Squaring the circle with 8 and 9

[Ainsloch]

Anyone interested in I Ching will know how important the numbers 8 and 9 are. So I thought I would give this ancient Egyptian solution to the problem of "squaring" the area of a circle. Basically a square of 8x8 gives an area of 64. By enclosing the 8x8 in a larger square of dimensions 9x9, and then constructing a circle on the perimeter of the larger square, you obtain a circle with an area approximately equal to that of the square.

To calculate the area of the circle you multiply the radius squared (4.5x4.5 = 20.25) by pi (3.1415...).

Of course, because pi is an irrational number you cannot obtain a whole number figure for the area (or the circumference) of a circle, but I think this attempt by the Egyptians is a noble one, invoking the numbers that it does. :cool:

[MythMath]

Please tell us more about 8 and 9 and 72...

[Kain]

Very interesting indeed, thanks Ainsloch. Since the circle and square have often been attributed to Heaven and Earth by many cultures (or the Unmanifest and Manifest by a more general comparison), I guess in a way this approximateness could be said to denote the essential (even if slight) quality "change" for the formulation of the Unformed. An essential grossening similar to the decreasing of a digital image's resolution takes place for the materialization of the Cause, yet this is the price we pay for interracting within Manifestation, or for "squaring the circle"...an action never 100% complete (as the approximateness would denote) but still doable in a way...

Kain

[Ainsloch]

Very interesting indeed, thanks Ainsloch. Since the circle and square have often been attributed to Heaven and Earth by many cultures (or the Unmanifest and Manifest by a more general comparison), I guess in a way this approximateness could be said to denote the essential (even if slight) quality "change" for the formulation of the Unformed. An essential grossening similar to the decreasing of a digital image's resolution takes place for the materialization of the Cause, yet this is the price we pay for interracting within Manifestation, or for "squaring the circle"...an action never 100% complete (as the approximateness would denote) but still doable in a way...

Kain

You could look at it that way. The very fact that everything about a square can be calculated, yet not so with a circle because it invokes an irrational number, means that a circle is all the more mysterious, and therefore cements its association with the "divine". Pi, along with other irrational numbers like phi and certain square roots suggest a realm of knowledge which man can only approach up to a limit, because the number stretches to infinity. Therefore "absolute" knowedge in certain areas is out of man's reach, and he must settle for an approximation. Intriguingly the same situation arose in quantum physics, where at the subatomic level of matter scientists discovered they can no longer know everything about a particle, but must resort to probability to predict its behaviour.

[Ainsloch]

Please tell us more about 8 and 9 and 72...

72 is a powerful number. I am sure you have heard of the 72 names of God. It is also one fifth of 360, the degrees in the circle. A circle's ratio divides its circumference into six equal sides, producing the hexagon. Whenever you construct a circle it will of course have a given ratio. Therefore, perhaps without even knowing it, you have mysteriously invoked the number 6 in relation to the circle, just by setting a ratio (or diameter) and drawing a circle! Now if you draw a pentacle in the circle you have divided the circle with 5 lines. Thus you have merged 5 and 6, and the pentagram/pentagon and hexagon/hexagram simply by the construction of the pentagram. The triangles of the pentagram will each have a pair of base angles of 72, and since there are 5 triangles they sum to 720, or 72x10. The pentagram and hexagram are age old symbols of the microcosm and macrocosm, and united they represent the old addage "as above, so below."

It is interesting to consider that every time you see a five pointed star within a circle, the circle is actually silently invoking the hexagon/hexagram through its ratio... which is the distance to the center of the circle from its circumference. Centering oneself is the key to overcoming the limiting constraints of dualistic perception; of returning to the Source, and this is best symbolised through the triangle, which gives the third side. Thus we find in the pentagram, with its 5 triangles and the number 72, and the hexagram with its two equilateral triangles, powerful symbols of the unification of opposites. 5+6 = 11, and this is also the number of Abrahadabra, which of course is a triangle of 11 rows. Which is why Crowley related it as a symbol of the Great Work. Simple, yet effective.

[Ainsloch]

Of course, all this 5+6 stuff relates directly back to the I Ching. Long ago, Chinese sages realised that the hexagrams did not give a complete picture by themselves. Therefore they introduced the five elements to supplement the hexagrams, and give a more comprehensive picture. So the pentagram and hexagram epitomise everything the I Ching stands for, in simple yet powerful symbols. Lurking within them are the numbers 8 and 9, which when multiplied together give 72. All things are connected.

[Ainsloch]

By the way, the above can be seen as a geometrical interpretation of Liber DCCCXIII vel ARARITA. The Twelve Rays are therefore the five sides of the pentagram, the six sides of the hexagon, and the ratio of the circle... a return path through the unification of micrcosm and macrocosm to the central Source. A circle begins as a dimensionless point. It becomes a line, and then the line rotates to form a circle. The line of course is the ratio of the circle. The dimensionless point outside of space and time represents Supreme Consciousness, from which all manifestation emerges. So we have a very basic and natural geometrical process to symbolise the emergence from, and return to, a central Source. Crowley dressed it up in a lot of prose, but it is very simplistic in essence, and it is found in many other cultures in different guises... the six hexagrams of the I Ching and the five elements, the six realms of Buddhism and the five elements, and so on. We can see that these schemes are derived from, or at least can be expressed through geometry, which is the stem of physical manifestation. Mathematics is the root. Maps are one thing though... making the journey is entirely another.

The Tree of Life is another such map, also with its roots in geometry, as Frater Achad revealed long ago in the Anatomy of God. The Vesica Piscis which underlies it generates the equilateral triangle, or Tetractys, which m1thr0s had the insight to overlay the tree on, through Abrahadabra, and thus reveal its dimensions. In doing so he stripped away another layer and got closer to the essence of the diagram. One good turn deserves another, and hence I give my interpretation of some of Crowley's work above. There are greater mysteries for sure, but they are not for the uninitiated.

[MythMath]

Thanks for all that...

The timing's perfect...
____________

Any insights on the THC/9x9=81...?

[Ainsloch]

Any insights on the THC/9x9=81...?

It relates also to what I have said above through the number 9. 9 is 3x3, linking it to the triangle. 72/8 = 9. So it sits alongside the I Ching here. In fact the two go hand in hand. Also, binaries and ternaries... 2's and 3's... 2+3 = 5, and 5 was the number of marriage to the Pythagoreans, because it is the sum of the first even number and first odd number beyond 1. The pentagram has five sides. Enough said!

[Kain]

Great stuff Ainsloch...:)

You could look at it that way. The very fact that everything about a square can be calculated, yet not so with a circle because it invokes an irrational number, means that a circle is all the more mysterious, and therefore cements its association with the "divine". Pi, along with other irrational numbers like phi and certain square roots suggest a realm of knowledge which man can only approach up to a limit, because the number stretches to infinity. Therefore "absolute" knowedge in certain areas is out of man's reach, and he must settle for an approximation. Intriguingly the same situation arose in quantum physics, where at the subatomic level of matter scientists discovered they can no longer know everything about a particle, but must resort to probability to predict its behaviour.Yes, pretty much my point as well. Also, I always felt that the inherent irrationality of such numbers and shapes also hints at the fact that for realization of our full potential and nature, we should ultimately look to cultivating direct Experience (or Samadhi) rather than reasoning alone, as it seems that reasoning, however useful, cannot bridge the ultimate paradox for us...

Kain

[Ainsloch]

Great stuff Ainsloch...:)

Yes, pretty much my point as well. Also, I always felt that the inherent irrationality of such numbers and shapes also hints at the fact that for realization of our full potential and nature, we should ultimately look to cultivating direct Experience (or Samadhi) rather than reasoning alone, as it seems that reasoning, however useful, cannot bridge the ultimate paradox for us...

Kain

You are absolutely correct Kain. Reason can take us quite some distance, but not the full distance. To bridge the gap intellectual knowledge must become the knowledge of actual experience, otherwise all we have done is developed a nice philosophy, a nice construct of ideas. To be honest, you could probably pick any one of a multitude of magical systems devised by individuals over thousands of years, and if you are willing to put it into actual practice, it should lead you to your goal. The goal in them is usually the same right across the board, just tailored to suit different tastes, and expressed with different terminology. But action is the true and final key, always.

[Kain]

To be honest, you could probably pick any one of a multitude of magical systems devised by individuals over thousands of years, and if you are willing to put it into actual practice, it should lead you to your goal. The goal in them is usually the same right across the board, just tailored to suit different tastes, and expressed with different terminology. But action is the true and final key, always.You speak my mind really, Ainsloch...I agree completely with your post. Also, it is based on this viewpoint that I often say that we should not forget that what we are essentially tracking through our theories and systems is a link with *Objectivity* Itself. Our approaches leading to it will essentially be subjective and prone to our own subjective background and perception/views yet if the subjective approach is tailored in a sufficiently fitting manner for our case (while also managing to adhere to the Objective Phenomenon with equally sufficient understanding of it's properties), we will manage to convey ourselves and our points of consciousness and perception all the way to making the realizational jump and attaining our goal. So the Great Work could be also reffered to as the Quest for Objectivity, in a sense...

Kain

[Ainsloch]

You speak my mind really, Ainsloch...I agree completely with your post. Also, it is based on this viewpoint that I often say that we should not forget that what we are essentially tracking through our theories and systems is a link with *Objectivity* Itself. Our approaches leading to it will essentially be subjective and prone to our own subjective background and perception/views yet if the subjective approach is tailored in a sufficiently fitting manner for our case (while also managing to adhere to the Objective Phenomenon with equally sufficient understanding of it's properties), we will manage to convey ourselves and our points of consciousness and perception all the way to making the realizational jump and attaining our goal. So the Great Work could be also reffered to as the Quest for Objectivity, in a sense...

Kain

Indeed. You use the word Objectivity, I like to use the word Reality. As Poimandres (Thoth) addressed Hermes:

"Let the man endued with a Mind mark, consider, and learn of himself, and with the power of his Mind divide himself from his not-self and become a servant of Reality."

[Anibis]

I wouldn't use the phrase objectivity, simply because it implies that the Real is a collection of objects... But yes, the Real, or the Outside (or our perceptual systems), or the Tao... the true 'ground' of existance....A pan-consistent account of the Real.
-Anibis
Edit: I'd be inclined to link Poimandres to Parmenides, myself. At least from what I've read His 'Being' becomes the trancendental mind, nous. In the first dialogue, Hermes Trismegistus (Thoth) is a man encountering this Being... Then again its entirely possible to consider HT and Poimandres conjoined to be Thoth... Just some meanderings...
-Anibis

[Kain]

Good point Ainsloch and Anibis. I agree, I think Reality is a quite apt way to describe this principle. By the way, that quote of Poimandres is spot-on.

Kain

[m1thr0s]

I'm a little late to this one but have been following it with a certain relish...your insights are very good ones Ainsloch. It's clear to see you've been tracking this beast awhile already...

The Tree of Life is another such map, also with its roots in geometry, as Frater Achad revealed long ago in the Anatomy of God. The Vesica Piscis which underlies it generates the equilateral triangle, or Tetractys, which m1thr0s had the insight to overlay the tree on, through Abrahadabra, and thus reveal its dimensions. In doing so he stripped away another layer and got closer to the essence of the diagram. One good turn deserves another, and hence I give my interpretation of some of Crowley's work above. There are greater mysteries for sure, but they are not for the uninitiated.The Ogdoad & the Ennead...the dance goes on forever and its mysteries know no limits. I am only just now beginning to really talk a little about trigrammal field theory, in part because this whole forum format is frankly a little chaotic. Just when I think it's just not going to work out someone new comes along who understands the language. A language I sure as hell did not invent, though at times I have almost thought myself the only one in my generation who even recognized it at all...Only a few such people operating in tangent are sufficient to warrant this public discussion. The rest will eventually filter in as it begins to be more apparent that Reality is the entire basis of it all and it therefor concerns them whether they wish it to or not.

I want to share something pertaining to the number 72 that is a little complex but has got my full attention and I think you will find this compelling...

We know of course that the Qabbalistic Tetragrammaton is rooted in the 4-fold "name of god" called YHVH which extends to the Twelve Banners (http://www.mazzaroth.com/Introduction/TheNamesOfGod.htm). We also know that this word alone, placed in the form of the Tetractys adds to 72 following Y=10 + YH=15 + YHV=21 + YHVH=26. We also know that a great deal has been made of the number 72 via the system called Shemhamphorasch, though in many ways the reasoning for this is a bit obscure since it has to do with encrypted passages from selected texts that really bears very little resemblance to anything purely alchemical in nature, yet it is clear that there exists a great sense of urgency surrounding it at least. But why should this concern Hermetic Alchemy specifically? This is the same old religionist nonsense we find all over the place really. So, in many ways it really doesn't matter, but here is something that really does...

The extended Word of Perfection was initially divided into Micropropsopus (YHVH) and Macroprosopus (AHYH) each word carrying its own unique system of banners. I have shown (in other posts) that there exists one other word (and one only) that can be extrapolated from this master-word sharing the same qualities as as the other two, which I deem to be the Jen Word, corresponding to the Man Line value in the 729 Ternary Hexagrams. This word also carries 12 unique banners and stands squarely in the middle of the Above and Below words. The full numeration on the Word of Perfection (AHYHVH)=32 but if you add its 3 parts AHYH=21 + AHVH=17 + IHVH=26, the grand total is actually 64.

Interesting, but not as interesting as this...

We only actually get 12 banners per word so long as we are only counting the letters since the rule is that any duplicates get ejected so that there only can remain 12 unique spellings before we run into duplications. But this is not the case with their elemental constitutions, since in this case we always have a clear distinction between earth and water (symbolically) so that the true number of elemental banners we can derive from each division is actually 24. 24 (banners) x 3 (divisions) = 72! I have been meaning to get to this article but that is the *punchline* of it so to speak, at least insofar as establishing an unseen precedent to 72 that is in all conceivable ways exceptionally alchemical in nature...

You'll have to do the math yourselves but there is no mistake. What this means of course (among other things) is that the elemental spelling of the Word of Perfection itself extends to 72 proper banners without incurring duplications and thus completes the circle of its own accord and we need not resort to obscure and garbled texts to achieve this for us. By simply adding a Shin, uniformly, to each of the 72 banners, we get an exact 360 degree circle with a letter at each degree. Thus the formula YHShVH-YVShHH takes on a whole new alchemical significance. It also gives us a very intriguing alternative to the 72 Barbarous Names, so-called...

I hope that is at least mostly clear. A little scratchwork should tie up any loose ends, The trick is to use elemental spellings to distinguish each banner. One way to do this is to include elemental symbols as superscripts adjacent to letters so that the Heh's can always be clearly distinguished... It requires this formal spelling of letters + elements to get the true alchemical tally. I don't actually have a standard cross-browser font that can do this so this has held up the article a bit...

Addendum (for Kain in particular): It happens that this formal alchemical spelling method also resolves the proper chronological order of the Banners, since it is possible to assign numbers in place of (or else adjacent to) elements. For reasons I won't completely go into here, the best way to do this is to assign Fire=0, Water=1, Air=2, Earth=3. Thus a spelling of IHVH=0123 which we can reasonably assume to come before a spelling of IVHH=0213. To be most precise, following this method, every letter value receives a superscript elemental value which in turn receives a superscript numerical value. In this way we can clearly identify unique chronological positions within either 12 or 24 Banners per division, depending on what we want to emphasize. I mention this because it turns out that the conventional Banners are not legitimately chronological, as is so often the case with traditional Qabbalah. This historical predilection for pseudo-chronologies is just one of the reasons modern science feels confident of accusing occultism of being a pseudo-science. The good news is that this is mostly a matter of sloppy mental habits, not really anything that cannot be logically overcome. Occultism is much better by far at whole systems thinking than modern science ever was with its fetish for divisive and opportunistic essentialsm...

m1thr0s

[Kain]

...wow...that's really good m1thr0s...

OK, let's make sure I have this straight. By differentiating the letters of the 12 Banners elementally (thus distinguishing between Heh of Water and Heh of Earth) we get instead of 12 possible banners, 24 possible banners which also bear a directly visible alchemical constitution of the 4 elements. Since the expanded Word of Perfection is AHYHVH, three possible 4-letter arrangements that meet the prerequisites can be extracted from it, namely IHVH, AHVH and AHYH. Since each can support 24 banners, we thus get 72 of them...

Now, the elemental addition to each letter in turn receives a superscript of it's own, one of a numerical nature, thus allowing for a Chronological Arrangement of the Banners to successfully emerge, as that is visible through the base-4 system of counting. Correct?

This is big...hehe...

Kain

[m1thr0s]

yes, that's it...once you run a few tests we can look at a few additional factors but they aren't complicated. The main thing is identifying a workable system, which is what this is. At some point I will set up a chart to demonstrate all of this but my simple explanation seems to have sufficed for now...

sorry it has taken so long to get back to you on this Kain...at least now you have the essential nuts & bolts...

m1thr0s

[Kain]

yes, that's it...once you run a few tests we can look at a few additional factors but they aren't complicated. The main thing is identifying a workable system, which is what this is. At some point I will set up a chart to demonstrate all of this but my simple explanation seems to have sufficed for now...OK, great. So here's another question...we have Heh of Water and Heh of Earth. Does this mean that Yod stands for Fire and Vau for Air? Also, what about Aleph in such a case (as it appears in the Jen Word)? Would that stand for "Spirit"?
sorry it has taken so long to get back to you on this Kain...at least now you have the essential nuts & bolts...Much appreciated...thanks m1thr0s. It was worth the wait too...

Kain

[m1thr0s]

So here's another question...we have Heh of Water and Heh of Earth. Does this mean that Yod stands for Fire and Vau for Air? Also, what about Aleph in such a case (as it appears in the Jen Word)? Would that stand for "Spirit"?In the full word AHIHVH what we have is AIV + HHH, sometimes referred to as the three Fathers / Mothers respectively (not to be confused with the more generic "Mother Letters" in Qabbalah which is a different context). In cases like this we are looking at a situation where Tetragrammaton has been extended to incorporate the Shin (spirit) element in its tally, so we would get A=Spirit (Yang), H=Spirit (Yin), I (or Y)=Fire, H=Water, V=Air and H=Earth. But when we fall back to the 4-Fold standard we drop the Shin and view letters according to their balanced familial placement values, so we basically fall back to the standard of Bigrammaton itself with its Father-Mother-Son-Daughter structure.

So in the Heaven Line:
A=Father(Fire), H=Mother(Water), I=Son(Air), H=Daughter(Earth)

In the Man Line:
A=Father(Fire), H=Mother(Water), V=Son(Air), H=Daughter(Earth)

In the Earth Line:
I=Father(Fire), H=Mother(Water), V=Son(Air), H=Daughter(Earth)

There is a tendency to want to preserve the WoP placements and mix and match them between the lines but the truth is that it serves no useful purpose to do so. It just winds up asserting a molecular imbalance and eventually you'll get bored with the novelty and return to a more productive application of letter placement values. At least in field work this is the case...

One has to always remember that no letters in themselves are any more or less uniquely qualified to one elemental valuation than any other...things achieve a certain stature because we say they do. To the extent that we are able to believe our own assertions, these things may in fact be true and this is why we need rules and laws and principles to guide us...this is how we may know that our assertions carry a certain inherent authority at the level of principle.

But an Aleph is actually no more or less uniquely Air or Spirit than a Qoph is or a Kaph or any other letter from any other language. These are lofty (and sometimes confusing) matters since none of it has any value at all without Being itself driving the whole process. But Being must always negotiate a certain internal/external equilibrium for its assertions to carry the "ring of truth", without which all of our assertions are a complete waste of time & energy.

So these rules that I have outlined work consistently and correctly throughout all of Tetragrammaton and all of Trigrammal Field theory as well...

addendum: even the elements, in a very real sense, are matters of convention. We actually do know this since we can swap them out for Lingam, Yoni, Sun and Moon or other elements we might happen to take a fancy to, at any time we like. We could totally make shit up if we wanted to and divide the whole universe into crockodiles and zebras and snakes and lions or whatever we felt like! If we are heavy into genetics we might prefer to look at everything as combinations of Acids & Sugars! If we are more into particle physics it may all be quarks and gluons or whatever. One might think that all this subjective flexibility renders the whole thing impossibly chaotic. Beautifully chaotic I'd say...but one thing remains very strong and very stable and that is the underscoring Father-Mother-Son-Daughter relationships and this is why Bigrammaton is so vitally important for us to consciously integrate into our thinking. With the elements, we are better off to say that certain elements stand in the position of Father, Mother, Son or Daughter, which are then usually defined as Fire, Water, Air & Earth...in the context of Western Qabbalah, etc...

This way of thinking will stand you in good stead and make your assertions very strong and very balanced in all cases. This is the freedom obtained from building on the numbers in the first case...they have the widest range of natural expression of anything at our disposals. So Bigrammaton is really at the heart of it all Kain, and that's finally the point of this little diatribe (most of which you already know)...that's about the only thing we actually cannot afford to dispense with at the end of the day.

m1thr0s

[Kain]

I see...so since 24 banners are derived from each of the three short versions of the WoP, which you have connected with each of the 3 lines (Heaven, Man, Earth), does that mean that each of the Words (and thus it's related department of banners) is used in the scope of it's respective line only? Thus giving us 24 elemental mantric variations of expressing the content of each of the 3 line values?
even the elements, in a very real sense, are matters of convention. I see your point and building on the numbers is certainly one of the more powerful and certainly real approaches possible in this field. I think that there is also a factor of adhering to principles as they are directly perceived and experienced, for they are revealed instances of the fully Objective Fact. For instance, ever since the first years of my life, I used to hear very distinct sounds emanating from parts of my body that had no actual counterpart in what others around me could hear. I paid it no attention until this sense faded around my adolescent years...eventually, I found it to return in particular intensity while conducting energy work, and also while being in altered states of consciousness in general. The sounds haven't really changed through the years and it was relatively recently (compared to the years I have been perceiving them) that I realized their connection with bija-mantras. A further surprise was that the sounds were naturally correctly placed, as far as the theory of the bija-mantra system was concerned. So I accepted such placements, even though the bija-mantras are largely "dictated" in that system without a very solid logical background or explanation as to the reasoning behind their placement.

So, I think that a firm base of logical deduction is a huge factor of adhering to Truth, but direct experience is also a factor to keep in mind, a factor that usually has a contracting effect to our field of possible choices regarding accurate symbolical representations.

Kain

[m1thr0s]

I see...so since 24 banners are derived from each of the three short versions of the WoP, which you have connected with each of the 3 lines (Heaven, Man, Earth), does that mean that each of the Words (and thus it's related department of banners) is used in the scope of it's respective line only? Thus giving us 24 elemental mantric variations of expressing the content of each of the 3 line values?that's pretty good Kain...you have apparently been looking at different ways of combining these already...yes, at the end of the day I found it was more stable and a lot less cluttered to confine words to line values no matter where they show up in the structures. There are other possibilities...we could try to base everything on positions (for instance) and arrange alternate pronunciations for different line values but it very soon gets too convoluted to be believed...much too *contrived* basically.

What I settled into was simply assigning The Heaven Word (AHIH) to Yang Line values, The Man Word (AHVH) to Jen Line values and the Earth Word (IHVH) to Yin Line values. I also take directions into account so that if I am running in a counter-clockwise direction I will pronounce I-H-V-H but if I am running a clockwise direction I will pronounce I-V-H-H. I believe that this is (possibly) of lesser importance but there are some compelling reasons for considering doing things this way on a regular basis. I will try to get into that more as I begin to address the actual creation of fields in future articles. It will probably have been observed that the Man Word (AHVH) will not get used at all in creating Binary Hexagrams but will only come into play when creating Ternaries. If so, this is quite correct. In the Binaries, the Man Line principle exists solely in the background and becomes apparent only in the Closing Action (Hua-AThh)...

I see your point and building on the numbers is certainly one of the more powerful and certainly real approaches possible in this field. I think that there is also a factor of adhering to principles as they are directly perceived and experienced, for they are revealed instances of the fully Objective Fact.Observed phenomenum...even seemingly stable phenomenum...should not be defined as "objective fact" I think. All we really know is that the phenomenum itself appears to be holding steady over time. That still doesn't tell us what it is in a purely "objective" sense I think. But otherwise, I think I see where this is going. You seem to be saying that we don't really just pull shit out of our ass so much as there has been a concerted effort to chronolog this kind of experienced phenomenum as it has been repeatedly observed (and thus confirmed) by numerous people across time. This is a legitimate point of order I think and probably one of the main reasons the whole 4-Elemental Universe Construct seems to surface and resurface all over the world, in only very slightly different ways really... This appears to be something rooted in human consciousness itself...if not built right into the fabric of all consciousness in general...

note: in re-reading that highlighted sentence I think I may have misinterpreted your intent. The "objective fact" you are referring to is the Bigrams? I think it's probably fair to agree to this, so far as I understand objective fact at least. They certainly exist independant of personal experience in any case. Fortunately you were spared any extreme tyrade on objective vs subjective relativities...:cool:

m1thr0s

[MythMath]

So, I think that a firm base of logical deduction is a huge factor of adhering to Truth, but direct experience is also a factor to keep in mind, a factor that usually has a contracting effect to our field of possible choices regarding accurate symbolical representations.
Perhaps this accounts for the times when the different cultures do
differ in their respective correspondences (i.e. south at the top)...

[Kain]

that's pretty good Kain...you have apparently been looking at different ways of combining these already...yes, at the end of the day I found it was more stable and a lot less cluttered to confine words to line values no matter where they show up in the structures. There are other possibilities...we could try to base everything on positions (for instance) and arrange alternate pronunciations for different line values but it very soon gets too convoluted to be believed...much too *contrived* basically.Thanks m1thr0s...yeah, I've been trying to flex the joints this way and that, sort of getting a feel of the possible movements of the system...a very interesting structure emerging...I would agree from what I've seen of the Banners that this is a quite stable configuration, perhaps the best really.
What I settled into was simply assigning The Heaven Word (AHIH) to Yang Line values, The Man Word (AHVH) to Jen Line values and the Earth Word (IHVH) to Yin Line values. I also take directions into account so that if I am running in a counter-clockwise direction I will pronounce I-H-V-H but if I am running a clockwise direction I will pronounce I-V-H-H. Since you have assigned each of these Words to a particular line value, and ternary fields are built out of 3 possible values, to what end are you using the other 69 possible mantric variations of the Words? It would seem that this freedom of 24 banners per line value would imply a particularized and internal elemental system for each of the 3 values, similar to the Thelemic "Fire of Air", "Earth of Air" etc. . If so, this would greatly expand the variability of ternary fields, thus allowing instead of 729 possible fields alone, a greater resolution subset of the 729 hexagrammal fields wielding 156,238,908 possible hexagrammal variations, of slighter differences of course (different configurations within the same line value). Am I correct here?
It will probably have been observed that the Man Word (AHVH) will not get used at all in creating Binary Hexagrams but will only come into play when creating Ternaries. If so, this is quite correct. In the Binaries, the Man Line principle exists solely in the background and becomes apparent only in the Closing Action (Hua-AThh)...Yes, I assumed so, as it would function just like the Jen Line Value does.

But otherwise, I think I see where this is going. You seem to be saying that we don't really just pull shit out of our ass so much as there has been a concerted effort to chronolog this kind of experienced phenomenum as it has been repeatedly observed (and thus confirmed) by numerous people across time. This is a legitimate point of order I think and probably one of the main reasons the whole 4-Elemental Universe Construct seems to surface and resurface all over the world, in only very slightly different ways really... This appears to be something rooted in human consciousness itself...if not built right into the fabric of all consciousness in general...That's pretty much where I was getting at...also, I agree, the 4-Elemental Universe is indeed one of the best examples that we are dealing with something substantial in such cases. Bigrammaton itself qualifies too I think...the interraction of the opposites are equally universal and "all-time classic" assertions which I think hint at an equally deeply rooted experience. So both your original response and your edited note have me on absolute agreement m1thr0s, very good examples...Perhaps this accounts for the times when the different cultures do
differ in their respective correspondences (i.e. south at the top)...That's quite a good point MythMath. Still, it's even more important I think when different cultures actually completely agree on matters of extreme subtlety of nature...Due to the essential difficulty of testing those fields enough to actually define the "truth" of the matter, it is such close agreements from completely geographically or temporally unconnected sources that tip one off for humanity actually nailing (or at least being very close to nailing) a universal "fact" of some sort...

Kain

[m1thr0s]

Since you have assigned each of these Words to a particular line value, and ternary fields are built out of 3 possible values, to what end are you using the other 69 possible mantric variations of the Words? It would seem that this freedom of 24 banners per line value would imply a particularized and internal elemental system for each of the 3 values, similar to the Thelemic "Fire of Air", "Earth of Air" etc.It's a huge engine Kain...I haven't even tried to use all of these variations. This whole thing becomes even more intense when you realize that we can also work in layers. Banners themselves simply set up elemental fields but directing those fields is wide open. I hinted at some of this in my article on Talismanic Magick. I have primarily worked in tight around the IHShVH-IVShHH standard itself since I now have good reason to suppose that this formula is indeed a direct extension of the Word of Perfection. I have primarily explored the most basic applications corresponding to the Body of Light and unlocking its core properties & potentials. What you are talking about would go a bit further down the road into astrological kinds of applications, calender stuff and beyond. I haven't really gone there much but just surveyed the landscape. It's big.

If so, this would greatly expand the variability of ternary fields, thus allowing instead of 729 possible fields alone, a greater resolution subset of the 729 hexagrammal fields wielding 156,238,908 possible hexagrammal variations, of slighter differences of course (different configurations within the same line value). Am I correct here?not quite sure how you got that number but your essential assertion is correct. Much of my work at this pass is still in the distillation phase...still boiling things down to a methodology that can be employed to *raise the foundation* with as little wasted energy as might be logically affordable. Seems to me that is basically about enough for one incarnation but the extended possibilities are also very promising...

m1thr0s

[Kain]

It's a huge engine Kain...I haven't even tried to use all of these variations. This whole thing becomes even more intense when you realize that we can also work in layers. Banners themselves simply set up elemental fields but directing those fields is wide open. I hinted at some of this in my article on Talismanic Magick. I have primarily worked in tight around the IHShVH-IVShHH standard itself since I now have good reason to suppose that this formula is indeed a direct extension of the Word of Perfection. I have primarily explored the most basic applications corresponding to the Body of Light and unlocking its core properties & potentials. What you are talking about would go a bit further down the road into astrological kinds of applications, calender stuff and beyond. I haven't really gone there much but just surveyed the landscape. It's big.Certainly so, the expanse of possible applications and variations is almost breathtaking...it requires an equally pragmatic approach to allow one to not get lost in senseless over-complexity. Enough work to keep one occupied for lifetime after lifetime in fact...
not quite sure how you got that number but your essential assertion is correct. Much of my work at this pass is still in the distillation phase...still boiling things down to a methodology that can be employed to *raise the foundation* with as little wasted energy as might be logically affordable. Seems to me that is basically about enough for one incarnation but the extended possibilities are also very promising...Of course. I was just testing the water I guess...You're right, the number is wrong...sorry...However, what I tried to calculate is the possible hexagrammal fields that could be generated with 72 possible values per line. For the Binary Hexagrammal fields, this would be 2^6 = 64. For this occasion, I figure it would be 72^6, which gives us 139,314,069,504 (as I return to it).

This is quite a lot of potential, especially if one were to build fields in layers...

Kain

[m1thr0s]

well here is one thing to consider when we are addressing the whole size of things...if we look at this whole enginery as a systematic "language" of energy/consciousness itself that manages to codify all possibilities of Mind-Matter Creation/Destruction in some way...then we are really ultimately discussing a means of achieving anything as a matter of focused thought. It's the codification principle in itself that is especially intriguing since it suggests the idea of being able to do (and undo) anything the mind can possibly imagine according to a uniform technology of consciousness itself. This codification mechanism also preserves a technical distinction between imagining and doing, such that both passive and active states of consciousness are clearly maintained throughout.

In part, the only way to really begin to get a handle on how stark that is is to really reflect on what is implied to have Intelligence (Jen) placed on an exact even footing with Space (Yin) and Time (Yang) itself as happens in the Ternary system. Life as we know it achieves all of its manifest innovations via the codification mechanism of DNA/RNA which is at bottom reduceable to the 64 binary hexagrams! How much more vast than this must be this unseen codification mechanism incorporating the 729 ternaries!

The whole concept here is the idea that Mind achieves all things via the agency of Law in some way. In training the Mind to speak this particular language we are opening up the floodgates to an actual enginery of higher consciousness that follows very specific rules as to getting things done. Ultimately this becomes essentially autonomic, yet where a precise mechanism is involved it can all be broken down at any point in any process to exact mathematical procedures. Only in this way does the principle of Right Thinking attain to a true universiality in things, since unless there be some "wrong" way to go about accomplishing things, there must also be no "right" way.

We know that life itself follows such a system of Law or Rules in everything it does...why would we think that Mind does not do this as well? The whole issue really is identifying a mechanism that is not ultimately more oppressive than it is beneficial. The 8²/9³ Matrixes of Binary/Ternary Hexagrams is at this time the most promising lead we have got.

m1thr0s

[Kain]

You know, that's exactly the way I approach things, and that's also why I am so interested in practicing energy manipulation related with direct physical effects (as in the case of telekinesis etc). The potential of managing to consciously understand and speak this language of Universal Law in it's entirety is what I am most interested in, and try to approach and understand it better at every pass. It may look weird or even relatively pointless to some, trying to bring about direct effects through pure thought while those effects are possible through simple physical movement, and yet understanding the nature of the Mind's language of Law and testing that language in practical application is what such an approach is all about in my view. So yes, I think that this is a most important thing to consider m1thr0s, especially when taking into account the magnitude of possible variations presented in an elemental system of such dexterity of nature...

Kain

[m1thr0s]

Beethoven's Ninth...

Our ability to create complex structures at the level of thought itself attains for us a personal freedom not limited by the constraints of the Body.

Ultimately the two are probably the same thing in some incomprehensible sort of way...If one were a Universe for instance, wouldn't ones thoughts and limbs be all about the same thing?

m1thr0s

[Kain]

Ultimately the two are probably the same thing in some incomprehensible sort of way...If one were a Universe for instance, wouldn't ones thoughts and limbs be all about the same thing?Yes, exactly...so it all comes down to the reconcilation of the apparent "gap", and that's where elemental systems come in with their respective ability of mobility I think.

Kain

[MythMath]

http://i133.photobucket.com/albums/q48/MythMath/aBrainonTHCcopy.jpg

[m1thr0s]

THC = Tai Hsuan Ching...

That's actually a pretty accurate analogy MM...

it's the whole synergy thing that's never really been understood...the mysterious and extremely dynamic interplay between these two very powerful mathematical engines...the Binary & the Ternary...the 2 (yin) & the 3 (yang), which also comes to bear in the Ogdoad (2³) and the Ennead (3²)...

m1thr0s