Using a calculator to cast the hexagrams - who decides what the boundary values should be?

[Graham_Giles]

I've got a question (actually part question, part statement) about
divination methods.

I've recently been using an old electronic calculator to consult the I
Ching. It's one of the very advanced ones with a graphics display for
drawing graphs, a program function for ease of repeating sequences of
commands, and - most importantly - a random number generator which
generates numbers at random between any two limits you type in.

The way I've been using it is to think of the question I want to ask, and
then run the random number generator to generate a random decimal number
between 0 and 1; depending on what the number comes out as, I then draw a
line of the hexagram. And of course I repeat this six times, to get the
hexagram.

In my dividing out of the numbers (I'll spare you the exact figures for
now), the very smallest numbers generated by the random number generator
generate a moving yin line, then the numbers between these and 0.5
generate a stable yin line. After that the next band up of numbers (larger
than the stable yin lines but not the very biggest ones) generate a stable
yang line, and finally the very largest ones (going all the way up to 1)
generate moving yang ones.

I feel this works for me and would like to continue with it. The trouble
is, I've seen an online reference which tells me that I've in fact got it
wrong and the stable bands of generated numbers should be the other way
round. In other words, in increasing order of size the bands of numbers
should go; moving yin, stable yin, stable yang, moving yang.

How much does this really matter? Does the I Ching know in advance which
outcomes from the divination process you've assigned to which lines, or
does it not work if you don't assign the outcomes to lines in the correct
way?

Thanks in advance.

 

[Liselle]

Have you come across how the four types of lines (yin, yang, moving yin, moving yang) are represented by 6, 7, 8, 9? If I was doing this, I think I'd set it up that way and not between 0 and 1.

Here are instructions about that in the context of casting with coins. Maybe you could emulate that process with your calculator.

 

[Graham_Giles]

Hi Liselle, thanks for replying. The way I'm working with it is in line with Stephen Karcher's technique of casting the lines by selecting marbles from a bag.

He sets it up in line with the probabilities you get from casting the lines using yarrow sticks, so all of the lines have different probabilities of occurrence. That seems to me to be correct and so I'm duplicating it in the way I assign values from the random number generator on my calculator.

I don't know if I'm telling you something you already know here, but in Karcher's system there are sixteen marbles in a bag and of four different colours. One of the marbles corresponds to moving yin, three of them to moving yang, five to stable yang and seven to stable yin. Thus, you have an equal probability of getting either a yang or a yin line but the probabilities of getting a stable yin or stable yang line are not the same and nor are the probabilities of getting a moving yin and a moving yang line.

 

[Liselle]

Could you pre-assign a line type to each number between 1 and 16, and then have the calculator generate random whole numbers between 1 and 16? That way you'd emulate the marble method exactly, using exactly 16 of something (16 whole numbers).

If the calculator can't be limited to whole numbers, how about ignoring the decimal portion? E.g. 1.0003478 = 1, 5.748327 = 5, 16.948477 = 16.

For instance (you could probably mix this up however you'd want):
1 = moving yin
2, 3 ,4 = moving yang
5, 6, 7, 8, 9 = stable yang
10, 11, 12, 13, 14, 15, 16 = stable yin

 

[Graham_Giles]

Could you pre-assign a line type to each number between 1 and 16, and then have the calculator generate random whole numbers between 1 and 16? That way you'd emulate the marble method exactly, using exactly 16 of something (16 whole numbers).

If the calculator can't be limited to whole numbers, how about ignoring the decimal portion? E.g. 1.0003478 = 1, 5.748327 = 5, 16.948477 = 16.

For instance (you could probably mix this up however you'd want):
1 = moving yin
2, 3 ,4 = moving yang
5, 6, 7, 8, 9 = stable yang
10, 11, 12, 13, 14, 15, 16 = stable yin

Thanks Liselle. My understanding is that it's the probabilities that are important, not so much the means of getting them; after all, Karcher's method uses sixteen marbles but it duplicates the probabilities obtained from the yarrow stick method which uses fifty (I think it is) sticks. And my method does make the probabilities pretty much equal to the Karcher method because the random number generator on my calculator has 9 decimal places.

My question is more about how much it matters in which order the stable and moving yin, and stable and moving yang, bands are stacked on top of each other. In my method all the yin probabilities go together as do the yang probabilities, but in the method I've seen online they're divided up amongst each other (I'm not sure in what order, but I think it goes moving yin: stable yang: stable yin: moving yang).

 

[Liselle]

Sorry. I got stuck on the decimals, which seemed complicated to me.

I wonder if the probabilities aren't even that important? The two most common methods are three coins, and yarrow stalks (a.k.a. 16 marbles). Those have quite different probabilities, but people use both and get good readings.

I used marbles in a bowl for a while, a long time ago. I probably did it the way Hilary describes here, which sounds the same as Karcher's, going by what you said. But mostly I've used three-coin odds. I also tried a method for a little while that always gives you exactly one moving line. I found I didn't magically understand (or not understand) my readings any better or worse with one method than the other, or get good advice from one and lousy advice from another. Yi seems to get its message across.

But still, different methods make varying degrees of sense to me. For instance, it doesn't "make sense" (to me) to limit readings to exactly one moving line, no less and no more, but there are people who are very happy with the advice that gives them.

I have no idea about the online source that divides things up differently from Karcher. Would you want to link to it?

 

[Graham_Giles]

Thanks for replying again Liselle.

I'll see if I can find that reference. It's not so much that it divides things up differently from Karcher; it's more that because of the way it arrives at the values, the "stacking" (i.e. the order in which they appear) is important in a way it isn't for the Karcher method. The proportions are still the same; 1:3:5:7.

You're probably right that the probabilities aren't even that important, it's just that I have difficulty processing that information; how does the I Ching "know" ahead of time which probability set you're using, the 3 coins one or the yarrow sticks / marbles one? And if the probabilities don't matter, maybe the "stacking order" doesn't either and I'm making a fuss about nothing here?

 

[Graham_Giles]

I couldn;t find the original article but this one presents much the same ideas and so will do for this purpose;

Yijing Dao - Probabilities with coins and yarrow stalks

Yijing Dao - Calling Crane in the Shade: A website dedicated to reviews of books on the Yijing or I Ching, the ancient Chinese oracle known as the Book of Changes, but also containing a complete 'Introduction to Yijing' for beginners, an accurate transcription of the 1935 Harvard-Yenching...

www.biroco.com

BTW, Karcher is a very important figure for me in my own background with the I Ching. The first book I ever bought about it was his and Rudolf Ritsema's big reference book, published by Element Books in the UK (I still refer to it sometimes). I've also got his book "Total I Ching", though it's buried somewhere amongst all my other books.

 

[Hans_K]

How much does this really matter? Does the I Ching know in advance which
outcomes from the divination process you've assigned to which lines, or
does it not work if you don't assign the outcomes to lines in the correct
way?

In my opinion, it does not matter, as long as it is clear beforehand what is what.
It is the same when you use the coin method which value you give heads and tails. Some give heads the value 3 and tails 2 and vice versa.
Both are fine as long as it is clear beforehand (and perhaps you stay consistent in using the assigned value from then on).
So there is no correct way

 

[Graham_Giles]

In my opinion, it does not matter, as long as it is clear beforehand what is what.
It is the same when you use the coin method which value you give heads and tails. Some give heads the value 3 and tails 2 and vice versa.
Both are fine as long as it is clear beforehand (and perhaps you stay consistent in using the assigned value from then on).
So there is no correct way

Thanks Hans, that makes sense. So, if you are clear in your own mind which outcomes from, say, the coin method represent which lines, it should work?

 

[Hans_K]

Thanks Hans, that makes sense. So, if you are clear in your own mind which outcomes from, say, the coin method represent which lines, it should work?

Yes, if you assign head the value 3 then 3x head is a moving yang line.
What is fixed, of course, is that yang is always about the odd numbers and yin the even

 

[Graham_Giles]

Thanks again Hans. So, if the lines are obtained from the coin method the yang numbers are always odd and the even ones, yin?

 

[Hans_K]

Thanks again Hans. So, if the lines are obtained from the coin method the yang numbers are always odd and the even ones, yin?

Yes, but that does not only apply to the coin method. In general, yang is odd and yin is even.
In a hexagram, for example, positions 1, 3 and 5 are yang positions and 2, 4 and 6 are the yin positions.
Odd numbered hexagrams are the yang hexagrams and the even numbered ones are the yin hexagrams, etc.

 

[remod]

How much does this really matter? Does the I Ching know in advance which
outcomes from the divination process you've assigned to which lines, or
does it not work if you don't assign the outcomes to lines in the correct
way?

Hi @Graham_Giles , I've done quite a lot of work on I Ching probabilities. As some of the regulars here know, I can be quite boring on these topics .

I do think that probabilities matter while the method you get those probabilities does not.

If you generate a random number between 0 and 1 and you want to map it to one of the possible 4 lines with the same probabilities as the 16 marbles one, you can use this table (which I believe is what you are using now, right?):



Which says that if you get a number below 0.0625, then it's a moving Yin.
Otherwise, if it's lower than 0.5 is stable Yin. And so on.

Or you can use this table:


Where if you get less than 0.0625 it's a moving Yin, if you get less than 0.25 is a moving Yang, less than 0.6875 is a stable yin, otherwise is a stable yang.

You can build many of these tables (exactly 24 of them) and as long as you are consistent, you will get the lines with the 16-marbles probabilities.

Having to decide which table to use is similar to having to decide which face is 2 and which is 3 in the three-coins method. The probabilities are ensured by the way the table is arranged.

The only thing I want to highlight is that a calculator will not produce numbers that are really random, the are called pseudo-random (but you may know it already).
Some pseudo-random number generators are good (meaning that you can't really distinguish the sequences they produce from really random sequences) and some are not.
So, you just have to decide if the RNG used in your calculator is good enough for you.

If the calculator allows you to seed the rng (and I guess it does), just choose a really random seed and start from it. For a six number sequence I would say that would be as good as a real random number generator.

 

[Graham_Giles]

Thanks for replying remod. And you were right, this was the table I used;


I did a check on the accuracy of the RND function of my calculator where I calculated a large number of random numbers (into the thousands0 and then added them together. The total I got was close to 0.5 but not exactly so, so I might look into seeding the rng as you suggest.

 

[remod]

Thanks for replying remod. And you were right, this was the table I used;

View attachment 5673
I did a check on the accuracy of the RND function of my calculator where I calculated a large number of random numbers (into the thousands0 and then added them together. The total I got was close to 0.5 but not exactly so, so I might look into seeding the rng as you suggest.

I'm sure you noticed already but that table had the Moving/Stable Yang switch (the 7 and 9 where correct).

I corrected the one in my previous post and this is the table for Moving-Stable Yang (in that order):

Sorry for the confusion!
(p.s. just in case anyone is interested in how to build one of this table, I'll explain ...)

 

[my_key]

Why not just miss out the statistical middle man and use a bowl with the apposite number of marbles in? I have been swirling up Yi readings for years through this simple approach.

 

[remod]

Well in that case the statistical middle man would hide in the bowl among the marbles.

Any method you use to cast the lines has some statistical properties.
I belong to the faction that believes that those properties have significance and that they are part of the overall process of interacting with I Ching, but I know that others feel differently and I respect that.

Personally, in all these years, I felt a greater and greater closeness to the I Ching by using methods that I devised, possibly using objects that were dear to me. Most probably, if I still had my TI30-LCD (the first programmable calculator I ever had) I would surely try to squeeze an I Ching program into its 30 steps memory

I fully understand @Graham_Giles desire to use his old calculator.

 

[Graham_Giles]

Hi my_key (and remod, whose post I've just seen),

One reason is that I already have an advanced calculator (in fact I have *two, both with random number generators on), and so it's natural for me to think of using one in this context. If it doesn't work out for me then maybe I'll think of getting the bowl and the 16 marbles.

Also, one of the best things about the I Ching for me is that there's no one way of doing it, and for me concentrating on my question and pressing a button feels right; it has a feeling of certainly for me that I don't get in a situation where there are sixteen marbles in a bowl and I have to select one.

Different strokes for different folks :0

*In case anyone's interested; a Sharp EL-9400 and a Texas TI-85, both programmable and with graphical displays.

 

[Hans_K]

and for me concentrating on my question and pressing a button feels right;

If it feels right then it's definitely a way to do it that way, but you don't have to focus on the question. That's another one of those Western-made rules, endlessly copied in Western translations.
A question is basically already unnecessary, a few keywords will suffice and then only for the questioner.
So if focusing on the question is the only reason to use a calculator because it is easier....

 

[my_key]

Well in that case the statistical middle man would hide in the bowl among the marbles.

Any method you use to cast the lines has some statistical properties.

I belong to the faction that believes that those properties have significance and that they are part of the overall process of interacting with I Ching, but I know that others feel differently and I respect that.

I agree. Apart from the soothing swirly sound and the feeling of connection when I disturbed the marbles with my hands in the bowl, I chose the marbles because the statistical probabilities are closest to that which occur in the yarrow stalk method.

Personally, in all these years, I felt a greater and greater closeness to the I Ching by using methods that I devised, possibly using objects that were dear to me. Most probably, if I still had my TI30-LCD (the first programmable calculator I ever had) I would surely try to squeeze an I Ching program into its 30 steps memory

I fully understand @Graham_Giles desire to use his old calculator.

I do too. It is important that connection is made through methods that we each feel are the right ones for us.

I worked for many years in a role with statistical analysis as a key part of of my day: every day. So I have spent a long time bathing in probability, ANOVA, process capability, regression, t-tests, and all the rest. These days I prefer to wallow in a pool of a different hue. Although, I still recognise the invisible 'statistical middle man' that resides at the root of many, if not all, of life's wonders and mystery.

As @Graham_Giles said " Different strokes for different folks" and long may that continue.

 

[dobro p]

I've got a question (actually part question, part statement) about
divination methods...

How much does this really matter? Does the I Ching know in advance which
outcomes from the divination process you've assigned to which lines, or
does it not work if you don't assign the outcomes to lines in the correct
way?

In my opinion, it does not matter, as long as it is clear beforehand what is what.

Like Hans suggests, set your own mind first. Decide what the rules are for you, and then consult the Yi. It will adjust to your mind. It can't help it. It works with what's there.

 

[Graham_Giles]

Thanks. I've got a program set up on my calculator that not only generates the number but subtracts each of the three boundary values (between moving yin and stable yin, etc) in turn from it, so that I don't have to remember what the values are; all I have to do is count the minus signs from the results of the subtractions (no minus signs = moving Yang, three minus signs = moving Yin, one minus sign= stable Yang and two minus signs = stable Yin).