How "learnable" are mathematics?

[Suicidesoldier#1]

Layra-chan

Wait a second. Exactly what do you mean when you distinguish between how and why? What exactly would constitute an answer for "why"?
When someone asks for an answer as to why hot things burn skin, the typical answer is that human skin is sensitive to heat and that heat tends to flow from hotter things to colder things. Is this an answer for how, or why?

"Why" is, at least as far as I understand the word, is asking for a cause-and-effect relation. "This is true, therefore this is true." People with blood-type A and people with blood-type B typically don't interbreed, therefore blood-type AB is rare. Is this a how or a why?

That would be a how. Why is it that way, when AB blood poses a dominant hold over the other human species blood types and would easily cancel out every other blood type? That is the WHY factor.

How explains how something works- lighting bolts work becuase enough static energy builds up between extremely volatile and high moving water particles that help suspend dust in the air, and the temperature changes cause these clouds to vibrate and move even more, creating such a strong build up of electrons that the electric energy is so powerful that the static charge can reach the ground.

Why does this work? Because there are natural laws of physics ingrained into our universe that never fail and always repeat themselves. Why is there such a system? Nobody knows.



Some examples!




Question 1: How does god make puppies?
Answer 1: He just does.

Question 2: Why does god make puppies?
Answer 2: Um... to entertain us?






Question 1: So how did you blow up that building?

Answer 1: I used ANFO- a Mixture ammonium nitrate fertilizer and cheap gasoline, a mixture that becomes volatile once you combine hydrocarbons with a nitrate- in this case, despite being a mixture, it is still very volatile. Naturally, fertilizer and gasoline are relatively cheap compared to other explosives, and readily available to the public, and this is how I got 8000 pounds of it and blew up the building.

Of course, I used a rented van with the identification on it covered by a sticky note say "Sorry I'll move later" so it wouldn't be spotted. Then I drove it into the building, hiding it becuase I didn't get caught, and left. It had a 30 minute timer, more than enough time to allow me to escape.



Question 2: Why did you blow up that building; what was your motive?

Answer 2: I just felt like killing some peeps today.  

[VorpalNeko]

If your interpretation of "why" is entirely teleological, then asking "why" something exists is an inquiry to its purpose. And while lots of physical things do have a purpose (e.g., we can coherently talk about the purpose of electron transport in chloroplasts, or whatever), others have a vacuously trivial answer at best, since asking "why" presupposes something that just isn't necessarily true. That you can always ask a question doesn't mean it's always coherent.  

[Suicidesoldier#1]

VorpalNeko

If your interpretation of "why" is entirely teleological, then asking "why" something exists is an inquiry to its purpose. And while lots of physical things do have a purpose (e.g., we can coherently talk about the purpose of electron transport in chloroplasts, or whatever), others have a vacuously trivial answer at best, since asking "why" presupposes something that just isn't necessarily true. That you can always ask a question doesn't mean it's always coherent.

Err, yes. Except coherent may be a slightly misplaced adjective, considering the wide variety of contexts it could pertain to.  

[Basilia Ann E]

StandingOnTheMoon

I once made the snarky comment to Layra in the ED Sci & Tech forum in reference to her mathematical ability: "So, are you Asian, South Asian, or Jewish?" (I may be paraphrasing)

Given that there is certainly SOME expectation from SOME people that (East) Asians, South Asians, and Jews will be better at mathematics than other demographic groups, and further given that large populations will approach a perfect bell curve of distribution of aptitudes, doesn't this imply that learning higher order mathematics and the like may not be entirely aptitude but cultural? Does anyone have any hard numbers on this? Certainly it's a little from column A, and a little from column B, but in what proportions?

It basically comes down to attitude and expectations. Parental expectations of the "gifted" group are often centered around cultural expectations. Even if the parents - themselves - weren't educated. Education, in many of these cultures was the only way out of poverty.

In North America small business, in addition to education, provides a path out of poverty. As such, the necessity of an education is not considered in the same manner is it is in cultures were there are no other options.

A sample study of this need only be a look into the structure of school society. Identify what it means to be a nerd (geek, etc.) and compare it to the rest of the groups. Then add the immigrant into the equation. Remember, Asians were excluded from North American culture (by-law) until about 1975 - so they were culturally isolated.

 

[Suicidesoldier#1]

Einstein was one of the best mathematicians ever known.

To my knowledge, he's not Asian.





I highly doubt that people are genetically inclined to be good at math; people aren't even born with concepts of numbers. And if they were, it would be a random occurrence, nothing linked to a specific "genetic code" among various ethnic populations.

If someone was inherently good at math, they'd probably be good at music and and identifying sounds as well, as many studies have indicated that these things are linked and stimulated in the same portion of the brain. It would be a strong connection in that area of the brain, more or less, and not necessarily "math".

The real reason why we notice higher American Asian scores on the SAT is really more or less due to the constant increase in Asian Immigration. At this moment, a large number of Asian countries are seeking to expand and strengthen their country. A large majority of the people who we see in "American" schools are people who scored well in their old school in China, and were given payed way to the United States, or who were rich, relatively, so they could afford better schooling and move to the united States. This can easily out balance the small 4% Asian population living in the United States.

Right now, in a lot of Asian countries, there is a growing trend in appreciating mathematics as the primary academic schooling tool. First of all, history is something that doesn't necessarily carry over to other countries. Learning Chinese history is great, but it's hard to expand your economy that way. Being a good historian is great, but Historians only exist in societies that can support them, and generally are historians in one particular era or place in human history. "English" or language comprehension is obviously irrelevant; if your going to be moving around a lot, to other countries so that you can learn their language, the complex understanding of your own isn't necessarily methodically important to promote transport to another country. Science is a form of academics that can truly transcend multiple language and societal barriers, however, if these places had great science research and education centers than the need to ship their children off would be obsolete.




Math is relatively easy to move across barriers and teach. What do you not know how to do in math? Most of it is application. What is 2 + 2. What is 2 x 2. What is 1028 x 1028?

Numbers are easily understood and very well defined. Algorithms for solving mathematical problems are usually relatively simple, and bigger numbers simply take more time and scale easily. If you judge the speed of questions answered to the number of correct answers, then you can determine how "good" a person is at computing math problems. Math is very simple in the fact that there is a definitive right answer and a objective way to measure it.




A lack of technology we take for granted, such as calculators and computers, makes counting and other forms of math incredibly important. If you take a look at education in during the Industrial period of the United States, you'll see that people were more motivated to learn math, and at this time period human calculators were extremely important. Now a days math in places with advanced computers has become less integral, as we no longer require geniuses to compute math problems instantly and quickly- now we have calculators.

If anything, being good at math has more to do with a geographic and societal constraint placed on math.





But there's no use in speculating reasons for random data. Statistics are a way of counting. Their a way to mathematically determine a set objective criteria. They provide neither a solution nor an explanation for an event; they merely record it. It's useless to pretend that it means something.  

[StandingOnTheMoon]

Suicidesoldier#1

Einstein was one of the best mathematicians ever known.

To my knowledge, he's not Asian.

1) my initial post about about demographics was a joke

2) see my initial post  

[Suicidesoldier#1]

StandingOnTheMoon

Suicidesoldier#1

Einstein was one of the best mathematicians ever known.

To my knowledge, he's not Asian.

1) my initial post about about demographics was a joke

2) see my initial post

Have you ever heard of the Chaos theory?

Why is it that flipping a coin 100 times doesn't produce 50 tails and 50 heads every single time?

Could it be for a reason?

Or could it possibly be random occurrences, and that statistics collected on said data are arbitrary and random at best?




There is an expected "Margin of Error" in everything.

Sure, now a days Asians are a small percentage above everyone else in math, but in the future it could possibly be anyone.

The explanation for these differences is that there is an expected random statistical difference.

Namely due to thousands, and millions, and trillions, and infinite amounts of variables, and possible variables, that come into play.