The Fourier of the ring
The DFT over Shao Yong's circle Z/64
Walk the magnitude spectrum and find which cyclic harmonic dominates the King Wen sequence on the circle.
The site's other geometry. The Shao Yong circle is Z/64, and the discrete Fourier transform decomposes any sequence on it into cyclic harmonics. We apply it to the same signal as Fourier over the cube (at each position of the circle, the King Wen number of the hexagram), but with another geometry: there the cube (Z/2)⁶, here the circle. Same signal, two geometries, two spectra.
harmonic k = 8: magnitude |F| = 388.42 · period 8.00 positions
The dominant harmonic is k = 8: the King Wen sequence resonates with the period of the 8 trigrams, the 8×8 structure that organizes the book. The spectrum satisfies Parseval (energy is conserved), the DFT of a constant is a delta at k=0, and the inverse transform recovers the exact signal: verified in the suite. Where the Fourier of the cube saw interactions between pairs of lines, the one of the circle sees periodicities: two different questions asked of the same sequence.
The DFT over Z/64 (the Shao Yong circle) decomposes the King Wen sequence into cyclic harmonics and satisfies Parseval; the DFT of a constant is a delta and the round trip recovers the signal.
verificar_fourier · source: Terras, 1999The dominant harmonic is k = 8, the period of the eight trigrams; it is the same signal as the Walsh experiment in another geometry: the circle Z/64 instead of the cube (Z/2)^6.
verificar_fourierThe types of claim and the full bibliography (APA) are in Foundations.