## Humans Hard-wired for Geometry 235

Posted
by
CowboyNeal

from the pythagoras-notwithstanding dept.

from the pythagoras-notwithstanding dept.

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."*
## 3D world (Score:4, Insightful)

## That's nothing. We're hardwired for calculus. (Score:5, Insightful)

dogscan do calculus, even when the birds they're after are using anti-calculus to try to defeat them.## Re:3D world (Score:3, Insightful)

## Not Geometry, pattern recognition (Score:5, Insightful)

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.

## Seems like a "non discovery" to me, really... (Score:4, Insightful)

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.

## Scientific? (Score:3, Insightful)

## Re:That's nothing. We're hardwired for calculus. (Score:5, Insightful)

consciously applyinggeometry. 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.

## Re:That's nothing. We're hardwired for calculus. (Score:3, Insightful)

## Seen in kids, too (Score:3, Insightful)

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.

## Re:That's nothing. We're hardwired for calculus. (Score:2, Insightful)

## Re:Not Geometry, pattern recognition (Score:5, Insightful)

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 [nyud.net] before calling it pseudo-science.

## Re:Yes (Score:0, Insightful)

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.

## You can't invent math. (Score:4, Insightful)

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.

## Gee... (Score:2, Insightful)

alwaysostracizing those that aren't part of the group! Definitely the best at that skill...## That was not a geometry test though (Score:5, Insightful)

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.

## That's not a two-dimensional problem (Score:1, Insightful)

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.

## Re:Partial Differential Equations, too! (Score:5, Insightful)

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... (Score:5, Insightful)

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).

## Re:That's nothing. We're hardwired for calculus. (Score:3, Insightful)

## Re:Partial Differential Equations, too! (Score:3, Insightful)

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 stillnot reality).## Not Geometry! (Score:4, Insightful)

Have them write some proofs or identify the magnitude of some angles and I'll be impressed.

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

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.

## hmmm (Score:1, Insightful)

## Re:Partial Differential Equations, too! (Score:3, Insightful)

thoughtmy post boiled down to : 'saying that someone/thingsolvesan equation, just because that equationmodelssomething that someone/thing is doing, can end up making you sound pretty silly'.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.

## Re:Not Geometry! (Score:3, Insightful)

It seems what you are saying is that perhaps the brain is composed of neural networks, but is not limited to this. I suppose I would agree with that.