Clarity,
Office 17622,
PO Box 6945,
London.
W1A 6US
United Kingdom
Phone/ Voicemail:
+44 (0)20 3287 3053 (UK)
+1 (561) 459-4758 (US).
L
lightofreason
Guest
The I Ching is a filter through which we interpret reality by using self-referencing of a dichotomy - in this case that of yin/yang.
When focusing on the dynamics of the 'traditional' I Ching, through the IDM filter, we find the representation of meaning in the form of considering one trigram operating within, or emerging from, a context described by another trigram. The representation is as one trigram atop another.
Thus given the trigram of heaven (111) we can set it into a context represented by, for example, the trigram of water (010) to elicit some overall meaning - and so the hexagram 010-111 (010111) where we read the symbols left-to-right but representing a vertical stacking of 'yin' and 'yang' lines read bottom to top (general to particular, context to text) thus:
--- 1
--- 1
--- 1
- - 0
--- 1
- - 0
Through the use of the emotional I Ching (http://members.iimetro.com.au/~lofting/myweb/EmotionalIC.html ) we can derive representations of a context through our feelings. For example, the current issues in the Middle East repeatedly come up with a context of water (010). Through IC+ and IDM we find the associations with water cover issues of:
Rejection/Rejecting
Protection
Socialisation
"us vs them"(bounding) where the boundary acts to contain, to keep someone/something 'in' or 'out' and so the focus on protection.
We can then map out the eight hexagrams of the I Ching that cover this basic context:
07 - the army, uniforming
04 - youthful folly, masking
59 - disperse, dispelling illusions
29 - abysmal, containment/control
40 - relaxed structuring
64 - incompleteness, remain open, mis-sequence
47 - exhaustion, forced containment (willing or not)
06 - conflict, compromising (50/50 no more, no less, it is all about borders as such)
Given this map one can then figure out which one is the 'best fit' for the current situation, where it will then order the eight into a best-fit/worst-fit sequence in that they are ALL applicable to the moment but with varying intensities of expression.
If we use the same method of stacking trigrams atop each other, so we can stack hexagrams atop each other. What this does is give finer details of what is possible in some context represented by one hexagram.
Thus, given the hexagram 010010 - hexagram 29 that covers all aspects of water where in the lower position the trigram represents containment but in the upper position - it represents containment doubled and so the notion of control. Thus hex 29 'reads' from bottom to top "with/from containment comes control" and this generic meaning is reflected in all of the octet of hexagrams through the link to the bottom trigram in all of those hexagrams - water.
If we now shift gears and move to dodecagrams, 12-line representations, where we now use hexagram atop hexagram as compared to trigram atop trigram, so we extract more details where ALL of the 64 hexagrams of the IC can form dodecagram relationships with EACH hexagram. Thus we can have:
010010-010010 (29 atop 29) or 010010-111110 (43 atop 29) etc.
What do these represent? Given the general-to-particular, context-to-text forms of representation these represent the top hexagram being expressed through/in/from a context set by the bottom hexagram.
Thus the overall meaning of, for example, 43 atop 29 (010010-111110), is isomorphic to the meaning derived using XOR-ing of hexagrams where here we have the quality described by analogy to the expression of 43 THROUGH 29 - OR, in other words, the 43-ness of 29.
Since the 43-ness of a hexagram covers a generic association, so too can this be refined, exaggerated, when we consider 43 as emerging from, and so 29 changing into, a context of 43. Thus we have (a) an aspect of 29 and so a structural focus, and (b) the changing of a context from one to the other - IOW a temporal focus.
These two forms of representation are standard for the I Ching in that they are standard for our brains where the structural (space) and the temporal (time) share the same set of meanings/categories.
Elsewhere I have shown that the notion of a 'changing line' stems from taking line representations and compressing them such that we have:
00 - 0
01 - 0 changing into 1
10 - 1 changing into 0
11 - 1
As such, we can compress dodecagrams into 'hexagrams with changing lines' as we can hexagrams into 'trigrams with changing lines'. (see my wave-oriented perspectives on the IC in:
http://members.iimetro.com.au/~lofting/myweb/WaveInterpret.html
http://members.iimetro.com.au/~lofting/myweb/WaveStructure.html )
Combining the dodecagram perspective with the XOR material allows us to derive the meanings of these dodecagrams through the X-ness analogies. For example, 43 atop 29 is representing the 43-ness of 29; 43 operating in in/through a 29 context. The description of this expression is derived by analogy to:
010010 (29)
111110 (43)
------ XOR
101100 = 55
Since 55 is a hexagram and we are using it to describe a dodecagram, so the description needs to include that difference through exaggeration of the meaning of 55 to get close to what is being represented. We can see this 'issue' with, for example, the range of meanings for hexagram 23 where, in its under-exaggerated form it represents 'housekeeping' but in its exaggerated form it represents the high priest/priestess establishing the 'core' belief focus - BOTH as such represent 'pruning' but there is a difference in intensity.
We must also take into consideration the context. IOW given 43-ness of 29, the context is 'bounding' and the description sourced from 55 'fits' into that context. On the other hand, if we have the context as 43 and so the 29-ness of 43 we get the same analogy to 55 but now in a context of bonding.
If we compress the dodecagram of 29-43, 010010111110 we get:
001111 changing into 100110 and so hexagram 33 changing into 17. Given the compression so the 55 meaning still stands and so describes this 33 to 17 change; if we compress the 55 then we have the trigram of 110 changing into 010 and so a transition from bonding to bounding - interpretable in general as sharing space with another in competitive format (33) to encapsulation for protection (17).
If we order the dodecagrams in binary top hexagram sequence WITHIN the one bottom hexagram sequence so we get an ordering of, for 29 as an example,
010010-000000 = XORed = 29
..
..
010010-111111 = XORed = 30
There are TWO sequences of hexagrams that reflect this ordering from the poles of 29/30.
Since we are holding the 29 constant, and ordering the top in binary order, so the next dodecagram after '29' is:
010010-000001 = XORed = 59
At the other end we have:
010010-111110 = XORed = 55
Thus, using hexagrams as analogies, we have a sequence of 64 starting with 29,59 and ending with 55,30. This is the sequence of hexagrams representing changing lines through 29/30 but *rotated* (see the material in http://members.iimetro.com.au/~lofting/myweb/icmatrix.html covering the horizontal vs vertical sequences of hexagrams) thus the set of dodecagrams with 29 as base will give an ordering describable by analogy to hexagrams thus (this will apply to 30 as well but in reverse):
MATRIX-A
30 55 13 49 22 36 37 63
21 51 25 17 27 24 42 03
14 34 01 43 26 11 09 05
38 54 10 58 41 19 61 60
56 62 33 31 52 15 53 39
35 16 12 45 23 02 20 08
50 32 44 28 16 46 57 48
64 40 06 47 04 07 59 29
For 29-based dodecagrams, read matrix-A from bottom-right to top-left, right-to-left. Note that these are the ANALOGIES for some hexagram A atop 29 where a matrix of those A hexagrams is the binary ordering of hexagrams (below, in matrix-B, for 29, read bottom right to top left, right to left):
MATRIX-B
01 43 14 34 09 05 26 11
10 58 38 54 61 60 41 19
13 49 30 55 37 63 22 36
25 17 21 51 42 03 27 24
44 28 50 32 57 48 18 46
06 47 64 40 59 29 04 07
33 31 56 62 53 39 52 15
12 45 35 16 20 08 23 02
.. and so 02 atop 29, XOR-ed top with bottom = 29 in the same position on matrix-A, 23 atop 29 XORed = 59 in the same position on matrix-A, 08 atop 29 XORed = 07 and so on.
IOW matrix-A is the result of XOR-ing each of the hexagrams in the binary order (matrix-B) with 29. What is of note here is that matrix-A ordering is also derived from the rotation of the ordering of changing line hexagrams 'up' 29. That order is given in this matrix:
MATRIX-C
30 56 14 50 21 35 38 64
22 52 26 18 27 23 41 04
13 33 01 44 25 12 10 06
37 53 09 57 42 20 61 59
55 62 34 32 51 16 54 40
36 15 11 46 24 02 19 07
49 31 43 28 17 45 58 47
63 39 05 48 03 08 60 29
(iow no change of 29 = 29, change line 1 of 29 = 60, change line 2 = 08, change 1 & 2 = 03 and so on, changing lines in binary order to the last position where we change all lines of 29 to get 30. ROTATE the hexagrams in matrix-C and you get matrix-A)
This association of XOR-ing with rotation is not something unique to the IC, it is a property of brain function using self-referencing to derive meaning. We can replace all of the hexagrams etc with 'blending, bonding, bounding, binding' labels and the same patterns would apply.
Thus, from the I Ching perspective, we can derive generic meanings of dodecagrams, 4096 of them, from forming pair relationships of hexagrams, one atop the other. This methodology applies to ANY dichotomy-derived system of categorisation.
Chris
When focusing on the dynamics of the 'traditional' I Ching, through the IDM filter, we find the representation of meaning in the form of considering one trigram operating within, or emerging from, a context described by another trigram. The representation is as one trigram atop another.
Thus given the trigram of heaven (111) we can set it into a context represented by, for example, the trigram of water (010) to elicit some overall meaning - and so the hexagram 010-111 (010111) where we read the symbols left-to-right but representing a vertical stacking of 'yin' and 'yang' lines read bottom to top (general to particular, context to text) thus:
--- 1
--- 1
--- 1
- - 0
--- 1
- - 0
Through the use of the emotional I Ching (http://members.iimetro.com.au/~lofting/myweb/EmotionalIC.html ) we can derive representations of a context through our feelings. For example, the current issues in the Middle East repeatedly come up with a context of water (010). Through IC+ and IDM we find the associations with water cover issues of:
Rejection/Rejecting
Protection
Socialisation
"us vs them"(bounding) where the boundary acts to contain, to keep someone/something 'in' or 'out' and so the focus on protection.
We can then map out the eight hexagrams of the I Ching that cover this basic context:
07 - the army, uniforming
04 - youthful folly, masking
59 - disperse, dispelling illusions
29 - abysmal, containment/control
40 - relaxed structuring
64 - incompleteness, remain open, mis-sequence
47 - exhaustion, forced containment (willing or not)
06 - conflict, compromising (50/50 no more, no less, it is all about borders as such)
Given this map one can then figure out which one is the 'best fit' for the current situation, where it will then order the eight into a best-fit/worst-fit sequence in that they are ALL applicable to the moment but with varying intensities of expression.
If we use the same method of stacking trigrams atop each other, so we can stack hexagrams atop each other. What this does is give finer details of what is possible in some context represented by one hexagram.
Thus, given the hexagram 010010 - hexagram 29 that covers all aspects of water where in the lower position the trigram represents containment but in the upper position - it represents containment doubled and so the notion of control. Thus hex 29 'reads' from bottom to top "with/from containment comes control" and this generic meaning is reflected in all of the octet of hexagrams through the link to the bottom trigram in all of those hexagrams - water.
If we now shift gears and move to dodecagrams, 12-line representations, where we now use hexagram atop hexagram as compared to trigram atop trigram, so we extract more details where ALL of the 64 hexagrams of the IC can form dodecagram relationships with EACH hexagram. Thus we can have:
010010-010010 (29 atop 29) or 010010-111110 (43 atop 29) etc.
What do these represent? Given the general-to-particular, context-to-text forms of representation these represent the top hexagram being expressed through/in/from a context set by the bottom hexagram.
Thus the overall meaning of, for example, 43 atop 29 (010010-111110), is isomorphic to the meaning derived using XOR-ing of hexagrams where here we have the quality described by analogy to the expression of 43 THROUGH 29 - OR, in other words, the 43-ness of 29.
Since the 43-ness of a hexagram covers a generic association, so too can this be refined, exaggerated, when we consider 43 as emerging from, and so 29 changing into, a context of 43. Thus we have (a) an aspect of 29 and so a structural focus, and (b) the changing of a context from one to the other - IOW a temporal focus.
These two forms of representation are standard for the I Ching in that they are standard for our brains where the structural (space) and the temporal (time) share the same set of meanings/categories.
Elsewhere I have shown that the notion of a 'changing line' stems from taking line representations and compressing them such that we have:
00 - 0
01 - 0 changing into 1
10 - 1 changing into 0
11 - 1
As such, we can compress dodecagrams into 'hexagrams with changing lines' as we can hexagrams into 'trigrams with changing lines'. (see my wave-oriented perspectives on the IC in:
http://members.iimetro.com.au/~lofting/myweb/WaveInterpret.html
http://members.iimetro.com.au/~lofting/myweb/WaveStructure.html )
Combining the dodecagram perspective with the XOR material allows us to derive the meanings of these dodecagrams through the X-ness analogies. For example, 43 atop 29 is representing the 43-ness of 29; 43 operating in in/through a 29 context. The description of this expression is derived by analogy to:
010010 (29)
111110 (43)
------ XOR
101100 = 55
Since 55 is a hexagram and we are using it to describe a dodecagram, so the description needs to include that difference through exaggeration of the meaning of 55 to get close to what is being represented. We can see this 'issue' with, for example, the range of meanings for hexagram 23 where, in its under-exaggerated form it represents 'housekeeping' but in its exaggerated form it represents the high priest/priestess establishing the 'core' belief focus - BOTH as such represent 'pruning' but there is a difference in intensity.
We must also take into consideration the context. IOW given 43-ness of 29, the context is 'bounding' and the description sourced from 55 'fits' into that context. On the other hand, if we have the context as 43 and so the 29-ness of 43 we get the same analogy to 55 but now in a context of bonding.
If we compress the dodecagram of 29-43, 010010111110 we get:
001111 changing into 100110 and so hexagram 33 changing into 17. Given the compression so the 55 meaning still stands and so describes this 33 to 17 change; if we compress the 55 then we have the trigram of 110 changing into 010 and so a transition from bonding to bounding - interpretable in general as sharing space with another in competitive format (33) to encapsulation for protection (17).
If we order the dodecagrams in binary top hexagram sequence WITHIN the one bottom hexagram sequence so we get an ordering of, for 29 as an example,
010010-000000 = XORed = 29
..
..
010010-111111 = XORed = 30
There are TWO sequences of hexagrams that reflect this ordering from the poles of 29/30.
Since we are holding the 29 constant, and ordering the top in binary order, so the next dodecagram after '29' is:
010010-000001 = XORed = 59
At the other end we have:
010010-111110 = XORed = 55
Thus, using hexagrams as analogies, we have a sequence of 64 starting with 29,59 and ending with 55,30. This is the sequence of hexagrams representing changing lines through 29/30 but *rotated* (see the material in http://members.iimetro.com.au/~lofting/myweb/icmatrix.html covering the horizontal vs vertical sequences of hexagrams) thus the set of dodecagrams with 29 as base will give an ordering describable by analogy to hexagrams thus (this will apply to 30 as well but in reverse):
MATRIX-A
30 55 13 49 22 36 37 63
21 51 25 17 27 24 42 03
14 34 01 43 26 11 09 05
38 54 10 58 41 19 61 60
56 62 33 31 52 15 53 39
35 16 12 45 23 02 20 08
50 32 44 28 16 46 57 48
64 40 06 47 04 07 59 29
For 29-based dodecagrams, read matrix-A from bottom-right to top-left, right-to-left. Note that these are the ANALOGIES for some hexagram A atop 29 where a matrix of those A hexagrams is the binary ordering of hexagrams (below, in matrix-B, for 29, read bottom right to top left, right to left):
MATRIX-B
01 43 14 34 09 05 26 11
10 58 38 54 61 60 41 19
13 49 30 55 37 63 22 36
25 17 21 51 42 03 27 24
44 28 50 32 57 48 18 46
06 47 64 40 59 29 04 07
33 31 56 62 53 39 52 15
12 45 35 16 20 08 23 02
.. and so 02 atop 29, XOR-ed top with bottom = 29 in the same position on matrix-A, 23 atop 29 XORed = 59 in the same position on matrix-A, 08 atop 29 XORed = 07 and so on.
IOW matrix-A is the result of XOR-ing each of the hexagrams in the binary order (matrix-B) with 29. What is of note here is that matrix-A ordering is also derived from the rotation of the ordering of changing line hexagrams 'up' 29. That order is given in this matrix:
MATRIX-C
30 56 14 50 21 35 38 64
22 52 26 18 27 23 41 04
13 33 01 44 25 12 10 06
37 53 09 57 42 20 61 59
55 62 34 32 51 16 54 40
36 15 11 46 24 02 19 07
49 31 43 28 17 45 58 47
63 39 05 48 03 08 60 29
(iow no change of 29 = 29, change line 1 of 29 = 60, change line 2 = 08, change 1 & 2 = 03 and so on, changing lines in binary order to the last position where we change all lines of 29 to get 30. ROTATE the hexagrams in matrix-C and you get matrix-A)
This association of XOR-ing with rotation is not something unique to the IC, it is a property of brain function using self-referencing to derive meaning. We can replace all of the hexagrams etc with 'blending, bonding, bounding, binding' labels and the same patterns would apply.
Thus, from the I Ching perspective, we can derive generic meanings of dodecagrams, 4096 of them, from forming pair relationships of hexagrams, one atop the other. This methodology applies to ANY dichotomy-derived system of categorisation.
Chris