A Conversation for Ask h2g2
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The 4D HyperCube - its all a matter of perspective..
~ jwf ~ scribblo ergo sum Posted Feb 19, 2008
I simply cannot pass up this opportunity to familiarise you all with a quote from Canadian historian, broadcaster, authour and gardener, the late Pierre Berton, who inspired us all by saying: "Landscaping is the only true four dimensional art form." I believe he came to that observation after his exhaustive study of Canada's first trans-continental railway upon which this country was built - rather linearly.
~jwf~
The 4D HyperCube - its all a matter of perspective..
toybox Posted Feb 19, 2008
Incidentally, if we could move around freely in a 4th spatial dimension, then we wouldn't have a left and right hand - they would be equivalent.
Similarly, on a straight line, you can have arrows pointing in one direction and arrows pointing in the other; if you allow rotating in a plane both arrows are essentially the same (because you can turn one into the other).
The 4D HyperCube - its all a matter of perspective..
TechNoiZ Posted Feb 23, 2008
Also incidentally ...
Has anyone tried modelling a 3 dimensional cube (given only a 2 dimensional plane - and a phantasy 3rd 'depth' dimension) in the same manner one models a 4 dimensional tesseract from a 3 dimensional cube.
The results are quite interesting. A 2 dimensional creature could quite easily believe from what they found that in the third dimension planes could pass through each other, the outside of containers could become the inside, and that an incredible amount of elasticity of form would exist.
Try it ......
There are some incredibly confusing, and also conflicting interpretations of what the forms generated by rotating a cube joined by 4D edges mean. Surely we must recognise some degree of 'compatability' and 'interchangeability' between all dimensions involved if we are to make any real sense of what we see.
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The 4D HyperCube - its all a matter of perspective..
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