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."

Comments

Now I understand why...

[Anonymous Coward]

People are always calling me square.

3D world

[Anonymous Coward]

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?

That's nothing. We're hardwired for calculus.

[ScentCone]

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.

[Mattintosh]

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.

Tell my teacher that, sheesh

[Jim in Buffalo]

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.

Not Geometry, pattern recognition

[Wind_Walker]

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

[tadmas]

Agreed.

Actually, they've done previous studies on these people to investigate whether they had innate arithmetic abilities 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

[KaushalParekh]

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 before calling it pseudo-science.

old news

[Snafoo]

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

[$carab]

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

Kant died in 1804.

That was not a geometry test though

[roman_mir]

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.

Re:Partial Differential Equations, too!

[greginnj]

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.

My nominee for...

[constantnormal]

... the Ig Nobel Prize.

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).