Tests for the non-random character of the I Ching

[wandelaar]

I like to start a new topic suggested by these posts from another topic:

 

Wandelaar:

Quote

That's an interesting question! Subjective experiences of 'uncanny relevance' don't mean much because people are notoriously bad at evaluating statistical data. I almost always find when asking what happened that they didn't properly research how improbable the results actually were. So my opinion on this is that the I Ching gives surprising results because it puts the intuition of the user at work, and the results are than considered surprising because the user generally doesn't know (or doesn't want to know) how the results could be scientifically explained. It's even possible that the I Ching works better for those users that believe the I Ching to deliver information that they don't know themselves, because those people are more motivated to use it and work with the results.

 

I tried the I Ching myself and found out that it works, but as the sceptical person I am I than looked at some other hexagrams and they also proved relevant. So I think the I Ching when used as an oracle is a tool that puts our intuition and creativity at work, without objectively delivering any relevant new information of its own. It does however contain timeless wisdom of general relevance.

 

Michael Sternbach:

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With all respect, I strongly disagree with this view. The Yijing's answers are far too specific and accurate in order to attribute them to the kind of psychological projection you are referring to. For me, anyways (I can't speak for others, though).

 

Which doesn't require that they would be repeatable in the way of a modern scientific experiment. I believe that the Yijing can indeed answer a question in more than one way, to be sure. However, I stopped "pestering" it with the same question over and over again long ago. I only did that in my very early days of Yijing divination on some occasions, and then I would get reprimanded by receiving hexagram 4 (Youthful Folly) so many times that I soon stopped trying  (just like somebody else posting in this thread has observed).

 

I have made quite similar experiences also with other oracles. E.g., when using Tarot for divination and asking essentially the same question again and again, they often start reflecting the querent's state of mind rather than the topic he or she inquires into. However, if the same basic topic is explored with more composure over a period of time and/or across various decks, typically the same cards show up again and again.

 

However, all that being said, I don't deny the inquirer's own mind playing an important role in the divinatory process, even though this goes far beyond what could be explained by your usual "inkblot psychology". At any rate, there isn't just a receiver (projecting meaning into a basically arbitrary message), but also a transmitter involved, sending the former a very specific message. This is not to say that the latter is not part of yourself too - consider how you are sending yourself a message in a dream sometimes, and more generally, when you make yourself aware of something by way of intuition.

 

Thus, intuition indeed comes into play, as well as the phenomenon known today as synchronicity. This is linked to the reality that is - to some extent - described by quantum mechanics and chaos theory, which are already speaking to there being implicit order in what, on the surface, seems arbitrary.

 

However, these are phenomena that we are just beginning to understand. The study of divinatory methods is key, starting with C.G.Jung and his quantum physical colleague Wolfgang Pauli - but by no means limited to the exploration of this topic that they undertook so many years ago.

 

Wandelaar:

Quote

@ Michael Sternbach

 

Thanks for your opinion. If as you say there are certain patterns in the way the I Ching works that go beyond the common sense explanation I gave, then it should be possible to set up experiments to show those patterns. Or do they disappear when we try to explore them?

 

Michael Sternbach:

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Sounds interesting... I'm all for it! What kind of experiments do you have in mind, though?

 

The purpose of this topic is exploring ways to test whether or not working with the I Ching shows patterns in the found hexagrams that are impossible to explain when the hexagrams that turn up are purely random. This topic is expressly not about belief or disbelief or anecdotal evidence! So please don't spam this topic to death as happened with previous topics of mine. If you are not interested in exploring systematic ways to test the I Ching than please leave us alone.

[wandelaar]

Now as regards the yarrow-stalk method there is the possibility of (consciously or unconsciously) influencing the probabilities of the lines that turn up by how you divide the heap of stalks. So perhaps for test purposes using the coin method seems to be better because of itself it is more closely random. Do you agree?

Edited June 17, 2018 by wandelaar

[Harmen]

Can you define what kind of 'patterns' you are referring to?

[OldDog]

I think there must be confusion between the mechanics of the hexagram creation and interpretation.

 

Almost by definition, the hexagrams are patterns that are limited mathematically. On the other hand the significance that one places on a particular hexagram is highly subjective ... that is, an interpretation ... and highly variable and likely non-replicable. 

 

That said, I have long believed that the I Ching is a unique structure in the mathematical sense. If one has a high degree of expertise and understanding of system dynamics in a given subject ... and if the same ones have undertanding of the mechanics of the I Ching ... then it should be possible to map the system dynamics of the subject onto the I Ching structure and thus produce a tool. Divination is one such mapping. Others might be medicine and martial arts.

 

I am curious to see how this thread evolves.

[wandelaar]

@ Harmen

 

I am looking for patterns that:

1. Can be repeatably and objectively verified.

2. Would be extremely unlikely to appear if the hexagrams found are completely random.

 

Michael Sternbach already gave the following example: "receiving hexagram 4 (Youthful Folly) so many times that I soon stopped trying".

See:

Quote

Which doesn't require that they would be repeatable in the way of a modern scientific experiment. I believe that the Yijing can indeed answer a question in more than one way, to be sure. However, I stopped "pestering" it with the same question over and over again long ago. I only did that in my very early days of Yijing divination on some occasions, and then I would get reprimanded by receiving hexagram 4 (Youthful Folly) so many times that I soon stopped trying  (just like somebody else posting in this thread has observed).

 

However he writes:

Quote

Which doesn't require that they would be repeatable in the way of a modern scientific experiment.

 

But why is that?

Edited June 17, 2018 by wandelaar

[wandelaar]

@ OldDog

 

The only thing about the I Ching I am sceptical about is the claim that the hexagrams that are found are specific to the questions or situations concerning which it is consulted in a way that goes beyond what is to be expected when the hexagrams that are found were purely random. But I am open to correction when it can be shown by way of experiment that I am wrong.

 

I am also interested in any special mathematical properties of the I Ching, but that would be another topic.

Edited June 17, 2018 by wandelaar

[Harmen]

38 minutes ago, wandelaar said:

Michael Sternbach already gave the following example: "receiving hexagram 4 (Youthful Folly) so many times that I soon stopped trying".

See:

 

However he writes:

 

But why is that?

Michael received H4 when he asked the same question several times. Is that also how you want to test for patterns? Ask the same question multiple times?

 

I think you want to see if the answers of the Yi (and their quality) can be scientifically tested, and if patterns emerge during its consultations? Patterns that can be objectively measured? I have attached a few articles by Lance Storm who conducted similar studies. I can find more if you are interested. The Yijing has been tested during several parapsychological investigations.

I_Ching_Storm_2009.pdf

I_Ching_Storm_2008.pdf

para-ac07_Storm_2003a.pdf

para-ac07_Storm_2003b.pdf

Storm_2002.pdf

Edited June 17, 2018 by Harmen

[wandelaar]

1 hour ago, Harmen said:

Michael received H4 when he asked the same question several times. Is that also how you want to test for patterns? Ask the same question multiple times?

 

Not necessarily, but it's an example of a pattern that could be objectively investigated if it indeed has a repeatable character.

 

1 hour ago, Harmen said:

I think you want to see if the answers of the Yi (and their quality) can be scientifically tested, and if patterns emerge during its consultations? Patterns that can be objectively measured? I have attached a few articles by Lance Storm who conducted similar studies. I can find more if you are interested. The Yijing has been tested during several parapsychological investigations.

I_Ching_Storm_2009.pdf

I_Ching_Storm_2008.pdf

para-ac07_Storm_2003a.pdf

para-ac07_Storm_2003b.pdf

Storm_2002.pdf

 

I must have seen those pdf's somewhere before. The results of those experiments are mixed. It appears that very little parapsychological research concerning the I Ching has been done.

[wandelaar]

Ideally the test would have to be such that anybody wishing to see for himself whether the I Ching objectively performs above chance could do it.

[Lost in Translation]

If you really want to "test" the I Ching then try the following:

 

1) Using 3 coins generate a dozen "responses'. Write down the response values but do not look them up.

2) Over the course of several days "ask" the I Ching questions. Look up the response from the next available response that you had previously generated.

3) Write down your impression of the relevancy of the response.

 

A truly prescient oracle would have no problem answering your questions before you think to ask them. A truly prescient oracle with a strong personality might see through your game and decide to chide you for your behavior.

 

I haven't done this but it would probably be an interesting experiment.

[wandelaar]

2 minutes ago, Lost in Translation said:

If you really want to "test" the I Ching then try the following:

 

1) Using 3 coins generate a dozen "responses'. Write down the response values but do not look them up.

2) Over the course of several days "ask" the I Ching questions. Look up the response from the next available response that you had previously generated.

3) Write down your impression of the relevancy of the response.

 

A truly prescient oracle would have no problem answering your questions before you think to ask them. A truly prescient oracle with a strong personality might see through your game and decide to chide you for your behavior.

 

I haven't done this but it would probably be an interesting experiment.

 

Problem with this experiment is that it doesn't prove or disprove that the results are objectively above chance. According to my current view of the I Ching almost all hexagrams can be interpreted as relevant for almost all questions or situations. See also: https://en.wikipedia.org/wiki/Barnum_effect

 

That's why subjective evaluations of the relevance of results (even by myself) don't count as objective evidence of an above-chance performance of the I Ching.

[wandelaar]

I have read about the parapsychological experiments with the I Ching done so far, and the results found are not very robust. Even if there is an objective effect that goes beyond chance, it appears to be small. Now small effects are not per definition unimportant, in modern physics small effects can even be extremely important as soon as there are reliable methods to measure them. So scientifically speaking it all depends on finding a smart experimental set up that allows the small effects to manifest themselves, and make further research possible. Lets see. With the use of modern computers it is possible to calculate with huge amounts of random numbers, and that would make even small differences in the probabilities of different hexagrams stand out in their relative frequency of appearing. In this way one could try out perhaps thousands of throws in one run to generate a picture of the relative frequencies of the different hexagrams instead of just one hexagram a time with or without moving lines by the usual methods of throwing the I Ching. By this new methods even small differences in the probabilities of the different hexagrams would show up.

[OldDog]

8 hours ago, wandelaar said:

In this way one could try out perhaps thousands of throws in one run to generate a picture of the relative frequencies of the different hexagrams instead of just one hexagram a time ...

 

Sure, you could do this but all you would be doing would be coldly (objectively?) mapping out the occurences of hexagrams that are already fully described by the mathematics of the casting method. Such an experiment would not map out any meanings of any particular hexagram. That would require context, which the experiment seeks to exclude as a variable. Indeed, the process seems to recognize that context as a variable would be so vast as to be impractical to manage. Tantamount to mapping out the possibilities of all existence. What you seem to be seeking is predictability in something that is inherently unpredictable. It is not unlike the Uncertainty Principle ... you may be able to show the probability of an occurance in a particular location but not where it is going. A totally unsatisfying situation.

[wandelaar]

@OldDog

 

Some extra explanations might be necessary.

 

One can use the proposed method of throwing the I Ching as an alternative to the coin or yarrow stalk method. If by using the I Ching concerning a real life question or situation it is more likely for specific hexagrams to turn up then others, than this should become visible in the picture of relative frequencies per run. The type of questions or situations concerning which the I Ching is consulted could be same as when using the coin of yarrow stalk method. One could use a ritual if one wanted. And also the method of interpretation need not be fundamentally different form the usual one, you just looks up the hexagram (or hexagrams) with the largest relative frequency and explores how those hexagrams relate to the question or situation. It can all be done at home, provided the computer program is developed and a true random generator is available.

The scientific aspect of this proposed experiment consists in the pictures of the relative frequencies that result as one goes about consulting the I Ching. Could such pictures of relative frequencies have resulted by pure chance? When the I Ching somehow selects relevant hexagrams, the answer is NO. A preference of the I Ching for giving specific relevant hexagrams as answers must show up in the pictures of relative frequencies. And such a deviation from chance could then be investigated. 

 

Any more questions about the set up of this experiment?

Edited June 19, 2018 by wandelaar

[wandelaar]

In the proposed experiment each throw of the I Ching would consist of many thousands of randomly generated hexagrams. Because of the large number of hexagrams generated the number of times a particular hexagram turns up will be a measure for the likelihood of that particular hexagram to turn up for the question or situation investigated in the circumstances as they were at the moment. So in stead of just one hexagram this method gives a picture of all hexagrams with their measured likelihood of appearing in case a more conventional method had been used. 

 

Now if the hexagrams turn up purely by chance than no consistent pattern will be visible in the pictures (or histograms), but if the I Ching selects particular hexagrams appropriate to the questions or situations for which it is consulted than each (or most) pictures would have to show that with each throw (consisting of many thousands of randomly generated hexagrams) some hexagrams are much more likely that others.

 

Is the general idea clear now?

 

Edited June 20, 2018 by wandelaar

[Lost in Translation]

I'm interested to see how this play out, but I suspect it will end the same as my attempt to predict lottery numbers based upon past occurrences. 

[wandelaar]

The method I propose here can be used for serious real life consultations and interpretations of the I Ching so it does not misuse the I Ching for materialistic purposes. Unless of course you ask the wrong questions. The only extra benefit of my method is that we get a picture of the relative frequencies (a histogram) of all hexagrams in stead of just one hexagram. The picture then gives us scientifically interesting information about whether there is a deviation from pure chance in the results of the I Ching. I don't know whether the proposed method of throwing the I Ching has already been described by someone else. 

Edited June 20, 2018 by wandelaar

[wandelaar]

Has anybody here seen something like the proposed method of throwing the I Ching before? It would be very strange when something like it wasn't thought of and researched before. But in that case it would be interesting to see what were the results then. 

Edited June 23, 2018 by wandelaar

[Michael Sternbach]

I haven't.

 

Your experiment sounds interesting, but you will still have to subjectively link the predominant reply to the question asked, so probably there will be no hard evidence there. At best, this may turn out to be just another method of consulting the oracle, made possible by the use of computer technology. Not sure if this would be an improvement, though.

 

True, if with each question,there was a particular hexagram showing up way beyond what is probable, that would be an indication that something remarkable is going on. But is that really how it works? What if Yijing divination, in order to create meaning, is using what we think of as "chance", rather than defying it? The "hidden order" concept of quantum mechanics comes to mind.

 

But I am just thinking aloud and do not mean to discourage you in any way. And I will continue watching this with curiosity.

[wandelaar]

@ Michael Sternbach

 

I can think of two uses of the proposed method:

 

1. An alternative method for throwing the I Ching.

2. A way to scientifically verify whether or not something special is happening with the chances of finding specific hexagrams.

 

Personally I am most interested in 2. because it would be a revolutionary scientific discovery when the chances of random experiments would behave radically different from normal in case they are used in throwing the I Ching. That would then be the long sought after repeatable experiment proving the reality of paranormal phenomena beyond doubt.

 

Sadly I am not very experienced in computer programming myself...

[Lost in Translation]

2 hours ago, wandelaar said:

Sadly I am not very experienced in computer programming myself...

 

If you are serious about testing this hypothesis I  found several projects on Github that might help you get started.

 

This project shows how to calculate a single line using the yarrow method via Javascript.

https://github.com/Brianfit/I-Ching

 

This project gives a full reading using Javascript.

https://github.com/ablwr/i-ching

 

This project also gives a full reading, but using Python.

https://github.com/roorco/CliChing

 

I tested each of these and they nominally work. At least they don't show obvious coding errors. I don't see anything that does what you are looking for explicitly but if you are comfortable modifying either Python or Javascript you can probably produce what you want.

[wandelaar]

Thank you, but I have no experience with either Javascript or Python. We could do something else though. Could you consult the I Ching about the question on how to proceed with this topic?

[Lost in Translation]

3 hours ago, wandelaar said:

Thank you, but I have no experience with either Javascript or Python. We could do something else though. Could you consult the I Ching about the question on how to proceed with this topic?

 

I wrote a program to calculate I Ching responses using the yarrow method.

 

Question: What do you (the I Ching) think about this topic of discussion?

 

Response:

 

$ gcc i-ching-blaster.c -o i-ching-blaster
$ ./i-ching-blaster 500000 | sort | uniq -c | sort -n > results.txt
$ head -5 results.txt 
   5344 111111
   6101 211111
   6123 111112
   6140 111211
   6142 121111
$ tail -5 results.txt 
   9833 221222
   9852 222122
   9880 122222
   9969 212222
  11114 222222
$ 
 

Already we can see that the results are skewed away from pure yang and towards pure yin. This might be a statistical anomaly since there is a greater likelihood of receiving yin via the yarrow. 500 thousand is a huge number of iterations. I'll reduce it to 50 thousand.

 

$ ./i-ching-blaster 50000 | sort | uniq -c | sort -n > results2.txt
$ head -5 results2.txt 
    552 111111
    587 121111
    596 111211
    604 111112
    607 211111
$ tail -5 results2.txt 
    991 222221
    994 212222
    996 221222
   1000 222212
   1137 222222
$ 
 

Again the results are skewed towards pure yin. What if I reduce the results to only five thousand?

 

$ ./i-ching-blaster 5000 | sort | uniq -c | sort -n > results3.txt
$ head -5 results3.txt 
     46 111111
     56 211211
     56 212111
     58 111112
     58 111122
$ tail -5 results3.txt 
     98 212212
     98 222212
    102 222122
    112 222221
    120 222222
$ 
 

We see the same pattern. I think this is the problem with these kinds of tests. As the sample size increases the variation in the output decreases.

 

I'll put the program code in my PPD if you want to review.

 

[wandelaar]

Thank you very much! This is getting interesting. 

 

A few questions:

 

- How are the random numbers generated: are they really random (for instance derived from noise) or pseudo random?

- Do the codes like "212212" represent the hexagrams?

- And are the numbers before the codes the number of times of the 5 most frequently found hexagrams in the current run?

 

Quote

We see the same pattern. I think this is the problem with these kinds of tests. As the sample size increases the variation in the output decreases.

 

That should be so according to the law of large numbers:  https://en.wikipedia.org/wiki/Law_of_large_numbers

 

But when using a random number generator to throw the I Ching would cause large and consistent deviations from the law of large numbers than that would prove the presence of a paranormal component in this method of throwing.

Edited June 23, 2018 by wandelaar

[Lost in Translation]

1 hour ago, Lost in Translation said:

$ gcc i-ching-blaster.c -o i-ching-blaster
$ ./i-ching-blaster 500000 | sort | uniq -c | sort -n > results.txt
$ head -5 results.txt 
   5344 111111
   6101 211111
   6123 111112
   6140 111211
   6142 121111
$ tail -5 results.txt 
   9833 221222
   9852 222122
   9880 122222
   9969 212222
  11114 222222
$ 

 

In this example the first column represents the number of occurrences for the hexagram, e.g. 5344 occurrences of hexagram 111111. The numbers 111111, 211111, 221222, etc are the actual hexagrams. 1 is a solid line. 2 is a broken line.

 

7 minutes ago, wandelaar said:

How are the random numbers generated: are they really random (for instance derived from noise) or pseudo random?

 

The numbers are pseudo random. I'm swapping out the random generator and testing now to see if the values change.