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Geometry may be hard-wired into brain, study shows
Reuters ^ | Thu Jan 19, 2006 | Anon

Posted on 01/20/2006 3:11:23 AM PST by Pharmboy

Amazonian hunter-gatherers who lack written language and who have never seen a math book score highly on basic tests of geometric concepts, researchers said on Thursday in a study that suggests geometry may be hard-wired into the brain.

Adults and children alike showed a clear grasp of concepts such as where the center of a circle is and the logical extension of a straight line, the researchers report in this week's issue of the journal Science.

Stanislas Dehaene of the College de France in Paris and colleagues tested 14 children and 30 adults of an Amazonian group called the Munduruku, and compared their findings to tests of U.S. adults and children.

"Munduruku children and adults spontaneously made use of basic geometric concepts such as points, lines, parallelism, or right angles to detect intruders in simple pictures, and they used distance, angle, and sense relationships in geometrical maps to locate hidden objects," they wrote.

"Our results provide evidence for geometrical intuitions in the absence of schooling, experience with graphic symbols or maps, or a rich language of geometrical terms."

Geometry is an ancient field and Dehaene's team postulated that it may spring from innate abilities.

"Many of its propositions -- that two points determine a line, or that three orthogonal axes localize a point -- are judged to be self-evident and yet have been questioned on the basis of logical argument, physical theory, or experiment," the researchers wrote.

There was no way the Munduruku could have learned these ideas, they added.

"Most of the children and adults who took part in our experiments inhabit scattered, isolated villages and have little or no schooling, rulers, compasses, or maps," they wrote.

"Furthermore, the Munduruku language has few words dedicated to arithmetical, geometrical, or spatial concepts, although a variety of metaphors are spontaneously used."

They designed arrays of six images, each of which contained five conforming to a geometric concept and one that violated it.

"The participants were asked, in their language, to point to the weird or ugly one," the researchers wrote.

"All participants, even those aged 6, performed well above the chance level of 16.6 percent," they found. The average score was nearly 67 percent correct -- identical to the score for U.S. children.

"The spontaneous understanding of geometrical concepts and maps by this remote human community provides evidence that core geometrical knowledge, like basic arithmetic, is a universal constituent of the human mind," they concluded.


TOPICS: Culture/Society; Foreign Affairs; Front Page News; News/Current Events
KEYWORDS: brain; cognition; crevolist; hardwired; hunting; math; southamerica
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Geometric constructs are key to understanding a 2 dimensional and 3 dimensional world. This is not surprising.
1 posted on 01/20/2006 3:11:26 AM PST by Pharmboy
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To: PatrickHenry; blam; voletti; aculeus; SunkenCiv; Physicist; thefactor

Math ping...for your personal interests and not meant for you to ping your lists.


2 posted on 01/20/2006 3:14:51 AM PST by Pharmboy (The stone age didn't end because they ran out of stones.)
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To: Pharmboy

Geometry is crucial to land navigation. It's not surprising that hunters understand


3 posted on 01/20/2006 3:26:38 AM PST by SauronOfMordor (A planned society is most appealing to those with the hubris to think they will be the planners)
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To: Pharmboy

They should've done their study in a pool hall... er... billiards parlor.


4 posted on 01/20/2006 3:30:03 AM PST by Pete'sWife (Dirt is for racing... asphalt is for getting there.)
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To: Pharmboy
"Adults and children alike showed a clear grasp of concepts such as where the center of a circle is and the logical extension of a straight line, the researchers report in this week's issue of the journal Science"

My geometry course was more demanding than this but then, I went to a Catholic High School

5 posted on 01/20/2006 3:33:28 AM PST by muir_redwoods (Free Sirhan Sirhan, after all, the bastard who killed Mary Jo Kopechne is walking around free)
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To: Pharmboy
"All participants, even those aged 6, performed well above the chance level of 16.6 percent," they found. The average score was nearly 67 percent correct -- identical to the score for U.S. children.

So, primitive hunter-gatherers who have never been inside a classroom score as high on geometry as American children who are being "educated" at $10,000 per head per year.

6 posted on 01/20/2006 3:43:52 AM PST by Junior (Identical fecal matter, alternate diurnal period)
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To: Junior

Great point...don't tell the teacher's union.


7 posted on 01/20/2006 3:48:19 AM PST by Pharmboy (The stone age didn't end because they ran out of stones.)
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To: SauronOfMordor
"Many of its propositions -- that two points determine a line, or that three orthogonal axes localize a point -- are judged to be self-evident and yet have been questioned on the basis of logical argument, physical theory, or experiment," the researchers wrote.

There was no way the Munduruku could have learned these ideas, they added.


They are self evident to all but mathematicians! Even the most primitive tribesman knows that the shortest way to go from point A to point B is a straight line! Three axis defines a point – go east 100 paces, turn north go 50 paces. Climb up 4 body lengths. A point has been defined. What did they have to learn from a book?
8 posted on 01/20/2006 3:52:04 AM PST by R. Scott (Humanity i love you because when you're hard up you pawn your Intelligence to buy a drink.)
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To: Junior

"So, primitive hunter-gatherers who have never been inside a classroom score as high on geometry as American children who are being "educated" at $10,000 per head per year."

But US students educated at 10,000/year can read and write whereas the "primitive" hunters cannot - er, well, never mind.


9 posted on 01/20/2006 3:53:17 AM PST by razoroccam (Then in the name of Allah, they will let loose the Germs of War (http://www.booksurge.com))
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To: Pharmboy
"Many of its propositions -- that two points determine a line, or that three orthogonal axes localize a point -- are judged to be self-evident and yet have been questioned on the basis of logical argument, physical theory, or experiment," the researchers wrote.

Oooh, we have grant money to spend! Let's question obvious, self evident minutiae!

yay for science!

10 posted on 01/20/2006 3:57:44 AM PST by ovrtaxt (I looked for common sense with a telescope. All I could see was the moon of Uranus.)
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To: razoroccam

I speculate that this concept could be turned around, using pictures like this to reinforce intuitive ideas of geometric concepts before the formalities are introduced. Such as work on boosting the 67% picture choosing scores to something much higher using colloquial explanations of the differences.


11 posted on 01/20/2006 3:59:21 AM PST by HiTech RedNeck
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To: Pharmboy
Chimpanzees have been documented in their ability to continually locate and find their own chimp-made tools (special rocks for breaking nuts, etc) that they store in different areas of their territory. Based on the descriptions I read of the process, they must have been using geometric reasoning and a mental map to do this.

Other animals may rely primarily on scent and scent-memory for finding things -- but it would seem that primates evolved with a different set of capabilities to solve the same problem.

12 posted on 01/20/2006 4:06:40 AM PST by WL-law
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To: Junior
So, primitive hunter-gatherers who have never been inside a classroom score as high on geometry as American children who are being "educated" at $10,000 per head per year.

High School Geometry is easily mastered by students if the basis of real-world concepts is in place.

Many students need to re-visit childhood activities ... drawing maps, writing directions, designing something to build or arrange, basic play and games, etc.

Computer activities and xeroxed work sheets can work for lots of necessary pre-requisites to Geometry success, but the hands-on aspects early man wired our brains with created the need for hands-on real-world type experiences to fully develop them.

So, if you know a child who can't do or learn Geometry, bring him or her out to play!

13 posted on 01/20/2006 4:09:07 AM PST by grania ("Won't get fooled again")
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To: SauronOfMordor
Eggs-actly.
14 posted on 01/20/2006 4:16:34 AM PST by kinsman redeemer (the real enemy seeks to devour what is good)
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To: Pete'sWife
LOL - very good!

but be sure to use a little "running english" to make sure that geometry is not overcome by physics.

15 posted on 01/20/2006 4:18:20 AM PST by kinsman redeemer (the real enemy seeks to devour what is good)
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To: razoroccam

Do you believe that 67% of government school education children in the country can read and write?


16 posted on 01/20/2006 5:17:28 AM PST by OldFriend (The Dems enABLEd DANGER and 3,000 Americans died.)
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To: TR Jeffersonian

ping


17 posted on 01/20/2006 5:21:02 AM PST by kalee
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To: Pharmboy; RadioAstronomer; longshadow; Doctor Stochastic; tortoise; Right Wing Professor; ...

Great thread. Wouldja believe it, I once toyed with the idea of a math ping list. I didn't assemble many names, and I soon dropped the project. Someone else should pick it up. Anyway, this topic is broader than math, so I'll add a few others ...


18 posted on 01/20/2006 5:40:56 AM PST by PatrickHenry (Virtual Ignore for trolls, lunatics, dotards, scolds, & incurable ignoramuses.)
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To: WL-law

And somewhere a honeybee is doing a happy dance...playing charades...and using geometry. :)


19 posted on 01/20/2006 5:54:15 AM PST by Graymatter
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To: All
This is neat. I was always really bad at most advanced math but geometry was such a no brainer for me. It was so simple and easy for me to grasp the concepts. I always wondered why that was the case. I spent my youth in the woods and navigation is what I am best at doing. I always know what direction I am facing regardless of the situation and stuff like that. I did get lost in Prague once. I kept trying to get to the dang river and kept going the wrong direction. It was either jet lag or absinthe I'm not sure which.
20 posted on 01/20/2006 6:10:33 AM PST by The Toll
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To: OldFriend

Nope, which is why I said never mind............


21 posted on 01/20/2006 6:12:41 AM PST by razoroccam (Then in the name of Allah, they will let loose the Germs of War (http://www.booksurge.com))
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To: Alamo-Girl; betty boop; P-Marlowe

AG, you ole salty dog, you.

You called this ahead of time.

"The unreasonable effectiveness of math." (or something like that.)

HA! Designer indeed!


22 posted on 01/20/2006 6:16:35 AM PST by xzins (Retired Army Chaplain and Proud of It!)
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To: PatrickHenry

Definitely not for me. Attending to one ping list is already more than I can properly handle!


23 posted on 01/20/2006 6:23:03 AM PST by AntiGuv ()
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To: razoroccam
I've been very critical of public schools but truth to tell I had one child in public and one in private and my public school child got a MUCH better education.

However, it was the environment that was just not acceptable for younger child. We always had to supplement the education she got in private school but the learning environment and the social norms were world's better than in public school

All in all, we wouldn't have done it any differently.

Every parent needs to take responsibility for their child's education and make sure it's not left to the school!

24 posted on 01/20/2006 7:21:41 AM PST by OldFriend (The Dems enABLEd DANGER and 3,000 Americans died.)
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To: muir_redwoods
My geometry course was more demanding than this but then, I went to a Catholic High School

LOL! Me, too. My own first thought on seeing the title was that, in my HS geometry class, it seemed clear that those of us who were good at geometry got at sight and just had to learn the vocabulary, and those who weren't good, well, just would never get it (I got the same feeling about logic in college!).

25 posted on 01/20/2006 7:25:06 AM PST by maryz
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To: Pharmboy
Geometry may be hard-wired into brain, study shows

Hadn't thought about it from this angle before.

26 posted on 01/20/2006 7:37:38 AM PST by Ken H
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To: R. Scott

These self-evident truths are interrogated not for their confessions but for their universality.

Imaginatively, we speak of extra dimensions but logically we can only account for three.

What is better displayed here is the seeming fact that not all children come equipped with the same ability to intuit the obvious and that is a phenomenon for social study, not the science of mathematics, per se.


27 posted on 01/20/2006 7:40:10 AM PST by Old Professer (Fix the problem, not the blame!)
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To: Pharmboy

"points, lines, parallelism, right angles simple pictures, distance, angle, relationships"

All of these exist in the Amazon and tribe. All are used in hunting, farming, cooking and taking care of the tribe.

Look at what has been built over 1,000 years where modern math did not exist - we cannot duplicate today - maybe modern math is incorrect.


28 posted on 01/20/2006 7:43:11 AM PST by edcoil (Reality doesn't say much - doesn't need too)
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To: Pharmboy

This whole article is based on a completely faulty premise. The whole point of High School Geometry is not to teach people how to compute areas of rectangles or know that two points make a straight line. Students are expected to intuitively know that coming in.

High School Geometry is meant to introduce axiomatic thinking and theorem proving.

All this proves is that the hunters know geometry and the guys who designed the study do not!


29 posted on 01/20/2006 7:43:53 AM PST by Netheron
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To: Ken H
...from this angle...

Hmmm.

Cordially,

30 posted on 01/20/2006 7:47:26 AM PST by Diamond
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Comment #31 Removed by Moderator

To: Ken H

Good one...


32 posted on 01/20/2006 7:55:29 AM PST by Pharmboy (The stone age didn't end because they ran out of stones.)
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To: Netheron

I only wish that there was such as thing as Angle-Side-Side congruence. It would have made Geometry class a little more fun. :)


33 posted on 01/20/2006 7:59:49 AM PST by dfwgator
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To: xzins
"HA! Designer indeed!"

You rang?

34 posted on 01/20/2006 8:07:11 AM PST by Designer (Just a nit-pick'n and chagrin'n)
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To: Pharmboy

Sounds more like plain old spatial relations.


35 posted on 01/20/2006 8:10:00 AM PST by TX Bluebonnet
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To: Pharmboy

I recall that Kant said the same thing more than 200 years ago.


36 posted on 01/20/2006 8:10:09 AM PST by RobbyS ( CHIRHO)
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To: dfwgator

Well, at least you narrow it down to two solutions. With angle-angle-angle, you have an infinite number.


37 posted on 01/20/2006 8:11:42 AM PST by Netheron
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To: Junior

That's because their instruction never goes much beyond this intuitive level. Many educators--many math teachers--do not know that Euclidiean geometry is an application of logic, that it is the only opportunity for the school to teach formal logic to ordinary students.


38 posted on 01/20/2006 8:14:28 AM PST by RobbyS ( CHIRHO)
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To: RobbyS

Well, Kant said that there were three dimensions of space, and that that was all there could be, since it was clearly the case that there couldn't be any others.

Special Relativity blew a hole in that. General Relativity nailed the coffin shut. Quantum Field Theory and String Theory are currently dancing on the grave.


39 posted on 01/20/2006 8:16:06 AM PST by Netheron
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To: Ken H
I have a theory that at least in some students, it also takes time to mature the "wires" until they are hard. I didn't understand geometry at all in junior high school. Retook it in summer school, still didn't get it but when I later took it in college,... Voila... it all made sense, and was in fact easy to understand.
40 posted on 01/20/2006 8:20:53 AM PST by tertiary01 (Dems ..the party that repeats history's mistakes over and over and....)
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To: Netheron
Relativity is counterintuitive, an intellectual contract on the same order as atomic theory. Kant was right to say that we can only perceive three dimensions. Science as a whole has gone beyond our ability to imagine in the original sense of the word. It has become a code, and only the code-breakers can interpret it.
41 posted on 01/20/2006 8:34:10 AM PST by RobbyS ( CHIRHO)
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To: Pharmboy

Fascinating article. Thanks for posting it.


42 posted on 01/20/2006 8:34:52 AM PST by RightWingAtheist (Creationism Is Not Conservative!)
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To: tertiary01

It could be you were mistaught. Many math teachers really don't understand their subject.


43 posted on 01/20/2006 8:36:12 AM PST by RobbyS ( CHIRHO)
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To: Old Professer
What is better displayed here is the seeming fact that not all children come equipped with the same ability to intuit the obvious and that is a phenomenon for social study, not the science of mathematics, per se.

Just as some people have a great sense of direction and others seemingly don’t. For some math comes easy, others have to struggle. I think much of it has to do, not with the wiring of the brain but with upbringing – nurture, not nature.
But my opinion might be a result of having a degree in Sociology.
44 posted on 01/20/2006 8:48:45 AM PST by R. Scott (Humanity i love you because when you're hard up you pawn your Intelligence to buy a drink.)
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To: RobbyS

But Kant didn't say that we could only perceive three dimensions. Kant said that there WERE only three dimensions. He was directly saying that the existence of four or more dimensions was absolutely impossible. Kant made specific statements about the actual structure of the universe which have been proven false.

Anyhow, there are two refutations to the perceiving three dimensions issue.

1) Many mathematicians, who spend a long time working with four (and higher) dimensional objects, actually do develop the ability to perceive them in the same way that people normally perceive three dimensonal ones.

2) Physics experiments are perception, that's why we do them.


45 posted on 01/20/2006 8:49:12 AM PST by Netheron
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To: RobbyS

I took that into account. Maybe it was due to a difference in textbooks, but I think most explain Geometry in the same linear fashion.


46 posted on 01/20/2006 9:10:20 AM PST by tertiary01 (Dems ..the party that repeats history's mistakes over and over and....)
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To: tertiary01

>> I think most explain Geometry in the same linear fashion. <<

Well...


47 posted on 01/20/2006 9:45:33 AM PST by dangus
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To: Pharmboy
Geometry may be hard-wired into brain, study shows

Personally, I have always had a thing for nice curves and shapes. It almost seems programmed into me...

48 posted on 01/20/2006 11:54:17 AM PST by Onelifetogive (* Sarcasm tag ALWAYS required. For some FReepers, sarcasm can NEVER be obvious enough.)
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To: Junior
["All participants, even those aged 6, performed well above the chance level of 16.6 percent," they found. The average score was nearly 67 percent correct -- identical to the score for U.S. children.]

So, primitive hunter-gatherers who have never been inside a classroom score as high on geometry as American children who are being "educated" at $10,000 per head per year.

To be fair, the comparison was for 6-year-olds. Not many 6-year-olds are getting any kind of "education" beyond how to sit at their desks, color within the lines, and playing well with others. The "$10,000 per head" education comes when they get older.

Now let's compare the abilities of the US students versus the hunter-gathers on, say, trigonometry when they're 18.

49 posted on 01/20/2006 11:58:01 AM PST by Ichneumon
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To: Junior
So, primitive hunter-gatherers who have never been inside a classroom score as high on geometry as American children who are being "educated" at $10,000 per head per year.

The $10,000 figure is because someone has to cosine for those under 18.

50 posted on 01/20/2006 12:31:37 PM PST by Ken H
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