Beta
×

Welcome to the Slashdot Beta site -- learn more here. Use the link in the footer or click here to return to the Classic version of Slashdot.

Thank you!

Before you choose to head back to the Classic look of the site, we'd appreciate it if you share your thoughts on the Beta; your feedback is what drives our ongoing development.

Beta is different and we value you taking the time to try it out. Please take a look at the changes we've made in Beta and  learn more about it. Thanks for reading, and for making the site better!

Humans Hard-wired for Geometry

CowboyNeal posted more than 7 years ago | from the pythagoras-notwithstanding dept.

Math 235

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."

cancel ×

235 comments

Sorry! There are no comments related to the filter you selected.

Now I understand why... (5, Funny)

Anonymous Coward | more than 7 years ago | (#14526533)

People are always calling me square.

Re:Now I understand why... (1, Funny)

Wolfrider (856) | more than 7 years ago | (#14526864)

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! ]

OMG (-1, Offtopic)

Anonymous Coward | more than 7 years ago | (#14526935)

The test!! The test!! How did everyone do?!!!!

3D world (4, Insightful)

Anonymous Coward | more than 7 years ago | (#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?

Yes (0)

Anonymous Coward | more than 7 years ago | (#14526571)

Of course it's a wonder that we can deal with two-dimensional problems. Dogs can't, cats can't, cows can't. The very fact that we live in a 3-D world makes it surprising that we have the equipment to deal with abstract patterns on a flat surface according to their own logic.

It would be much less surprising if, upon seeing two similar triangles, we always thought the larger one was closer.

Re:Yes (2, Insightful)

fredrated (639554) | more than 7 years ago | (#14526813)

Of course it's a wonder that we can deal with two-dimensional problems. Dogs can't, cats can't, cows can't.

Of course they can. Finding your way home is solving a 2 dimensional problem, and animals have amazing ability to do that, even if dropped of somewhere they have never been.

That's not a two-dimensional problem (1, Insightful)

Anonymous Coward | more than 7 years ago | (#14526960)

To your human mind, finding your way home seems like a two-dimensional problem. You've got an abstract idea of a map in your head, and that's how you'd do it.

It isn't anything like a two-dimensional problem in life. You've got obstacles, roads that pass under and over each other, hills and valleys, and the only input a cat or dog has to deal with all this visually is the fairly black-and-white input they get from the world.

They have other senses that are very acute. Their smell and their hearing are far better than ours.

The result is that to a cat or a dog's mind, no two-dimensional aspect is involved in going home. They go in the direction that feels homeish. Part of that is based on sun directions, part on the smells of areas they've passed over, part on things they've heard near your house you never knew about. It's not geometric.

The very fact that you think it's a two-dimensional situation shows how deeply this approach is imprinted on the modern human mind, largely because humans are so visual. Most mammals do not have the visual acuity to make anything out on a map. Without that kind of acuity, they're not going to have that kind of detailed visual mental imagery.

On the other hand, for a dog a smell or a sound isn't "It's about this smelly" or "it's about this loud, and rightish." For a dog, a smell has a size, a shape, and even a direction. A sound is a precise three-dimensional location. With that kind of input available, it's almost like having a direct three-dimensional sense of where things are, rather than the two-d projection you're used to on your retinas. They're not going to abstract things into two-d.

Signal to noise (1)

AllenChristopher (679129) | more than 7 years ago | (#14527014)

"Finding your way home is solving a 2 dimensional problem, and animals have amazing ability to do that, even if dropped of somewhere they have never been."

Birds have an amazing ability to do that. Maybe not so amazing, because a bird sees everything from above and doesn't have to worry about finding a traversable route.

Cats and dogs? Nope. There are some amazing documented cases of cats and dogs finding their way home. There are about seventeen million documented cases of cats and dogs not finding their way home even without being dropped somewhere. These are animals that just wandered off and got lost.

If we could rely on dogs and cats to just go home we wouldn't have pounds.

Re:Yes (2, Funny)

Kierthos (225954) | more than 7 years ago | (#14526881)

No, no... dogs can't. Cows can't. Cat's won't. Why should cats bother when people will do everything for them?

Kierthos

Re:3D world (1)

J_Darnley (918721) | more than 7 years ago | (#14526581)

It's a great deal harder to create a 3D object from some material where as a 2D object han be represented on a surface alone. Cave paintings, stone tablets, paper, and a computer screen can all display 2D images extremely easily.

Re:3D world (2, Insightful)

DeafByBeheading (881815) | more than 7 years ago | (#14526591)

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.

Math world (0)

Anonymous Coward | more than 7 years ago | (#14526651)

We're also wired for math, and look at how poorly people do at that

Re:3D world (1)

The evil non-flying (947059) | more than 7 years ago | (#14526596)

Isn't the human brain programmed to see faces? I remember reading once about how the brain will recognize faces in natural formations (i.e. face on mars, clouds, etc). Perhaps this is just an extention of that?

Re:3D world (2, Funny)

SIGFPE (97527) | more than 7 years ago | (#14526817)


I remember reading once about how the brain will recognize faces in natural formations (i.e. face on mars, clouds, etc).

Um...if you have a brain of your own (borrow one if you don't) you could try this out for yourself. It's not exactly some obscure experiment that you can only "read about".

Re:3D world (1)

The evil non-flying (947059) | more than 7 years ago | (#14526898)

Judging by the behavior of people on message boards, I guess hurling insults and/or abuse at total strangers is also hard wired into the human brain.

Re:3D world (1)

lawpoop (604919) | more than 7 years ago | (#14527051)

That's nothing. The incredible human mind can recognize faces in computer monitor pixels or even ink spots on paper.

Re:3D world (1)

chris_eineke (634570) | more than 7 years ago | (#14527179)

In God's Debris [ucomics.com] , Scott Adams discusses how and why the Human brain is an illusion generator. A good read, nonetheless.

Re:3D world (0)

Anonymous Coward | more than 7 years ago | (#14526982)

The fusiform face area is the part of the brain you are thinking of. You may want to look at the art work of Guiseppe Arcimboldo

Geometry Jokes Here (0, Offtopic)

TubeSteak (669689) | more than 7 years ago | (#14526551)

Q: What'd the Acorn say when he grew up?



A: Gee, I'm a tree

(say it fast if you don't get it)
(I'll be here all week)

Here's one (0)

Anonymous Coward | more than 7 years ago | (#14526659)

What is the compliment to a 45 degree angle?

"Wow, you're looking acute today"

Re:Geometry Jokes Here (0)

Anonymous Coward | more than 7 years ago | (#14526688)

(say it fast if you don't get it)
(I'll be here all week)


So I'll be able to ask you about this when I still haven't figured it out by next Friday?

Re:Geometry Jokes Here (0)

Anonymous Coward | more than 7 years ago | (#14526701)

Ha!

That's like the story about little Mozart...

Little Mozart was playfully tucked away in a closet in his room. His mother prepared supper and was looking for little Mozart.

Little Mozart's mom: Little Mozart, were are you?
Little Mozzart from the closet: I'm hiddin'!

(tip: Haydn was Mozart's teacher)

Re:Geometry Jokes Here (0)

Anonymous Coward | more than 7 years ago | (#14526807)

You suck!

That's nothing. We're hardwired for calculus. (5, Insightful)

ScentCone (795499) | more than 7 years ago | (#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. (1)

lawpoop (604919) | more than 7 years ago | (#14526612)

Dag nabbit! They got me with their Anti-calculus!

Re:That's nothing. We're hardwired for calculus. (5, Insightful)

Mattintosh (758112) | more than 7 years ago | (#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. (1)

roman_mir (125474) | more than 7 years ago | (#14526891)

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. (0)

Anonymous Coward | more than 7 years ago | (#14527022)

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.

Thanks for the elegant solution! Otherwise I will be trying to solve this geometry problem for a long time :-)

Now have to work out only the details. Is the string cut using scissors or saw?

Re:That's nothing. We're hardwired for calculus. (3, Insightful)

poeidon1 (767457) | more than 7 years ago | (#14527214)

I am not sure if it has not been patented yet by someone.

Re:That's nothing. We're hardwired for calculus. (3, Insightful)

Luke PiWalker (946528) | more than 7 years ago | (#14526630)

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. (2, Funny)

CentraSpike (947642) | more than 7 years ago | (#14526778)

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. (1, Insightful)

flynt (248848) | more than 7 years ago | (#14526669)

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 naturally. That does not mean that is what is actually happening in the real world. Remember, it's not where we find math, it's where we put math.

Re:That's nothing. We're hardwired for calculus. (1)

lawpoop (604919) | more than 7 years ago | (#14526950)

"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's actions are not a purely mechanical event, like water flowing. In order to successfully run, jump, or throw a ball, any body, from ants to gazelles, has to model the natural world and how the body will move within it. If the body and its neurons are *not* using calculus, then they must have another method of solving these equations. Are you claiming they are not using math?

They're not using calculations, no. (1)

AllenChristopher (679129) | more than 7 years ago | (#14527063)

The neurons in your hand are reacting according to finely tuned lookup tables. If they were doing math, they wouldn't get better through practice. Practice is adjusting the lookup tables.

Not that there are really tables stored in memory. The neurons themselves are the table elements. If you miss the ball because you moved your hand too fast, your body tells the neurons to move slower next time.

This is called "approximation."

Think also about this: When you do calculus in the normal way that we speak of doing calculus, what does a mistake do? A misplaced sign or a confusion about division gives you a terribly inaccurate answer. You can end up with the wrong answer by orders of magnitude.

Your body almost never does that. You rarely reach up to catch a ball that's a foot above your hand and accidentally throw yourself across the room. Even slashdotters aren't that bad.

Does your car do calculus when its automatic transmission shifts over at the precise right moment to match the torque of the higher gear with the speed the wheels are currently going and get a smooth shift? No. It's just been adjusted that way. Engineers did the math, but your engine just does it. Conversely, do you do the math when you shift in a manual? No. You just know how the engine sounds when it's time to shift. Stimulus response, honed by trial and error.

Re:They're not using calculations, no. (2, Interesting)

lawpoop (604919) | more than 7 years ago | (#14527129)

" Not that there are really tables stored in memory. The neurons themselves are the table elements. If you miss the ball because you moved your hand too fast, your body tells the neurons to move slower next time."

Except there is no "next time". You will never have to catch a ball with those exact same parameters again. Your body will be in a different position, the ball will be at a different speed, angle, and trajectory, different wind and environment conditions, etc.

"Think also about this: When you do calculus in the normal way that we speak of doing calculus, what does a mistake do? A misplaced sign or a confusion about division gives you a terribly inaccurate answer. You can end up with the wrong answer by orders of magnitude.

Your body almost never does that. You rarely reach up to catch a ball that's a foot above your hand and accidentally throw yourself across the room. Even slashdotters aren't that bad.
"

Yes, but you have millions of years of evolution that have weeded out mistakes and orders-of-magnitude errors in your nervous system.

Furthermore, a mistake in your look-up table would be as deadly as a mistake in doing the calculus.

Do you have any references for your 'lookup table' theory, or is this just a pet theory?

I'm not good with math, but isn't the idea of calculus so you can sum *infinite series*? How are you going to have a look-up table for an infinite series?

"Conversely, do you do the math when you shift in a manual? No. You just know how the engine sounds when it's time to shift. Stimulus response, honed by trial and error."

I'm not saying you are consciously doing the calculus, but your spine is, and sending the commands to your limbs. The problem with stimulous response is that you will never get the same stimulous again. You can't 'hone' in an ever-changing environment. You have to be able to calculate all the variables -- i.e., do the math.

Re:That's nothing. We're hardwired for calculus. (1)

irc.goatse.cx troll (593289) | more than 7 years ago | (#14527095)

"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 spiraling it made it fly straight, I just know that it did, so thats how I threw it. Thats the beauty of sciences..They exist to explain what happens, but you don't have to understand them to use them or for them to occur. What difference does it make if you think lightning is god punishing you or an ionized beam of air with a current going through it? We might find one more accurate than the other now, but in the end you both know its bright, loud, and can cause destruction.

Re:That's nothing. We're hardwired for calculus. (1)

lawpoop (604919) | more than 7 years ago | (#14527162)

"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 done. No chance to be trained on that! An organism that survives has to be able to handle new and unexpected scenarios. So seeing how an organism behaves in a repeated stimulous-response situation doesn't really tell us anything about what the nervous system evolved to handle.

Partial Differential Equations, too! (2, Interesting)

IAAP (937607) | more than 7 years ago | (#14526694)

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! (0)

Anonymous Coward | more than 7 years ago | (#14526799)

Maybe our sub-con is better at math then the concious mind.

Re:Partial Differential Equations, too! (1)

TubeSteak (669689) | more than 7 years ago | (#14526832)

"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! (1)

PitaBred (632671) | more than 7 years ago | (#14526963)

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! (1)

swillden (191260) | more than 7 years ago | (#14527123)

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 different problems, but the neural network can only cope with problems that fit into a certain space of problems for which it has been trained.

The two approaches are completely different and have nothing in common except that they happen to be able to solve some of the same problems.

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

greginnj (891863) | more than 7 years ago | (#14527135)

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:That's nothing. We're hardwired for calculus. (1)

AtomicBomb (173897) | more than 7 years ago | (#14527008)

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

New uses for geometry in everyday sentences! (-1, Troll)

maxrate (886773) | more than 7 years ago | (#14526570)

"large 'cylindrical' objects pertruding from my anal cavity"

Re:New uses for geometry in everyday sentences! (1)

maxrate (886773) | more than 7 years ago | (#14527066)

Score: -1 ??

Typical /. - No sense of humus

Tell my teacher that, sheesh (4, Funny)

Jim in Buffalo (939861) | more than 7 years ago | (#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 (1)

DaHat (247651) | more than 7 years ago | (#14526763)

Only 10th grade? It took me 3 attempts to pass calculus 1 in college!

Not Geometry, pattern recognition (5, Insightful)

Wind_Walker (83965) | more than 7 years ago | (#14526593)

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 (1)

MOBE2001 (263700) | more than 7 years ago | (#14526689)

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 (1)

Shar-Kali-Sharri (890290) | more than 7 years ago | (#14526695)

I concur. It reminds me of the sometime 'misuse' of the work of Jean Piaget (basically arguing for an biologically determined set of stages in intelligence that all children everywhere pass through). Where the fourth stage, 'formal operational intelligence' is representing the ability to think abstractly, - This stage is often interpreted to be a scientific intelligence - understood as the ability to think in hypotheses and test them. This is overinterepretation - resulting in an 'eurocentric' evolutionary view where we in the west have accomplished the highest intelligence-potential of our biological brains. Studies have shown that this is indeed pseudoscience, as modern hunter-gatherers doesn't neccesarily think in a western liniar scientific way.

Re:Not Geometry, pattern recognition (0)

Anonymous Coward | more than 7 years ago | (#14526711)

This is what happens when you have anthropologists (instead of psychologists) run behavioral studies that supposedly tell us something about human evolution...

Re:Not Geometry, pattern recognition (5, Interesting)

tadmas (770287) | more than 7 years ago | (#14526724)

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 (5, Insightful)

KaushalParekh (896920) | more than 7 years ago | (#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 (1)

Vellmont (569020) | more than 7 years ago | (#14526930)


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 (0)

Anonymous Coward | more than 7 years ago | (#14527053)

Rotation and translation of shapes is geometry, at a basic level

Re:Not Geometry, pattern recognition (1)

StateOfTheUnion (762194) | more than 7 years ago | (#14527180)

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 of angles represents a cultural bias. In other words the statement implies that because one learns that angles denote different kinds of triangles, then everyone differentiates different types of triangles by the angles.

I think that it it is very possible that people can denote different types of triangles without any understanding of angles. If I can change the size of a shape in my mind and rotate the shape in my mind and superimpose it on another shape in my mind, then I can perform pattern recognition without an understanding of angles.

Now if I can take that same shape and flip it over in my mind (like flipping over a leaf, a turtle, flat rock, or any other fairly flat object existing in nature) then I can pattern match clockwise or counter-clockwise items also.

Again I think that the cultural construct of clockwise and counter-clockwise may make one believe that the concept requires cultural education, but if one reduces the concept to flipping over an assymetrical leaf, it doesn't seem like an unnatural expression of pattern matching.

Re:Not Geometry, pattern recognition (1)

qwyeth (944726) | more than 7 years ago | (#14526949)

But pattern recognition is exactly what's so incredible about our predilection for geometry! It's only recently (with the rise of fast and powerful computing machines) that we've been able to define iterative equations that model the natural world with any kind of precision, and yet we've modeled objects around us with simple polygons & polyhedra for ages.

It seems obvious to us because we're the beings who are "hardwired" for it, but one of our most profound abilities is that of simplification. Isn't it fascinating that we can look at a pine tree, then at a rhinoceros's horn, and think "cone" about each? Truly regular polygons and polyhedra don't occur in nature, but we can look at something that's pretty close and identify it with one.

Geometry relies on our ability to think in symbols, but symbols are useless, even meaningless without the patterns they represent. The two are inextricably tied, and while I did RTFA and I agree that the study itself leaves a lot to be desired, you touched on what I believe is an important insight on how we are able to do geometry at all.

Socrates (2, Interesting)

AlastairMurray (537904) | more than 7 years ago | (#14526594)

Plato wrote about an incident where Socrates demonstrated a knowledge of geometry in an uneducated boy over 2000 years ago, this isn't exactly an entirely new discovery. See here [focusing.org] for a description.

Re:Socrates (1)

Doc Ri (900300) | more than 7 years ago | (#14526645)

From TFA:

According to Plato's writings, Socrates attempted to determine how well an uneducated slave in a Greek household understood geometry, and eventually concluded that the slave's soul "must have always possessed this knowledge."

So it seems like you actually read it!

Re:Socrates (1)

Mr Z (6791) | more than 7 years ago | (#14526712)

Shhh... He's trying to look smart to the people who didn't read the article. :-)

Explains a lot (0, Troll)

LiquidCoooled (634315) | more than 7 years ago | (#14526595)

It certainly explains why politicions and RIAA executives look lost most of the time.

Seems like a "non discovery" to me, really... (3, Insightful)

King_TJ (85913) | more than 7 years ago | (#14526600)

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... (0)

Anonymous Coward | more than 7 years ago | (#14526631)

I agree, these results are not astounding. OF COURSE we are "hard wired" for spatial concepts... the real question is, are we genetically programmed with the concepts and thus hard wired, or does the hard wiring occur as a result of developmental exposure to our environment. I am more convinced that it is acquired... but its neccesarily there or we wouldn't be able to function. This study does not show that it's somehow in our genes and present before we are infants.

Re:Seems like a "non discovery" to me, really... (1)

lawpoop (604919) | more than 7 years ago | (#14527034)

"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 that this experiment is lousy, and didn't demonstrate it.

"The fact that adults tended to score better on these tests than kids did further illustrates this. "

Not necessarily. An adult mind is different than a child's mind. It could mean that, instead of the adult learning over a lifetime, and adult brain is fully developed and has all the innate abilities up and running, whereas a childs' mind doesn't.

"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."

There is a famous studies with babies and their perception of 'impossible' scenes. You can read about it in Stephen Pinker's _How the Mind Works_. The babies in the studies were 2-12 months -- they weren't walking around, they didn't have fully developed minds, and they certainly didn't have much experience. However, they showed the babies 'possible' scenes, such as a ball knocking into another ball, and the second ball moving. Then they showed the babies 'impossible' scenes through optical illusions -- such as a ball dissapearing, a ball hitting another ball and coming to a dead stop, etc. The babies stared longer at the impossible scenes than the possible scenes. This seems to imply that they perceived some sort of difference between the possible and impossible scenes. We can reasonably conclude that the babies had some innate sense of physics -- what is possible and impossible in our world -- and therefore were befuddled by the illusions and stared at them longer. 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.

Scientific? (3, Insightful)

teklob (650327) | more than 7 years ago | (#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.

Hmmm.. (0, Redundant)

TubeSteak (669689) | more than 7 years ago | (#14526615)

So, I just read TFA and since they're trained professionals, I won't argue with their methodology.

What I wonder about is their conclusion. Finding the 'odd' shape seems more like pattern recognition to me.

Maybe the ability to recognize patterns also represents some basic concept of geometry, but then again, maybe it just means we're good at noticing differences/relationships.

I guess by abstracting the excercise away from physical objects, they're able to draw these conclusions?

scepticism (1)

Doc Ri (900300) | more than 7 years ago | (#14526704)

since they're trained professionals, I won't argue with their methodology

Maybe you should be a little more sceptical. A specific training or authority does not strengthen any evidence or methodology per se. (Although it might serve as a rough first filter to avoid getting flooded).

old news (5, Informative)

Snafoo (38566) | more than 7 years ago | (#14526617)

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 (1)

bblazz (746281) | more than 7 years ago | (#14526761)

There is also a story about how Socrates tryed to prove that geometry is hard-wired into humans. He did that by questioning some uneducated slave about geometry to extract some knowledge out of him.

Re:old news (1)

kwoff (516741) | more than 7 years ago | (#14526907)

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

I barely even made it through your Slashdot comment. Whew.

Re:old news (5, Informative)

$carab (464226) | more than 7 years ago | (#14527058)

Kant figured this out back in the mid-nineteenth century...

Kant [wikipedia.org] died in 1804.

Seen in kids, too (2, Insightful)

FreshMeat-BWG (541411) | more than 7 years ago | (#14526662)

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.

Then how the bloody hell... (1)

MoogMan (442253) | more than 7 years ago | (#14526673)

...am I crap at Pool?

Re:Then how the bloody hell... (1)

xenoandroid (696729) | more than 7 years ago | (#14526992)

Just because you can see the geometric path you want to take doesn't mean you have the coordination to execute it exactly.

Because.... (1)

Khyber (864651) | more than 7 years ago | (#14527077)

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.

This is a surprise! (0)

Anonymous Coward | more than 7 years ago | (#14526680)

Because it was thought that early geometry teachers taught hunter-gatherers before they could remember where all that juicy juicy fruit was in the forrest. This study hints at the fact that this stuff is built in.

Hardwired indeed (2, Interesting)

dada21 (163177) | more than 7 years ago | (#14526691)

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. (3, Insightful)

Inoshiro (71693) | more than 7 years ago | (#14526823)

"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. (3, Informative)

mightybaldking (907279) | more than 7 years ago | (#14526953)

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.

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

JaxWeb (715417) | more than 7 years ago | (#14527010)

That is merely your opinion. Do not state it as fact.

Re:You can't invent math. (1)

swillden (191260) | more than 7 years ago | (#14527168)

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:Hardwired indeed (1)

lawpoop (604919) | more than 7 years ago | (#14526897)

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 of the class where we were to find triangles in a complex, overlapping shape. Most people found 10-15. The 5 or so of us who were really great at it found 32 (one guy found 31), which I believe is the maximum number in that figure.

Re:Hardwired indeed (1)

dada21 (163177) | more than 7 years ago | (#14526978)

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

Kidding!

simple epistemology (1)

Gothmolly (148874) | more than 7 years ago | (#14526716)

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. This is why old Terrapin Logo was so fun for kids - they GOT it. Contrast this with math (remember how superior you felt when you mastered long division?), where its much more abstract... imaging a 5 year old trying to take a pile of blocks and divide the total (73) by some smaller number (7)... its not intuitive with physical entities.

Does this mean (1)

p0 (740290) | more than 7 years ago | (#14526742)

... that students can no longer take their brains to the exam halls?

Results are possibly unreliable (0)

Billosaur (927319) | more than 7 years ago | (#14526764)

From MSNBC: Using a series of nonverbal tests, scientists claim to have uncovered core knowledge of geometry in villagers from a remote region of the Amazon who have little schooling or experience with maps and speak a language without the mathematical language of geometry.

I knew Amazon was big, but where could a remote region be? Now I know how Jeff Bezos is keeping costs down and why deliveries sometimes get delayed.

How much learned (2, Interesting)

MyLongNickName (822545) | more than 7 years ago | (#14526780)

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, he adapted a strategy of "get in front of the ball and wait for it instead of going right at it." Later, he was able to refine to where he would do the same thing, but meet the ball at exactly the right time.

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.

Don't believe me? Try to come up with a formula to find the optimal path when given fixed speeds, distance, and angle rolled. Bet 90% of Slashdot doesn't have the math skills required. Yet a two-year old's brain is capable of figuring it out.

Re:How much learned (1)

m-laboratories (840170) | more than 7 years ago | (#14526904)

You would be surprised how well neural networks can model some aspects of cognitive development (see here [blogspot.com] for a summary of Elman's work).

In fact, a lot of NN researchers are now modeling child development, based on a growing consensus that true artificial intelligence will have to be capable of learning from its environment in much the same way human infants do. --- Developing Intelligence: http://develintel.blogspot.com/ [blogspot.com]

Re:How much learned (1)

PitaBred (632671) | more than 7 years ago | (#14527001)

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.

Art School (2, Interesting)

Lord_Dweomer (648696) | more than 7 years ago | (#14526785)

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?

Re:Art School (1)

protocoldroid (633203) | more than 7 years ago | (#14527122)

I can't explain the left vs. right brain espects of it, but... The author and artist Betty Edwards can and does in her book Drawing on the Right Side of the Brain [amazon.com] (which, imho is a great read for any accomplished artists, and also any person who'd like to improve their skills in drawing from observation)

intrinsic knowledge or common sense? (2, Interesting)

m-laboratories (840170) | more than 7 years ago | (#14526831)

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 think anyone's surprised that humans can do this. But if this truly is intrinsic knowledge, as opposed to just the human ability for abstract reasoning, we should see similar results even in human infants, from discrimination studies with looking-time measures.

Far more interesting work could be done in animal experiments: what primates can do the same thing? If this is really a case of specific intrinsic knowledge, can we selectively disrupt 'geometric' abilities through brain lesioning? Or is this ability really just a by-product of more general-purpose cortical machinery?

Actually (1, Funny)

Anonymous Coward | more than 7 years ago | (#14526845)

God compiled geometry into our kernel.

An odd comment on left- and right-handedness. (1)

dhilvert (608753) | more than 7 years ago | (#14526882)

'Finding the one "left-handed" image from five "right-handed" images below proved difficult, and the Mundurukú study participants did not do much better than chance.'

'Only 23 percent chose the bottom right as the weird or strange image.'

From 6 choices, this is still about 40% better than chance.

Gee... (2, Insightful)

ericdfields (638772) | more than 7 years ago | (#14526886)

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 (4, Insightful)

roman_mir (125474) | more than 7 years ago | (#14526945)

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.

Mom see I'm a scientist (0, Troll)

Stan Vassilev (939229) | more than 7 years ago | (#14526993)

There are two popular studies. One is that multitasking makes you stupid:

http://www.clarkeching.com/2004/12/multitasking_is .html [clarkeching.com]
http://www.sauria.com/blog/misc/103 [sauria.com]

Also we have all the studies that women are better at multitasking.
So I just added 2 and 2 there...

This is true for asian villagers but (-1, Troll)

Anonymous Coward | more than 7 years ago | (#14527056)

does this also apply to african-americans?

My nominee for... (4, Insightful)

constantnormal (512494) | more than 7 years ago | (#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).

Load More Comments
Slashdot Login

Need an Account?

Forgot your password?

Submission Text Formatting Tips

We support a small subset of HTML, namely these tags:

  • b
  • i
  • p
  • br
  • a
  • ol
  • ul
  • li
  • dl
  • dt
  • dd
  • em
  • strong
  • tt
  • blockquote
  • div
  • quote
  • ecode

"ecode" can be used for code snippets, for example:

<ecode>    while(1) { do_something(); } </ecode>