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can you apply OR exclusive operator on multiple changing lines from fan yao?

Topher

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like you do it to get the resulting hexagram could you possibly do it with the changing and their fan yao? just curious what it would look like (or you only could get a shadow hexagram for said line?) then it is a good advice to not act such way then?
 

Liselle

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Sorry, I don't understand this, Topher. What's an "OR exclusive operator"? How do you mean you get the resulting hexagram that way? Etc.
 

dfreed

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I’m not sure what you mean either? Are you wondering about looking at the shadow hexagram of the resultant hexagram?

Regarding the fan yao: as it’s most commonly used the resultant hexagram doesn’t have ‘changing lines’, and therefore no fan yao.

Or perhaps you mean something else?
 
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hilary

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Can you give us a couple of examples with hexagrams?
 

moss elk

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Good luck guys. :rofl:
I am delightedly remembering Talkie Toaster.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

From IMDB/Red Dwarf:

Holly : [her IQ has been increased to 12,000] Strike a light! I'm a genius again! I know everything! Metaphysics, philosophy, the purpose of being-everything! Ask me a question, any question, and I'll answer it.

Talkie Toaster : Any question?

Holly : Yes.

Talkie Toaster : How to break the speed of light? How to marry quantum mechanics and classical physics? Any question at all, truly anything and you will answer?

Holly : Yes.

Talkie Toaster : OK, here's my question: Would you like some toast?

Holly : No, thank you. Now ask me another.

Talkie Toaster : Do you know anything about the use of chaos theory in predicting weather cycles?

Holly : I know everything there is to know about chaos theory and predicting weather cycles.

Talkie Toaster : Oh, very well. Here's my second question: Would you like a crumpet?

Holly : I'm a computer with an I.Q. of 12,000. You don't seem to understand; I know the meaning of the universe.

Talkie Toaster : That's not answering my question.

Holly : [irritated] No, I would not like a crumpet! Now ask me a sensible question, preferably one that isn't bread related.

Talkie Toaster : Very well. I have a third question. A sensible question. A question that will tax your new I.Q. to its very limits and stretch the sinews of you knowledge to bursting point.

Holly : This is going to be about waffles, isn't it?

Talkie Toaster : Certainly not. And I resent the implication that I'm a one-dimensional, bread-obsessed electrical appliance.

Holly : I apologise, toaster. What's the question?

Talkie Toaster : The question is this: Given that God is infinite, and that the universe is also infinite... would you like a toasted teacake?

Holly : That's another bready question.

Talkie Toaster : It's not just bready. It's quite curranty, too.
 
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dfreed

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Talkie Toaster : OK, here's my question: Would you like some toast
The only problem here is you’re asking yes / no questions. And since we don’t yet know or understand what’s being asked - and since even asking (what some might think of as) silly questions is sometimes advised, all is right with the world.
 
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Topher

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Can you give us a couple of examples with hexagrams?

what I mean could you possible apply the resulting hexagrams for XOR ? example

63.1.2 -> 48

63.1 -> 39.1
63.2 -> 5.2

between 39.1 and 5.2 I assume they cant?

39.1 says obstruction and 5.2 waiting while nourished

obstructed waiting while nourished -> something stagnant that could nourish while you wait for it(to be fixed?).. maybe the image of the well?

in a way these have to be related to result in the same meaning at the combination of words.
 

dfreed

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... could you possible apply the resulting hexagrams for XOR .... and

63.1 -> 39.1
63.2 -> 5.2
between 39.1 and 5.2 I assume they cant?
* I don't know what XOR is ???? (A xany organic rooster?)

* And between these two lines (the fan yao for 63.1 & 63.2), they 'can't' what? - what is it they can not do?

This is still very unclear to me, and I'm getting farther away from understanding, not closer. Please advise, and please spell out XOR. And is it safe to assume this has nothing to do with Shadow Hexagrams (which you mentioned in your original post, above)?

Thanks
 
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Liselle

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Are you trying to understand how steps of change interact with the relating hexagram? Interesting question.

(What DFreed said - I still have no idea what an XOR is, could you tell us, please?)


63.1 zhi 39 - first step of change
63.2 zhi 5 - second step of change

Then how do 39 and 5 sort of "make" 48 in this reading, is that right?

-----

I have a recent reading where I wondered a similar thing (I think, if I understand you right). I'll explain it with some background, maybe it'll help.

I'd had a skeptical-eyebrow-raising exchange with a friend, in which I strongly implied she was nuts. We dropped the subject, and I have no desire to revisit it with her. Then a few days later I wanted to ask her an unrelated question, but given the still-fresh friction I thought that might be awkward. Asked Yi, "What if I phone her about 'x'?" Got 26.3.4 to 38.

(Quoting Hilary's book)
26.3 zhi 41: "A fine horse for pursuit. Constancy in hardship bears fruit. Daily training, chariot driving, protecting. Fruitful to have a direction to go."

26.4 zhi 14: "Young bull’s hornboard. From the source, good fortune."

I thought the reading overall meant don't call her, and I didn't.

38 was surely our irreconcilable difference over the original topic.

I think the moving lines might mean there's a chance she'll think about what I said to her about Original Topic, and maybe come to understand my point. (26's training and hornboard.) But calling her blithely like nothing was going on would probably - at the very least - dilute the process, and might even make her angrier. ("You fuss at me and then call me like nothing's going on??!")

Zhi gua 41 I took to mean I should decrease my involvement for a while. Zhi gua 14 - I value (or ought to value) our friendship enough to handle a spat carefully. What Hilary says in her commentary:
Also, tying on a hornboard marks the bullock out as an exceptionally fine creature, worthy to be used in offering – one to be carefully nurtured and protected. To apply restraint in this way to a young, growing thing is a sign of how much you value it.


If your question would be how or whether 41 and 14 add up to 38... um... I guess I'm not sure they directly do in this one. 38 seems more about the original tiff. A sentence about 26 to 38 might be something like, "Greatly Taming a Difference," as a frame for the reading. 41 and 14 seem more specific, to do with my question about phoning her.

I'm still not sure what you're trying to do with fan yaos, but here are my two:
41.3: 'Three people walking, Hence decreased by one person. One person walking, Hence gains a friend.'
14.4: 'It is not for you to dominate, No mistake.'

The "three people" could be (1) her, (2) me, and (3) our disagreement, I guess. If I let her and the disagreement alone with each other for a while, maybe she'll approach me when she's ready.

14.4 - I should shut the heck up, is my guess. :lol:
 

dfreed

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... I still have no idea what an XOR is, could you tell us, please?
It seems you have made a noble stab in the dark, but unless I know more of what's being asked, I can't begin to respond. I don't even know where to begin. Of note: for me, the 'steps of change' include the fan yao, but if I'm remembering correctly, they go much further in how they are used and applied. And again, is that even what's being asked about here?

Or, as the Bard once said, 'to XOR or not to XOR, that might, maybe, possibly, could be the question!'

:LOL: :LOL: :LOL: :LOL: I think in England they have a Shadow Government (or more correctly, a shadow ministry); whereas we here in the USA just have the 'deep state'. So, could XOR be a code name for a deep state operative?
 

Liselle

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for me, the 'steps of change' include the fan yao
They're related, at the very least. I usually think of steps of change being the zhi guas, and fan yaos are part of the line pathway - it's in my head that way because that's how Hilary teaches it. The steps of change Foundations course module talks about zhi guas but not fan yaos (I say without re-reading it).

But as said it's ultimately all related.

I made a stab only at the part I thought I did understand - watch me be wrong...
 

hilary

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Public service announcement: XOR is short for 'exclusive or'. An 'exclusive or' is like the 'or' in 'Would you like tea or coffee?' - only one answer can be true. (Unlike the 'or' in 'do you like classical music or jazz?' - you could reply 'both'.)

Always marry a mathematician before setting up a Yijing forum.

Unfortunately this hasn't got me any closer to understanding what Topher is getting at.

what I mean could you possible apply the resulting hexagrams for XOR ? example

63.1.2 -> 48

63.1 -> 39.1
63.2 -> 5.2

between 39.1 and 5.2 I assume they cant?
What can't they do?

I don't understand where you are thinking of applying XOR, as you have to change both lines to get to the resulting hexagram... can you describe this in another way without using the mathematical terminology at all?

39.1 says obstruction and 5.2 waiting while nourished

obstructed waiting while nourished -> something stagnant that could nourish while you wait for it(to be fixed?).. maybe the image of the well?

in a way these have to be related to result in the same meaning at the combination of words.
63.1 zhi 39 - first step of change
63.2 zhi 5 - second step of change

Then how do 39 and 5 sort of "make" 48 in this reading, is that right?
If that's what you mean, then yes, it is an interesting question, and we can safely expect all these things to be meaningfully related, because the people who put this oracle together knew what they were doing. Whether we can retrace their steps, or whether we'll be any wiser about our readings afterwards, is a whole other question, of course.

In this example, 39 and 5 are what Karcher would call 'steps of change', and he would consider them as stages, steps through the reading. I find I get on better when I think of them as part of the moving lines - 63.1 is the 39-ish-ness of 63, its difficulty and struggle; 63.2 is its 5-ish-ness, requiring confident patience. But yes, you might also add them together: 'hard work waiting' is somewhat well-like.

is it safe to assume this has nothing to do with Shadow Hexagrams (which you mentioned in your original post, above)?
Bear in mind that 'shadow hexagram' is not a copyrighted term ;) and different people can and no doubt do use it to mean completely different things. I think you can safely assume this has nothing to do with Karcher's shadow hexagrams.
 

dfreed

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XOR is short for 'exclusive or'. An 'exclusive or' ... Would you like tea or coffee?' - only one answer can be true.

Bear in mind that 'shadow hexagram' is not a copyrighted term ;) and different people can and no doubt do use it to mean completely different things.

Unfortunately this hasn't got me any closer to understanding what Topher is getting at.
Good to know what XOR is (I think?) and it helps me to understand the title of the thread a bit - but I am still confused what it all means and how it’s being applied?

And what you're saying is, there are multiple meanings for a ‘shadow hexagram’, but we don't really know which 'shadow hexagram' we're talking about, OR if we are even talking about one at all!

And it strikes me as odd that there are so many possible answers being offered here, as to what this thread might be about, OR might not be about - when people don't know what this thread is actually about.

And I'm still confused.
 
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remod

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what I mean could you possible apply the resulting hexagrams for XOR ? example

63.1.2 -> 48

63.1 -> 39.1
63.2 -> 5.2

between 39.1 and 5.2 I assume they cant?

39.1 says obstruction and 5.2 waiting while nourished

Hi Topher.
Is this something you want to do only when you have two or more changing lines?

To see if I understood your example (line 6 is the most significant digit):

63 -> 010101

39 -> 010100
5 -> 010111

their xor is 000011 -> 19 (Approach)

Is this what you meant?

If I understood correctly, with two moving lines you are xoring the primary and secondary hexagrams.
The result will be the hexagram that has yang lines for the changing lines and yin lines for the non-moving lines:
63.1.2 -> 48
010101 -> 010110

xor -> 000011 -> 19 (Approach)

One could say that you are focusing on the hexagram where moving lines are considered "yang" (dynamic, changing) and non-moving lines are considered "yin" (stable, foundational).

I never considered doing it and I don't know if there's anyone that examined the relationship between hexagrams obtained with this method and the original response. Maybe someone else can shed a light here.

If I did not understand correctly, please disregard what I said :)

Remo

PS. The text above assumes that you meant you want to consider the hexagrams as binary number and do the xor between them.
00 -> 0
01 -> 1
10 -> 1
11 -> 0
 
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Liselle

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Topher has been around in the meantime, so hopefully will come back here and clear this up since it has several of us interested in it now.

Fully in agreement with this from Hilary:
can you describe this in another way without using the mathematical terminology at all?
 

moss elk

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Ask him what motivates the question. :rofl:

Wheat or Rye?
 

dfreed

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Topher. Is this something you want to do only when you have two or more changing lines? .... if I understood your example (line 6 the most significant digit):
63 -> 010101 / 39 -> 010100 / 5 -> 010111

their xor is 000011 -> 19 (Approach) Is this what you meant?
I don't find what you've shared here to be helpful, nor understandable, and I'm not sure that it even address the question that has be asked - which remains a mystery to us, until Topher responds.
 

Liselle

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David, there's no law against taking stabs in the dark. Though I do share your wish that Topher come help us out.
 

dfreed

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David, there's no law against taking stabs in the dark.
There's no law against me pooping in my kitchen either, as long as I come back and clean it up, which is what we've been asking Topher to do; otherwise, I just don't think it's of much use to me or anyone else. And as I said, I don't know if what's being shared here is all that helpful, much of it is not understandable (as you, and I, and others have said), and I'm not sure that it even addresses the question that has been asked - which remains a mystery to us, until Topher responds.

What's happening here very much reminds me of Male Answer Syndrome Meets Giving Directions: I don't really know where you want to go, so I don't really know how to direct you there, but let me give you some directions anyway.

But if you want to stab in the dark, please do so - I have no law against it either.
 
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hilary

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Remo's provided a nice clear explanation of what XOR-ing two hexagrams actually looks like, which I - for one - appreciate. And...

If I understood correctly, with two moving lines you are xoring the primary and secondary hexagrams.
The result will be the hexagram that has yang lines for the changing lines and yin lines for the non-moving lines:
63.1.2 -> 48
010101 -> 010110

xor -> 000011 -> 19 (Approach)

One could say that you are focusing on the hexagram where moving lines are considered "yang" (dynamic, changing) and non-moving lines are considered "yin" (stable, foundational).

I never considered doing it and I don't know if there's anyone that examined the relationship between hexagrams obtained with this method and the original response. Maybe someone else can shed a light here.

...it's what I would call the yang change pattern, and Stephen Karcher these days would call the yang change operator. (He's been influenced by Andreas Schoter, who speaks fluent Boolean.) There's an introduction here -
- and a mini-course inside Change Circle, here
that talks about how they work in readings.

You can also always search these forums, or Amazon, for the work of Chris Lofting (who was 'lightofreason' here). He could XOR until the cows came home.
 

remod

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...it's what I would call the yang change pattern, and Stephen Karcher these days would call the yang change operator. (He's been influenced by Andreas Schoter, who speaks fluent Boolean.) There's an introduction here
Hi Hilary,
Yes, that exactly it! Xor-ing the two hexagrams is equivalent to the yang-change operator.
I was not aware it existed, it's good to learn new things every day :)

Thanks.

p.s. if anyone is interested, I believe I can explain what xor is better than what I did in my previous message but, please, don't shoot me if it gets too boring :)
 

Liselle

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it's what I would call the yang change pattern
Ah, thanks. You've unglazed my head, and now I can see that in Remod's post. (Hilary claims she's allergic to math, hm. :mischief: )
 

IrfanK

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p.s. if anyone is interested, I believe I can explain what xor is better than what I did in my previous message but, please, don't shoot me if it gets too boring :)
Please do! If it helps me understand Karcher's yang change operator, I'd be happy to hear it. I always understand Karcher better when someone else other than him explains what's going on.
 

dfreed

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what I would call the yang change pattern, and Stephen Karcher these days would call the yang change operator.
You mention ‘change operators’ and also ‘steps of change’ which are different things, correct?

And is it also correct that both LiSe and Hatcher also mention methods which ‘step thru’ the hexagram changes?

But I’m still not sure if either of these is what Topher’s post is about. It’s still not clear. Do you know?
 

hilary

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You mention ‘change operators’ and also ‘steps of change’ which are different things, correct?
Yup - see the above link to 'hexagrams of change'.
And is it also correct that both LiSe and Hatcher also mention methods which ‘step thru’ the hexagram changes?
Yes, but they're different. LiSe links each line in her translation to the step of change, and uses the connection in her interpretation. Bradford (and Mondo Sector) came up with an alternative approach to multiple moving lines that involves stepping through the different hexagrams formed by each line change. So for instance if you cast 1.1.2.3 to 12 you'd read not 1.1.2.3 but 1.1, 44.2 and 33.3.
But I’m still not sure if either of these is what Topher’s post is about. It’s still not clear. Do you know?
No.
 

remod

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Hi IrfanK.
Get ready, here comes the xor :)

1. Hexagrams as binary numbers
Any Hexagram can be considered as a binary number where each digit is either 0 or 1 (a representation mostly used with computers). Luckily, for our purpose, there is no need to convert numbers between their binary and decimal forms; one complication less :)

Commonly, broken lines are replaced by 0 and solid lines by 1; there is no general consensus on the order of digits but it doesn't really matter as long as the usage is consistent. I consider line 1 (the lowest in the hexagram) to be the least significant digit (i.e. the rightmost one) and line 6 to be the most significant digit (i.e. the leftmost one). With this convention, the binary form of hexagram 63 is 010101:
1620116109961.png
2. The XOR operator
To eXclusive OR (XOR) operator can be defined by saying that:
(A xor B) is true if one between A and B is true but not both
Using 1 for "true" and 0 for "false", the following table shows all the possible results:
1620117749941.png
To xor two binary numbers you simply line up the numbers and use the table above to calculate the result for each bit:
1620117996873.png
you can see that the result has 1 in the positions where the two bits are different and 0 where they are the same.

3. XOR-ing Hexagrams
Considering that XORing two binary numbers highlights the positions where the digits are different, doing so with hexagrams will indicate the lines that changed from one to the other. Here is in graphical form the example given by the OP:
1620120453486.png
where you can see the result calculated by xor-ing each line.

4. Conclusion
The example and the long description above show that there is absolutely no need to talk about XOR, you can just replace any non-moving line with a broken line and any moving line with a solid line to get the same result.
It may be marginally interesting (for math-oriented people like me) to know that the yang-change operator is equivalent to a xor but there is no practical benefit whatsoever :)
As I said I was not aware of Karcher operator but I can see his attempt is to relate the response to other hexagrams that focus on the moving (or not-moving) lines. Personally, I don't think I'll ever use this approach, but it's good to know it exists.


Hope this clarifies a bit.

Remo
 
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IrfanK

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Hi IrfanK.
Get ready, here comes the xor :)

1. Hexagrams as binary numbers
Any Hexagram can be considered as a binary number where each digit is either 0 or 1 (a representation mostly used with computers). Luckily, for our purpose, there is no need to convert numbers between their binary and decimal forms; one complication less :)

Commonly, broken lines are replaced by 0 and solid lines by 1; there is no general consensus on the order of digits but it doesn't really matter as long as the usage is consistent. I consider line 1 (the lowest in the hexagram) to be the least significant digit (i.e. the rightmost one) and line 6 to be the most significant digit (i.e. the leftmost one). With this convention, the binary form of hexagram 63 is 010101:
2. The XOR operator
To eXclusive OR (XOR) operator can be defined by saying that:
(A xor B) is true if one between A and B is true but not both
Using 1 for "true" and 0 for "false", the following table shows all the possible results:
To xor two binary numbers you simply line up the numbers and use the table above to calculate the result for each bit:
you can see that the result has 1 in the positions where the two bits are different and 0 where they are the same.

3. XOR-ing Hexagrams
Considering that XORing two binary numbers highlights the positions where the digits are different, doing so with hexagrams will indicate the lines that changed from one to the other. Here is in graphical form the example given by the OP:
where you can see the result calculated by xor-ing each line.

4. Conclusion
The example and the long description above show that there is absolutely no need to talk about XOR, you can just replace any non-moving line with a broken line and any moving line with a solid line to get the same result.
It may be marginally interesting (for math-oriented people like me) to know that the yang-change operator is equivalent to a xor but there is no practical benefit whatsoever :)
As I said I was not aware of Karcher operator but I can see his attempt is to relate the response to other hexagrams that focus on the moving (or not-moving) lines. Personally, I don't think I'll ever use this approach, but it's good to know it exists.


Hope this clarifies a bit.

Remo
Okay. I think I'm more in the poetry faction than the maths faction, but I was surprised to see I could pretty much follow.
 

Topher

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Topher has been around in the meantime, so hopefully will come back here and clear this up since it has several of us interested in it now.

Fully in agreement with this from Hilary:
I was wondering if you applied xor to the changing line hexagram you obtained something something like the related hexagram since the fanyao has different hexagrams but I assume it cant be done it has to be the same hexagram. jsut i found curious that mixing both changing hexagram lines's name ended getting the related hexagram

hex 5 39 describes a well apparently ti is just the same result of using xor on the main hex changing lines
 

dfreed

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you can just replace any non-moving line with a broken line and any moving line with a solid line to get
And you can do the ‘opposite’ too: replace any-non moving line with a solid (yang) line, and any moving lines with a broken (yin ) line.

These then are the two Change Operators you can apply to any hexagram.

Another way to see it / do it:

Start with hexagrams 1 and 2. In whatever location you have a moving line, make a change in these two hexagrams. So:

If you have 46.5.6, then you’d change the two top lines of hexagram 1 to broken lines ( giving you 34) as one change operator; and you’d change the two top lines of hexagram 2 to solid lines (giving you hexagram 20) as the other change operator.

And so 34 and 20 are the change operators of 46.5.6, AND these two are also the change operators for any hexagram with the top two lines changing: 13.5.6, 63.5.6, etc.

I have never thought of them in binary or in XOR terms however.
 
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Liselle

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the fanyao has different hexagrams
Well, the fan yao is a line in a hexagram... if there are multiple moving lines, the various fan yaos are in different hexagrams...


Are you trying to think about this?

63.1.2 to 48

63.1 to 39
63.2 to 5

48.1 to 5
48.2 to 39

You get the same two zhi guas (resulting hexagrams), 5 and 39, but in opposite order, because you're coming back the opposite way.

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

========.....=== ===
63...........48......


I assume it cant be done it has to be the same hexagram
What can't be done? (Hilary already asked this question.)


5 + 39 describes a well
Hilary seemed to agree with you, that Waiting + Difficulties could be well-like. (I can't say my imagination has caught up with her, but that's nothing new :lol: )

I suppose we'd have to keep looking at readings through that lens to see if it holds up, and I bet it would get harder to see the more resulting hexagrams you're trying to combine.

It seems similar to trying to combine the meanings of multiple moving lines. Sometimes two lines put together indeed seem to become kind of a separate idea - Hilary has an ongoing series of blog posts about this:
 
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