Question: How do the online yijing readings actually work?

[breakmov]

Just to highlight a detail... talking about probabilities implies talking in the context of large numbers... just look at the calculation of the error associated with a given probability, dependent on the average of the errors divided by the number of times the experiment was repeated.



... The larger the value of N, the smaller the value of the associated error calculation.



breakmov

 

[surnevs]

First, as I became aware that the thread here is specific about online readings in this forum I may have raised my quisten the wrong place.
Very briefly: Reality doesn't obey or follow statistical analysis or probability calculations - for the most part. A long way down the line they may show up though surprisingly accurate.
For my part, I will stay away from using such even if they showed up accurately 99 of 100 times. Reality is the factor from which statistics have been learned and probability formulas have been discovered.
But the reality is the reality.

 

[surnevs]

I'm not clear what you mean. The probability of not getting any 1 in six throws is 33.49% (which is a little bit higher than 1/3).
For an event to have probability 1/6 doesn't mean that if you repeat the experiment 6 times you will get that even at least once.

Probably I missed your point.

Sorry, yes you are right. I should at least have picked up one of the books about and written by Blaise Pascal I still have kept from back when I was puzzling with his probability theory in the nineteen-seventies to make sure I was remembering right.

 

[surnevs]

I wish you all good with your work concerning this algorithm and - I could remember wrong - your work with AI concerning the approach to attain deeper insight in fields of divination in this relation, which I'm not in touch with.
To conclude: I have been down that road, but it doesn't mean that in the dark end I found there, wasn't a gem open, hidden for my eyes. ( Grammarly will have me to write "hidden from my eyes" ??? Maybe I should turn back to the days when I didn't use this editing program)
Finally: 3 coins are real.

 

[remod]

Finally: 3 coins are real.

Fully agree. So are sticks, dice, marbles, cards, ...

I find it interesting that we can make all these physical objects perform the same process (casting I Ching hexagrams).
And also that we can abstract this same process to make a computer perform it.

 

[hilary]

(A computer is also a physical object.)

 

[hilary]

Sorry, I don't mean to be glib. What I'm suggesting is that if I cast with coins, marbles or sticks, I'm interacting with ordinary physical objects, and they create a hexagram that answers my question, and how they do so is a mystery to me. And if I consult with a computer... exactly the same thing is happening. It's just that the physical stuff doing the creating is smaller, and some of it is electrical currents or what-have-you.

I can't see or touch the computer casting process, so it seems very different - but in fact, whatever it is that gives rise to a hexagram that answers my question is exactly as invisible and intangible either way. So maybe these different ways of casting are not as different as they seem.

 

[remod]

I can't see or touch the computer casting process, so it seems very different - but in fact, whatever it is that gives rise to a hexagram that answers my question is exactly as invisible and intangible either way. So maybe these different ways of casting are not as different as they seem.

I understand your point, Hilary

However, for me it's different because I can see what's inside the computer, it is not invisible to me.

When I throw the coins, I can't really influence the way they will face in the end. They will rotate a bit, roll, bounce on the table etc in a way that is not governed by me,

When I do it with a computer, I know what has ben "told" him to do. It's like if I it were able to tell each coin exactly how to spin, roll and bounce. That's why the type and quality if the Random Number Generator is important: it's the only thing that will ensure that the end result is not biased towards a certain result.

That's why I keep computers in a separate category of devices,

 

[eowyndernhelme]

Never heard of a 2 coin method.

Hello, Trojina, I have to look up where I read about it. Been really sick for a while here, just starting to get back to normal.

Anyway: First throw, 2 heads = 2, any other combo = 3. Second throw, heads = 2, tails = 3. Add them up, that's your line. Repeat for all lines ordering them from bottom to top.

I'm probably not being very clear. If that's so, will try to reframe it, plus will look up where I read it. You know, thinking about it, I probably read it right here on Clarity Next, somebody's going to tell me I've been doing it wrong this whole time

 

[eowyndernhelme]

Hello, Trojina, I have to look up where I read about it. Been really sick for a while here, just starting to get back to normal.

Anyway: First throw, 2 heads = 2, any other combo = 3. Second throw, heads = 2, tails = 3. Add them up, that's your line. Repeat for all lines ordering them from bottom to top.

I'm probably not being very clear. If that's so, will try to reframe it, plus will look up where I read it. You know, thinking about it, I probably read it right here on Clarity Next, somebody's going to tell me I've been doing it wrong this whole time

Just to snip the end of this thread, here it is. Wikipedia has an entry on "I Ching divination" that includes the 2-coin method, but here it is as well:

2 coins

In addition to reproducing the yarrow probabilities, this method has all the advantages of the three coin method: practical, simple, and no special equipment required. Of course, you can still opt to light a candle or burn incense, or use special Chinese coins - whatever helps your focus on what yo

www.onlineclarity.co.uk

Not sure which place I first found it.

 

[eowyndernhelme]

I see that Hilary already provided the link earlier, I guess I should have reread things before I posted. Sorry all.

 

[Introvist]

A computer most of the times will use a PSEUDO Random Number Generator, a "formula" that produce outcomes that are not distinguishable from real random numbers but that could potentially be knonw in advance (by knowing the initial random generator state).

Does that mean that the RNG is in a certain state from the minute I turn on my computer and until I activate it the first time to get the first line of the hexagram - and that the RNG's programming determines the selection of a line based on this initial state? And then it is fixed in that new state and remains there until I press again to get the second line...etc?

If so, at least the first line is destined to be the same whatever I ask about! (or whenever I press the button). Well, the same goes for the rest of the lines, since they are destined upon the first line.

If this is so... which I don't hope...I could just as well throw a hexagram right now, so I have a hexagram readily available for future reference whenever I wish to consult the I Ching at a later time....?

 

[remod]

Does that mean that the RNG is in a certain state from the minute I turn on my computer and until I activate it the first time to get the first line of the hexagram [...]

If so, at least the first line is destined to be the same whatever I ask about! (or whenever I press the button). Well, the same goes for the rest of the lines, since they are destined upon the first line.

If this is so... which I don't hope...I could just as well throw a hexagram right now, so I have a hexagram readily available for future reference whenever I wish to consult the I Ching at a later time....?

Hi Introvist. No, that's not the case! I trust the programmers to have set up things correctly to avoid the scenarios you described in which you always get the same hexagram or get a hexagram that had been pre-determined (which are possible scenarios that must be avoided).

Let me be clear: doing "random" things on a computer is difficult but is a very well-studied topic because it's related to crucial aspects of programming (from cryptography to the fairness of dealing cards on online poker sites). Programmers (should) know how to deal with these details.

The task of initializing a PRNG (setting its initial state) is called "seeding" and is done (usually) using some form of true randomness. From that point on, the sequence of numbers is completely determined by the seed.
A very simple way of doing it (not particularly good, but adequate in some scenarios) is to use the current time (say, up to milliseconds). In the case of an online I Ching casting program, the RNG might be seeded with the difference between the time the page has been loaded and the time you click the button to get the first line. This interval will vary every time and it's entirely dependent on you (i.e. how long you wait before clicking the button to get the first line).

Consider that Pseudo-RNGs rely on chaotic functions, i.e. functions whose results vary greatly even if the function arguments vary very little; this means that waiting just one millisecond more (or less), would generate a completely different set of lines.

Another possibility, if the PRNG is managed on the server, is to seed the PRNG once when the system starts up and have all users access the same generator. This means that the line you will receive depends not only on when you click the button but, also, on when other people click the button to get their lines (which is unpredictable).

On a mobile phone, you could ask the user to shake the phone and read the phone accelerometer to seed the PRNG.

There are many, many ways to make the casting process right. Programmers will find the right balance between what is practical and what is acceptable.

You are right that, even if seeding is done properly, the entire hexagram might be determined by the first click you do, but I wouldn't be too worried about this: it's like instead of throwing 3 coins 6 times, you throw 18 coins at once and then divide them into groups of three. Clicking on the button to get the next line is like revealing the next group of coins. (Similar examples can be made for stalks and marbles ...)
I would say that this is entirely acceptable.

Our modern operating systems can generate TRUE random numbers distilling them from physical events like the pattern of network traffic, the disk access frequency, the keyboard typing, etc. However, collecting (and properly cleaning) these events is a very slow and costly process. That's why we use PRNG in our applications that are faster and computationally cheaper. Those (relatively few) true random numbers are best used for seeding PRNG than for being used directly.

For the small app I created for my site, I went for true random numbers collecting physical events (user clicks and mouse movement) to generate each line; I collect 5 random bits for each line. It's a little bit slow but the result only depends on user actions, no PRNG is involved.
I'm pretty confident that the way I collect and clean the events results in a uniformly distributed random variable but, I must confess, I did not go up to the extent of formally (mathematically) proving it.
Another reason to rely solely on user's events is that the resulting hexagram feels (to me) more related to the specific question; a sort of bigger intimacy.

That said, let me disclose that I prefer physical objects (stalks, coins, dice, cards, ...) to cast hexagrams. I surely understand the comfort of having a hexagram directly generated on the computer but I can't escape the feeling of being too detached from it if all I had to do was to click on a button. Just my preference.

Hope this clarifies things a bit, do not hesitate to ask if I've not been able to explain things clearly.

 

[eowyndernhelme]

Hello, remod! I was waiting and hoping you'd see this and answer Introvist's question.

 

[blewbubbles]

The same problem occurs in computer backgammon games where pseudo random number generators are used to produce dice rolls which make the computer seem to "cheat", by favouring itself with higher rolls and better combinations. Some backgammon programs I have played against have a function to simply switch the opponents' sides so that the human player plays the "favoured" rolls. Surprisingly, it is sometimes difficult to determine weather the computer doesn't still cheat when the sides are flipped. This is an argument which is used by inexperienced or poor players only, since the outcome of the game really depends heavily on the momentous decisions made after each roll and not only on the actual dice numbers. The computer's strength can only be adjusted to make more poor decisions during a game to give the human player an advantage, rather than making it play better. A program called BGBlitz has the choice to use true random numbers received from random.org. In my experience the game always feel more natural when random.org numbers are used in stead of the preudo random numbers, but maybe only because a sequence of number cobbinations from random.org doesn't have any predictable pattern, which is the case with pseudo random numbers.

I posted a link sometime back in another thread of a pdf called HEXAGRAM-ALLOCATED TABLE OF SHAO YONG’S 129,600-YEAR SUPREME WORLD-ORDERING PRINCIPLES.

These lists remind me very much of the printouts of pseudo random numbers used in these backgammon engines I'm on about. So, maybe, referring to what introvist says..

If this is so... which I don't hope...I could just as well throw a hexagram right now, so I have a hexagram readily available for future reference whenever I wish to consult the I Ching at a later time....?

..yes, why not? According to Shao Yong (as I understand it so far) the future is determined for several thousand years in advance. So, I think that some benifit can be drawn by predetermined hexagram patterns, simular to the predetermined "random" strings of a pseudo random generator, but I think it has to be interplayed with other readings based on a more tactile method, viz. Yarrow Stalks, coins, etc.

I'm not trying to suggest that anyone in this thread has to strart playing backgammon, which in my honest opinion is a vice. I only want to point out that the need for real random is as strongly felt by computer- or online backgammon players as it is for yijing players, if i may call myself and others so.

I wholly agree with remod, that physical objects are by far preferable over electronic simulations. My own readings are far more accurate using sticks when I consider serious matters (or so it feels to me in any case).

This is a very enjoyable thread, thanks to all.

 

[blewbubbles]

I never put together all the sources but from what I've gathered, yarrow stalks-based divination was in use for a long time before using coins, sometimes as an alternative method to confirm/enlight oracles got with scapulomancy (using tortoise shells or ox bones). The exact method used, however, has been lost to us.

Then the three-coins method became common and only much later the yarrow stalks method we know has been "reconstructed" based on previous commentaries.

So, it's true that yarrow stalks were in use before coins but it is also true that the yarrow stalks method we know is more recent than the three coins.

Sooner or later I will muster the energies and will required to diligently read and report all the sources. For now, this is what I can remember on top of my mind .

In the Po Hu T'ung (the comprehensive discussions in the white tiger hall), it says that "the King alone uses for his divination a tortoise-shell twelve inches long, a milfoil-stalk nine feet in length."

This may suggest that milfoil in ancient China may have been a different plant from the yarrow we know, or else, yarrow may actually grow to that length, which I haven't seen physically, or reported elsewhere. I have picked yarrow growing up to about four feet, but it has to be trimmed to around 18 inches to get a decent stalk. I'm wondering weather the ancient kings used yarrow raw off the fields, untrimmed, from parts where it grows very tall... or did they use a different species altogether, implying shi 蓍 ?

 

[Introvist]

You are right that, even if seeding is done properly, the entire hexagram might be determined by the first click you do, but I wouldn't be too worried about this: it's like instead of throwing 3 coins 6 times, you throw 18 coins at once and then divide them into groups of three. Clicking on the button to get the next line is like revealing the next group of coins.

I can live with that - actually I like it better that way. (I have always thought it should not be necessary to click 6 times, and that the reason the program is constructed this way simply is because it feels more similar to a manual cast). If it's only the first click that counts, I don't have to obsess about avoiding new chains of thoughts during a cast. Like: Should I go to the wedding - click, ...oh, god, I also have to buy a gift, what should I buy? - click... And then it's hard to tell afterwards what the answer really is about.
From your answer, I gather that there is a possibility of it being this way or not, but maybe your answer was regarding a not specified program. Do you know how Resonance Journal is constructed?

 

[remod]

From your answer, I gather that there is a possibility of it being this way or not, but maybe your answer was regarding a not specified program. Do you know how Resonance Journal is constructed?

Whether the "first click" determines the entire hexagram or not is entirely up to the programmer. I would say that the most common solution is that it does as it is much simpler to implement it this way.

Actually, the simplest way to cast a hexagram is to generate a single random number between 0 and 16.777.215 (2^24 - 1) and derive the lines from groups of four bits. However, I would not recommend it as it would be very sensitive to any pseudo-random number generator imbalance (for example the less significant bits being "less random" than the most significant bits).
Drawing 6 numbers, instead, would make it more robust against this issue.
This is just an example of the considerations and trade-offs between simplicity and accuracy you must make when dealing with random numbers.

As for the Resonance Journal, I understand it is a desktop application, and the source code is not available for analysis. We should ask the software developers about it.

 

[buzzurro]

Actually, the simplest way to cast a hexagram is to generate a single random number between 0 and 16.777.215 (2^24 - 1) and derive the lines from groups of four bits. However, I would not recommend it as it would be very sensitive to any pseudo-random number generator imbalance (for example the less significant bits being "less random" than the most significant bits).
Drawing 6 numbers, instead, would make it more robust against this issue.

Hi RemoD,
I've just taken a look at your JS code on GitHub, looking forward to read it thoroughly and learn how it works, but the idea is really cool!
And I want to tell you that it's a honour for me that you linked one of my scripts.

Just for the sake of curiosity, the Tumbling Coins online reading draws at least 3 numbers for each line (some numbers are discarded, so the PRNG may be called more than once to move each coin). Moreover the user can "shake" the coins at will during the cast, and each "shake" draws 3 more numbers.

 

[remod]

Hi RemoD,
I've just taken a look at your JS code on GitHub, looking forward to read it thoroughly and learn how it works, but the idea is really cool!

Thanks! Let me know if you spot something "strange". As I said, I did not prove that generating random numbers that way gives a uniform distribution. I don't see how it could not, but you know how tricky these things are.

Just for the sake of curiosity, the Tumbling Coins online reading draws at least 3 numbers for each line (some numbers are discarded, so the PRNG may be called more than once to move each coin). Moreover the user can "shake" the coins at will during the cast, and each "shake" draws 3 more numbers.

I find it to be a great way to link more directly the response to the user's questions.

I really liked reading your code.

 

[ultraviolet]

****
Title:: Math of the Lines on Hexagram Sequences
*****
Preface, 5/22/2024
****
There are some mathematical features of the I Ching, but recognizing that math by itself is not a complete answer or consensus of readers. The reader is bringing his own human intuition and his teacher's intuition to the interpretation. of the hexagram. This article proceeds from basic thoughts and analogies on Hexagrams to a more intuitive discussion. In effect, the I Ching has been a collaboration of human endeavors and human intuition for many centuries in China. In modern times, each country brings its own skills, knowledge set, and innate wisdom to the I Ching Oracle Book, everywhere the I Ching is cultivated.
***
The Hexagram Sequences
***
1. Math of the hexagram sequences: Richard S. Cook's work on Classical Chinese Combinatorics has shed light on the derivation of the King Wen Sequence KWS in the I Ching or Book of Changes. By examining the mathematical patterns and relationships within the hexagrams, researchers and readers have gained a deeper understanding of the underlying mathematical structure and symbolism of this ancient text.
****
2. Mathematical sophistication in the I Ching: The I Ching, or Book of Changes, is known for its intricate system of 64 hexagrams, each composed of six lines that can be either solid or broken. These hexagrams have been found to exhibit a high degree of mathematical sophistication, with patterns similar to Fibonacci sequences and the Golden Ratio. The findings from Dr. Cook highlight a high level of mathematical understanding found in the ancient Chinese texts and commentaries.
*****
3. Linear recurrence sequences and Golden Ratio: The study of the hexagram sequence in the I Ching has revealed connections to linear recurrence sequences, such as the famous Fibonacci sequence. The Fibonacci sequence is characterized by each number being the sum of the two preceding ones. Additionally, there are indications of division in extreme and mean ratio, also known as the Golden Ratio, a ratio found in nature and art that is considered aesthetically pleasing and harmonious. While these mathematical connections and theory may not be definitive or represent a consensus of scholars, the Cook theory certainly provides an interesting perspective on the possible relationships between the I Ching, the Fibonacci sequence, and the Golden Ratio. Note. A theory is a set of hypothetical ideas or thesis with pros and cons, which is not proven beyond all doubt. I do not have all the answers.
****
4. Combinatorics History: The Yarrow Stalk Method for generating hexagrams was first recorded during the Western Zhou Dynasty in China, which lasted from 1046 to 771 BC. At that time, mathematical developments in China included arithmetic, geometry, and the use of the counting board or counting rods, which were precursor methods to the development of the abacus. The concept of zero as a placeholder digit had not yet been introduced in Chinese mathematics during this period. In India, the Bhagavati Sutra had the first Indian mention of a combinatorics problem; the problem asked how many possible combinations of tastes were possible from selecting tastes in ones, twos, threes, etc. from a selection of six different tastes (sweet, pungent, astringent, sour, salt, and bitter). Indian physician Sushruta asserts in Sushruta Samhita that 63 combinations can be made out of 6 different tastes, thus computing all 2**6 − 1 possibilities. These Indian problems are of interest in that the Indians were working with 6 objects or 6 concepts.
****
5. The power of human intuition in interpretation: Mathematics can provide valuable insights into the patterns and sequences of the I Ching Oracle Book. Ultimately, the interpretation of a hexagram relies on the individual's own intuition and understanding. The hexagrams serve as a tool for reflection and guidance, allowing individuals to tap into their inner wisdom and navigate the complexities of life with clarity and insight.
*****
References
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Dr. Richard Sterling. Cook, Jr., ( 曲理查 博士) University of California, Berkeley. Department of Linguistics
Book: Classical Chinese Combinatorics 《周易》卦序詮解, Classical Derivation of the Book of Changes Hexagram Sequence.
(Berkeley: STEDT Monograph 5, 2006)
Note. Includes James Alan Matisoff (simplified Chinese: 马蒂索夫) writing “Introduction.”
****
*****
Book:: I Ching by Hilary Barrett, 2018
Book: I Ching: Walking your path by Hilary Barrett, 2010
****