Re: Trigram Data Disks, etc.

by Nancy Killia

(Private email between the authors. Reprinted by permission.)

(Editor's note: The issues discussed here are in response to an email from John Compton. See also the email from Vincent deGuy.)

Hi Martin!

Great to hear from you again! My, you must be busy lately -- I haven't heard from you or Mike in ages. What have you two been up to recently (besides IBT)? Thanks for forwarding the Compton email for comment. Been mulling it over a bit before responding.

As always, it's hard to comment on an "abstract" instead of a full journal article. There's a lot of bald claims without the evidence, arguments, interpretations and details needed to make an informed critique. You know how hard it is to reconstruct the distant past with any certainty and keep your own projections out of the way, especially in archeocomputing. Nonetheless, many of his claims are intriguing to consider.

Trigram Data Disks

Let me pull up the relevant quotes about the data disks:

I note from para. 3 of your "Introduction to the Q-Ching", that primative computing devices were found in the Oracular Temple.

Do you have any personal knowledge of these artefacts. If so, can you please advise me if these consist of circular trigram arrangements or any 8 x 8 square matrix boards. (Photographic copies would be appreciated).

I Ching forms part of an ancient computer system. It uses a combinatory series of "trigram" cyclic discs for data storage i.e., information is stored in a symbolic manner similar to that of the floppy disc where information is stored magnetically.

To date, there is sufficient archaeological evidence to suggest that over forty thousand combinatory trigram cyclic discs exist.

My research conclusively proves the existance of a computer program which manipulates data to recreate a series of unique hexagrams. i.e, a repeatable oracle program.

Now, I'm not an expert on the digs at the Oracular Temple. I'm more of a theorist than a field worker anyway, but I haven't heard of any field reports that explicitly mention devices like these. Of course, it's dangerous to argue anything from a lack of evidence. I'm sure there were always 8 by 8 charts of trigrams around for use by the priests, but whether they were used in the computational devices at the Temple is an entirely different matter. I don't recall mention of any data disks in any of the journals either, but I have some curious observations on them, should they turn out to exist.

Maybe John can correct me if I'm wrong, but it sounds like he's describing some kind of disk with the 8 trigrams printed or encoded somehow around the periphery. I presume that different disks would have the trigrams in different orders. From an information theory point of view, if they all contain the same 8 symbols, the only thing distinguishing one disk from another would be the order of the symbols. These sequences are simply permutations of the 8 trigram symbols. Incidentally, we may be seeing faint echos of these disks in the various mappings of trigrams onto the 8 directions in the Shuo Kua ("Discussion of the Trigrams") of the I Ching itself, or the mechanism of the Ba Gua in Feng Shui.

First of all, the claim that there's approximately 40,000 such disks. The number of permutations is simply 8 factorial:
          8 ! = 8*7*6*5*4*3*2*1 = 40320
So the number of disks is purely a matter of combinatorics. I'm not sure why he appeals to "archeological evidence" when mathematics will do. If 40,000+ disks have actually been dug up somewhere, I guess it's a testament to the thoroughness of the old sages, particularly since this is already 4 times the "10000 things" that constituted infinity for them.

As I recall, the Oracular Temple was not that big of a structure, considering how many priests it housed, and the library section was only a small part of the site. Even if these data disks were reasonably small (say, 10 cm. in diameter), storage for 40,000 of them would take up quite a lot of space. I think it's unlikely the fieldworkers would have overlooked a cache of that size. I suspect that the computational devices at the Temple probably worked on other principles.

However, trigram disks like these could easily have been used to generate sequences of hexagrams without repetition. If you choose two disks at random, let the top trigram on one disk be the lower trigram, and let the top trigram on the other disk be the upper trigram, you form a hexagram. Rotate the upper disk one position, you get the next hexagram. After 8 turns, the upper disk is in its original position, so rotate the lower disk one position and continue. I call this algorithm for rotating the disks "the odometer method", since it resembles the odometer on your dashboard. This would generate all 64 hexagrams in turn without repetition. Each pair of disks would give a distinct hexagram sequence. Seemingly impressive.

Unfortunately, this is not a very efficient way to create hexagram permutations. There are 8 factorial squared ways to pick two disks and hence the corresponding sequences, but (8!)**2 is only about 1.625e9 (a little over a billion). The total number of hexagram permutations is more like 64! = 1.268e89. Thus the use of the trigram disks with the odometer method only produces 1 in 7.8e79 of the total number of sequences, which is roughly like being able to find a single atom out of the entire universe. Even if you use more complicated schemes than the odometer method (assuming it's still deterministic), you might be able to knock off a few orders of magnitude, but it's still a pretty sparse coverage of the entire set of sequences. I doubt the old sages would have been content with such a hit-and-miss operation and surely (in my opinion, at least) would have tried something else.

Interestingly enough, the entire collection of disks would be isomorphic to the group S(8), the permutation group of 8 objects. Given that S(8) is a perfectly well behaved mathematical object, I suspect the more mystically inclined programmers would have studied this group and somehow built it into their computers. It makes more sense than maintaining a huge disk library in the back of the Temple.

One last note: using a number of symmetries within the S(8) group and the symmetries of the disks themselves, it's possible to read out at least 32 distinct permutations from a single disk. This reduces the disk library down to 1260 separate disks, a much more doable number. However, you'd probably want to maintain a duplicate set of disks, so that you don't lose any possible hexagram sequences.

Hexagrams as Pixels in a Picture

This was one of his more delightful suggestions:

An ancient CPU manipulates this data to create a series of hexagrams to form a pictographic image.

I have also discovered, that each hexagram actually represents an individual computer "pixel", and that a series of such "pixels" forms a pictographic image which can be displayed on a VDU screen (board).

To date many interesting images have been recreated from the symbolic data incorporated on a number of trigram discs.

I conclude, from the results of my research, that the data extracted suggests that the pictographic images contain advanced geometrical and scientific information known some 3000 to 4000 years ago.

From my own research criteria, I have realized that it is extremely important to understand the actual mathematical methodology and programming techniques used, in order to achieve a meaningful interpretation of each individual image.

Such interpretation may be almost impossible in some cases, as in many instances the image obtained appears to form a unique digital language - thus I conclude from my research that The I Ching was used by the ancient Chinese as a means of communication in a digital format.

Yes, I suppose it's extremely easy to have a hexagram represent a pixel. For instance, each digram in a hexagram could be a number from 0 to 3 (or 6 to 9 in the traditional numbering), with the lower digram representing the red channel, the middle is green, the upper blue. (What? No alpha channel?) This gives a crude but useful 64 valued RGB pallette. Further, the moving lines allow a pixel to change colors, providing a simple animated GIF format. (You would need to use some of McFnordland's hyperlines to get more complicated animations.) It might be fun to whip up a program and experiment with this concept. I have a few reservations, however.

First is the sheer size of these picture files. It's said that a picture is worth a thousand words, but what "they" didn't tell you is that the picture probably takes up more bytes than the text does. A small 64 by 64 pixel picture (about the size of a postage stamp on a 72 dpi video display) requires 4096 hexagrams or about 6144 bytes (possibly less with appropriate data compression), a sizeable text file. Obviously no one person is going to have the patience to throw that many yarrow sticks. Even with a large group of people tossing sticks all day, it might take days to create a "picture" like this. It's reasonable that such an undertaking could only be done with a computer, not manually. Of course, the pictures you get then depend on the program you use, which leads to other questions.

Clearly, the program is not simply random or a simulation of the yarrow stick algorithm. This reminds me of a high-tech version of the "100 typing apes" scenario with a vengence. A stream of random hexagrams viewed as pixels is overwhelmingly likely to produce static, akin to watching the "snow" on your television after the TV station has gone off the air. Maybe once in a lifetime, you might see a grainy and static-y "image" that resembles something, but I wouldn't hold my breath waiting for it. Mind you, I'm not trying to disparage the use of TV snow as a divinatory tool (I'm sure it can be used to channel something, if only a stream of hexagrams), but I don't think it's very useful. Besides, there's always the subjective issue of who decides what is a "meaningful image" or not, one of the critical issues for any oracle system. Even harder, how would you recognize a new, never before seen "meaningful image" for an idea you've never thought about before -- the psyche literally has no experiences to serve as a basis for "seeing" the meaning. For instance, to a culture that has no prior knowledge of atoms, a picture of a helium atom (whatever that means, Heisenberg and all that) would more likely be "recognized" as a mandala, not an atom.

So obviously, the program must have numerous heuristics about what a "meaningful image" looks like or what kind of content it might have before you can start producing such images in a timely fashion. At this point, you need to ask whether the intelligence you are channeling is from the cosmos or from the smarts put in the program by the programmer. If the latter, you have a serious "garbage in, garbage out" problem, as John seemed to hint at. It's unlikely such artificial intelligence could reveal the secrets of the universe, although stranger things have definitely happened.

I'd be curious to see some of these meaningful images that John claims to have uncovered, as well as the programs that produced them. Without seeing the data, it's impossible to have an opinion about these claims. As for the digital communication assertion, it's possible but I'm skeptical about it. Once more, there's not enough information in this email to have a useful opinion.

Finally, I have a "stylistic" objection to these pictures. Given the love of calligraphy in the Chinese mind, a part of me seriously doubts whether the old ones would have even thought in terms of pixels. It's more likely that they would have translated sequences of hexagrams into brush strokes instead of mechanically churning out pixels -- how boringly yang! I fail to see how static-y postage stamps could be viewed as revealing the Tao.

Miscellaneous Issues

For your information - The Golden Code program, which you refer to in your Q-Ching notes, is probably an I Ching code that was utilized to obtain all the major mathematical constants of the universe i.e., Pi, Log e, Golden Section ratio, etc.

I raised my eyebrows the most when I read this sentence. It's generally conceded among scholars studying the Q-Ching material that "Golden Code" was a spiritual ideal that the Wise Ones aspired to, an experience of the Tao that their efforts pointed to. I've never heard of anyone refering to anything called "The Golden Code program". Granted, the younger initiates undoubtedly tinkered with such programs in their spare time (or at least talked about them at the beer hall), but it would have been the height of arrogance to call such a program Golden Code. None of these young guys would have risked the old Zen two by four like that.

I can't say I've ever seen much evidence concerning computations of such mathematical constants at this early date, with the possible exception of the natural log of e :-)

The ancient scribes "programmers" understood the basic molecular structure of DNA and electron nuclear theory.

From your notes, it would appear that as the I Ching predates the Q-Ching. As such the original methodology of data manipulation to form the original "10 thousand images" was lost, no doubt, due to the many "burning of the books" that has taken place in the past 4000 thousand years.

For the record, the I Ching (as measured from the time of King Wen, c. 1150 BCE) probably predates the Q-Ching, but not by much. Compared to the intervening 3 millennia, a century or two is insignificant. Note that the I Ching itself took quite a few centuries to take its final form in the time of Confucius (551 to 479 BCE), centuries after Lao Tse Kaud was dead and gone. Undoubtedly, the various oracles influenced each other heavily back and forth.

Granted, there was a Great Burning under Ch'in Shih Huang Ti in 213 BCE and possibly others, but proof of destroyed evidence is not evidence of a forgotten Golden Age. I tend to hold forgotten Golden Age theories up to an extremely high level of proof, because it's way too easy to fill in the historical blanks in a self-serving or self-fulfilling manner without even trying. This is obviously shifting ground. Two decades ago, no scholar would have seriously predicted the high culture of the Oracular Temple, however there are currently raging arguments as to how advanced this priesthood truly was. Did they understand modern sciences like nuclear physics and biochemistry or even advanced mathematics? The jury is still out. Did they understand spiritual disciplines we can only dream of? Possibly. All we can say with certainty is that they understood the world in a way wholy different than modern people, for better or worse. Beyond that, you must tread carefully.

I find it extremely curious that most Golden Age theories tend to describe ancient cultures as being "advanced" in terms that are strictly important to moderns. Why should progress in science, mathematics, computers, medicine, government, etc. be the only yardsticks of advancement? Old cultures had their own unique areas of expertise (and I truly mean expertise) that probably don't mean squat to modern Western sensibilities. "They were advanced because they were so like us" is a red flag of projection in my book.

Also recall that King Wen and Lao Tse Kaud were 3000 years closer to their Golden Age than we are, not to mention part of the culture that produced it, so it's interesting to ask what they thought of their own cultural peak. In terms of systems of divination, the seminal figure of that previous era was the legendary Fu Hsi, the inventor of the trigrams. Yes, trigrams are important, but the I Ching and other oracles are so much more. The use of yarrow sticks and tortoise shells was codified. Wilhelm describes this era as a time of "hunting and fishing and of the invention of cooking", without a doubt an underestimate of a fine culture. But was it a time of atom smashers and computers? I think we moderns have to be extremely careful that we don't create a lost esoteric tradition out of whole cloth, especially if that tradition is in our image, not that of the culture that spawned these advances. Maybe I'm totally wrong (this would be a terribly exciting field if I was). Falsifiabililty is the mark of good science. Data trawling through old symbol systems until you find the evidence you seek (think the Bush administration and Iraq) probably isn't.

In conclusion...

I don't mean to be a wet blanket and a nay-saying nit-picker. There's part of me that hopes John is onto something important. I just want to see the beef first before I sign on. This email was fun, but show me a big fat journal article of peer-review quality and I might even be convinced. In the meantime, I'll reserve judgment.

It's hard enough to keep your feet on the ground, even harder to keep them out of the swamp.


P.S. -- Either of you know what Vinnie is up to these days??