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## Humans Hard-wired for Geometry235

Posted by CowboyNeal
from the pythagoras-notwithstanding dept.
hcg50a writes "An article on MSNBC reports that, according to a new study, even if you never learned the difference between a triangle, a rectangle and a trapezoid, and you never used a ruler, a compass or a map, you would still do well on some basic geometry tests, because we are hard-wired for geometry, rather than learning it from teachers or cultural influences."
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## Humans Hard-wired for Geometry

• #### Now I understand why... (Score:5, Funny)

by Anonymous Coward on Saturday January 21, 2006 @11:29AM (#14526533)
People are always calling me square.
• #### Re:Now I understand why... (Score:2, Funny)

Arr, my hardwiring sucks; I failed geometry -- twice. But it was teh teacher, I tell yaz - I got a C in night school and an A in summer school. So put THAT in your pipe and smoke it, Mister Moor from Gordon Tech!

[ God, I feel old - I just looked up the faculty list and he's STILL THERE! ]

• #### 3D world (Score:4, Insightful)

by Anonymous Coward on Saturday January 21, 2006 @11:31AM (#14526542)
We live in a 3-dimensional world. Is it any wonder that we've managed to develop an inherent ability to cope with 2-dimensional problems?
• #### Re:3D world (Score:3, Insightful)

Right. Saying that humans are hard-wired for geometry is only a little less silly than saying that humans are hard-wired for breathing. It's almost a truism.
• #### Re:3D world (Score:2)

According to archeologists, we developed the ability to process geometry because that skill was required in order to make a spearhead from a block of flint. The flint would only cleave a sharp edge if hit in a particular direction, so this required geometric processing in order to determine the correct striking point.
• #### That's nothing. We're hardwired for calculus. (Score:5, Insightful)

on Saturday January 21, 2006 @11:35AM (#14526565)
Watch a little kid running down a hump-shaped hill and managing to catch a slowing, banking frisbee that's drifting in an accelerating gust of wind and you'll know what I mean. Hell, my dogs can do calculus, even when the birds they're after are using anti-calculus to try to defeat them.
• #### Re:That's nothing. We're hardwired for calculus. (Score:2)

Dag nabbit! They got me with their Anti-calculus!
• #### Re:That's nothing. We're hardwired for calculus. (Score:5, Insightful)

on Saturday January 21, 2006 @11:47AM (#14526624)
But we're hard-wired for consciously applying geometry. If I gave you a board, a piece of string, scissors, and a saw, you could cut the board exactly in half in a short amount of time. How? You'd lay the string out on the board, cut them to match length, fold the string in half, and lay the string out on the board again, making the cut at the end of the string.

That's geometry, and a practical application of it. You wouldn't think about it for too long before coming up with the method of how to accomplish that, either.

Meanwhile, mental "calculus" (the observation of the rates of change of things) and metal "statistics" (the counting of how many times something is going to happen a certain way across repeated attempts) are usually something we can't quite quantify. We do these things automatically, but we can't put them on paper so easily. Geometry, however, works on a sheet of paper, and can be demonstrated there. Notice how all math homework is numbers and letters and symbols except in geometry, where you draw pictures, using the numbers/letters/symbols only to annotate what is going on in those diagrams.

It's not the calculations or even the practical application that sets Geometry apart. It's the fact that we can easily record what's going on in our minds and reuse that recorded information quickly and easily, without having to dredge the rules up from our memories.
• #### Re:That's nothing. We're hardwired for calculus. (Score:2)

I just used the string method you described a week ago for splitting a spruce beam into two halfs, you don't need to cut the string though, just fold it.
• #### Re:That's nothing. We're hardwired for calculus. (Score:3, Insightful)

I am not sure if it has not been patented yet by someone.
• #### Re:That's nothing. We're hardwired for calculus. (Score:2)

Actually, in modern math pretty much everything is numbers and letters and symbols. Pictures can lie and mislead, as Gauss, Bolyai and Lobochevsky discovered (and others, but them most famous). A picture does not replace or serve as a proof, unless it's been proven that the picture is rigorous, in which case it's probably superfluous.

Basically, what the article's saying is that the branch of geometry that deals with the world as our brain perceives it is hardwired into our brain. There's a reason geometry
• #### Re:That's nothing. We're hardwired for calculus. (Score:3, Funny)

If I gave you a board, a piece of string, scissors, and a saw, you could cut the board exactly in half in a short amount of time. How? You'd lay the string out on the board, cut them to match length, fold the string in half, and lay the string out on the board again, making the cut at the end of the string.

Sounds overly complicated to me - I'd just cut it corner to opposite corner.
• #### Re:That's nothing. We're hardwired for calculus. (Score:3, Insightful)

Indeed, I think the parent really points out the absurdity of this article. Of course humans are good with some forms of geometry, seeing as we deal with geometry on a day to day basis in the world we live in. Some previous poster pointed out that dogs can't do geometry problems. Well, dogs can't really do any "problems" of the form we humans can. We are used to thinking abstractly and solving problems.
• #### Re:That's nothing. We're hardwired for calculus. (Score:2, Funny)

who says dogs can't solve problems that humans can - i'm sure it's just a question of motivation :)
• #### Re:That's nothing. We're hardwired for calculus. (Score:2, Insightful)

Well it is appealing to think that we're "hard-wired" for things, it's really not that way. We have found models for describing things like you're talking about (catching frisbee's, etc.), but do you really think we (much less your dog) are solving differential equations in your head in order to catch a frisbee? Even if you could somehow do that, how would someone who hasn't been exposed to the maths do it? Things like geometry and calculus are simply really helpful tools to *model* things that occur nat
• #### Re:That's nothing. We're hardwired for calculus. (Score:2)

"We have found models for describing things like you're talking about (catching frisbee's, etc.), but do you really think we (much less your dog) are solving differential equations in your head in order to catch a frisbee?"

I don't think anyone is consciously doing algebra in their imagination when they throw a ball (for that matter, I think dogs are hardly conscious, even though I am a dog person). However, the nuerons in the brain, spinal cord, and arm probably are doing calculus.

Remember that the body'
• #### Re:That's nothing. We're hardwired for calculus. (Score:2)

"then they must have another method of solving these equations"

Past experience? I don't think that a labrat knows a thing about physics or circuitry design, but if every time he hits the button he gets knocked across the room, he'll quickly learn to not hit the button.

We've got much bigger and more powerful brains so we're more capable of "just understanding" stuff from past experience. I still remember learning how to throw a football, purely from experience of what works vs what didn't. I didn't know why
• #### Re:That's nothing. We're hardwired for calculus. (Score:2)

"Past experience? I don't think that a labrat knows a thing about physics or circuitry design, but if every time he hits the button he gets knocked across the room, he'll quickly learn to not hit the button."

That's the problem with the labratory-oriented experiment. The idea of the lab is to get rid of all variables except one. In the real world where this organism evolved, they will never have the same experience twice -- there are many variables, and they are all different! Once you get eaten, you're don
• #### Partial Differential Equations, too! (Score:2, Interesting)

We can subconsciously solve graduate level mathematical problems every time we go up or down stairs.

Which makes me wonder: is math really that hard or is our notation making it more difficult than it really is?

• #### Re:Partial Differential Equations, too! (Score:2)

"We can subconsciously solve graduate level mathematical problems"

While you can train yourself to control subconscious processes, I don't think math is one of them.

RoboCop is probably the only person who consciously does graduate level math in his head.
• #### Re:Partial Differential Equations, too! (Score:2)

Define "love". Just because it's hard to define doesn't mean that it's not easy to do. When walking, we work with continuous input from many sources, and use a fuzzy, inexact way of reacting to it. That's why people sometimes trip. Math has nothing to do with it.
• #### Re:Partial Differential Equations, too! (Score:2)

We can subconsciously solve graduate level mathematical problems every time we go up or down stairs.

Now apply that same subconcious "mathematics ability" to calculating an orbit.

We have sets of neurons which have been trained/structured to produce adequate approximate solutions to the stair-climbing problem, and we can also solve the same problem through a completely different process of mathematical symbol manipulation. The same symbol manipulation techniques can be applied to solve lots of radically

• #### Re:Partial Differential Equations, too! (Score:5, Insightful)

on Saturday January 21, 2006 @01:12PM (#14527135) Homepage Journal
We can subconsciously solve graduate level mathematical problems every time we go up or down stairs.

Yee-haa, let's apply this epistemological principle elsewhere:

Birds fly -- they must be able to solve aerodynamical problems!

Acorns fall -- they must be able to solve second-order differential equations!

Water makes waves -- it must understand turbulent flow better than humans do!

Sheesh. Stop banging everything with your big Anthropomorphism Stick. Equations modeling some behavior are not 'understood' or 'solved' by whatever exhibits that behavior; the equations are just a model. Living being climbing steps or whatever are using highly-evolved real-time feedback mechanisms, not solving anything.
• #### Re:Partial Differential Equations, too! (Score:3, Insightful)

Please, oh please, if there is any intelligence, justice or wisdom in the Slashdot universe, please MOD PARENT UP!!!!

It never ceases to amaze me how frequently even otherwise intelligent people confuse the map for the territory. Any abstract model you've ever conceived of or used is not reality. It is just a model that corresponds more or less well to reality. Please read and understand the parent post if you want to have any notion of how human knowledge differs from reality, and how human knowledge progre
• #### Re:That's nothing. We're hardwired for calculus. (Score:2)

I don't to be a troll.... But, as a person with dysparxia, I guess many around here probably are not hard-wired for calculus.

But, on the other hand, many of us may have deep understanding in advanced maths. I guess it is literal meaning of "my maths only look good on paper" :p
• #### Re:That's nothing. We're hardwired for calculus. (Score:2)

What exactly do you mean by "calculus"? A bucket is an example of an integrator; applied calculus is rather trivial stuff. Catching a frisbee is an example of a very interesting feedback system, but i don't see any calculus there. Your brain doesn't calculate the precise trajectory of the frisbee; it simply assesses its position, velocity, and environmental factor and produces an appropriate response. Apart from the requisite vision and locomotion systems, it's not really that complicated. The fascinat
• #### Re:That's nothing. We're hardwired for calculus. (Score:2)

Your brain doesn't calculate the precise trajectory of the frisbee; it simply assesses its position, velocity, and environmental factor and produces an appropriate response

I guess I have to disagree, to a certain extent. To get your, say, 150-pound body where it needs to be to catch a frisbee that's going to be there some seconds later, you've got to do a lot more than respond to a condition. You have to evaluate the de/acceleration, what gravity's doing, and take those changing velocities/vectors into a
• #### Tell my teacher that, sheesh (Score:4, Funny)

on Saturday January 21, 2006 @11:38AM (#14526583)
We're hard-wired for geometry? Sheesh, let's tell my 10th-grade Math teacher that... she'd point over to me and laugh in your face.
• #### Re:Tell my teacher that, sheesh (Score:2)

Only 10th grade? It took me 3 attempts to pass calculus 1 in college!
• #### Not Geometry, pattern recognition (Score:5, Insightful)

on Saturday January 21, 2006 @11:39AM (#14526593) Homepage Journal
Wow, what horrible pseuo-science. There's nothing "Geometric" about those shapes at all. Every single one of those "example" tests (as well as their interactive "do you own geometry" test) were all based on pattern recognition. 5 of the things are roughly the same, and the 6th is quite different in a very visual sense.

If they did this same test with the numbers "1" and "2" oriented in different directions, or in different sizes (with five 1's and only one 2) I think these tribal people would be just as good at finding the pattern, but that does not mean they know basic arabic numbers.

We've always known that the Human Brain is incredibly good at pattern recognition. This article, and this study, are full of crap.

• #### Re:Not Geometry, pattern recognition (Score:2)

We've always known that the Human Brain is incredibly good at pattern recognition. This article, and this study, are full of crap.

I agree. We learn the natural geometry of the world automatically. We also learn to recognize musical tunes. It's all in the learning mechanism. There is nothing hardwired about it. I have seen 4-year old kids who swear that the moon follows them as they walk. Sooner or later, they figure it out.
• #### Re:Not Geometry, pattern recognition (Score:5, Interesting)

<`david' `at' `tadmas.com'> on Saturday January 21, 2006 @12:03PM (#14526724) Homepage

Agreed.

Actually, they've done previous studies on these people to investigate whether they had innate arithmetic abilities [sciencemag.org] by seeing if they could add large numbers, which they could only do approximately. As long as the numbers would fit on two hands, they were exact, but over that, not so much. It seems to me that the large number tests would just be comparing sizes of physical objects rather than actual math. (I don't think they gave them arabic numerals to add, but probably tick marks or other objects. It's just a guess: I don't know their exact methodology.)

What I find most revealing about this is their results on "handedness", which to me would help weed out pattern recognition versus spacial thinking (geometry). According to TFA, only 23% got it right... but 16% would get it right by guessing alone, so it's really not much better. Like the previous study, that seems to conflict with their conclusion rather than support it.

• #### Re:Not Geometry, pattern recognition (Score:5, Insightful)

on Saturday January 21, 2006 @12:11PM (#14526772)
I dont agree with you there. Although it seems as if the odd-one-out tasks are childs play, they are not. Some of them, especially the triangles (equilateral v/s isosceles) and the X's (perpendicular v/s otherwise) need the ability to think in terms of angles. And the last one requires you to see if the figures are clockwise or counter-clockwise. Its definitely not simple patterns recognition, all 6 images in each set are very similar in terms of "pattern".

And what you probably read was only the article was on MSNBC for the average reader. It was published in Science, so maybe you should go and read the full article [nyud.net] before calling it pseudo-science.

• #### Re:Not Geometry, pattern recognition (Score:2)

Some of them, especially the triangles (equilateral v/s isosceles) and the X's (perpendicular v/s otherwise) need the ability to think in terms of angles.

That's one way of thinking of it. But in all these examples you don't need to do any geometry, they're all just patterns. The X's example can be rotated in your head to compare them. The triangles can be rotated and reduced in size in your head. This doesn't have anything to do with geometry, but is just pattern matching.
• #### Re:Not Geometry, pattern recognition (Score:2)

And how, pray tell, could one characterize the rotation and scaling of two dimensional figures as anything other than geometry? Did we create a new sub-dicipline of mathematics outside of geometry just for 2D figure scaling and rotation while I wasn't looking?

FYI my dictionary gives this for geometry:

the branch of mathematics concerned with the properties and relations of points, lines, surfaces, solids, and higher dimensional analogs.( pl. -tries)

a particular mathematical system describing such properties
• #### Re:Not Geometry, pattern recognition (Score:2)

Of course, that's like saying that your eye knows geometry, because it's able to bend light in very specific ways and be flexible across a wide variety of situations. Not only that, but it adjusts to geometrically position objects in your visual field to give maximum light exposure. But eyes don't know geometry.

I'm not saying that there aren't some very neat aspects of our visual systems. I study visual systems. But this seems more like an artifact of visual systems than it does "knowledge of geometry".
• #### Re:Not Geometry, pattern recognition (Score:2)

I'll agree with you. And the one they found difficult, (the rotating notes) they probably mentally flipped the object over, making it the same as the other six, hence the diffficulty in realizing it was any different than any of the others. Now if they'd shown a variety of the 'note' objects, with one side colored blue, the other side colored red, and one of them had the colors on the two sides reversed, I'm sure that more of them would have recognized the one out of the ordinary.
• #### Re:Not Geometry, pattern recognition (Score:2)

Some of them, especially the triangles (equilateral v/s isosceles) and the X's (perpendicular v/s otherwise) need the ability to think in terms of angles. And the last one requires you to see if the figures are clockwise or counter-clockwise. Its definitely not simple patterns recognition, all 6 images in each set are very similar in terms of "pattern".

But pattern recognition for two dimensional shapes requires an implicit understanding of angles. I think that the statement the ability of think in terms o

• #### Re:Not Geometry, pattern recognition (Score:2)

Spatial pattern recognition in 2D is a kind of geometry. No one is saying that we are hard wired to prove theorems. The study simply says that people are hard wired to recognize simple geometric patterns such as distinguishing right angles from acute angles, and closed figures from open figures.

As usual, Ring TFA helps here. The knee-jerk dissing of anthropologists of the kind demonstrated by some of my peer posts just makes them look like blowhards who didn't RTFA.
• #### Re:Not Geometry, pattern recognition (Score:2)

Pattern recognition studies are often very interesting, though. I remember watching a video in science class about pigeons beating entire classes of university students on certain types of pattern recognition problems. It was neat, but like this one, I'm not sure how much it says about any species' geometry abilities :)
• #### Seems like a "non discovery" to me, really... (Score:4, Insightful)

on Saturday January 21, 2006 @11:41AM (#14526600) Journal
This study would have a profound impact if it was really discovered that humans are born with this basic sense of geometry. But it doesn't show that at all! Rather than implying that we might have an "innate sense of geometry" - it merely shows that we're able to pick up basic concepts of 3D objects by working and interacting with them every day as we go through our lives.

The fact that adults tended to score better on these tests than kids did further illustrates this. The longer you've been around on this planet (formally educated or not), the more time you've had to work with objects and draw conclusions about what makes an object "different" from other similar ones.
• #### Re:Seems like a "non discovery" to me, really... (Score:2)

"Rather than implying that we might have an "innate sense of geometry" - it merely shows that we're able to pick up basic concepts of 3D objects by working and interacting with them every day as we go through our lives."

Correlation is not causation. It seems that from this experiment you can't make a conclusion one way or the other. If this study *does not* show that we have an innate sense, that doesn't mean that it therefore must be learned. Say that in reality we do have an innate sense -- it just means
• #### Re:Seems like a "non discovery" to me, really... (Score:2)

Remember, these are babies that are still being carried around by their mothers, no older than 12 months. The have very little experience with everyday physics.

Right - this argument is known as "the poverty of the input." Basically you can conclude that a skill is at least partially innate if the sensory input the child has before acquiring the skill it is too small to have taught the child the skill from ground zero. This, for example, is why linguists and neurologist universally believe that human beings
• #### re: possibilities (Score:2)

Ok, I agree that this study doesn't prove anything one way or the other. Point taken there.

But as for the "impossible scenes" study, I'm lost as to how it means one can "reasonably conclude that the baabies had some innate sense of physics"? Even as young as 6 months to 12 months old, a child is already experiencing all sorts of basic laws of physics. Every time you dress them, for example, they're experiencing certain rules. (EG. They're unable to see their own skin through the material, and they can'
• #### Scientific? (Score:3, Insightful)

on Saturday January 21, 2006 @11:43AM (#14526606)
This test was not as scientific as it could have been. The natives were presented with 43 sets of 6 images, and asked to choose the 'odd' one, such as 5 equilateral triangles and 1 isosceles. You could use the same type of test by showing 5 photos of happy people, and one photo of somebody badly injured and say humans are hard-wired for medicine. The results of this test are interesting, but not ground-breaking.
• #### Re:Scientific? (Score:2)

You could use the same type of test by showing 5 photos of happy people, and one photo of somebody badly injured and say humans are hard-wired for medicine.

Or psychology ...

• #### old news (Score:5, Informative)

on Saturday January 21, 2006 @11:46AM (#14526617) Homepage
Kant figured this out back in the mid-nineteenth century. He proved that spatial and temporal conception is a prerequisite of consciousness.

Not that anyone except the five people that made it through the 'Transcendental Deduction' noticed, however.

• #### Re:old news (Score:5, Informative)

on Saturday January 21, 2006 @12:59PM (#14527058) Journal
Kant figured this out back in the mid-nineteenth century...

Kant [wikipedia.org] died in 1804.
• #### Re:old news (Score:4, Funny)

<rob AT rob-squared DOT com> on Saturday January 21, 2006 @01:36PM (#14527253)
Yeah, but everyone knows he did his best work as a zombie.
• #### Re:old news (Score:2)

Damn, that would explain a lot! I nearly became a zombie just by reading Kant. Why wasn't I warned?
• #### Re:old news (Score:2)

Make that six.

[Phil. major specialized in Kant, but mostly his ethics. Hume is the man w.r.t epistemology *grin*]
• #### Re:old news (Score:3)

There's a big difference between a philosopher's speculations and actual scientific evidence. Kant also believed that our percieved universe was Euclidean and that we couldn't conceive of a non-Euclidean geometry.
• #### Seen in kids, too (Score:3, Insightful)

<bengoodwyn AT me DOT com> on Saturday January 21, 2006 @11:52AM (#14526662) Homepage
I watched a show a couple of years back on kids recognizing things that "should be impossible". The researchers would setup demonstrations using various techniques that would make impossible sequences of events occur and watch the astonishment on the very young childrens faces (12-18 months).

One example was a ball rolling down a ramp. About halfway down the ramp there was a small blind where the ball disappeared, but the ball never appeared on the other side of the ramp. This surprised the children and it surprised me that it surprised them so much.

I know kinetics and geometry are quite different, but apparently there is a lot we are "hard wired" for.

• #### Re:Seen in kids, too (Score:3, Informative)

I;m a Human Development & Family Studies major - Social worker major, basically (For me, it's pre law)

The really interesting thing that they're demonstrating is "Object Permenance" - Younger infants do not know that when an object leaves their point of view that it still exists! IIRC, they get that starting around 9 months. When it happens, it's sudden - one week the kid doesn't care, the next minute, "Huh?! Where'd it go?!" Even your attachment to your own mother wasn't there from the very start! You k
• #### Then how the bloody hell... (Score:2)

...am I crap at Pool?
• #### Because.... (Score:2)

you're only using half of the sciences needed to play pool. Math is one part (geometry for the mathematics part like angles) and you also need physics to accomplish the rest.
• #### Re:Then how the bloody hell... (Score:2)

...am I crap at Pool?

Seriously? Because you've not practiced enough, or you've never learned from a good player.

Conceptually, shooting an arrow is a pretty simple thing, but you need to work at it to become good. Same for pool.

Pool is one of those things with a lot of 'knack' to it, and a fair bit of non-obvious things -- like applied spin (top = follow, bottom = stop or roll back, left and right = redirect cue ball/object ball on impact) and knowing where the balls will end up. There's also a lot of te

• #### Hardwired indeed (Score:3, Interesting)

I find myself completely hardwired for geometry. In fact, I honestly believed I invented the calculus when finding some shortcuts for algebraic equations in the 7th grade.

All my life I found myself aggressive trying to find the most efficient geometry. Looking back, maybe I had some OCD that I never realized.

Wide aspect ratio TVs always made more sense to me than the squarish ones we used to use. The golden ratio [wikipedia.org] is for sure a mythical creature that proves that the ancients were just as bright as we are today, and that humans are locked in to geometric perfection.

Feng shui, symmetrical balance and all that garbage don't make me feel at ease -- geometric balance does.

I'm turning into Monk, aren't I?
• #### You can't invent math. (Score:4, Insightful)

on Saturday January 21, 2006 @12:20PM (#14526823) Homepage
"I honestly believed I invented the calculus when finding some shortcuts for algebraic equations in the 7th grade."

No, you rediscovered (independently) principles of calculus perhaps, but you did not invent it. You cannot invent calculus anymore than you can invent gravity or hydrogen -- they already exist, and are waiting to be discovered by the fertile human mind.
• #### Re:You can't invent math. (Score:3, Informative)

Please don't open that can of worms! I hold the view that anything other than the natural number system (Integers greater than zero) is invented. However, people far more educated than I have been arguing [google.com] this for centuries.
• #### You make a good point, but (Score:2)

If calculus was already "invented" by Newton and Leibnitz, I doubt that scholars would say that a person in grade 7 had also invented it. When someone in the past has invented something, even if the knowledge is lost, the term is rediscovery.

This person "rediscovered" it in that sense, or merely "discovered" it in my assertion. In no sense was it invented, thus my original point is still valid.
• #### Re:You can't invent math. (Score:3)

That is merely your opinion. Do not state it as fact.
• #### Re:You can't invent math. (Score:2)

You cannot invent calculus anymore than you can invent gravity or hydrogen

There are plenty of mathematicians who disagree with you, and plenty who agree with you as well. Your statement is a point of debate, not a fact.

• #### Re:You can't invent math. (Score:2)

"I honestly believed I invented the calculus when finding some shortcuts for algebraic equations in the 7th grade."

No, you rediscovered (independently) principles of calculus perhaps, but you did not invent it. You cannot invent calculus anymore than you can invent gravity or hydrogen -- they already exist, and are waiting to be discovered by the fertile human mind.

No, GP said 'I honestly believed I invented ...' and I take him at his word. Do you have reason to believe that he didn't believe that --

• #### Re:Hardwired indeed (Score:2)

I've always had a problem with sentence-style math. Anything beyond long division I can't handle. However, I am very good at visual gemoetry.

In my high school, the sophomore math class was geometry. We constructed shapes and did geometric proofs. A lot of people just couldn't get it. Some of them were vrey frustrated because they were really good at regular math, but they just weren't visual thinkers.

There were about 5 of us, including me, who were great at it. I remember one homework at the beginning
• #### Re:Hardwired indeed (Score:2)

It is easier to discover geometric shapes when one is used to rolling 3d6 or 1d20 in the basement 12 hours a day. :)

Kidding!
• #### Re:Hardwired indeed (Score:2)

I'm not quite sure what you mean by calculus when you say you "[found] shortcuts for algebraic equations in the 7th grade." - I presume you mean shortcuts for solving them. Calculus has nothing to do with solving ordinary equations; it devises new functions, new operations you can do on functions, and thus new kinds of equations that were unexpressible without it (ODE's, PDE's, fxns defined by integrals, etc.).

When you say you "aggressive"ly tried to find the most effecient geometry, and that you prefer ge
• #### simple epistemology (Score:2)

This works well, even in young people, because once you master counting from 1 to 10, its trivial to distinguish shapes that have from 1 to 10 sides. Its trivial to integrate them (all pointy shapes) and differentiate them (square shapes vs. pointy shapes), and even create more advanced concepts like acute and obtuse angles. Granted, a child may not use those words to describe a star shape vs. a hexagon. At a young age, you can easily form shapes out of simple materials, further reinforcing the concepts.
• #### How much learned (Score:2, Interesting)

It is fun to watch children learn. They are capable of doing things and adapting in ways that I could never teach a computer... even one that simulates neural networks.

My oldest is almost three, and youngest is one. If you roll a ball, not directly at her, she will walk directly at the ball, constantly changing her path to reflect the fact that the ball has moved as she is moving. The ball will get past her, and she will continue to go after it.

My almost three-year-old did the same thing at that age. Then,
• #### Re:How much learned (Score:2)

Math is exact and descriptive. Human actions are inexact and reactionary. I'm not saying that it's not amazing what your kid does. But everyone does it. And it's because of the way our brains work. And it's not math. It's an effect of how our brains are inexact, fuzzy calculators. Very fast, and usually close enough to get what needs done, done.
• #### Re:How much learned (Score:2)

Is this amazing? Yes and no. Practically every kid developes this skill (except for Cleveland Indian players). Yet it is very amazing, because it is real time processing of information that is quite complex when you try to break it down. Defining the optimal path to the ball requires fast image processing combined with low level calculus.

Wrong, wrong, wrong. Small children (and also adults who are not world-class athletes) trying to intercept a slow-moving object are not doing anything even approximati

• #### Art School (Score:3, Interesting)

on Saturday January 21, 2006 @12:15PM (#14526785) Homepage
While some people have pointed out that we are not hardwired for geometry but rather pattern recognition...I was wondering if someone could clarify on the left-brain vs right-brain aspects of it.

For example, I have been absolutely horrible at all forms of math throughout my entire life with the SOLE exception of geometry, which I never had to study for once, and got straight A's in. It just "made sense" to me on an intuitive level.

And apparently I'm not the only one. You see, I went to an art school, where a whopping 40% of people were left-handed and the vast majority of people at that school completely sucked at all forms of math....EXCEPT GEOMETRY! Now, it could just be that geometry is the easiest form of math, but I wonder how much of it has to do with pattern recognition, and how that might relate to kids at an art school where people have an inherently higher level of innate pattern recognition ability.

Now.....all of this is just me explaining my observations, but I was wondering if someone could shed some scientific light behind this. Is there any correlation between the two?

• #### intrinsic knowledge or common sense? (Score:2, Interesting)

All they've determined is that nonverbal reasoning tests appear to be culturally neutral, which shouldn't be a surprise because this is precisely the part of IQ tests that was designed to be culturally neutral.

They even admit this test could have required only the concept of similarity; they proposed the 'map test' to rule out this alternative (but which suffers from the same problem, in my opinion).

Call it what you like - intrinsic geometric knowledge, nonverbal reasoning, or common-sense - I don't thi

• #### Gee... (Score:2, Insightful)

We have an innate ability to pick apart those that don't belong in a group (all the article talked about)? No wonder why Western civilization has become the most powerful one on Earth: we're always ostracizing those that aren't part of the group! Definitely the best at that skill...
• #### That was not a geometry test though (Score:5, Insightful)

on Saturday January 21, 2006 @12:39PM (#14526945) Homepage Journal
it was a pattern recognition test.

A geometry test would be different. Ask them what is the shortest distance between two points on a plane, see if they can explain what it is and why. Ask them how to find areas for different shapes. Those are the kinds of questions that geometry really answers, not the questions that require simply to notice difference between shapes.
• #### Re:That was not a geometry test though (Score:2)

I think you miss the point.

For example, most people can catch a ball. This requires the brain to do calculus at some level; However most people can not sit down and do calculus.

• #### My nominee for... (Score:5, Insightful)

on Saturday January 21, 2006 @01:20PM (#14527175)
... the Ig Nobel Prize [improbable.com].

Of COURSE we are hard-wired (in some manner) for geometry!!!

We're visual creatures operating in (a perceived) Euclidean space!

How could we not be (geometry-aware)?

As to the implication that we have some innate ability to reason geometrically, I think the folks at MSNBC and the AAAS must not have tried any mathematical proofs recently (or perhaps ever).

THERE's an area where there is ample evidence that we have zilch in the way of pre-wiring (a.k.a. "instinct"), and must undergo extensive pain and effort to wire ourselves to perform logical reasoning -- a skill that is foreign to most of the human population.

There's a pretty substantial chasm between the ability to recognize lines and shapes, and the ability to develop a method for bisecting an angle (using straight edge and compass) and showing that such a method is correct (i.e., develop a proof).

• #### Maybe hard-wired but still "innumerate" (Score:2)

It's an odd situation that humans are so expert at navigating their way through three-dimensional space, which suggests some familiarity with mathematics, and yet we are so uncomfortable with numbers, and math is dreaded in schools in a way no other subject ever is. Paulos's classic work Innumeracy [amazon.com] shows that the average man suffers from a serious lack of interest or skill with mathematics, and as a result we're victim to all manner of scams and failures. So, an article title like "Humans Hard-wired for G
• #### Not Geometry! (Score:4, Insightful)

on Saturday January 21, 2006 @01:50PM (#14527333) Homepage
Looking at the examples in the article, I saw very little evidence of Geometry. To me the questions were all a matter of pattern recognition, which it has long been known was THE strongest benefit of Neural Nets. Since the human brain is a neural net, I'm not particularly surprised that it is capable of recognizing patterns.

Have them write some proofs or identify the magnitude of some angles and I'll be impressed.
• #### Geometry is Intuitive (Score:2)

That must be why I rebelled against the stifiling formalisms thrust upon me in math class. It was easier to find the answer than to go through the theorem and proof steps. Math class took all the fun out of Math.
• #### Learned vs. Intuitive (Score:2)

A Mundurukú villager in a remote region of the Amazon weaves a basket -- a task illustrating that knowledge of geometry is spontaneously imposed upon many of the acts of everyday life.
How about another possiblity that the villagers are confronted with basic Geometry on a day-to-day basis since birth, and such things were learned out of necessity to live? These folks weave baskets to live and such things require dexterity and a spacial knowledge that is akin to Geometry. Suppose their culture was all

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