Where Does Mathematical Ability Come From?, page

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reply posted on 11-2-2013 @ 02:16 AM by WaterBottle
Where does it come from? The instinct to survive. Simple mathematics is ingrained in our brain from birth.

Monkeys Do Math Like Humans

To see how far back more advanced capabilities such as addition might go, researchers at Duke University in Durham, N.C., focused on somewhat distant relatives of humans—rhesus monkeys. While the ancestors of chimpanzees—humanity's closest living relatives—diverged from us about 6 million years ago, humans and rhesus monkeys parted ways roughly 25 million years ago. In comparison, the age of dinosaurs only ended roughly 65 million years ago.

The scientists tested two monkeys and 14 college students on a math task where they had to add two sets of dots together. They were each shown one set of dots on a computer touchscreen for a half-second, and then another set a half-second later. They were then shown two separate clusters of dots at the same time, one of which was the correct sum of the first two sets. The monkeys were rewarded with Kool-Aid for choosing the right answers.

"When I first began training the monkeys on the addition task, I thought I would have to wait for many weeks before they understood the task," said researcher Jessica Cantlon, a cognitive neuroscientist at Duke. "We started the monkeys out on an easy version of the addition task, and the plan was to increase the difficulty of the problems gradually over time."

However, when Cantlon looked at the data from the first sessions, "it turned out that the monkeys were already performing the easy problems very well, and so I had to scramble to program the more difficult version of the task," she recalled.

Why they do it

Cantlon and her colleagues suggest math could help monkeys and other animals choose larger amounts of food or gauge the size of a rival group.

"Although we can never travel back in time to know exactly why or how this arithmetic ability evolved in humans, social battles might have something to do with it," she said. "Finding the perfect spot in the forest to stop and forage might also have something to do with it."

The researchers now want to learn more about what this primitive math system in monkeys is capable of "and whether it is the evolutionary basis of human mathematical thinking," Cantlon said. "We are also interested in whether this primitive mathematical system forms the basis of mathematical development in human children."

www.livescience.com...

Like Monkeys, Babies Know Math

In the study, seven-month-old babies were presented with the voices of two or three women saying "look." The infants could choose between looking at a video image of two or women saying the word or an image of three women saying it. The babies spent significantly more time looking at the image that matched the number of women talking.

"We conclude that the babies are showing an internal representation of 'two-ness' or 'three-ness' that is separate from sensory modalities and, thus, reflects an abstract internal process," said Elizabeth Brannon of Duke University.

www.livescience.com...

Pigeons Are Brilliant in Math

Pigeons have just tied with non-human primates in terms of math competence.

- Pigeons can not only discriminate quantities, they can also learn abstract mathematical concepts.

Pigeons may be ubiquitous, but they're also brainy, according to a new study that found these birds are on par with primates when it comes to numerical competence.

The study, published in the latest issue of the journal Science, discovered that pigeons can discriminate against different amounts of number-like objects, order pairs, and learn abstract mathematical rules. Aside from humans, only rhesus monkeys have exhibited equivalent skills.

news.discovery.com...

Now, I've never been good at math, as soon as it got complicated. I studied and tried but it never stuck. Other than geometry..... I don't know why, but then again I didn't go to the best of schools as a child. I guess that's why I ventured to the more creative side of life. I'm a designer, but then again a lot of that has to do with geometry, in a creative way.

reply posted on 11-2-2013 @ 04:08 PM by Wang Tang

You have provided overwhelming evidence that we are born with mathematical ability, and that is it an instinct to survive. So now I ask, how does this mathematical ability manifest itself? Obviously if someone is extremely good at math, they have mathematical ability. But what about other things like logical reasoning, learning a new language, common sense, and an ability to build and fix anything. Does mathematical ability cause these things, or are they just correlated?

And can you have repressed mathematical ability?

reply posted on 11-2-2013 @ 05:13 PM by Wang Tang

I'm not buying that hand-eye coordination is directly correlated to mathematical ability. I have a friend who is very good at math but can barely keep his balance while playing basketball. He frequently mishandles passes, shoots airballs, and misses the ball completely when going up for a rebound.

An interesting correlation I've noticed is great musicians I've known have all been good at math. I don't know if this stems from mathematical talent though, I think it has just as much to do with the ability to focus for long periods of time, and high levels of self motivation and initiative.

reply posted on 11-2-2013 @ 06:09 PM by schuyler
Originally posted by Wang Tang
post by schuyler

I'm not buying that hand-eye coordination is directly correlated to mathematical ability. I have a friend who is very good at math but can barely keep his balance while playing basketball. He frequently mishandles passes, shoots airballs, and misses the ball completely when going up for a rebound.

Not really the point. I'm not saying there is a correlation between abilities. I'm saying that your body performs mathematical functions all the time yet many people cannot, for whatever reason, do the mathematical formulas. In other words, there's a disconnect between the two, not a correlation. Your friend may be uncoordinated, be he still plays basketball. He doesn't have to be a star and coordination problems, for that matter, may have a completely different cause.

The point is that we've got mathematical functions physically. We perform trigonometric functions without needing any formulas. Your friend does catch the ball once in awhile, right? Well, his body computed a trig function to do so. He walks, and that requires multiple mathematical calculations per second to stay balanced and upright. When you catch a ball I throw to you, just once, reach out and grab it, you just computed a number of formulas analyzing speed and trajectory plus the movements of your own body, arm, and hand to get them to the place where the ball was going to be to intercept and catch it. It's not a trivial process. Try to figure it out on paper sometime.

The interesting aspect here is that we've actually got math down in many ways, yet so many of us can't seem to "put it on paper," as it were. I maintain there are a couple of reasons for that. One is the way we typically teach advanced math. Frankly, it's boring. Unless you find the process intellectually gratifying, there's little purpose to it. My personal experience was that once I had a real purpose and goal in mind, those regression equations became a lot more interesting. Combine a dull approach to teaching math with a little intellectual laziness, and voila! You have someone who "just can't do math."

But the larger question here is, What is knowledge? If you can DO something, but not express it in abstract terms, does that pertain to your ability and knowledge to DO it, or is it simply a matter of your inability to express it?
edit on 2/11/2013 by schuyler because: (no reason given)

reply posted on 11-2-2013 @ 08:35 PM by Wang Tang

I'm not sure what the purpose of mentioning physical mathematical functions. I just don't see how it relates to our mathematical ability. After all, there is math constantly going on in nature, with the planets orbitting around the sun and the tides of the ocean, but that doesn't mean nature has mathematical ability.

So I see you are saying the laws of nature are in mathematics... or... mathematics are in the laws of nature. Either way, being able to discover these mathematical laws while sitting in a math class seems to only be one manifestation of mathematical ability.
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