Comments on: Parallel Lines Never Cross, Even in Remote Amazonia

By: vmaxxed

vmaxxed — Tue, 29 Nov 2011 21:14:35 +0000

No news, philosphers have known that since middle ages.

The idea or concept of parallel lines is defined by Euclidean geometry as lines that never cross. So the regular answer is: No, they never cross, because then they will not be parallel according to Euclid.

But, I’m sure the questioner is not asking about Euclidean geometry but about reality.

In this sense some people will say: No, parallel never cross because there is no such a thing in real life. Parallel lines only exist in our mind.

But this answer is too simplistic. There is “reality” in our “ideal” concept of parallel lines. If reality was so disconnected from our geometric and logical constructs we would not be able to interact with the real world. We can walk, see and reason reality because we find circles, lines, logical constructs and 2 as the sum of 1 + 1, in the “real” world. Or at least, a very close approximation to that, though never “perfect” circles or lines.

Kant clearly demonstrated that these ideas are “hard coded” in our mind, not learned, because we need this idea “framework” to rationalize perception in the first place. There has never been a society where 1+1=3 and where parallel lines cross at say, 100 feet.

Questions like these are the beginning of modern philosophy, beginning with Plato who had not other option but to conclude that these ideas have an existence of their own in some kind of idea heaven. Of course the point is not whether this idea heaven exists, but to point out the real problems: Why do we have this constructs in our mind? What is the relationship to reality? Where do ideas come from?

So, in summary, yes, parallel lines in our mind never cross, and yes, they seem not to exist in reality. But there is a very real connection between the idea and the “real” thing, but since we can only “see” the “idea” we can not now in “reality”.

By: Holden

Holden — Tue, 31 May 2011 01:23:08 +0000

Hey joasnosmae,
Your contribution is one word too long. There’s no need for that.

By: John

John — Mon, 30 May 2011 09:52:57 +0000

“Socratese and the Slave Boy” is in one of the late Martin Gardner’s antholigies (such as “The Mathematical Mag Pi”). A classical story.

If we were to ask a chimp those questions (like Washo) what would the sign language answers be? Or an African Gray Parrot?

Might we find that geometry was instinctive?

By: Iain

Iain — Sun, 29 May 2011 02:12:55 +0000

Younger American children, however, ages 5 to 7, did poorly by comparison,
I’m assuming that the Amazonians kicked ass here as they spend most of their time in the world, not a virtual world.

By: Ryan

Ryan — Fri, 27 May 2011 18:29:29 +0000

I’m sure many of these tribal people are better human specimens than much of the detritus that inhabits our “advanced” societies. In their world, the gap between success and fatal failure is much smaller.

By: joasnosmae

joasnosmae — Thu, 26 May 2011 22:52:49 +0000

Tom, i don’t think they guessed by within 5 degrees numerically. As the article states, they used measuring tools, or their hands, to estimate the angles. Duhhhhhh.

By: Tom Hanna

Tom Hanna — Thu, 26 May 2011 16:45:36 +0000

If these people, in the amazon, were able to guess the angles by within 5 degrees, something tells me someone was there before to educate them on the fact that there are a total of 360 degrees in a plane!

By: Juris Zars

Juris Zars — Wed, 25 May 2011 19:15:50 +0000

I am reminded of the many times, in an effort to bolster the confidence of my mathematics students at the start of the school year, I paraphrased Plato’s so called “Socretes and the Slave Boy” story. The results of the above study and the wisdom expressed by Plato point in the same direction, and the implications of this principle are of value to both the teacher and the student.

By: Jordan C

Jordan C — Wed, 25 May 2011 17:00:17 +0000

Of course nature v nurture is going to rise up. After all, we are talking about people who need to understand angles in order to hunt. Hunting a moving animal is akin to understanding the trajectory and relative path of a snooker ball. If you fail at geometry in the real world where angles = kills and therefore food for your tribe/family, then you will fail at life!!

By: Michael Berry

Michael Berry — Wed, 25 May 2011 15:07:03 +0000

Like Kevin, I also assumed these types of things were innate, or rather learned through natural experiences of trial and error, or as the the article phrased it “acquired through general experiences with space, such as the ways our bodies move.” To me, it seems the Amazonian children might simply be extrapolating their spatial reasoning from the real world to the exercises in geometry they were given.

Interesting study.