A102241 Hexagrams of the Yi Jing [or I Ching] interpreted in base 10, with the top line = 2^5 (most significant bit) and the bottom line as 2^0 (least significant bit).

63, 0, 17, 34, 23, 58, 2, 16, 55, 59, 7, 56, 61, 47, 4, 8, 25, 38, 3, 48, 41, 37, 32, 1, 57, 39, 33, 30, 18, 45, 28, 14, 60, 15, 40, 5, 53, 43, 20, 10, 35, 49, 31, 62, 24, 6, 26, 22, 29, 46, 9, 36, 52, 11, 13, 44, 54, 27, 50, 19, 51, 12, 21, 42

Offset

1,1

Comments

Traditionalists insist that the hexagrams were built from trigrams, which were in turn built from single lines. Historians point out that this is not supported by facts, the hexagrams came first and the rest has evolved from commentary.

There are at least 5 orderings: The popular book order (known as the Wen-Wan ordering, this sequence), the MaWangDui order (A125638), the Lian-Shan ordering (partial), the Kuei-Tsan ordering (partial) and the most recent binary ordering, known as the Fu-Hsi ordering (probably by Shao Yung, +1000 most certainly influenced by Yang Hsiung's Tai Hsuan Jing +10).

In a similar vein the Tai-Hsuan Jing (Han Dynasty, Yang Tze-Yun or Yang Hsiung about +10). This book uses four layers of unbroken, broken once and twice-broken lines that result in the numbers 00 - 80 arranged in a base-three number system order. This book may have also influenced Leibniz.

To my knowledge the orderings of the hexagrams have not been explained mathematically (apart from the obvious fact that each hexagram is followed by its binary reversal or binary complement if it is a binary palindrome).

References

D. E. Knuth, The Art of Computer Programming, vol. 4A, Combinatorial Algorithms, Section 7.2.1.7 (p. 486).

Unknown author, Yi Jing (also known as the Chou Yi). Translation by Richard Wilhelm (Chinese to German) and Cary F. Baynes (German to English).

Unknown author, Yi Jing, English Translation of the MaWangDui text (which has a different ordering).

Links

Table of n, a(n) for n=1..64.

Andreas Schoeter, Yi Jing Algebra

Greg Whincup, The I Ching on the Net

Wikipedia, I Ching

Example

The original hexagrams (in binary) are 111111, 000000, 010001, 100010, 010111, 111010, 000010, 010000, 110111, 111011, 000111, 111000, 111101, 101111, 000100, 001000, 011001, 100110, 000011, 110000, 101001, 100101, 100000, 000001, 111001, 100111, 100001, 011110, 010010, 101101, 011100, 001110, 111100, 001111, 101000, 000101, 110101, 101011, 010100, 001010, 100011, 110001, 011111, 111110, 011000, 000110, 011010, 010110, 011101, 101110, 001001, 100100, 110100, 001011, 001101, 101100, 110110, 011011, 110010, 010011, 110011, 001100, 010101, 101010.

Crossrefs

Cf. A125638.

Sequence in context: A115460 A116270 A324018 * A255915 A351341 A234692

Adjacent sequences: A102238 A102239 A102240 * A102242 A102243 A102244

Keyword

nonn,fini,full

Author

Patrick A. Kirol [Sun Wu Kong] (sunwukong(AT)hananet.net), Feb 18 2005, Nov 28 2008

Extensions

Corrected by David Applegate, Nov 28 2006

Status

approved