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Humans Hard-wired for Geometry
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."
People are always calling me square.
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?
A: Gee, I'm a tree
(say it fast if you don't get it)
(I'll be here all week)
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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.
Don't disappoint your bird dog. Go to the range.
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.
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.
This sig, aah-ah, is comin' like a ghost-sig...
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.
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 for a description.
It certainly explains why politicions and RIAA executives look lost most of the time.
liqbase
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.
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.
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?
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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.
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We're also wired for math, and look at how poorly people do at that
What is the compliment to a 45 degree angle?
"Wow, you're looking acute today"
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.
...am I crap at Pool?
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.
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 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?
Which makes me wonder: is math really that hard or is our notation making it more difficult than it really is?
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).
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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.
I want to delete my account but Slashdot doesn't allow it.
... that students can no longer take their brains to the exam halls?
This is my sig. There are thousands more, but this one is mine.
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.
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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.
See my journal for slashdot ID's by year. Mine created in 2005. http://slashdot.org/journal/289875/slashdot-ids-by-year
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?
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"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.
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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?
God compiled geometry into our kernel.
'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.
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...
eric http://www.ericdfields.com/
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.
You can't handle the truth.
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.
There are two popular studies. One is that multitasking makes you stupid:
s .html
http://www.clarkeching.com/2004/12/multitasking_i
http://www.sauria.com/blog/misc/103
Also we have all the studies that women are better at multitasking.
So I just added 2 and 2 there...
"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.
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.
Typical /. - No sense of humus
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.
Still waiting on Serviscope_minor to wake up to fucking reality and realize that Jessica Price isn't going to fuck him.
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).
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 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 Geometry" makes us really seem more competent than we actually are, since this simple ability to amble about doesn't actually give any useful skills with numbers.
http://www.msnbc.msn.com/id/10931608/
You answered 100% of questions correctly.
Pfft, they should have made those questions a bit harder than that...
Kaetemi
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.
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Give 'em a twist, a flick o' the wrist...
The article raises a very old question, as they pointed out; it has a historical reference at least as old as Plato. I agree with some of the assertions made by the team from the university in France. However, if there test was made up of similar pictorial questions as are posted in there article on MSNBC, there are significant flaws in their research. Notice in the second set of diagrams that the one in the lower right is the only shape that is convex! This could also be a legitimate response. As far as the last set of images, these bare a striking resemblance to patterns one could encounter on insect, such as butterflies. We have no information on the cultural relevance these people give to such markings and as such they may choose the one that has some spiritual taboo in their society. It is clear that the team must include a mathematician, i.e. Geometer, and a cultural anthropologist that is an expert in such areas. Although I agree with the findings of this study, the work that is published makes me believe it should be classified as junk science.
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.
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The only thing I was able to find was this article http://www.bioedonline.org/news/news.cfm?art=1207 which shows that the ability to count even in small quantities is not naturally inherent in humans. How much of our "basic" abilities are truly nature or nurture?
The BBC ran an episode of Horizon concerning this called "The Day We Learned To Think". They talk about how early man (and woman... gotta be politically correct these days) underwent the first steps of learning to think by drawing geometric shapes, with sets of parallel and lines etched into cave floors and walls.
Didn't people INVENT geometry? "Hey everybody! This glove fits my hand!!!"
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.
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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 about dancing and then food would rain from the sky. If this was the case, they would be great dancers but poor Geomtricians.
Horns are really just a broken halo.
Someone else mentioned a pouncing preditor, and that is an example of a problem preditors solve: the location of a perticle in space at time t based on observation and estimation of preys speed, direction and acceleration; and the need to calculate the muscle contractions necessary to get it to the same point at the same time. As the prey evades, the preditor has to constantly adjust its own velocity and acceleration to match until it can get close enough to solve the following vector problem for t and Preditor Velocity:
Preditor Location + t * Preditor Velocity = Prey Location + t * Prey Velocity
This certainly involves an understanding of geometry.
According to Plato's philosophy, we already know everything, we've just forgotten it (anamnesis).
Per Aspera Ad Astra.
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't just kick around and have their feet or hands pass through the clothing, leaving it behind them someplace.) Certainly, by age 12 months, they've also done such things as batted at items dangling overhead (say on a mobile in their crib?) and watched the results of those actions.
I'm pretty sure Immanuel Kant wrote about that over two hundred years ago. I wouldn't consider it exactly 'new'.
Mathematics is made of 50 percent formulas, 50 percent proofs, and 50 percent imagination.
I teach geometry in a Bronx high school. My students regularly confuse angles with sides and even points. This is commonplace in the inner city high schools where as bad as we observe our students algebra skills to be, the ability to see and understand geometric shapes is even worse. I have seen many students fail to reasonably depict in their notebooks a simple right triangle that I have drawn on the chalkboard.
If we are so hardwired for calculus why is it that so many ancient Greek mathematicians actually used geometry to solve their hardest problems (See Alexander to Actium) and never really reached a firm understanding of calculus? Much of the work that could have been done easier with calculus was done with painful geometric representations.
Wikipedia says that Archimedes came close, but other (more informed) sources say that he wasn't close and used geometry as everyone else did.
Get your Unix fortune now!
The Inuit have an absurd number of words for what we call snow.
Not really. Various Inuit dialects have a lot of compound words, analogous to English snowdrift, snowflake, snowball, etc. You might find the E2 article and the Wikipedia article interesting.
Similarly, it is not clear that everyone in the world takes 'length' and 'angle' to be significant.
Especially to the Pirahã.
From 6 choices, this is still about 40% better than chance.
When you're aiming for a typical 95 percent confidence interval, a mere 40 percent over chance is "not much". Do you know your student's t test from your chi squared test?
This guy also has something to say on this subject: http://fleen.org/?p=60
duh -- we're hardwired for geometry because of problems like this:
* misty haze rises - 300,000 years ago:
ancient man talks to his son, points and grunts the following instructions:
"go 300 yards over there, take a left and go 600 yards. thats where the women were. go get 'em boy..."
What I'm missing from the discussion is a reference to the Sapir-Whorf hypothesis (see http://venus.va.com.au/suggestion/sapir.html): does our language shape/limit our thought! And this study clearly seems to contradict it...
I want an anthropomorphism stick!
I'm willing to bet there's are bunches of neurons modelling/mirroring/simulating the perceivable world in your brain. And that's used to help predict what might happen next, or what could happen.
;).
Such a predictive ability is very useful to most animals. And I believe "models" are a fairly simple way to do things with neurons AND they can be used to solve more than a few problems - they are not a "premature optimization", unlike many of those simplified equations.
I suggest that most humans are able to tell whether a tree branch or even a plank or sheet of metal is unlikely to safely hold their weight, just from looking at the object and having a previous experience of the strength a sample of the material the object was made of.
I believe that sort of thing is more like modelling and simulation in your brain, than calculation and equations.
It is more like building a scaled down model of a river and a dam and pouring water in to see if something will overflow.
Sure your neurons probably do the equivalent of some analog math to simulate some stuff, but I believe "simulation" is more useful and accurate for what our brains do for this sort of thing. Otherwise it would be like someone saying that the water in the scaled down model of a dam is doing calculus. May be true in a way, but not very useful.
Lastly, I suspect a fair bit of consciousness is you modelling and predicting yourself. To quote Dune: "Solve thyself". BUT I don't think that's all of it because there're still a few other things
I know a mentally challenged lady who can't understand geometry. But she can knit quite well. She learned by copying the steps her grandmother made.
It's like confusing a script kiddie with a true hacker.
SIL Linguists tell me that 50 year-old people from pre-literate societies can't seem to get the square pegs in the square holes and the round pegs in the round holes. Child's play, but they've never dealt with abstract shapes. When they start teaching reading and writing, the first steps are teaching the kids to draw vertical lines like grass. Then they work on horizontals. It takes a while before they can get to basic letters. You'd be amazed at what you've learned in your preschool years.
I've spent time in China and Taiwan (amongst other places). The Chinese as a culture have a poor sense of geometry or geography. Amongst other things, ever notice how their streets and houses are a hopeless maze?