Is Geometric Knowledge Learned or Inherited?

How long does it take them to get the hang of HALO: Combat Evolved, or any of the 813 other games available for the Xbox 360 today.

I have an acquaintance whose ten year old son is a self-described 'Wizard' at such games, and I know this lad at least has trouble trying to "manipulate numbers larger than five.".

A sad commentary on American education households, this. I hardly believe this to be an exclusive example of how the next generation of Americans is being raised.

Does this kid understand geometry? I cannot tell you; he refuses to play along with anything I have tried in the way of mental (or physical, for that matter) exercise.

Heck I know financial officers, business owners, and other highly paid management people who obviously cant manipulate numbers greater than five as well and God knows they cant pay Xbox either.

Whats that say about the business ownership and management level mental capacities of today as well?

Can these tribes people rationalize the difference between personal wants and good business tactics? If so I have a few dozen jobs for them! No counting over five required either!

Plato's Dialogue between Socrates and Meno suggested that such knowledge is innate. I have my doubts, but the debate is quite old.

Until one gets to analytic geometry, geometry is largely visual rather than numerical, so the tribal capabilities need not be surprising.

There may be some geometric principle involved in the common objects of that culture, but little or no use of counting. Even crows can count to eight, and monkeys (not even apes) instinctively deal with money the same way we do, focusing on the same bargaining points and missing the same good deals.

I was also fascinated to learn that Eskimos, who were raised in Igloo domes, have no extra difficulty in reading text and diagrams presented in any orientation.

The same tribe was described in Alex Bello's book, "Alex's Adventures in Numberland". The Indians have learned what they need to survive in remote primitive environments.I believe they think in logarithmic terms as it best suited there sense of survival. Our number system is linear but their system is logarithmic to reflect the dangers they would encounter. It kind of gave them some idea of ability to outrun some preying animal. I do not recall all the details so I am sorry I can't expand very much on the theory. However, when I get the book back (it is on loan!!), I will review it. The book is a terrific read and has many facets of numbers to intrigue all of us. FYI.

Sounds interesting! I'll look for your review (if the book returns home). Meanwhile, off to Amazon....

Even ancient tribes in south america,africa and asia have built geometrical shaped structures(homes) without any education in arithmetic. Drawing a straight line using the shadow of a pole in sunlight was known to them. Brick or stone laying in temples/ pyramids vertically and horizontally in a straight line is normally done by uneducated bricklayers and uneducated carpenters check linearity/straightness in wood/timber by using their eye sight without using any implements.

As geometric shapes are visible to the eye it may be easier to conceive than addition, subtraction,division,multiplication etc which need to be done by mind.

I'm not sure any 'debate' is necessary.
We have certain inate cognitive and motor abilities. What we choose to use them for is what hones them to a level of usefulness even if it's not formalised mathematically.
A great appreciation of the geometry of a parabola is needed to shoot an arrow accurately, but I don't s'pose the Mundurucu realise this. Similary the building of shelter from various natural materials requires a great deal of skill and understanding.
Although to be fair they have the great advantage of not having CAD systems and accountants.
The basics are learned in the sand pit or with building blocks, sticks, xbox or whatever the cultural equivalent may be. Deprive a child of these learning tools and they will have their development stunted.
Without nice neat rectangular bocks maybe the natives learn more subtle geometries than us 'civilised' types. It then takes brave bold architects to shun the straight edge and the corner in favour of more natuaral forms.
<AWOOGA> brevquot error process terminated
Del

One only has to look at some of the fine stone work at Macchu Picchu in Peru to know that they were not done by someone without some knowledge of Geometry. Of course, there are some who contend that the aliens helped them. The Indians in the Amazon probably had some contact or common ancestry with the Mayans and Incas.

There are not many masons alive today who could duplicate that construction and it was all done without the use of cement.

I think the act of 'seeing' is much more complex than we realize. Neurospsychologists have identified a number of different areas of the brain where specific visual processing operations takes place outside of the visual cortex. Some of these areas seem to be specifically involved in identifying lines and angles, an ability that is critical to locating the edges of physical objects. This is one of those areas that are very difficult for AI but are 'second nature' for the brain. If you are going to hunt successfully in a jungle, a quick decision must be made when releasing an arrow, dart or spear about which path between the intervening trees and brush your missile needs to follow. This requires the brain to develop a 'map' of the local space in real time. I would suggest that to a large extent the mental tools needed to develop this skill are innate, and are honed over time through trial and error, and by helpful advice from the more experienced hunters. (I'll go way out on the limb and suggest that this ability is common to predators of other species as well) It is great that our ancestors (probably in India) were able to sort out the math behind geometry, giving us a formal system for numerically describing our world, but the ability to use geometry is a fundamental part of the human toolkit, and is more ancient still. Without this ability we probably wouldn't be here to have this discussion.

I'd say it boils down pretty much to 3D vision. Our eyes are placed to create this effect from the light images entering them. There are many animals that don't have this placement and therefore experience the world much differently from us. The brain is wired for each case. Our minds "think" in 3D.

Ordinary geometry is "spatial." (No Church Lady jokes. ;) ) The consciousness in our brains "devised" a formal discipline called geometry, but it arose out of our visual experience. If animals with non-3D vision could devise a "system" encompassing their "view" of the world, what sort of math would they need or use? And what would their version of "reality" look like?

Interesting question. I don't have an answer but I'd note that many birds have sideways facing eyes but probably have much better spatial sense than critters like us with forward facing (3D) eyes.

From our understanding, it gives them more of a 360 degree view, but I wouldn't think it would be 3D by our definition, or experience -- not depth perception, as we experience it. It would still be more like closing one eye for us.

I think 3D, as we experience it, is just as dependent on how the brain organizes the "data" from each eye into a composite result. This truly makes our experience of the world possibly unique. I've seen figures that say between 75%-83% of our experience is through the eyes. And there is enough variation in what is called IPD (interpupillary distance) that the angle between the 2 images is, likely, not highly critical. Apparently. This brings up a similar question of, How do we know for sure what any one of us "sees" is the exact same image that is constructed in another persons brain/perception?"

I think that it is both learned and innate, these people build small and medium sized dwellings, and to do this does require a certain amount of geometrical knowlege, and the results of this test do not surprise me, I have seen similar before!

Spencer.

Compare with an Aborigine making a boomerang and an aeronautical engineer trying to analyse it...
Del

Exactly !