¶ Powering: Fourth Dimension and Sixth Dimension
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Index Entry
“. . . Whereas we can only get eight cubes around a point. . . 90 degreeness uses up all the space around a point. When I am dealing in 60 degreeness, when I am using tetrahedron as unity, we can get the whole volume of 20 tetrahedra around one point. The tetrahedron is unity. Then we are getting 20 around a point instead of eight around a point. Eight is the third power of two. When I have a stack of cubes coming together around a point, the edge count is two cubes. Unity is two there. There is just one set of radii from the center of gravity in the system and you can only have a total volume of eight which is the third power of two. If I have a volume of 20 around a point, then two to the fourth power is 16, plus two to the second power. I can then accommodate two to the fourth power plus two to the second power around a point. It is very easy to make models of the fourth dimensionality. We discover that when we do that-- this is what we call the vector equilibrium-- the edge count is now one. When the edge count is one we have a vector equilibrium, not two as in the cubes. The volume is 20. You start with unity as 20. . . And we find that we are able to accommodate sixth powering.”
¶ Citations
- Oregon Lecture i#4, pp. 137-138. 6 Jul’62
