Center of Gravity in 2D

Ideas about how a world with more than three spatial dimensions would work - what laws of physics would be needed, how things would be built, how people would do things and so on.

Center of Gravity in 2D

Postby somashekart » Fri Feb 24, 2012 5:36 am

I wonder where is the Center of Gravity in 2D and how do the 2D beings visualize it? According to Flatland and other 2D analogies, the 2D beings seem to float along their plane (and not grounded over the line at the bottom of the plane - in fact flatland analogy doesn't have any line as the starting boundary of emergence to the 2D beings. The plane is infinitely expanded in all four directions). Where as in our 3D world, we are grounded on a surface (in contrast to what I thought the 2D beings should have grounded over a line as a second version of flatland analogy) and our center of gravity is below our feet.

So where is the center of gravity in the 2D world? And how the 2D beings visualize it? Are they unaware of the concept of center of gravity itself? Is Center of Gravity insignificant in flatland? According to flatland analogy, if at all there is any center of gravity (as I see) it seems like it is in a direction perpendicular to the body of 2D beings (and not below their feet), but strangely the flatlanders cannot visualize that direction!

And also I'm surprised at one more thing. A flatlander is always in a threat of attack from all 4 directions around him (Another being can easily stamp over his head by moving around him) whereas in our 3D world, the direction of attack is limited to left-right, front-back. The top-bottom attacks are possible only if we use airways, missiles and explosions. (In brief, all flatlanders can literally fly in their world, where as in our world we have both living forms. OR is there a possibility that even the 2D World has both living forms?)

One more thing... How do a flatlander greet and shake hand with a friend in his land? It is only by touching each others hand through a linear contact, and they can't cross over the hands (because it needs a third dimension to do so)

I have several other doubts regarding 2D analogy (Probably I'm failing to understand the 2D analogy fully just like 4D. Do others also feel the same OR can I be clarified?)
Last edited by somashekart on Fri Feb 24, 2012 9:48 am, edited 1 time in total.
somashekart
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Re: Center of Gravity in 2D

Postby somashekart » Fri Feb 24, 2012 9:42 am

Also they tell the view of 2D beings is 1D. So even a square will look like a vertical line (or horizontal line). But I'm not clear how it will appear to them (Vertical or Horizontal). But in any case, the line will have a thickness (and that thickness should exist in the third dimension - I mean 3D). But then the 2D beings will not remain 2D in this analogy! So we have probably not understood the 2D concept (at least me) let alone 4D.

A 2D being would understand a square by moving around it and seeing 4 nodes (and 4 edges) and will visualize a circle again by moving around & not finding any sharp node. But a 2D being would not be aware of the full picture (face on) of a 2D Shape (if I am not wrong). Likewise shall we say we have not actually seen a sphere's shape properly. To do that we may have to get into the 4D world?
Last edited by somashekart on Fri Feb 24, 2012 9:51 am, edited 1 time in total.
somashekart
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Re: Center of Gravity in 2D

Postby somashekart » Fri Feb 24, 2012 9:47 am

Hmmm... I also feel that if a flatlander is rooted to ground (line) in their plane (center of gravity over a line), then their movement will be limited to only one direction (front & back). The other movement will be flying above and digging the ground. Life becomes really difficult/tedious then! Overtaking someone becomes impossible (unless you jump or fly over him). So I think the floating flatland analogy is better served.
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