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When people think of square roots and numbers to certain powers many tend to think of them as "numbers". Numbers only describe geometry. All numbers and equations are ALWAYS describing only geometry. In this diagram each "cube" is the number one. There are eight cubes to each side (8 cubes high, 8 cubes wide and 8 cubes in length). So this is literally the number "Eight cubed" or 8 to the power of three. This is the easiest way to see it. Eight to the power of 3 can also be written as 2 to the power of nine. Both 8 to the power of three and 2 to the power of nine equal 512 cubes. This is what square roots and exponents are, literally. Beautiful symmetry of space time created from limits. The shapes of 'numbers' and 'equations' are the key to understanding our universe.
October 18th, 2008
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