rarely useful _in daily life_ while ignoring things that are actually critical in many situations. 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.
pimmen 7y ago
The math in high school was more relevant 50 years ago than now, though. Most students who learn calculus will never, ever, integrate a function again in their life. Most people who don’t learn statistics will get bombarded with arguments based on statistical analysis, often done sloppily but only obvious to someone with training in the subject. So, if your choice is between calculus or Spanish, Spanish might be the better choice.
- gshubert17 7y ago
  Steven Strogatz in his book "Infinite Powers" shares the story of author Herman Wouk interviewing Richard Feynman about his role in the Manhattan Project. Feynman asked Wouk if he knew calculus. When Wouk replied, no, Feynman said "You had better learn it. It's the language God talks". 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.html https://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.htm...
  - pimmen 7y ago
    I agree, learning calculus does enhance one’s life. Statistics enhances your life even more though since you will actually use it. I use calculus sometimes at work and I use it when learning new mathematical concepts but it still doesn’t even come close to how important statistics is to me. 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.
otabdeveloper2 7y ago
Why not both? Seems to work for the rest of humanity.
feinstruktur 7y ago
Or walk and chew gum, like the rest of the world does.
floki999 7y ago
Can't disagree more. Learning a spoken language is much more than picking-up a communication tool - it opens a world of culture and thought that is bigger than the language itself. Yes, the same can be said of mathematics, and both are as valuable. 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.
- bernardv 7y ago
  Totally agree. A second language expands your world dramatically.
bigred100 7y ago
This sounds like wonderful advice to me. If you are an English speaker, I frankly don’t see the return on the immense investment of time and energy learning a language requires unless you will eg live there or do much business there. Unfortunately for the average person I’d imagine learning math might not be extraordinarily useful either.
gumby 7y ago
Why are they mutually exclusive? 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.
m0llusk 7y ago
What you should learn depends on your interests. Curious about metallurgy? Then German holds a great reservoir of hard won knowledge. Culture, aesthetics, and hard math? There French has profound influence. And so on. Buddhist wisdom is scribed in Sanskrit, Hindi, Chinese, and many others. Extend and spread your knowledge using whatever language and idioms are most appropriate and useful.
babayega2 7y ago
From my experience (and I emphasize on that) I can tell you from us (I'm from East Africa, speaking English, Swahili, French and two other natives languages) being proficient in at least English/French is an existential question. I really understand why a US citizen may think twice before starting learning a new language. For us, if you want a "normal" life, you do have to learn other 2 languages. We do not have that luxury.
beenBoutIT 7y ago
There's no shortage of Math advocates, one of you needs to put together the Math equivalent of DuoLingo. A math textbook isn't the only way to work on math daily.
masayune 7y ago
So is there a better way to learn math now? I haven’t taken a course in over a decade and would love to understand proofs. I admittedly memorized a lot to get through math during K-12 and most of Uni.

174 points by abrax3141 7y ago

Note that the Wikipedia claim about total speakers, the Wiki page notes that "Speaker totals are generally not reliable because they sum estimates from different dates and sources, usually uncited."

cromwellian 7y ago

Why not learn multiple? Why make a false dichotomy? Math, programming languages, and alternative spoken languages are distinct useful things you can learn. Otherwise what if someone said, don’t learn Math, learn Modula-2?

coldtea 7y ago
>Why not learn multiple? Why make a false dichotomy? Because of opportunity cost
- buzhidao 7y ago
  not really. if you are waiting in a line, or taking public transportation, you can use you smartphone to practice some natural language, but not math which requires deep focus.
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- almostdeadguy 7y ago
  Okay if you want to treat life like an RPG you need to minmax the right skills in, fine. That's a very strange, naively calculated, and from my perspective, totally unfulfilling way to live life.
  - antidesitter 7y ago
    That’s a very strange reading of the parent comment.
  - jasode 7y ago
    >you want to treat life like an RPG you need to minmax the right skills in, fine. That's a very strange, naively calculated, and from my perspective, totally unfulfilling way to live life. 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.)
    - almostdeadguy 7y ago
      > It's not naive to try and optimize learning to help maximize a fulfilling life. The time in life to learn is finite and therefore choices have to be made. 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.
- malaxii 7y ago
  The opportunity cost of learning a language at school is very small.
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mpoteat 7y ago
I've always had a suspicion that one person can't be a master of all things due to the physical limitations of human memory. Isn't that why we specialize?
- whatshisface 7y ago
  More like the physical limitations on lifespan.
  - coss 7y ago
    But probably memory as well. If I start specializing elsewhere I'll forget the intricate details of the thing I'm already specialized in.
    - pen2l 7y ago
      Don't think it works like that. 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.
      - colordrops 7y ago
        It does work like that. As you get older your ability to retain information wanes.
        Apocryphon 7y ago
        That could be physical degradation from age, not necessarily the "running out of disk space".
        colordrops 7y ago
        Why does the cause matter?
rolltiide 7y ago
Eh read the article, there are more interesting points worth discussing or disagreeing with in it

mistermann 7y ago

I would argue that an individual (and in turn, the entire world) would be benefit more from learning the "languages" of, or getting a good grounding in, logic and epistemology. 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.

tzjmetron 7y ago

Plain retarded tripe.

finnjohnsen2 7y ago

«there are no studies that suggest that learning math as a “native speaker” does not have at least the same, and perhaps even more benefit», this reasoning is so flawed.

melling 7y ago

I collect math, machine learning, statistics, etc urls. The ones discussed on HN have the HN discussion below the article: https://github.com/melling/MathAndScienceNotes/blob/master/math.md https://github.com/melling/MathAndScienceNotes/blob/master/m... https://github.com/melling/MathAndScienceNotes/tree/master/statistics https://github.com/melling/MathAndScienceNotes/tree/master/s... https://github.com/melling/MathAndScienceNotes/blob/master/machine_learning.md https://github.com/melling/MathAndScienceNotes/blob/master/m... This recent HN was interesting, for example: https://news.ycombinator.com/item?id=19811715 https://news.ycombinator.com/item?id=19811715

siwatanejo 7y ago

That's like saying "learn to play an instrument, not cooking". Everyone has different tastes/needs.

Profan 7y ago

The article reads a bit like a rather long way for the author to excuse avoid learning a few of the natural languages of which it seems he would have much use. (Like French that they mention half their family speaking, or Mandarin with which they say they have a fascination..) 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..

Al-Khwarizmi 7y ago

I don't get the point they're trying to make. 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.

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js8 7y ago

Actually, math is not an universal language. There are several different languages within math, see http://math.ucr.edu/home/baez/rosetta.pdf http://math.ucr.edu/home/baez/rosetta.pdf

seanmcdirmid 7y ago

As someone who lived in China for 10 years, they aren’t wrong if we are just talking about earning potential. The number of bilinguals is pretty high, you would make more than a couple of thousand RMB a month if you knew English in addition to a native mandarin. On the other hand, a machine learning expert would easily start around 60k RMB/month. From a personal perspective, knowing another language is enriching, but don’t do it purely for the earnings gain.

Kaveren 7y ago
If you're living in a country where you don't speak the mainstream language, living there is more than reason enough by itself to learn it.
- whfeiabsvdv 7y ago
  And it’s embarrassing how many people live in a country for years but still can’t be bothered to learn the language. Especially in East Asia.
  - seanmcdirmid 7y ago
    That really isn’t China. You won’t survive without some mandarin, so you learn a basic level pretty quickly.
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- seanmcdirmid 7y ago
  A lot of foreigners working in China get by with only basic daily life mandarin. Mine was better than most, but no where useable for work. 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.
  - Kaveren 7y ago
    It's pretty embarrassing to live in a country for 10 years and not being able to use it for work.

malloryerik 7y ago

Maybe he should try studying math in Mandarin. It doesn't have to be so zero-sum...

twelve40 7y ago
haha that's very optimistic! I'm thinking about getting into gymnastics and also maybe skiing, a cork 720 backflip seems like a good first step!

xvilka 7y ago

There is a lot of unique content in Chinese already, and the number will grow substantially in the upcoming years. It includes scientific and not-scientific content. So I wouldn't call learning Mandarin a "waste of time".

AFascistWorld 7y ago
>It includes scientific 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.
- darklajid 7y ago
  Meeting someone half way is nice. 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..
- slaslasla 7y ago
  With that mentality I doubt that you speak a foreign language. If that's the case, of course you think that everything "important" is translated for you already - it's not going to show up on Google if you don't search it in its published language. Considering your tone I doubt I can convince you, so all I will say is that you don't know what you're missing.

draw_down 7y ago

Seems a bit silly. Americans typically learn enough math for the example problems he lists by the time they graduate high school. I don't think learning Mandarin is such a bad idea, personally.

mettamage 7y ago

You want to learn Mandarin to talk to people who cannot speak the languages you know, or because you’re interested in Chinese culture/history. 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.

jm__87 7y ago
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. 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.
- khuey 7y ago
  "My hobby is X and I want to be better at it" seems like a pretty strong and clear goal to me.
  - jm__87 7y ago
    Not really, though. I build software for a living. If I told my boss "we should make X better" they would probably want to know in what way will X be better, how much better do I want it to be, what will we gain from these improvements and approximately how long will it take me to make the improvements. That is, there should be a clear goal in mind that fits in to the bigger picture with a rough estimate of cost associated to determine if this task is worth undertaking. 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.

unixbeard1337 7y ago

My read on this is pretty complex. On the one hand, my verbal ability is off the charts - I never scored lower than an 800 on a PSAT or SAT. My math ability is good but not great. For some time I've felt I'd have been better served by being the worst math or CS student at my college rather than one of the best foreign language students. 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.

alexhutcheson 7y ago
Yeah, even for state schools there is often a foreign language requirement. For example, University of Maryland requires applicants to have taken at least 2 years of foreign language courses[1]. If you decide not to check those boxes, you’re just making the college application process unnecessarily difficult for yourself. Take 4 years of Spanish or whatever else and move on. [1] https://admissions.umd.edu/apply/requirements/freshman https://admissions.umd.edu/apply/requirements/freshman

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dvduval 7y ago

Math + Mandarin = X; Math + English = Y; Mandarin = 1.11; English = 1.12; Article Usefulness = Math(X-Y)

abrax3141 7y ago
You need to factor in: “English is the de facto language of Business, Engineering, Science, and, most influentially, The Internet.”
- dvduval 7y ago
  Ok, but spend a little time on the Chinese internet. Sure, they use "some" obligatory English, but the dependency is likely not what many imagine it to be.

throwaway072019 7y ago

Someone who's studying these as a hobby is likely going to run into more uses for Mandarin in their day to day life than, say, Calculus. You're more likely going to run into a situation where you're saying "I wish I could talk to that person" or "I wish I knew what that said" than you are going to run into a situation where you go "I wish I could calculate the second derivative of that formula." And though I doubt self-studying either of those is going to boost your career much, self-studying Mandarin is probably going to be more beneficial (it makes sense to stick "I speak Mandarin" on more resumes than "I know calculus"). 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.

superkuh 7y ago
Sure, you don't run into situations requiring math. Instead existing everyday situations are perceived in new ways because you understand calculus.
- throwaway072019 7y ago
  Can you give an example? I can't think of any everyday situation that most people would run into where calculus comes in handy. It's definitely necessary for certain specific applications, but not ones I'd call everyday situations.
  - im3w1l 7y ago
    A lot of things are governed by differential equations, so understanding how they behave is helpful. Financial models, physics models, biology models commonly use them.
    - abrax3141 7y ago
      Epidemics, zombie invasions, zombie epidemics, vaccination, vaccination against zombie invasions.
    - 7y ago

azangru 7y ago

I am sad I am not seeing a strong cultural push towards everyone learning a single common language (which, for historical reasons, could well be English) at least as a well-acquired second language. Instead, the received present-day norm is to insist on cultural and linguistic diversity. Learn Spanish. Learn Mandarin. Learn German. Learn French. Oh, and while you are at it, learn Welsh or Irish too... It’s bewildering. And those enormous corps of translators seem like such a wasted effort!

Tharkun 7y ago
Y Gymraeg is a lovely language. Music to my ears. 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.
- klodolph 7y ago
  “Literal lingua franca” might be a bit confusing, because Mediterranean Lingua Franca was a pidgin based on northern Italian dialects.
- seszett 7y ago
  English is already a mandatory second language in pretty much all countries of the EU. Where it isn't mandatory, it is still the de facto second language in education.
- azangru 7y ago
  > 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. 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.

ptaipale 7y ago

From article: "So, really, there are only five global languages: English, Mandarin, Hindi, Spanish, and Arabic." 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".)

bilbo0s 7y ago
I don't know man? 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.
- Apocryphon 7y ago
  At some point it just seems like semantics, appropriately enough. There are some significant regional languages like Arabic - or Portuguese, which hasn't been brought up yet - that a lot of people speak and potentially can be relevant depending on the industry or field. It's just that not all of those people are as widely distributed as the other languages.

thinkpad20 7y ago

> Just as natural languages derive directly from our needs to do things with, and communicate about, things in, and state of in the real world, such as running away from lions, attracting mates, and (more recently) engaging in commerce, mathematics derives directly from our needs to do the exact same sorts of things: count chickens (or the number of lions you are running away from), mark time, distance, and rate (as you run from them) and their relationships, and so on. 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.

Tharkun 7y ago

I feel like it's much easier to start learning Mandarin than Maths. I can't really put into words why I feel this way, given that there are great resources like Khan Academy out there. Maybe it's easier to gauge fluency in a language than it is in maths? When do you stop learning? Maybe you're proficient enough when you can order from an all-Mandarin menu? As soon as you can't read a bit on a menu, you know what you need to work on next. But what about maths? I know how to add and divide. I'm fluent at trig and pretty good at some bits of algebra. Pretty rusty in calculus and OK at stats. I'm sure having this knowledge makes parts of my job easier. But maths is such a huge and diverse field. 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.

alexhutcheson 7y ago

Another compelling point is that high school foreign language students almost never gain meaningful competence in the language they study: https://www.econlib.org/archives/2012/08/the_marginal_pr.html https://www.econlib.org/archives/2012/08/the_marginal_pr.htm... 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.

Kaveren 7y ago
As far as the U.S. goes, I doubt students remember much of the math they learn, or gain much more competency in math than they would via a language course.
- robertAngst 7y ago
  I teach a programming class and one of the 'easy' things I ask about is- "Have you taken algebra?" 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.
  - Kaveren 7y ago
    Knowing what functions and variables are is below high school level, and I'd say it'd be comparative to knowing basic greetings in a foreign language. I doubt that many students who don't go on to study math after high school remember what's taught in courses at or past the Algebra 2 level.
- alexhutcheson 7y ago
  There are lots of standardized tests that evaluate students’ math proficiency, and lots of research examining specifically how much math proficiency students gain from each year of school. Learning and retention could definitely be improved, but I’ve never seen research that claims it’s as low as it apparently is for foreign languages.

mantap 7y ago

Learning other languages has absolutely improved my life and changed the way I think, just as much as learning mathematics. It has opened my eyes to the world that exists outside the anglosphere. Just make sure that you have native speakers to talk to, the benefit of learning a language is being able to talk to people!

cosmodisk 7y ago

Languages are overrated.I was born in a country with population of only 3M people,so I had no choice but to learn English.Later on in life I also learned Russian,because I ended up living with Russians for more than a year.Yes, it's great to go out there and be able to talk to people but that's about where it ends. That's why, unless one has some useful skills(IT, engineering, plumbing,etc.), knowing languages won't take you very far.In my previous company most people spoke at least 4 languages.And what? Everybody was on crappy salaries,even though most were very well educated but very few could do anything outside linguistics sector.In business, languages help, however I'm yet to see any jobs that'd pay more just because one can speak German and Italian...

chmod775 7y ago

The author's argument immediately fails at the fact that math papers are written in natural language and you'll have no chance of understanding the paper if you don't speak that language. 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%95%B0 https://zh.wikipedia.org/wiki/%E8%BF%9E%E7%BB%AD%E5%87%BD%E6...

maoeurk 7y ago

The author raises a good point that I agree with: math provides more direct value than learning a foreign language to native English speakers. The author talks about what children should be learning and I don't know enough about children's education to disagree, but if you're an adult, I think it's a good idea to learn at least one second language. 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.

carapace 7y ago

Fun fact: more people speak English in China than in North America. - - - - In re: teaching math ASAP see Iconic Math http://iconicmath.com/ http://iconicmath.com/ and (the general idea of) "Proofs without words" https://en.wikipedia.org/wiki/Proof_without_words https://en.wikipedia.org/wiki/Proof_without_words

Apfel 7y ago
Having lived in China for several years, it's very important to stress that the average English level of those "English speakers" is lower than that of your average American toddler.
- deleted 7y ago
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TomMckenny 7y ago

The author makes a good point of course. 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.

iamvik 7y ago

I like learning languages because I like learning. There doesn't need to be a reason. This is a very engineery perspective, I don't like it.

ivan_ah 7y ago

I like the comparison between learning the language of math and learning a foreign language. In both cases, learning the language gives you increased access to more culture, history, knowledge, and means to express yourself. This is a good way to answer "Why do need to learn math?" which people often ask me. As in "What am-I going to use this for?" 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...

heisenbit 7y ago

Before one has learned a foreign language one has not a deep understanding of their first language at all.

nneonneo 7y ago

Basic math is _really_ important, and not uniformly taught well. Stuff like understanding compound interest would help a _lot_ of people avoid poverty or financial hardship. What's surprising to me is that mathematics education (in many places) emphasizes things that are rarely useful _in daily life_ while ignoring things that are actually critical in many situations.

marcolussetti 7y ago
> Basic math is _really_ important, and not uniformly taught well. Stuff like understanding compound interest would help a _lot_ of people avoid poverty or financial hardship. What's surprising to me is that mathematics education (in many places) emphasizes things that are rarely useful _in daily life_ while ignoring things that are actually critical in many situations. 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.

pimmen 7y ago

The math in high school was more relevant 50 years ago than now, though. Most students who learn calculus will never, ever, integrate a function again in their life. Most people who don’t learn statistics will get bombarded with arguments based on statistical analysis, often done sloppily but only obvious to someone with training in the subject. So, if your choice is between calculus or Spanish, Spanish might be the better choice.

gshubert17 7y ago
Steven Strogatz in his book "Infinite Powers" shares the story of author Herman Wouk interviewing Richard Feynman about his role in the Manhattan Project. Feynman asked Wouk if he knew calculus. When Wouk replied, no, Feynman said "You had better learn it. It's the language God talks". 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.html https://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.htm...
- pimmen 7y ago
  I agree, learning calculus does enhance one’s life. Statistics enhances your life even more though since you will actually use it. I use calculus sometimes at work and I use it when learning new mathematical concepts but it still doesn’t even come close to how important statistics is to me. 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.

otabdeveloper2 7y ago

Why not both? Seems to work for the rest of humanity.

feinstruktur 7y ago

Or walk and chew gum, like the rest of the world does.

floki999 7y ago

Can't disagree more. Learning a spoken language is much more than picking-up a communication tool - it opens a world of culture and thought that is bigger than the language itself. Yes, the same can be said of mathematics, and both are as valuable. 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.

bernardv 7y ago
Totally agree. A second language expands your world dramatically.

bigred100 7y ago

This sounds like wonderful advice to me. If you are an English speaker, I frankly don’t see the return on the immense investment of time and energy learning a language requires unless you will eg live there or do much business there. Unfortunately for the average person I’d imagine learning math might not be extraordinarily useful either.

gumby 7y ago

Why are they mutually exclusive? 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.

m0llusk 7y ago

What you should learn depends on your interests. Curious about metallurgy? Then German holds a great reservoir of hard won knowledge. Culture, aesthetics, and hard math? There French has profound influence. And so on. Buddhist wisdom is scribed in Sanskrit, Hindi, Chinese, and many others. Extend and spread your knowledge using whatever language and idioms are most appropriate and useful.

babayega2 7y ago

From my experience (and I emphasize on that) I can tell you from us (I'm from East Africa, speaking English, Swahili, French and two other natives languages) being proficient in at least English/French is an existential question. I really understand why a US citizen may think twice before starting learning a new language. For us, if you want a "normal" life, you do have to learn other 2 languages. We do not have that luxury.

beenBoutIT 7y ago

There's no shortage of Math advocates, one of you needs to put together the Math equivalent of DuoLingo. A math textbook isn't the only way to work on math daily.

masayune 7y ago

So is there a better way to learn math now? I haven’t taken a course in over a decade and would love to understand proofs. I admittedly memorized a lot to get through math during K-12 and most of Uni.