Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: cheryl j on 06/08/2013 22:18:32
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I'm not sure where to place this post. It could go under biology (brain stuff) but since most discussions about math appear on the physics forum, I thought I'd post it here.
Malcolm Gladwell's book, "Outliers" is about the intermingling of environmental influences and innate ability in intelligence and success. There is a chapter about why many people of Asian background are good at math.
Basically, he gives to reasons: 1) language differences regarding numbers and 2) a different kind of traditional work ethic related to farming rice.
Regarding language, Gladwell says that human beings store digits in a memory loop that lasts two seconds.We more easily memorize what ever we can say or read within that two second span. The Chinese words for numbers are shorter and simpler and more numbers can be retained in short term memory. Chinese school children learn to count more numbers at an earlier age than children who speak languages with longer, more complex names for numbers. "The regularity of their number system also means that Asian children can perform basic functions, such as addition more easily. Ask an English speaking seven year old to add thirty-seven and and twenty two in her head, and she has to do the math (2 + 7 is 9, and 30 + 20 is 50, which makes 59.) Ask an Asian child to add three-tens-seven and two-tens-two, and then the necessary equation is right there, embedded in the sentence - it's five-tens-nine, because that is how their linguistic representation of numbers works.
Okay, that's just addition and school kids. But Gladwell's theories are based on the concept that small boosts early in life, from either culture or individual circumstance have a huge accumulative effect. (Another chapter discusses how the vast majority of professional hockey players are born in January Feb and March, because Jan 1st is the cut off date in kids' hockey and they were are bigger and better than their teammates, get more ice time, better coaching, and are selected to advance to the next level.)
But getting back to math and #2. Gladwell's "rice paddy' theory is a bit more speculative, in which he compares Asian and Western agriculture and its effect on people's mind set and work ethic. Rice farming, Gladwell says, is hugely labor intensive and quite complex. Fields have to be level to maintain a uniform level of water, seedlings have to be spaced evenly apart, thinned, weeded, and fertilized at the right time. But the up side is, if one works hard and everything is done right, it is almost always successful. The pay off is directly proportional to effort. Growing corn or wheat or vegetables is less labor intensive, relatively speaking, especially with machinery, - you plow, you seed, you wait and you harvest. But it is much more risky. Not enough rain, too much rain, late frost, infestation by insects means that you can work your ass off for nothing, and working even harder next time still won't guarantee success. Gladwell claims this is one reason why Asian culture or any culture that traditionally sees success as simply a result of effort is particularly suited to mathematics.
Like me, you might be saying, not all Westerners grew up on farm and many Asian engineers never stepped foot on a rice paddy, but Gladwell claims the cultural or family mindset is passed on for generations and provides some interesting documentation of scientific studies to support this in other chapters.
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An interesting idea but that deals only with arithmetic which is not real mathematics. mathematics proper is very different and is more like a symbolic language in its own right although I have come across similar suggestions of some nations or tribes having linguistic advantages. In particular it was one particular native north american language whose method of dealing linguistically with relationships in families made the understanding of group theory particularly easy.
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I agree. The author's premise, though, was that small advantages early in life (like finding arithmetic simple and enjoyable and receiving positive reinforcement from it) motivate one to pursue a subject at a more advanced level. He claims Asian students move on to algebra and more interesting areas of math much sooner than because of this.
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I think we're at least geometrically intuitive. When it comes to other fields of mathematic we're going into pure logic, and then it's harder to define. But when you move a arm you better 'counted' on what you do, even if you didn't know you did. As for the rest of it we will always find 'prophets', people that sees connections we don't think of normally, and that make use of them. It's immaterial feelings relating to emotions and dreams to me, then relating that to if you find it easier to use logics. It's insubstantial, and hard to test as there are so many parameters defining anything you do, at any moment, from your inner state at that moment to what parameters exist outside yourself defining it.
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But I have seen other relating to thought processes differing between Asian Mathematicians and Western, and I have a this funny suspicion that Russian Mathematicians may put weight on slightly different fields of mathematics too. but that is also about what you learn, not only about your language, and also about the philosophy emanating the society one live in. But what really makes me bristle is the idea of 'work ethics'? What the he* is that. You are born here, and you die here. It's all you do. 'Work ethics' is what you need to live in the moment inbetween, and that differs everywhere, with cultures, history etc. It's a non linear life, and history too I suspect :)
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Work ethic probably isn't an ideal term. It implies something moral about the willingness to put time and effort into completing a task. I suppose it has a moral aspect when it comes to completing a task someone is paying you to do, but when you are doing it for yourself, does that really make sense? Diligence or laziness may be more of a calculation one makes - how much time and effort will the task require? What do I think the odds of my success are if I put that time and effort in? 100% 50% 20%? If it takes more time and effort than I predicted, should I keep going, and how long before I give up? Is the outcome even something I value, or would my time be better spent doing something else?
A weird finding the author also noted involved a standardized test in schools called the TIMSS given to elementary and junior high students around the world. In addition to academic questions, there is also a very long, detailed questionnaire with personal questions, like parent's level of education, occupation, number of siblings, extracurricular activities, etc. It is so long and tedious that many students don't bother finishing it. You can rank countries just by the number of questions completed on the personal questionnaire, and if you compare that to the math rankings (of correctly solved problems), the author says, "They are exactly the same."
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Wow! Cheryl! I knew there was always something that I loved about you! :)
Thanks for this. It gave me an idea. I always had trouble with the multiplication table and that was because, I came to learn, I have memory problems. Your comments above gave me an idea. We can seek out words of short phrases that will help students learn the multiplication table by doing so. Instead of remembering those long phrases we can remeber shorter ones! Awesome!
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I always had trouble with the multiplication table
Like most people (I suppose) I learned the tables up to 12x at school, when I had a fairly good memory. Many years later, I learned the 13x, as an experiment. Now, at 73, the 2-12x give little trouble, but the 13x needs to be refreshed periodically to be used with any facility.
I guess that says something about the value of early learning.
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I'm going to conduct Bill's experiment and see what happens.
It does seem true that you can memorize or learn things better when you are younger. People claim you can learn also learn a foreign language faster and better before puberty because the brain is "primed" to learned language at that time in development.
I once whined to a math teacher that there should be more directions in math books, more discussion. And she said she thought there wasn't because "they want you to learn to think in the language in math."
Another teacher I know said his objective in teaching French was to get kids "to think in French" instead of thinking in English, translating it into French, and then saying it, because it takes too long. I took French in high school and University, but I don't know if I ever reached that point, except maybe when I was finally able to read novels - then I sort of felt like I was "thinking in French", but never when speaking it.
Anyway, the question I wish to ask is: Is learning math possibly like like learning a foreign language and more easily done before puberty? And I would also like to know if physicists and mathematicians can think about math in their heads without translating those symbols into their spoken or written names, and can they think about math without writing it down? As a biologist, I'm just curious how it works in their strange and mysterious minds.
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I'm going to conduct Bill's experiment and see what happens.
Thanks for creating this thread. It highly motivated me to get off my butt and take advice that I've been putting off for a while, helping children learn math. I want to catch them while they're young and haven't gotten sick of math and hated it yet. So I contacted the School Department and offered to take children who are doing poor in things like arithmetic and math and help them learn math, even more advanced levels of math. I can't thank you enough for starting this thread!
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And I would also like to know if physicists and mathematicians can think about math in their heads without translating those symbols into their spoken or written names, and can they think about math without writing it down? As a biologist, I'm just curious how it works in their strange and mysterious minds.
Introspection is surprisingly difficult at this level, but from the point of view of applied physics and engineering I think the underlying mental process is similar to that of biologists. Some very general concepts like "vertebra" or "momentum" are applicable to analysing or describing many different systems, and knowing how they evolve, behave, or are conserved, allows us to make useful predictions. It just happens that the physical quantities are very easy to manipulate and predict through their mathematical properties because the components (dimensions) are orthogonal and well-behaved, whereas a living biological system involves a whole lot of interdependencies, most of which are not understood or even suspected until they misbehave.
The maths of physics is very simple: adding, subtracting, dividing and multiplying, plus a few bits of geometry. Calculus is just neat way of multiplying and adding (integration) or subtracting and dividing (differentiation) at the same time. The clever bit that requires physical understanding, is analysing the system to determine which properties will be conserved and which will vary under a particular input.
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And I would also like to know if physicists and mathematicians can think about math in their heads without translating those symbols into their spoken or written names, and can they think about math without writing it down? As a biologist, I'm just curious how it works in their strange and mysterious minds.
Yes. Sometimes when I'm studying or thinking about something really intensely for a long time I even have dreams about it.
One example was trying to figure out a relationship between the different definitions of tensors. I figured it out in my head, not on paper.
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[Do] physicists and mathematicians think about math in their heads without translating those symbols into their spoken or written names, and can they think about math without writing it down?
I often mentally translate mathematical functions into graphs, and manipulate them in my head graphically rather than as words or equations - especially since a lot of the functions I deal with are functions of time, or probability distributions, ie mostly representable in 2 dimensions.
It's pretty easy to add and subtract two functions graphically; multiplication (or modulation) is moderately easy, but I can't recall ever needing to divide two functions (at least ones that went through zero)..
In slightly more complex cases, I can sometimes work out the effects of phase shifts, filters, correlation, Fourier transforms, probability distributions and convolution of probability distributions.
And if it gets too complex to do in my head, or I need numerical precision, I can use a spreadsheet to draw the graphs.
But I guess the reason I can do this is because I worked through the algebra in High School and University, and know roughly what comes out when you manipulate two functions. Having practiced as an electrical engineer, I am familiar with viewing functions on an oscilloscope, and seeing what happens when you manipulate the signal in various ways (at least for functions which I deal with regularly).
One of these days I should buy a symbolic maths package with integrated graphics...
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I often mentally translate mathematical functions into graphs, and manipulate them in my head graphically rather than as words or equations - especially since a lot of the functions I deal with are functions of time, or probability distributions, ie mostly representable in 2 dimensions.
Same here. Symmetry also plays a role in helping one think things through.
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I think we're at least geometrically intuitive. When it comes to other fields of mathematic we're going into pure logic, and then it's harder to define. But when you move a arm you better 'counted' on what you do, even if you didn't know you did. As for the rest of it we will always find 'prophets', people that sees connections we don't think of normally, and that make use of them. It's immaterial feelings relating to emotions and dreams to me, then relating that to if you find it easier to use logics. It's insubstantial, and hard to test as there are so many parameters defining anything you do, at any moment, from your inner state at that moment to what parameters exist outside yourself defining it.
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But I have seen other relating to thought processes differing between Asian Mathematicians and Western, and I have a this funny suspicion that Russian Mathematicians may put weight on slightly different fields of mathematics too. but that is also about what you learn, not only about your language, and also about the philosophy emanating the society one live in. But what really makes me bristle is the idea of 'work ethics'? What the he* is that. You are born here, and you die here. It's all you do. 'Work ethics' is what you need to live in the moment inbetween, and that differs everywhere, with cultures, history etc. It's a non linear life, and history too I suspect :)
I recall the story of an Indian guy who had almost no proper prior education concerning maths : he figures in the Guiness book of records , if i am not mistaken at least ,he startled and stunned the global math community by being able to come up with some equations, formulas ....relating to high level maths , which took brilliant mathematicians years to figure out .
That story also reminds me of an interesting article i read in a French scientific magazine (Science & Vie ) , some years ago, which tried to prove the very biological origin of maths ....
That article made its case very well , as i can remember .
Later ...Gotta go ,duty calls .
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I don't think though that there is any correlation between the ability in maths and culture ....I think that maths is something innate , biological ,the environment or culture just help develop or otherwise ...
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Yeah 'work ethics' have more negative associations than positive to me. As for what motivates you to study I think will depend on where you are born, the educational system, availability of Internet too. It also depends on your parents education and interests. But it is also so that we all grow up, becoming individuals, finding new interests. That's why education shouldn't be limited to your youth, it need to be freely available through a persons whole life, if society want to utilize their citizens to their 'fulmost' capabilities.
As for what will motivate one (then) I can't say . It's so subjective although we have some crude external common nominators, as money, peer prestige, and all sorts of power over someone else of course. But the best motivators is your mind, and your dreams/ideals naturally.
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I agree that different situations in life motivate us to learn, and by and large, they have to do with survival in society. And I am glad when no matter what - a person is interested in learning something. A trait like curiosity is a good engine for progress. How many examples of geniuses who grew up in dysfunctional families. And if curiosity + persistence, you get a rattling mixture. Yeah, and they weren't motivated by power or money. They were just themselves, for example, solving math problems for fun here plainmath.net, for a dream. And they became great people.
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Hi.
Welcome to the forum etc.
I still consider myself to be quite new here so I hope you don't mind if I ask one thing: How do you find these older threads?
Best Wishes.
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@gerardseal
Hello & Welcome!
I am a bit old on this forum now, but still unable to dig up such old OPs.
Same Query as Above, how did You manage to pull this off?
🤔
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It has been suggested that language rather than culture plays an important part. For most of us, maths begins with arithmetic, and some languages have more logical names for numbers. I don't know any Japanese but I'm told that for instance 99 -74 is "nine ten nine minus seven ten four" and so forth consistently for all numbers, unlike French "four twenty ten nine minus sixty fourteen" which is tres chic et tout francais but not intuitive.
Early arithmetic with an abacus also leads to considerable facility with numbers. I recall seeing a Chinese enthusiast factorising the date quicker than a western nerd could program the question in Basic.
However the most extraordinary number theorist A deeply religious Hindu, Ramanujan credited his substantial mathematical capacities to divinity, and said the mathematical knowledge he displayed was revealed to him by his family goddess Namagiri Thayar. He once said, "An equation for me has no meaning unless it expresses a thought of God."
suggests it is all down to culture after all!
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However the most extraordinary number theorist
... was quite possibly French.
https://en.wikipedia.org/wiki/%C3%89variste_Galois
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Algebra, not number theory.
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Possibly Ramanujan was a Savant...
Who did not realise he was one.
Spitting out equations without understanding how, can also point towards possible conning or cheating.
I personally do not see culture or traditions playing any vital role in absorbing mathematics.
Ps - Yes, certain Rats do eventually form the capability of swimming.
But that is not due to their heroic courage or inner strength, it's just a side effect of causal over population burst on their island of birth.
(Lack of basic resources creates excessive competition in which only the most timid survive)
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Spitting out equations without understanding how
Is there any evidence of anyone doing that, or are you just trolling again?
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Algebra, not number theory.
Was this a different M Évariste Galois?
https://bibbase.org/network/publication/galois-surlathoriedesnombres-1830
Sur la théorie des nombres. Galois, É. Bulletin des sciences mathématiques, physiques et chimiques, 13:428–435, 1830.
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Spitting out equations without understanding how
Is there any evidence of anyone doing that, or are you just trolling again?
You should Ideally pay a lil more Attention to the Subject in discussion...
I was referring to " Ramanujan ".
& I do not understand what exactly you meant by...
1) Am i Trolling?
2) Again?
Ps - perhaps it's time you finally learn to take things light, this is a Science Forum, Not a WarZone!
✌️
(chill)
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Spitting out equations without understanding how, can also point towards possible conning or cheating.
Only if somebody else has published the proof, which nobody had.
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Spitting out equations without understanding how, can also point towards possible conning or cheating.
Only if somebody else has published the proof, which nobody had.
Agreed!
👍
I have Nothing personal against one of the youngest Fellows of the
" Royal Society " or Trinity College.
But if Einstein came up with
E = mc(squared) & had no way of explaining how he derived it, & rather mentions it's from his
" Goddess, who bleeds physics "...
What is a critical & logical thinker supposed to make out of it?
I only pointed towards a possibility of something fishy.
If tomorrow i come up with an out of the world beautiful equation, but cannot explain how i got there, except that some alien civilization put it inside my brain thru telepathy...what would You make of Me?
Ps - Perhaps misassuming that the Original Source was Someone Else isn't entirely invalid...bcoz i can Bet my Azz it surely wasn't the Goddess!
(_/*\_)
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Maths often works backwards. Think of all the auxiliary functions that you would have learned at school if you'd stayed awake:
"Multiply both sides by e-bx"
"Why, sir?"
"Just do it and see what happens"
"Oh yes, it's differentiable!"
and then look up Wikipedia's list of favorite proofs where famous mathematicians have thrown some arbitrary auxiliary function into the mix without explanation, and abracadabra.....
A lot of maths is about leaning back from the problem and imagining what it looks like in 3D, or thinking of something vaguely like it that you have seen before. Did you ever ask a painter for his proof?
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I Think i get the Point you made here Sir!
👍
Only an Utter Fool would compare His " Lost Notebook " to the likes of the Voynich Manuscript.
Ps -
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Thanks BC, that made for a interesting read. It also makes me think of that Russian mathematician that refused that prize? We're all human. Ah ýes. https://iq.opengenus.org/grigori-perelman/
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It is a simple understanding. But after years of learning differences and similarities of school programs (Western and Russian mostly) and of the factors about being ‘technical’ or ‘humanitarian’ thinking to be distinguished in a high school I came to accept the next.
The subject here is for very young brains, right? In some brains, mathematics is built in the same way as knowledge of the native language. Up to senior school those who get the mathematics easily, are successful in physics and chemistry and even biology by translating other subjects to equations, diagrams etcetera. This is more about logic, might be. And some pupils who are brilliant in languages might be troubled in mathematics if they don't put much effort into it.
Regarding the school programs, they are pretty much the same, as I mentioned for Western and Russian knowledge. Might be a difference in load intensity, but the result after senior school is the same.
I would agree that culture or traditions are not playing any vital role in absorbing mathematics. This opinion I could get from history and what I know from having Eastern acquaintance now.
There are a lot of differences, but when it comes to mathematics, everybody is on the same page.
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Thanks for post