aka_tom_w Posted February 12, 2005 Share Posted February 12, 2005 Since it is hard to try to directly picture the world of CMx2 in our minds, perhaps using analogy can help us. In 1884, Edwin Abbot wrote a book called "Flatland". (Think CMx1) The book writes about A. Square and his world, Flatland. You may have already guessed, but Flatland is a 2 dimensional, flat plane and A. Square is a square shaped guy who lives there. He has two dimensions of free movement. He can go left/right and back/forth, however because he is restricted to his 2 dimensional Flatland plane, he cannot go up/down off the plane. By analogy, we humans are restricted to our "plane" of existence... and it would be impossible for us to freely move in the fourth dimension.(some might say the forth dimension is time but we are not concerned about that here ) Let's go back to A. Square again. Note that A. Square can only see what lies in his plane of existence, (CMx1) which means if a 3 dimensional sphere (Like a vision of CMx2) were to pass through Flatland, A. Square would not see the sphere, but just 2 dimensional "slices". Taking this further, imagine if a sphere passed halfway through Flatland but stopped in the middle. the sphere would interesect Flatland as just one circle and A. Square could see it! Furthermore, imagine if as the sphere approaches Flatland, A. Square watches as the sphere slowly moves through his plane. What would A. Square see? Recall that A. Square can only see 2 dimensional slices of the sphere (or circles or BIG curved lines up and down) so what A. Square would percieve is a circle suddenly appearing, then growing... then reaching a maximum size as the sphere was halfway through and as it exited, the circle would grow smaller until it disappeared. This means that 3d objects could be explained to a 2d being as a bunch of "slices stacked" on top of each other. Try to imagine taking a bunch of circles and stacking them. They would begin to form a skeleton framework of the actual 3d image. Similarly if a 5d thing (or CMx2) would intersect our plane of existence, we would see a 3d sphere appear out of no where. It would grow until the hypersphere was halfway through, then it would shrink back to nothing. Theoretically, we could stack these spheres to form a a new thing, but we can't stack them in the usual sense, but rather it would have to extend into the fifth dimension which takes us back to the original dilemma of trying to visualize it. plagarized and incomplete sorry needs some work to make sense I'll be back later -tom w [ February 13, 2005, 07:21 PM: Message edited by: aka_tom_w ] 0 Quote Link to comment Share on other sites More sharing options...
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