...life can be translucent

Menu

Did I discover this grouping/sequence...

getojack

visitor
Joined
Jun 13, 1971
Messages
589
Reaction score
6
...or is it a traditionally known one?
Since it would take up far too much bandwidth on this forum, I've put it on a webpage (with lots of cool graphics for those of you who don't like to read). I'd be interested in feedback from more experienced Yi Jingers than me about whether this sequence is known or not. Check it out at

http://getojack.freehostinn.com/yijingsequence.htm

Thanks everyone.
:bows:

Getojack
 

Sparhawk

One of those men your mother warned you about...
Clarity Supporter
Joined
Sep 17, 1971
Messages
5,110
Reaction score
81
Nice one, Getojack.

I like the symmetry obtained in that sequence. I'll have to study it. Perhaps, Brad can shed some light on it as far as a precedent for it.

Cheers,

L
 

bradford

Supporter
Clarity Supporter
Joined
May 30, 2006
Messages
2,626
Reaction score
265
getojack said:
...or is it a traditionally known one?
http://getojack.freehostinn.com/yijingsequence.htm
Getojack

Haven't seen that one. I do note that your yellow and blue matrix is identical
to my own Fig 30, which also charts symmetry in two or more basic Gua
dimensions (nuclear, inverse, opposite & reverse), as in A is the inverse and
also the reverse of B, etc.
Do you know Andreas Schoter's site, Yijing Algebra? He loves stuff like this.
http://www.yijing.co.uk/
 

stevev

visitor
Joined
Jun 12, 2006
Messages
216
Reaction score
1
G'day Jack

When, on your site, you say "simply read the hexagrams in the table above from left to right and top to bottom" do you mean vertically or horizontally ?

Also do you have the Wilhelm hexagram number for this sequence ?

I'll drop them into my program and take the sequence for a spin.

Regards

Steve

 

getojack

visitor
Joined
Jun 13, 1971
Messages
589
Reaction score
6
bradford said:
Haven't seen that one. I do note that your yellow and blue matrix is identical
to my own Fig 30, which also charts symmetry in two or more basic Gua
dimensions (nuclear, inverse, opposite & reverse), as in A is the inverse and
also the reverse of B, etc.
Do you know Andreas Schoter's site, Yijing Algebra? He loves stuff like this.
http://www.yijing.co.uk/

Cool. Thanks for the info. I do love symmetry in nature. (.)(.)
;)
 

getojack

visitor
Joined
Jun 13, 1971
Messages
589
Reaction score
6
stevev said:
When, on your site, you say "simply read the hexagrams in the table above from left to right and top to bottom" do you mean vertically or horizontally ?

I think the groupings should stay intact, so that if you break the sequence into eight groups, the opposite pairs (1st & 8th, 2nd & 7th, 3rd & 6th, 4th &5th) stay opposite hexagrams. So that would mean, "read the hexagrams in the table above by rows left to right and then top to bottom."

stevev said:
Also do you have the Wilhelm hexagram number for this sequence ?

Don't have it on me right now, but I can put it up on the website.

stevev said:
I'll drop them into my program and take the sequence for a spin.

It's a new sequence, so break her in easy. :)
 

getojack

visitor
Joined
Jun 13, 1971
Messages
589
Reaction score
6
Stevev, here's the one-to-one comparison of the King Wen Sequence and the Structure-Based Sequence (for lack of a better name) on my webpage.


KWS 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16
SBS 01 08 52 30 41 46 22 24 33 10 57 64 19 17 15 40

KWS 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
SBS 20 21 50 32 12 35 16 36 28 49 44 45 06 03 47 61

KWS 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
SBS 55 25 48 43 51 26 31 54 58 60 09 37 56 29 38 13

KWS 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64
SBS 27 53 04 07 23 18 11 39 05 02 14 34 42 47 59 62
 

getojack

visitor
Joined
Jun 13, 1971
Messages
589
Reaction score
6
Whoops, messed up in the transcription. Be advised that this may also be wrong. Just look on my website and do the transcription yourself if you really care about this sort of thing. I'm an artist, not a data entry person... :)

Getojack


KWS 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16
SBS 01 08 52 30 41 46 22 24 33 10 57 64 19 17 15 40

KWS 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
SBS 20 21 50 32 12 35 16 36 28 49 44 45 06 03 63 61

KWS 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
SBS 55 25 48 43 51 26 31 54 58 60 09 37 56 29 38 13

KWS 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64
SBS 27 53 04 07 23 18 11 39 05 02 14 34 42 47 59 62
 

stevev

visitor
Joined
Jun 12, 2006
Messages
216
Reaction score
1
getojack said:
<snip>
I'm an artist, not a data entry person... :)

Art is data entry, just a different kind of data.

Thanx I'll have a look, now you know why I didn't want to do it.
 
L

lightofreason

Guest
getojack said:

KWS 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16
SBS 01 08 52 30 41 46 22 24 33 10 57 64 19 17 15 40

KWS 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
SBS 20 21 50 32 12 35 16 36 28 49 44 45 06 03 63 61

KWS 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
SBS 55 25 48 43 51 26 31 54 58 60 09 37 56 29 38 13

KWS 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64
SBS 27 53 04 07 23 18 11 39 05 02 14 34 42 47 59 62

this does not seem to reflect the matrix on your site that is more:

01 58 30 51 57 29 52 02
43 10 55 21 48 59 15 23
14 54 13 17 18 07 53 08
34 38 49 25 46 04 39 20
09 60 22 24 44 47 56 16
05 61 36 27 28 06 62 35
26 19 37 03 50 40 33 45
11 41 63 42 32 64 31 12

Each colum is made up of all hexagrams with a common trigram as base and so reflect the binary ordering at the group level but within each group there are variations - the left and right columns are in proper order top down and then we shift pair elements and pairs themselves etc.
Thus the columns are ordered in TRIGRAM binary order left to right:

heaven, lake, fire, thunder, wind, water, mountain, earth
The mixing is in the rows.

Chris.
 

stevev

visitor
Joined
Jun 12, 2006
Messages
216
Reaction score
1
Thanx Chris

that's it, your a very patient chap. I'm not sure what GetoJack was doing, but it's quite a pleasing sequence when animated. I'm going to try to generate sequences mathematically shortly, after I've done the other ten things on the list and I can figure out how.
 

getojack

visitor
Joined
Jun 13, 1971
Messages
589
Reaction score
6
stevev said:
I'm not sure what GetoJack was doing, but it's quite a pleasing sequence when animated.

Hey, I'm an idea guy, not an execution guy. Thanks Chris. I owe you a beer.

Getojack
 

getojack

visitor
Joined
Jun 13, 1971
Messages
589
Reaction score
6
lightofreason said:
this does not seem to reflect the matrix on your site that is more:

01 58 30 51 57 29 52 02
43 10 55 21 48 59 15 23
14 54 13 17 18 07 53 08
34 38 49 25 46 04 39 20
09 60 22 24 44 47 56 16
05 61 36 27 28 06 62 35
26 19 37 03 50 40 33 45
11 41 63 42 32 64 31 12

BTW, it's the same sequence as I posted above. I just ordered my sequence according to the King Wen hexagrams, whereas you ordered the King Wen Sequence according to my hexagrams.
 
L

lightofreason

Guest
In comparing this presented sequence with the binary (also read left to right top left to bottom right)

presented:

01 58 30 51 57 29 52 02
43 10 55 21 48 59 15 23
14 54 13 17 18 07 53 08
34 38 49 25 46 04 39 20
09 60 22 24 44 47 56 16
05 61 36 27 28 06 62 35
26 19 37 03 50 40 33 45
11 41 63 42 32 64 31 12

binary:

01 43 14 34 09 05 26 11 - heaven
10 58 38 54 61 60 41 19 - lake
13 49 30 55 37 63 22 36 - fire
25 17 21 51 42 03 27 24 - thunder
44 28 50 32 57 48 18 46 - wind
06 47 64 40 59 29 04 07 - water
33 31 56 62 53 39 52 15 - mountain
12 45 35 16 20 08 23 02 - earth


The ROW labels in the binary map to the COLUMN labels in the presented sequence.

The order in row 1 of the presented is made up of the order of hexagrams across the diagonal of the binary, top left to bottom right (91,58,30....02) - as is the diagonal of the presented maps to column 1 of the binary.

The binary is the 'natural' sequence of hexagrams where we apply self-referencing to yin/yang and build hexagrams bottom up.

In the natural sequence, if we rotate all of the hexagrams we get the 'vertical' sequence of changing line patterns (or XORs) 'up/down' hexagrams 01/02:

01 44 13 33 10 06 25 12
09 57 37 53 61 59 42 20
14 50 30 56 38 64 21 35
26 18 22 52 41 04 27 23
43 28 49 31 58 47 17 45
05 48 63 39 60 29 03 08
34 32 55 62 54 40 51 16
11 46 36 15 19 07 24 02

- from top to bottom left to right - XOR 01 with 02, XOR 01 with 24, XOR 01 with 07, XOR 01 with 19 etc etc

Since the binary sequence maps opposites (yin/yang) so it maps the hexagram relationship of 01 to 02 and we have developed a logic of relationships:

01 is to 02 as 01 is to 02
43 is to 23 as 01 is to 02
14 is to 08 as 01 is to 02
etc etc

Given this pattern derived from 'natural' recursion of yin/yang, and given the rotation process, so for ANY hexagram we can map out its 'logic of relationships' with its opposite by:

(a) calculate the vertical matrix and then (b) rotate it to give us a matrix that reflects the 'logic or relationships' mappings.

For example, consider the pair 29/30. We have the change line, vertical, matrix of:

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

Rotate each of the hexagrams gives us:

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

THIS is a matrix of the 'logic of relationships' for 30/29 where we have:

30 is to 55 as 30 is to 29
13 is to 49 as 30 is to 29
22 is to 36 as 30 is to 29
etc etc etc

We are here dealing with qualities. Just as 01 to 43 reflected the 01 nature of 01 as compared to a more 02 nature of 43 so here we have the 30 nature of 13 to the 29 nature of 49. etc etc

Thus given a hexagram pairing we can map out through analogy their relationships using other hexagrams. And so 'what is the relationship of 30 to 29' and we have a whole set to consider "it is like 13 to 49 or 22 to 36" etc etc

Thus in the binary sequence we focus on 01 and 02 such that "01 is to 02 as 44 is to 28 or as 58 is to 57"

The IC is a language and as such represents 'all there is' and so has a lot to say! A lot of these matrices etc are to be found in:

http://members.iimetro.com.au/~lofting/myweb/pairmatrix.html and
http://members.iimetro.com.au/~lofting/myweb/icmatrix.html

... and there is still LOTS to do.

Chris.
 

getojack

visitor
Joined
Jun 13, 1971
Messages
589
Reaction score
6
Yes, but my sequence is prettier than your sequences.

GetoJack
 

stevev

visitor
Joined
Jun 12, 2006
Messages
216
Reaction score
1
getojack said:
Stevev, here's the one-to-one comparison of the King Wen Sequence and the Structure-Based Sequence (for lack of a better name) on my webpage.

I named it the GetoJack sequence, if you invented it, it's yours. If you re-discovered it and the original is lost or unrecorded, and the guy's dead anyway, who's arguing ?
 
L

lightofreason

Guest
stevev said:
I named it the GetoJack sequence, if you invented it, it's yours. If you re-discovered it and the original is lost or unrecorded, and the guy's dead anyway, who's arguing ?

;-) the goal now is to figure out what is being said.

AS the binary sequence answers "tell us about the relationship of 01 to 02" - "well its like 01 to 43 or 14 to 34 or 09 to 05 or 26 to 11 or ..... 23 to 02"

so the traditional sequence appears to answer to "tell us about the relationship of 01 to 64" - "well, its like 01 to 02, or 03 to 04, or 05 to 06, or... 61 to 62 or 63 to 64"

etc etc etc

The relationship of the presented pattern to the binary sequence indicates a specialist focus on 'something' that can elicit meaning for the presented and in so doing meaning for the overlay of all other hexagram sequences 'over' the presented template.
 

getojack

visitor
Joined
Jun 13, 1971
Messages
589
Reaction score
6
lightofreason said:
The relationship of the presented pattern to the binary sequence indicates a specialist focus on 'something' that can elicit meaning for the presented and in so doing meaning for the overlay of all other hexagram sequences 'over' the presented template.

Chris, the relationship of the newly dubbed "GetoJack Sequence" to the binary sequence is an artifact of the method used to turn my logical grouping scheme into an orderly sequence. If I had used a different matrix to "filter" the groups, I would have come up with a sequence that had no visual relationship to the binary sequence.

The "something" that you mention is, I think, pretty clearly explained on my webpage. It's the grouping of hexagrams by structure where, for example, a hexagram with heaven and lake trigrams is labelled "TC" for "top change", meaning the top line is the only line that differs between the two trigrams, and so on down through all the groups... "NC" for no change, "IC" for inner change, "OC" for outer change, etc. This results in eight groups, each containing eight hexagrams.

Getojack
 
L

lightofreason

Guest
getojack said:
Chris, the relationship of the newly dubbed "GetoJack Sequence" to the binary sequence is an artifact of the method used to turn my logical grouping scheme into an orderly sequence. If I had used a different matrix to "filter" the groups, I would have come up with a sequence that had no visual relationship to the binary sequence.
Getojack

I think you are confused re the concept of discovery vs that of invention.

E.g. "Einstein's relativity theory" is more a discovery than an invention - IOW the material existed before he did and will (does) after him. Thus the association of Einstein with relativity is in error - the speed of light, bending by gravity etc existed before him. As such relativity is relativity and Einstein is in the comments "relativity was identified by many pre 1910 but formally identified in theoretical form, and eventually validated by experiment, in the theoretical work of Albert Einstein" (and this often said without reference to his chief supporter/aider and co theoritician - his first wife)

OTOH "Getojack's Secret Salsa" is an invention, it did not exist prior to its invention.

The presented sequence of hexagrams is one of the set of all permutations of the 64 hexagrams into a 64-hexagram sequence - IOW the identified sequence is one of a finite set. The ANALYSIS of that set has brought out one of them for analysis, as we do with the binary and the traditional and all of the others covered by others and myself (e.g. all those in the IC+ matrix pages)

These sequences need numbering, not naming with someone who did research on them! - what CAN be done is the sequences listed and your material linked to or commented upon -- "this is sequence XXXX It has been well analysed by getojack circa 2007 where he/she found..." This also goes for the many sequences covered in the IC+ pages, not as "Chris Lofting' sequence XXXX" but as a number accompanied by a note covering my work on it as well as that of others. This 'marking' of some discovery with the name of the person is a trait of vain cultures; OTOH no problem with associating a name with an invention.

The natural sequence, aka binary sequence, is sequence 0001 in that all hexagrams are created in that sequence from the natural recursion of yin/yang. Thus the hexagram's position is related to its meaning - in the other patterns we move from the literal to the figurative.

The INVENTIVE part of the I Ching is in the representation, its expressions in the form of rigid/broken lines etc so we can associate that INVENTION with a name such as Fu Hsi (if I used circles or arrows etc then a different name for that - and so XX version or YY version but the qualities represented are hard coded into our species nature and so relate to being discovered by someone not invented by someone.)

Chris.
 
L

lightofreason

Guest
BTW - number of permutations of 64 symbols into all possible sequences of 64:

(64!)/(64-64)! = 1.2688693218588414e+89

(note that 0! = 1 and so we have 64! / 1 sequences)

As you can see, the IC can cover a lot. BUT since the above would include a sequence in reverse as a different sequence then if we are working off 'reflection' so we have to divide the above by 2... UNLESS we include direction as an indicator of difference whereupon we are back to the original number.
 
L

lightofreason

Guest
... and then we compress each 64 into an 8 x 8 matrix for analysis of column/row patterns.

do ya wanna go for dodecagrams? (compressed into the perception of hexagrams with changing lines) and so 4096!/1
 
Last edited:

getojack

visitor
Joined
Jun 13, 1971
Messages
589
Reaction score
6
Last word on the subject... I'm not claiming to have invented anything. Just discovered (perhaps re-discovered) a logical grouping scheme whereby each of the 64 hexagrams can be grouped into eight categories. They could also be grouped by base trigram, as you are fond of doing, or upper trigram, as in the Mawangdui sequence. This is just another method of organizing the hexagrams, one that takes into account the structural relationship between the upper and lower trigrams.
 

martin

visitor
Joined
Oct 2, 1971
Messages
2,705
Reaction score
29
Hi Jack,

Earlier I didn't find the time to look at your site but I just did, it looks beautiful!

Let's see ...

BottomTrigram[row,col] = trigram 9-col in the binary order 000, 001, 010, ..., 111

TopTrigram[row,col] = trigram row in the binary order XORed with the bottom trigram

Yes?
Well, if there is XOR in it Chris must have seen it too :), but I don't spot it in his posts at the moment. Only glanced through them though.


As to discovering and inventing, some mathematicians believe that we never invent math. All math already exists in a kind of eternal platonic realm and sooner or later we discover it perhaps.
I don't know if that is true, but I like the idea. A pity that I didn't invent it. :D
 

martin

visitor
Joined
Oct 2, 1971
Messages
2,705
Reaction score
29
:D
Funny that you post here now, Rinda. I was just thinking about your 48.2.5 in another thread.
I have an idea about it, but it's not clear yet, must be my 48.2.
I will post something there if I progress to 48.5, I hope I will. :)
 

peter

visitor
Joined
Apr 12, 1970
Messages
168
Reaction score
0
Re

Getojack,

Nothing new really. This is the way the Jing Fang 8 palaces are organized. You didn't make the next step: assigned 8 patterns to trigrams. "NC" will be Heaven trigram, "OC" - Water trigram etc., because Yang reflects stable condition and Yin - moving condition. In every palace templates go in the following order: "Heaven" - "Wind" - "Mountain" - "Earth" - "Thunder" - "Lake" - "Water" - "Fire". Yes, there are some curious connections between inverse and opposite hexagrams in 8 palaces, but nobody discovered here a key to the King Wen sequence so far.
 

getojack

visitor
Joined
Jun 13, 1971
Messages
589
Reaction score
6
peter said:
Getojack,

Nothing new really. This is the way the Jing Fang 8 palaces are organized. You didn't make the next step: assigned 8 patterns to trigrams. "NC" will be Heaven trigram, "OC" - Water trigram etc., because Yang reflects stable condition and Yin - moving condition. In every palace templates go in the following order: "Heaven" - "Wind" - "Mountain" - "Earth" - "Thunder" - "Lake" - "Water" - "Fire". Yes, there are some curious connections between inverse and opposite hexagrams in 8 palaces, but nobody discovered here a key to the King Wen sequence so far.

Awesome. I thought there must be some historical precedent because it seems so logical to define the structural relationships between the trigrams. Do you have any more info on the Jing Fang 8 palaces? I've never heard of it before. I guess I could just Google it, but if you know of some good references, I'd be happy to hear about them. Thanks.
 

Clarity,
Office 17622,
PO Box 6945,
London.
W1A 6US
United Kingdom

Phone/ Voicemail:
+44 (0)20 3287 3053 (UK)
+1 (561) 459-4758 (US).

Top