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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?
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.
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.
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.
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.
- undoware.ca
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.
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?
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.
--
Internet Explorer (n): Another bug -- that is, a feature that can't be turned off -- in Windows.
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?
No, no... dogs can't. Cows can't. Cat's won't. Why should cats bother when people will do everything for them?
Kierthos
Mr. Hu is not a ninja.
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.
" 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.
Computers are useless. They can only give you answers.
-- Pablo Picasso
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).
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.
Big ones, small ones, some as big as yer 'ead!
Give 'em a twist, a flick o' the wrist...
I think the reason those abilities fall away is because they're not constantly exposed to geometric objects. I recall in a psych class the teacher explaining a certain optical illusion. I forget the illusion, but the point was this: people in western countries see horizontal and vertical straight lines more clearly than diagonal ones. Our visual cortices are hard-wired - yep - to pick up the lines which we see reinforced in our lives. By contrast, the illusion does not work on non-civilized people.
The purpose of calculus is to provide a mathematical framework to deal with change, not to sum infinite series (though you can indeed use it for that too).
In a sense, you are doing applied calculus when you react to stimuli in that way, but that's because change is a very easy thing for organisms to react to. You're not actually doing any math, but you are reacting to a situation that calculus can describe. It's like dropping something and knowing when it will land. You can usually guess pretty well when it will hit without knowing that gravity causes the object to accelerate at 9.81 m/s^2.
On the other hand, it is a learned behavior, so the "lookup table" idea is not as far off as you would think. It's almost like the rules themselves are dynamically learned (and refined), allowing them to be applied to many scenarios.
Are we sure those cats and dogs really can't find their way home? Maybe they just don't want to go home. :)