Slashdot Mirror
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."
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.
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.
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.
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.
"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.
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.
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.
Read the best of all of Slash: seenonslash.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).
Please, oh please, if there is any intelligence, justice or wisdom in the Slashdot universe, please MOD PARENT UP!!!!
It never ceases to amaze me how frequently even otherwise intelligent people confuse the map for the territory. Any abstract model you've ever conceived of or used is not reality. It is just a model that corresponds more or less well to reality. Please read and understand the parent post if you want to have any notion of how human knowledge differs from reality, and how human knowledge progresses by devising ever more sophisticated models (which are still not reality).
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...
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.
Didn't people INVENT geometry? "Hey everybody! This glove fits my hand!!!"
If by 'content-free', you're saying that there's no difference between saying 'that bird/that wind tunnel is solving a particular case of the Navier-Stokes equations' and saying 'the bird has a sort of real-time feedback mechanism'/'the wind tunnel has settled into an equilibrium state', then you'd better make that clear. If you're not saying that, then maybe my original note wasn't so content-free after all.
You seem to have confused what I actually said with a straw man you're capable of taking some weak potshots at.
Read the best of all of Slash: seenonslash.com