The golden ratio, below, is the separation between whole numbers that breaks a collection into is small set of whole numbers. Root five is the first root with a single set of continued fractions, a[2,4,4,4,4..]. It is the first number that can break up any sequence into whole numbered fractions, I presume. Pauli adds the third shape, the Null, and gets three shapes, the golden counter, than is multiplied by 2/3, and gives the continued fraction that can make fractions at integer three seperation.
becomes the continued fraction 3,3,3,3,3,3
The golden vacuum shapes, then differ by .61803....; and they are optimally packed and can hold thwo numbers. Add the third and count whole fractions by 2/3, with whole number (rational) fractions.
The two vacuum shapes for minus and positive are not equal, according to golden.
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