Clarity,
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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.Talkie Toaster : OK, here's my question: Would you like some toast
Can you give us a couple of examples with hexagrams?
* I don't know what XOR is ???? (A xany organic rooster?)... 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?
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.
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?... I still have no idea what an XOR is, could you tell us, please?
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).for me, the 'steps of change' include the fan yao
What can't they do?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.
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.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?
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.is it safe to assume this has nothing to do with Shadow Hexagrams (which you mentioned in your original post, above)?
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?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.
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
can you describe this in another way without using the mathematical terminology at all?
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.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?
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.David, there's no law against taking stabs in the dark.
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.
Hi Hilary,...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
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. )it's what I would call the yang change pattern
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.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
You mention ‘change operators’ and also ‘steps of change’ which are different things, correct?what I would call the yang change pattern, and Stephen Karcher these days would call the yang change operator.
Yup - see the above link to 'hexagrams of change'.You mention ‘change operators’ and also ‘steps of change’ which are different things, correct?
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.And is it also correct that both LiSe and Hatcher also mention methods which ‘step thru’ the hexagram changes?
No.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?
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.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 bothUsing 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
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 hexagramTopher 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:
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.you can just replace any non-moving line with a broken line and any moving line with a solid line to get
Well, the fan yao is a line in a hexagram... if there are multiple moving lines, the various fan yaos are in different hexagrams...the fanyao has different hexagrams
What can't be done? (Hilary already asked this question.)I assume it cant be done it has to be the same hexagram
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 )5 + 39 describes a well
Clarity,
Office 17622,
PO Box 6945,
London.
W1A 6US
United Kingdom
Phone/ Voicemail:
+44 (0)20 3287 3053 (UK)
+1 (561) 459-4758 (US).