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## Humans Hard-wired for Geometry235

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

• #### Socrates (Score:1, Interesting)

on Saturday January 21, 2006 @12:39PM (#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.
• #### Hardwired indeed (Score:3, Interesting)

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

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

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

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

I'm turning into Monk, aren't I?
• #### Partial Differential Equations, too! (Score:2, Interesting)

on Saturday January 21, 2006 @12:58PM (#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:Not Geometry, pattern recognition (Score:5, Interesting)

<david AT tadmas DOT com> on Saturday January 21, 2006 @01:03PM (#14526724) Homepage

Agreed.

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

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

• #### How much learned (Score:2, Interesting)

on Saturday January 21, 2006 @01:12PM (#14526780) Journal
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.

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

on Saturday January 21, 2006 @01:15PM (#14526785) Homepage
While some people have pointed out that we are not hardwired for geometry but rather pattern recognition...I was wondering if someone could clarify on the left-brain vs right-brain aspects of it.

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

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

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

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

on Saturday January 21, 2006 @01:22PM (#14526831) Homepage
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?

• #### Re:They're not using calculations, no. (Score:3, Interesting)

on Saturday January 21, 2006 @02:11PM (#14527129) Homepage Journal
" 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:Inherent Geometry (Score:3, Interesting)

on Saturday January 21, 2006 @03:10PM (#14527446) Homepage

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.

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