Big-Endian or Little-Endian?

[russell]

Hello; I would like to decide on a definite scheme for ordering and looking up the hexagrams based on their binary values. It is simple to look up a hexagram in this kind of list based on reading the trigrams as two octal (base-8) numbers. The problem is that, to me at least, the logical binary number sequence starts with the bottom line and works up, the way lines are chosen and numbered. But Shao Yong started his sequence by changing the top line and working down, and this seems pretty engrained in people’s minds; the earlier heaven sequence of trigrams works this way as well.

To illustrate: which of these hexagrams should have a value of 1?

==== ==== . . . =========
==== ==== . . . ==== ====
==== ==== . . . ==== ====

==== ==== . . . ==== ====
==== ==== . . . ==== ====
========= . . . ==== ====

On “my” side, Larry Schoenholtz in New Directions in the I Ching calls Shao Yong’s sequence a mirror image of the binary number system.

E. A. Harper has written a document illustrating exactly what I would like to do, listed as IChingPaper.pdf at http://www.magichypercubes.com/Encyclopedia/i/i.html.

See also, the I Ching Sequencer, in which the lines progress from bottom to top, at

http://taolodge.com/flash/sequencer.html

Also see http://www.biroco.com/yijing/sequence.htm

Does anyone have any opinons on this?

Thank you,

—Russell

 

[bradford]

The one on the right is 000001 in binary, both in the order in which is written and cast, and in the higher value of the left and bottom digits. Larry Schoenholtz is wrong.

 

[russell]

So if you were referring to the hexagram on the right by its trigrams, would you call it 01? Or 10?

 

[bradford]

So if you were referring to the hexagram on the right by its trigrams, would you call it 01? Or 10?

Zero One
Gua are always built and read from the bottom up.

 

[russell]

I think the dichotomy comes from the fact that we write and build text from left to right:

every
good
boy
does
fine

And we write numbers from left to right but build them from right to left:

000000
000001
000010
000011
000100

If yao are treated as numbers, and gua are built from bottom to top, then I see the left gua above as the number 000001. Or in octal, 01.

Another way to put it, if yao are numbers, then gua are no longer simply a bottom-to-top writing system,

f
e
d
c
b
a

they are a progression of values. So do the values progress from bottom-to-top,

100000
10000
1000
100
10
1

or top-to-bottom?

1
10
100
1000
10000
100000

I understand the upper lines of a hexagram to have a greater value than the lower.

—Russell