Threesology Research Journal
Trigrams or Bigrams? 1
Threes or Twos?

(The Study of Threes)

As a Threesologist, I am frequently placed into a position of playing the devil's (or a saint's) advocate. Much like church leaders who are called upon to investigate the claimed validity of a miracle taking place, I delve into claims that promote a particular threes perspective, whether or not it is labeled a theory, if an author outright asserts or even insinuates their idea(s) as an "all encompassing" ideology. When an ideology presents three-based information as a factual component supporting the emphasis of a perspective, it is necessary to re-examine this part of the ideology's premises. Can an ideology stand without a component part, such that a part is greater than the whole, or does the whole have enough equilibrium to remain standing without a part used as an expressed supportive component? Whichever way you lean, let us sway neither to or fro by giving an author the benefit of any presumed doubt, until such time as we have offered evidence in support of or suggesting something to the contrary might advantageously be considered.

As a researcher, my views are only as valuable as my knowledge, and the extent to which I am up front about my limitations in a certain regard. Although in many instances I forget to be so forthcoming, (divergent thinkers very often are absent minded or "distracted"); in the present respect let me acknowledge that I am not an expert in the study of Trigrams to the extent I do not have an intimate appreciation of Trigram symbology details as does one who is well versed in such a study. Nor do I read, write, nor speak Chinese and therefore am unable to decipher as to what may or may not have been meant and written by a Chinese philosopher several centuries ago. [It is well known that translators of ancient texts can make mistakes if not impose personal alterations.] For my purposes, such abilities are not warranted nor even justifiably needed since they could very well impose an unwelcome bias.

Just because we of the present think we know what was said since we think we understand the views of someone writing about someone else's views about someone else's views about the original author who passed away generations ago, does not mean we actually do know... and may only have a gist of what was thought so many years ago in a different time and place under particular conditions. Nonetheless, my knowledge of threes makes me an appropriate candidate for examining Trigrams through the prism of a Threesological perspective, after reading different views of those who would appear to have a larger Trigram knowledge base. However, something can be said for those who stand at the expanse of a parameter and look inwards towards the center as opposed to those in the center who attempt to look outwards at the expanse... even if you would care to describe my "expanse" as just another form of center looking towards another center claiming to be an expanse... ad infinitum.

As a further disclaimer, let it be understood that I do not readily accept information as being more truthful just because it or similarities to it can be found in ancient texts whether or not they have acquired academic, social or some more notorious distinction, whether deserving or not. An entire generation (and then some) of people can be wrong-headed and perpetuate this same failing to future generations. Hence, with respect to the present discussion, just because so-called Trigrams can be found in old texts, and are studied by those who have themselves acquired notability, does not automatically provide them with an unassailable truth value to go unquestioned; particularly in light of the fact that the symbols dubbed as Trigrams look more like bigrams masquerading like Trigrams through an act of repeating a singular or doubled-singularity; much in the manner of two political parties attempting to claim a diplomatic, melding-of-minds, confluent centrality commonly referred to as a "bipartisanship" approach as a third option... when the real third option, namely the referendum vote of the people through a Peoples Legislative Branch, is not even being considered at all.

Back in 2006 I wrote a webpage with the questions "8 Chinese Trigrams or 8 Chinese Bigrams?" I web-publish it again after a "Threes" colleague directed my attention to the site --- Triplex Unity Theory --- which contains a section dealing with Trigrams.

The author asserts that there is nothing like his Triplex Unity Theory to which I would agree, unless of course a reader encounters a similar perspective drawn up by someone else and lets me know about it. I will admit there are a few million books I haven't read, not to mention hundreds of movies I haven't watched. Nonetheless, the idea is creatively unique. However, many of us might take exception to some of the claims by the author who writes with a style that some may interpret as a prepared-for-confrontation stance, perhaps as a projected expression of his interest in martial arts; instead of as an invitation to explore "triplexity" through receptive discussions amongst those who have differing opinions based on differences in experience and knowledge. In any respect, I will let you be the judge as to the validity of the author's claims after reviewing some considerations involving triads, though my discussion is not in the least solely focused on this task.

Let us first recognize that the singular designation "Trigram" is a label promoted by the Western perspective and that the Chinese have used the two words "Pa" and "Kua" and not "Trigram." Since the author of the "Triplex Unity Theory" appears to be of Indo-European stock, our analysis of his theory must take into consideration that he is exhibiting an unconscious, Indo-European based, three-patterned orientation, whether he is aware of it or not. Developmentally speaking, with respect to the "Out of Africa" hypothesis for hominid development and expansion in evolutionary terms:

  1. Fossils found in Africa implicate that our hominid line first arose in Africa.

  2. Additional fossils and archeological materials suggest that our hominid line moved into what we today call Asia though we should not limit our comprehension of past migrations to present day artificially created territorial boundaries.

  3. Evidence for further "advanced" forms of hominids appears to be centered in areas referred to as Indo-European. However, this is not to say that there were no "advanced" hominid forms in Africa or Asia. Thus far, and this is not to say that the future won't hold any surprises, there is a predominant class of over-riding evidence purporting to and supporting assertions that Indo-Europeans are the third (baby of the hominid family) arrival. Along with this third arrival comes an increased usage of three-patterned expressions that may be called jokes, ideas, theories, common sense, or whatever label you prefer.

Those who are familiar with the 1-2-3 maturational development theory of human cognition, similarly expressed in the 1-2-Many concept of number-symbols and word-for-numbers development, not to mention the physiologically expressed single, double, triple germ layer progression; know that a "three" perspective has been most progressively dominant amongst Indo-European peoples, a "two" perspective has been most predominant amongst Asian peoples, and a "one" perspective, has been most predominant amongst African peoples...

Yes, there are African and Asian peoples who have and do express patterns-of-three. But these peoples as individualized wholes appear to have historically used predominant singular and dual concept perspectives, respectively, in past ages. This doesn't mean they can't change, it is a comment that simply establishes a baseline for comparative research. Please don't try to read-in prejudices where none exist.

For an author with an unrecognized Indo-European penchant for using three-patterned concepts is not unusual. If an African or Asian author subscribes to such a usage, we must wonder if their education has had an Indo-European influence, which would thus encourage them towards accepting and using three-patterned concepts... unless it describes an overall change taking place with the culture the author did or does reside in.

What is Pa Kua? In the direct translation, Pa means eight (8) and Kua means suspending or hanging. It is like hanging a picture on the wall, (or) in the living room, to observe it. Actually, in Yi Jing, Pa Kua is telling us there are eight phenomena among us, suspending in the Universe. Instead of calling them the eight phenomena, they were referred as Pa Kua.

Our (Chinese) ancestors were studying the Universe by observing the suspended objects (phenomena) on the universal wall. To the best of their abilities, they saw eight basic images. These images are sky, earth, thunder, wind, fire, water, mountain, and marsh (body of water).

Before any languages were written, one of our (Chinese) ancestors developed a (two-patterned) line symbol system to represent the universal images. He used a solid line to represent motion, elevation, harden and strong images. And a broken line to represent motionless, depression, soft and weak images. In later times, people called the solid line yang and the broken line yin.

The two different lines were stacked (bigram) and this only has four combinations. The bigram cannot be used to represent any images and serves no purposes. It is only a passive development stage. However, by adding one yang or yin line to the bigram it will become Pa Kua. Each Kua was assigned an ancient name to it.

--- The 8 Trigrams ---

8trigrams (1K)

In other words, by adding an additional representation of a duality (Yin/Yang) to the initial duality (bigram), the result is called a Trigram but it is in actuality two bigrams (or one and one-half bigram for those readers who are mathematically oriented and would prefer to assign the numerical values of 2 + 1 = 3... or 1 + 1 + 1 = 3.) The Western mind is viewing the alternating yin/yang/yin (etc.) arrangement as a compilation of three units, whereas a (non-Western influenced) Eastern mind views the compilation as a separate but connected entity. Such compilations must be interpreted from the perspective of an ancient counting scheme where there existed counting limits.

A distinction is clearly being made between the counting limit of two lines and the developmental transitional stage to the concept of "three," though it is being addressed from an abstract philosophical sense and not a strict mathematically oriented one. Nonetheless, an image of early man's primitive numerical awareness (and development) is being reflected via a philosophical avenue. This is not to say that some early Chinese did not think in advanced mathematical terms, it is simply an example of how the human brain begins to wrestle with more complex philosophical ideas by (unknowingly) using elementary mathematical formulations in its first attempts to express such ideas. This "attempt to progress by way of regression" towards (unknowingly) using elementary numerical/mathematical formulations is used in a variety of ways throughout the world. In other words, elementary numerical/mathematical concepts can be viewed as being exercised in all behavior if we would simply take the time to make the comparison. All present day philosophies, theologies, (and science) are being thought of and exercised within the scope of a very primitive arithmetic regardless of claims about sophistication in mathematical concepts, instrumentation, etc...

The so-called complexity appears to be nothing more than a compilation of simplicity, as if simplicity is a cognitive point of limitation that can not be progressed beyond with a true "stand alone" identity of its own. The so-called complexity, derived from a mere compilation of simplicity augmenting itself, is similar to our inability to construct a different word to represent, to describe. to articulate a size beyond large. Instead, we compile a series of X's. Whereas we adopt the word "medium" as a stand-alone distinction from the word "small," and the word "large" as a stand-alone distinction from the word "medium," there are no similar stand--alone words to describe the X, XX, and XXX--large sizing groups.

Analogously, we must wonder if greater intelligence much less genius, is but one or more "compilations of simplicity" instead of a stand-alone "emergent property." Along this same vein of consideration, while we can readily see that much of adult language is but a compilation of simple words learned in childhood, are there instances when adult language is truly a "stand-alone" emergent property of a "greater" cognitive complexity? While some may claim the "language" of mathematics is extremely complex and stands alone and apart from all other languages, symbolic or linguistically expressed, it too is a series of incrementally learned simplicities.

Even though a historian of mathematics might offer the view that trigonometry, geometry, algebra and the calculus are stand-alone mathematical ventures, each requiring an individualized set of cognitive skills before a student can progress into "higher" mathematics, thus representing inherent emergent properties, all of them are nonetheless serial compilations of simplicity and do not necessarily represent an "all encompassing" theory of realization no matter how much or to what elaborate an extent you mix and match separate fundamental concepts. Granted, a primitive's brain may not be able to grasp fundamental mathematical concepts enabling them to solve, much less develop a calculus problem, the whole of mathematics itself may be nothing more than the exercise of a simplicity relative to a modern brain's architecture.

Note: in terms of cognitive development, the re-usage of a solid or double line expresses a limit point in human thinking that is similar to the development of words-for-numbers such that there was a quantity one, a quantity two, but any quantity beyond the "two" was labeled "Many." Though the one-two-many is a pattern-of-three expression, it nonetheless describes a functional limiting capacity to the human mind. In our modern era, we have a similar example of cognitive limitation in our (America) usage of clothing sizes. We have small- medium- large, with larger sizes indicated by a re-usage of a "many" symbol: X- XX- and XXX large. In other words, the human mind appears unable to devise separate distinctions without some form of repetition.

Thinking out-loud in a number-related-to-word sense while looking at the eight (so-called) Trigrams, we might come up with:

  • Monad ["Moad"] = One (the first "line" symbol)

  • Biad [or Dyad/Diad] = Two (the second "line" symbol)

  • Triad = Three (the third "line" symbol)

In the above sense I am speaking of the order of arrangement of the lines and am not counting individual component parts which make up a single line. For example:

The first (Ch'ien) representation would be written:

Chien (1K)

The second (Chen) representation would be written:

Chen (1K)

The third (K'an) representation would be written:

Kan (1K)

Let's look at the list of 8 "Trigrams" with number symbol indicators instead of geometric symbols called lines:

8trigrams2 (2K)

Just like humanity's early attempts at number counting, there are many historical references to counting limits at the quantity two, one of which appears to be represented in the Chinese philosophy that is frequently referred to as the Trigrams. The developmental leap to the concept of "three" was frequently referred to as a representation of "many." (However, the development of number concepts as well as counting limits, in different places and times was represented by various symbols (including simple notches on sticks or stones).

trigram3 (1K) However, let's not lose sight of the fact that a true trigram, with respect to a 1, 2, 3 quantity-of-lines differentiation, would look like this.

morsegrams (2K)

Imaginatively, if we were so inclined to think in terms of Morse (or computer) Code, we could view the lines and spaces as either dots or dashes (or zeros and ones), whether or not we include the spaces between each successive line as either a dot or dash as well. And if you were further inclined to think of the so-called Trigrams as a secret code, a full Morse Code decipherment is awaiting some astute translator's disposition to unravel yet another great ancient Chinese secret... (mystery in metaphor). Just don't forget to mention my name in your book or movie that an indulgent public doles out millions for. But I would prefer not to be named after one of the Fast-food chains' give-a-way toys.

A western interpretation which imposes the label of "Trigram," can lead to a misidentification of a "Trigram" philosophy that is actually a series of "Bigrams" that are striving for a Trigram identity. (A numerical concept of "two" that is advancing towards a numerical concept of "three.") Another example of a two-patterned perspective striving for a Three-patterned identity can be found in the (usually black/white colored) concept of Yin and Yang, which adopts the philosophical formula of Yin- Unity- Yang that a Western perspective might interpret to be a triad, but is actually a "biad" arrangement with an "intimation" of being a three-patterned structure. No less, we find another example of this when we look at the names of Asian gangs which espouse two-patterned references such as White Tigers, Red Dragons, etc., and yet are striving for an identity with a Triad organization.

bigram (6K)

However, we find this same type of Bigram-striving-for-a-Trigram-stature philosophy in the usage of a Binomial architecture underlying computer systems. The on/off circuitry of present-day electrical components is readily aligned to the true/false statements found in Boolean Algebra, which finds an amicable analogy with the usage of 1's and 0's used for modern computing systems. It is a small step towards appreciating the association between the concepts of Yin- Unity- Yang with White- Grey- Black, and misleading oneself into thinking they are representative of a tripartite form of 3-patterned syllogistic logic. The "Unity" portion is an assumption of achievement from the perfect coalescence of Yin and Yang. In terms of a modern day representation being used in computer technology, yinyang (1K) a Bigram form of computer language is thus an impediment towards helping computers achieve a type of consciousness comparable to a true trigram form of biological thinking and not accepted as a reality, based merely on speculative philosophical conjectures.

boolean (4K)
--- Boolean Operators ---

In an attempt to acquire a trigram status, the duality of a Solid line/Broken line is coupled with the notion of Yang and Yin, which appears to be an unacknowledged mental maneuver of attempting to increase ascendency of stature in philosophical importance as is characteristic of a developing consciousness. However, if a true Trigram is to be achieved, then the use of a single line, double line, triple line configuration should be adopted:

trutrigrams (4K)

This 1- 2- 3 configuration is more closely aligned to the architecture of reality in the sense that in terms of biological development we find the following structure related to three fundamental constituents:

  • RNA is predominantly single stranded.

  • DNA is predominantly double stranded.

  • Proteins can have a single- double - tertiary structure with a composite of these three (a 3 to 1 ratio) labeled a quaternary.

By using a strict reference of the single, double, triple structure, RNA could be written with one single line- one double line, and one single line. The first line would represent the predominance of RNA strand structure and the two-element second line would represent the secondary (in this case, minor) double-stranded form occurrence. The third single line would thus represent singularity form dominance. In the case of DNA, a double line would come first, followed by a single line, followed by a double line. As for proteins, a triple line would come first, a double line second, and a single line third, though some might want to arrange these in a different formulaic array such as representing predominance of occurrence in the third line (in stead of the first line) position.

While it has been recognized by others that an 8 X 8 mix and match array of the 8 basic "Trigrams" yields a quantity of 64 which is the complement of amino acids arrived at by a similar method of mixing and matching triplet codons, a view that I had independently arrived at without any fore-knowledge of such a perspective having been developed elsewhere, we must reassess this notion based on the acknowledgment that the so-called Trigrams are actually Bigrams and yield a "wannabe" (want-to-be) attempt at such a formulization. In other words, even though the correct value of "64" was achieved, it was achieved by the usage of a false set of triple codings which, if continued to be used, will fall short of extended applications in the future. This would be like a geneticist using three-patterned (mixed and matched) variations of only two amino acids.

The building blocks of proteins are called Amino acids. RNA has four amino acids known as Adenine, Cytosine, Guanine, and Uracil. DNA has the same amino acids with the exception of Thymine substituted for Uracil. Hence, I refer to this distinction as a 3 to 1 ratio, because there are 3 (the same) amino acids in both RNA & DNA, and 1 different amino acid.

A simple table may be of some value:

RNA DNA 3 to 1 comparison
Adenine Adenine Three the Same
Cytosine Cytosine
Guanine Guanine
Uracil Thymine One is Different

As a correlation to the "64" representation in genetics, we find another occurrence in logic. Taken by itself, the presence of a "64" seems rather superficial and more in tune with a mystical excursion into numerology, but when we look at the underlying formula used to arrive at such, we identify a recurrence of a three-patterned structure (Major premise- Minor premise- Conclusion), that may have an underlying parallel to triplet coding pattern found in DNA, and triads found in Music. If such a case can be made, it must be ascertained whether or not this recurrence is due to an underlying pattern in the human brain that is exhibited by those humans who represent a particular type of brain development consistent with an evolutionary change.

We can cite a 3 to 1 ratio of references to the "64":

  • 1 of 3- 64 "word" vocabulary in genetics.

  • 2 of 3- 64 "moods" in logic (to be mentioned below).

  • 3 of 3- 64 "Trigrams" in I Ching Philosophy.

  • 1 of 1- "64 dollar question" (a recurring colloquial expression denoting an unanswered question.)

A categorical syllogism infers a conclusion from two premises. (Major premise ~ Minor premise ~ Conclusion). It is defined by the following four attributes. Each of the three propositions is an A, E, I, or O proposition:

Major premise Minor premise Conclusion

The subject of the conclusion (called the minor term) also occurs in one of the premises (the minor premise). The predicate of the conclusion (called the major term) also occurs in the other premise (the major premise). The two remaining term positions in the premises are filled by the same term (the middle term).  Since each of the three propositions in a syllogism can take one of four combinations of quality and quantity, the categorical syllogism may exhibit any of 64 moods. (43)

Each mood may occur in any of four figures--- patterns of terms within the propositions --- thus yielding 256 possible forms. One of the important tasks of syllogistic logic has been to reduce this plurality to just the valid forms.

Aristotle recognized these 19 "valid" forms, (seen here in their medieval mnemonic names) while others recognized 5 others called subalternate moods:

First figure:

Barbara, Celarent, Darii, Ferio
Subalternates: Barbari, Celaront

Second figure:

Cesare, Camestres, Festino, Baroco
Subalternates: Cesaro, Camestrop

Third figure:

Darapti, Disamis, Datisi, Felapton, Bocardo, Ferison

Fourth figure:

Bramantip, Camenes, Dimaris, Fesapo, Fresison
Subalternate: Camenop

As with a four base triplet codon system, we can find another arrangement of this 4/3 formula in western (Indo-European) music, philosophy, and some out-dated ideas as well, such as the notion of a Triumvirate list of courses (Grammar, Rhetoric, Logic) coupled with a Quadrumvirate list of academic courses (Arithmetic, Music, Geometry, Astronomy) as was once practiced by Medieval Universities.  What needs to be acknowledged is that the number 7 has a special significance as a symbolic reference to a sequential numerical placement, in that it is arrived at through addition of the two numbers 3 and 4, irrespective of what mythological, scientific, theological, metaphysical, etc., connotations are applied to these numbers as referential attributes with personal meaning.

Another example of the 3/4 model representation can be found in particle physics:

3 families of fundamental particles (9K)

--- Standard Model of Particle Physics ---

Links that may be of interest:

--- Basic Circuits for Computing ---

--- I Ching Meanings page 1 ---

--- Searching Electronic Databases Using Keywords (Boolean Operators)---

--- The San He Luopan ---

--- Trigrams of the I Ching ---

Your Questions or Comments are welcomed:
Herb O. Buckland