(or Triads, Trimurties, Triple Deity, Triunities, Trebles, Triangles, Triskelions, etc...?)
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~ The Study of Threes ~
http://threesology.org
Visitors as of 8/25/2018
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Whereas I could begin this page with a specific reference to one or another threes-related word, a reference to the word "three" in a numerical form should also be addressed, particularly in light of my encounter with a mathematician's perspective commenting on the recurrence of "threes" in the context of Why Do We Believe That Catastrophes Come in Threes?. While the article does in fact provide ample evidence that people can and do seek out given patterns, with and without flexible constraints that they sometimes need to shoe-horn into place, the article did not try to explain why the usage of three is so robust, just as is the small set of number patterns one may collate into a graph.
Let me provide a short hypothetical graph concerning various number patterns (not including the three basic geometric patterns of line-circle-triangle), as a means of illustrating, in general, the small quantity of recurring patterns-of-number out of all the trillions of numbers which exist:
Another type of graph that should be included is that which expresses human cognition with respect to geographical symbolization. For example, no doubt in different contexts you have encountered information which describes a settlement or eventual city having begun alongside a single river such as the Nile or Ganges, while at other times a single river (such as the Amazon) is used as THE major point of geographical reference. The true can be said for the usage of a single mountain, single mountain range or gorge. During other information encounters you may come across the usage of two-patterned geographical references such as when we find the (Greek) word "Mesopotamia" which means two rivers. With respect to the "two", (if I may be permitted a momentary digression), the phrase 'Never the twain shall meet' can be labeled part of a literary genre of cognitive mapping which includes the American reference of "Mark Twain". However, in saying "Half twain! Quarter twain! M-a-r-k twain!"... and describing "Mark Twain" as referencing 12 feet, it is of interest to note that Half and Quarter twains do not actually describe portions of the twelve feet, as the table below the following insert describes:
Lead Line
A weighted rope with marked increments that was used to measure the river's depth, mostly used on the Mississippi River. A sounding pole is generally used on the Ohio River. The cord is marked off into fathoms and fractions thereof: one fathom (six feet) is termed mark one; two fathoms is mark twain; three fathoms is mark three and four fathoms is mark four. Above mark four is no bottom. The person who takes the soundings with a lead line and calls them to the pilot is called the leadsman. The leadsman sang out the depth in a voice loud enough to be heard in the pilothouse.
Source: Steamboats.org
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When a pilot "calls for the lead" he gives the command with a signal from the whistle or bell. Soundings are taken from either side of the boat, and when necessary from both sides. One signal from the pilot house sends a leadsman to the starboard (right) side, two signals to the larboard (left or "port" side). The same signals from the pilothouse recall the leadsman from his post. Soundings are taken at the discretion of the pilot, when making a crossing, going through seldom used chutes, or at any time when there is doubt regarding the depth of the water. When a leadsman is at work the pilot expects to be informed of the depth of the channel about ever hundred feet. Throughout the leadsman's chanting, pilots listen hopefully for "No Bottom." To them this is the leadsman's sweetest song. When a boat can be kept in deep water the danger of going aground is avoided. - Steamboatin' Days - Folks Songs of the River Packet Era, Mary Wheeler. Louisiana State University Press, 1944. |
 Quarter Less Twain - ten and one-half feet Mark Twain - twelve feet (two fathoms) Quarter Twain - thirteen and one-half feet Half Twain - fifteen feet Quarter Less Three - sixteen and one-half feet Mark Three - eighteen feet (three fathoms) Quarter Three - nineteen and one-half feet Half Three - twenty-one feet Quarter Less Four - -twenty-two and one-half feet Mark Four (or Deep Four) - twenty-four feet (four fathoms) No Bottom - over twenty-four feet Ssource: Samuel L. Clemens' Steamboat Career |
In as much as some readers get caught up in literary accounts of repeating cognitive patterns that, for the most part, may go unrecognized much less labeled as a recurring cognitive pattern or decipherd in the context of a larger depth and breadth of other subjects, this genre of consideration should not distract one from taking an assessment of geographical representations of human cognition. From the "two rivers" example one can cite references in which three rivers are used as geographical points of recurring reference such as Trois-Riviéres Three Gorges, and Three Mountains are three (from China) examples. In terms of more than three, at least in the Jewish reference to Four Rivers, it appears to be a confabulated creation using the number 4 intermixed with religious dogma, even though four actual rivers may indeed have been referred to. In other words, it was made up to promote a religious perspective. Another example of a contrived "four" geographical reference is that referred to as the four corners region of the United States (Utah, Colorado, New Mexico and Arizona meet). Another contrivance, which I place here because it just came to mind, is that of the "seven toothed grill" on the front of a Jeep, which references it as the first vehicle having been to seven continents. While there is a reference to "Four Rivers" on the internet, not much else surfaced during an initial cursory query.
While I could find references to five, six, seven, eight (spanish: ocha) and nine rivers, upon reaching the 10th, I was met with a reference to When Rivers Collide: 10 Confluences Around the World. In short, as with geographical points of reference which represent an area of human cognitive grouping behavior that is largely overlooked, what is to be found is yet another form of limitation. In other words, the geography of Earth imposes itself on human cognitive development. If there were multiple references to 11, 12, 13, 14, 15, etc., rivers, gorges, mountains, etc..., humans might well have a different model of brain. And even though there are millions of trees, insects, stars, fish, birds, etc., these do not customarily come into play as cognitively-linked geographical references... despite the usage of stars being grouped into constellations, that most of us quite probably don't know anyway. In short, though humans can conceive of larger number references, there is what appears to be an (environmentally) imposed limitation that we should not rationalistically defend, but come to appreciate as a tell-tale sign that it is a measurement of humanity's duration of existence... which is slowing ticking away.
There is a conservation of number that exists. It is, in other words... a limitation. It is not that we humans (and other animals) can not think or perform in larger numbers, it's that something in the environment enforces a rule-of-thumb to use a few small-number references agaia and again and again. Despite all the arguments and rationalizations to explain one or another recurring usage of a given number, the fact remains that our usage is limited. Identifying the existence of such a limitation is one of the steps enabling us to further identify whether or not the scope and duration of the limitation is changing in concert with the deterioration of the planet and solar system. From another vantage point, we can describe the usage as "set-creating-behavior". However, we often do not use the word "set". Instead, words such as group, spoon, gang, collection, compilation, city, state, country, nation, company, container, etc..., may be used to describe a set... even if the contents are not differentiated into numerically referenced items place together, alongside, or apart. Just because you may not routinely describe the amount of money you have in a wallet or purse as a set of a specific quantity, the behavior of creating sets appears to be a part of human nature... a nature dependent on the functionality of the environment. While different environments will influence the development of different types of named groupings, whether or not the users are aware that they are participating in such an activity, the numerical values appear to be a very small number that re-occur across nationalities. Much like the behavior that all infants babble in similar patterns irrespective of culture, so does the usage of some number patterns, even though some cultures are interpreted by cultural anthropologists to have a preference for one type of number usage over others. Phyisiologically and biologically, the patterns appear to remain constant, so long as there is an external environment which influences the development there of.
In other words, while it is true one can find different patterns by looking for them, some pattern uses appear to be more stable then others, and we don't find particular patterns everywhere, particularly the pattern of those who collate instances of many non-three patterns with an intent to discover... if possible, the existence of a reason or at least influence of what appears to be a small set of numbers being used as pattern identifiers. In other words, out of all the available numbers, we don't find a recurrence of large number- patterns, (patterns with number values such as 6,968, 13,245, 822, etc... The recurring patterns involve small numbers and only a relatively few of the these are used over and over again. A deteriorating planetary and solar system (as well as galactic) environment forces the usage of a small set of numerically identifiable pattern repetitions. The following example displays a negative effect of a triple repetion, but this should not be used to convey the idea that all such pattern forms are likewise undesirable. If this were the case, then we would have to say that the triplet coding in all of DNA and RNA is bad for us and all of life.
And even though we are unable to access the recurrence of number patterns used in the distant past proceeding to the present, an examimantion of our present day usage of patterns indicates that not only do humans engage in a small array of small numbers, as well as subject long strings of numbers to small sets of reference, but that the recurrence of such patterns across cultures gives us an indication of cognitive activity and ability, subject to the constraints of an incrementally deteriorating planetary system and planetary environment. As the deterioration continues, there might well be an alteration in pattern usage... irrespective of cultural embellishments including the perceptions and definitions used by one or another authority. Like religious authorities who come to believe themselves an authority on all or most or many things religious, the same attitude can be found among physicians, dentists, mechanics, mathematicians, psychologists, biologists, sports players, actors/actresses, mothers, fathers, business professionals, teachers, cooks, chefs, gardeners, etc. In other words, a mathematician's take on a recurring phenomena involving one or more numbers should not be viewed as if it were a sanctified "written in stone" edict being presented as the last word on a given subject, no matter how well provisioned and articulated. Religious leaders do not own the words God, Morality nor the Trinity, just as Physicists do not own sub-atomic particles, or Mathematicians numbers and number theory.
An excursion into a discussion of "three" as both a quantity and quality, necessarily involves a reference to religious-based groups-of-three such as the Christian Trinity and Hindu Trimurti, though we might well include more ancient pantheons of gods or mythological creatures (both human and otherwise), even if peoples in the past did not use the words "Triad, Trinity, Trio, Trimurti" etc... Such a discussion also lends itself to being examined from various alternative perspectives, one of which is mathematical set theory, though its tradition has adopted the mind-set that it is not conventionally applicable to ordinary experiences (for example, three clothing sizes of small-medium-large (and the extended sizes beyond the "large" coupled to a 1X-2X-3X layout), the three-based fast food restaurant combo-meal of sandwich-drink-side order, knife-fork-spoon eating implements, etc..), such as these and others I will describe and therefore refute the ascribed set theory notion explicated as: |
Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. The language of set theory can be used in the definitions of nearly all mathematical objects. Source: Wikipedia: Set Theory |
Just because one might personally encounter a common run-of-the-mill University Mathematician who is so arrogantly lofted in their opinion of themselves and their applied perceptions, doesn't mean the recurrences of sets of one or another number pattern found in multiple subject areas doesn't constitute a cognitive equation that they neither know how to perceive, much less interpret and then describe as a mathematically illustrative paradigm related to evolutionary development, growth and an eventual definitive for futher consideration.
While mathematicians are noted for their ability to decipher analytical abstractions, this doesn't automatically mean they can perceive all abstract simplicities staring them in the face simply because they confine their interests to a single subject or only a few taught to them in a College setting. A wider breadth of knowledge would enable them to apprehend commonalities of cognitive occurrences susceptible to mathematical indices, since many of them... such as superstitions, already lend themselves to being labeled numerically. And as such, the fact that only a few numbers are being continually referred to one generation to the next, is indicative of a "set" of number references related to cognition that is related to influences that like-wise repeat, and if such influences are deteriorating, than so will these and other "sets" of one, two, three, four, five, six, seven, eight, nine, etc.. Putting such numerically identifiable occurrences on a graph details a closer look at human cognition. The implied psychological depths and dimensions of human cognition set into a system of mathematical referencing is far removed from typical mathematical inquiries. For example, the dimension of counting games used by children have a repetitive frequency that can be deduced as a product of linguistic matrices linked to auditory controls subject to physiological imprints and often as a result of adult additions. The enumerations we can decipher are coordinates enabling us to construct a map of human cognition by developing a relevant graphing system.
A bit of history concerning "Set Theory" is appropriate at this moment because its development and acceptance as a relevant mathematical discipline has historically met with opposition, similar to the opposition which has been confronted by those attempting to establish a "Threesological" set theory discipline as it makes its way through a research and development stage with its own, as yet undefined axiomatic parameters, because the formation of such requires the participation of a much broader collection of information reduced to numerical indices portraying a recurrency of cognitive application in seemingly divergent areas of human orientation that can offer applicable information for multiple disciplines such as Philosophy, Psychology, Sociology, Music, Literature, script writing, motion picture direction, character development, Political Science, protest options, Surveillance, Military Science, Computer programming, etc...:
Set theory, (is a) branch of mathematics that deals with the properties of well-defined collections of objects, which may or may not be of a mathematical nature, such as numbers or functions. The theory is less valuable in direct application to ordinary experience than as a basis for precise and adaptable terminology for the definition of complex and sophisticated mathematical concepts. Between the years 1874 and 1897, the German mathematician and logician Georg Cantor created a theory of abstract sets of entities and made it into a mathematical discipline. This theory grew out of his investigations of some concrete problems regarding certain types of infinite sets of real numbers. A set, wrote Cantor, is a collection of definite, distinguishable objects of perception or thought conceived as a whole. The objects are called elements or members of the set. The theory had the revolutionary aspect of treating infinite sets as mathematical objects that are on an equal footing with those that can be constructed in a finite number of steps. Since antiquity, a majority of mathematicians had carefully avoided the introduction into their arguments of the actual infinite (i.e., of sets containing an infinity of objects conceived as existing simultaneously, at least in thought). Since this attitude persisted until almost the end of the 19th century, Cantor’s work was the subject of much criticism to the effect that it dealt with fictions—indeed, that it encroached on the domain of philosophers and violated the principles of religion. Once applications to analysis began to be found, however, attitudes began to change, and by the 1890s Cantor’s ideas and results were gaining acceptance. By 1900, set theory was recognized as a distinct branch of mathematics. At just that time, however, several contradictions in so-called naive set theory were discovered. In order to eliminate such problems, an axiomatic basis was developed for the theory of sets analogous to that developed for elementary geometry. The degree of success that has been achieved in this development, as well as the present stature of set theory, has been well expressed in the Nicolas Bourbaki Éléments de mathématique (begun 1939; "elements of mathematics"): "nowadays it is known to be possible, logically speaking, to derive practically the whole of known mathematics from a single source, the theory of sets." Introduction To Naive Set Theory Fundamental set concepts In naive set theory, a set is a collection of objects (called members or elements) that is regarded as being a single object. To indicate that an object x is a member of a set A one writes x ∊ A, while x ∉ A indicates that x is not a member of A. A set may be defined by a membership rule (formula) or by listing its members within braces. For example, the set given by the rule "prime numbers less than 1" can also be given by {2, 3, 5, 7}. In principle, any finite set can be defined by an explicit list of its members, but specifying infinite sets requires a rule or pattern to indicate membership; for example, the ellipsis in {0, 1, 2, 3, 4, 5, 6, 7, ...} indicates that the list of natural numbers N goes on forever. The empty (or void, or null) set, symbolized by {} or ∅, contains no elements at all. Nonetheless, it has the status of being a set. A set A is called a subset of a set B (symbolized by A ⊆ B) if all the members of A are also members of B. For example, any set is a subset of itself, and ∅ is a subset of any set. If both A ⊆ B and B ⊆ A, then A and B have exactly the same members. Part of the set concept is that in this case A = B; that is, A and B are the same set... Source: Set Theory (Britannica) |
Here are a handful of different sets-of-three configuration which contain not only the set (1,2,3), but alternate configurations such as (one, two, many), (three -to- one, three in one, three from one, three as one, three/two, one-two-empty or void, transitions thereof, regressions there of, etc... [in words or numbers or other symbols... sounds... impressions... etc...]). Sometimes the "three" or any reference to quantity is not specifically labeled, or may be inferred such as using words like triad, trinity, treble, triune, triangle, tripod, plurality, Many, etc... In other instances not listed, patterns may exisit by inter-mixing sounds, muscle twitches, tastes, ordors, feeling, nuances, subtle energies, or the egnimatic "something there" or as a difficult-to-grasp shadow or glimer or stroboscopic impression, etc... For example, how many record a pattern-of-three upon hearing a dog bark three times, or finding three coins on the ground, or 1st hearing a sound, then seeing a shadow, and 3rdly, in succession, smelling an order? Patterns occurring due to successively different perceptions are not customarily identified nor recorded, though they leave an impression and may well have an effect on behavior, particularly if a person or group of people in the same context have recurring experiences thereof.
 Christianity's 3-in-1 TrinityOrigin: the Sun + dawn-noon-dusk |
 3 faces of 1 god representing creation, preservation and destruction, or dawn-noon-dusk |
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 (A Trinity amdist violence, like a medieval Christianity) |
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 3 small, 3 large pyramids of the Giza Plateau |
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 The First of three Major (cradle of civilization) Societies originating in one region Began about 4000 (+/-) BC |
 The Second of three Major (cradle of civilization) Societies originating in one region |
 The Second of three Major (cradle of civilization) Societies originating in one region Began about 1792 BC when Hammurubi ascended the throne |
Since "Mesopotamia" covers a vast region and multiple cultures of distinction arose over time, some readers may not like the usage of "Mesopotamia" to label a separate time period from Sumeria and Babylon, much less be used to describe a separate civilization because of the resulting overlap of cultural integrations (language, trade, customs, social divisions, laws, etc...). Whereas they would prefer to include or choose instead one of the other several major cities which arose, the usage of the above three to give a rough outline of historical development will suffice to bring to the point that from a "4" (or 3-to-1) to a three-part social class division. (The so-called "four" class divisions extended into the much later developing region of India where a recognized "out cast" division was treated by Georges Dumezil as an irrelevancy by by-stepping the situation in his focus on the Varna three-fold distinction with his Tripartite social functionality system of analyzing Indo-European cultures contrasted to non- Indo-European ones). Instead of arising at the consideration of a 3 -t- 1 ratio (because his focus was limited to a specific field of research and not a wider breadth of cognitive activity), he enaged in what can be described as a "rationalized adjustment" of the information on hand in order to fit within a constrained compilation of subject matter.
- Sumer is the earliest known civilization in the historical region of southern Mesopotamia, modern-day southern Iraq, during the Chalcolithic and Early
Bronze ages, and arguably one of the first civilizations in the world along with Ancient Egypt and the Indus Valley. Living along the valleys of the Tigris and
Euphrates, Sumerian farmers were able to grow an abundance of grain and other crops, the surplus of which enabled them to settle in one place. Proto-writing in
the prehistory dates back to c. 3000 BC.
The earliest texts come from the cities of Uruk and Jemdet Nasr and date back to 3300 BC; early cuneiform script writing emerged in 3000 BCSumerian civilization took form in the Uruk period (4th millennium BC), continuing into the Jemdet Nasr and Early Dynastic periods. During the 3rd millennium BC, a close cultural symbiosis developed between the Sumerians, who spoke a language isolate, and Akkadian-speakers, which included widespread bilingualism. The influence of Sumerian on Akkadian (and vice versa) is evident in all areas, from lexical borrowing on a massive scale, to syntactic, morphological, and phonological convergence. This has prompted scholars to refer to Sumerian and Akkadian in the 3rd millennium BC as a Sprachbund. Sumer was conquered by the Semitic-speaking kings of the Akkadian Empire around 2270 BC (short chronology), but Sumerian continued as a sacred language. - Mesopotamia is a historical region in Western Asia situated within the Tigris–Euphrates river system, in modern days roughly corresponding to most of Iraq, Kuwait, parts of Northern Saudi Arabia, the eastern parts of Syria, Southeastern Turkey, and regions along the Turkish–Syrian and Iran–Iraq borders. The Sumerians and Akkadians (including Assyrians and Babylonians) dominated Mesopotamia from the beginning of written history (c. 3100 BC) to the fall of Babylon in 539 BC, when it was conquered by the Achaemenid Empire. It fell to Alexander the Great in 332 BC, and after his death, it became part of the Greek Seleucid Empire.
- Babylonia, ancient cultural region occupying southeastern Mesopotamia between the Tigris and Euphrates rivers (modern southern Iraq from around Baghdad to the Persian Gulf). Because the city of Babylon was the capital of this area for so many centuries, the term Babylonia has come to refer to the entire culture that developed in the area from the time it was first settled, about 4000 BCE. Before Babylon’s rise to political prominence (c. 1850 BCE), however, the area was divided into two countries: Sumer in the southeast and Akkad in the northwest. (Britannica: Babylonia)
There is a conclusion amongst some that a representation of the "three" (or 3 to 1) is the apex of some development... that is until the 1-2-3 sequence begins anew, similar to our usage of a comma before beginning a new set-of-three in our numerical value system (ones/tens/hunreds)[comma] (thousands/ten-thousands/hundred-thousands). For example, the so-named Trilobites, Trichomonads, and Trichonodonta are extinct— having no doubt... or at least suggestively... along a one-two-three evolutionary pathway, just as it appears (in one mode of thinking) is the case for all Monoploblastic examples of development (except for perhaps the sponges). In other words, development proceeds to a "three" reference which could well involve the 3 digit fingers + 2 digit thumbs for each single hand and foot that are customarily counted together to give us a three-part "five", "ten" or "twenty" reference. In such a case as the Monoploblastic situation, one must ask if this is a tell-tale indication that the Diploplastic condition will also meet with such a fate of extinction, requiring a new developmental set-of-three? Similarly, because we can see a numerically identifiable "code of structure" with respect to the social organization of early cultures which reached a usage of a "4" (three to one ratio) that was followed by a three-part social structure defined by the Hammurubi codes of law and that subsequent cultures alternatively adopted a usage of one, two, or three class-systems; one must wonder if there is not an underlying mental, biological, anatomical (etc.) scaffolding or blueprint being used... and why this is being used as well as what cause its development... and if this refers to something we need to be conscerned with... or at least make widely known in our public conversations?
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Frequency distribution of word order in languages surveyed by Russell S. Tomlin in 1980s Subject- Object- Verb | ||||||||||||||||||||||||||||||||||||||||||
 The Typology of the World Order of Languages | ||||||||||||||||||||||||||||||||||||||||||
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Another perspective of the "trinity" (as a pattern-of-three not confined to religion) is found in Music Theory whether or not one focuses specifically on Triads in Music, since music frequently involves a usage of numbers related to sounds from a present day perception, and the ancient philosophical abstraction called Music of the Spheres or Musica universalis. Another comparison can be made with genetics, since it involves using numerical references when speaking about basic processes. And to mention but one more example (bringing the total to a 3-to-1 expression), let us include a reference to audiology since it involves language and grammer, both of which are used in the aforementioned examples.  |
However, let us not forget to mention and take into consideration (as an ideological contrast), the much older idea involving a "two" pattern articulated by the Yin and Yang philosophy. While some in the present add a third word called "unity", and there is a Westren (English Language) inclination to reference the Bagua or Pa Kua as a "trigram" because of a three-line format, it is of need to dispel such a notion and suggest that the so-called "trigrams" are actually a more primitive "bigrams" mental expression. While the lines are displayed in a triple format, a more fundamental "count" revels the three rows disply only two types of lines... a short and a long one. Hence, while some are focused on a "three" pattern, it actually is a two-patterned configuration displayed in a three-level way, like an incomplete metamorphosis that provides evidence for a transtion to a third realization, but never actually reaches it. additionally, whereas the "eight" quantity of the Bigrams may appear to be short of a "perfect nine" (3 X 3) count, the eight count is applicable to an 8 X 8 (64) count seen in genetics with respect to an amino acid chart. Whereas we can see a type of reversal or mirror-image portrayal with respect to the 3' and 5' configuration related to the strands in DNA and RNA, this observation has some comparative relevancy to the Bigrams (and Monograms) of the Bagua because both are referenced as fundamental illustrations related to life, as well as being viewed as models that can be applied to technology... such as the binary formula (ASCII codes) used in computers that must be assisted by an application of a triple-based boolean logic applied to electronic circuitry which are typically described as AND, NOT, OR, but could be substituted using the letters A, B, C, or the numbers 1, 2, 3... or any se-of-three so long as one keeps the analogies coherent and consistent from one application to another... unless one wants to create something unexpected by a serendiptious application of jumbling different values and applications.
In other words, in making comparisons of different binary systems, one might include the following simplified examples:
- The dual Yin/Yang philosophy coupled to a "short and long" lines within the context of a so-called eight "trigrams" profile found in the I-Ching. (8 X 8 = 64)
- The paired groupings of four compounds (Adenine- Thymine, Guanine- Cytosine) into a triad (or trinity) (called a triplet code) which create amino acids that different proteins arise from chains thereof. The triplet code references of DNA and RNA (due to their differences of Thymine and Uracil), can be viewed as a 3-to-1 ratio. DNA has been referred to as the "medium" by which an internalized message is encapsulated. (Let us say like a message in a three-shaped bottle.) [Using a triplet code arives at a 64 amino acid complement.]
- The dots and dashes of the Morse Code involving a third segment called "the silence of a pause": The duration of a dash is three times the duration of a dot. Each dot or dash is followed by a short silence, equal to the dot duration.
- Braille is a Binary system of dots set on two rows of three.
- The Binary code used in computers uses a space for every grouping of eight bits (of 0's and 1.s), though the two-pattern ensemble could be represented by other symbol references. If a space isn't used, the "zero" or a pause of some other sort can be utilized.
- Another type of binary code associated with a triadic structure is that seen in the aformentioned musical triads with Major and Minor scales as a duality and the Augmented/Diminished as a complement. Then again from another perspective we could pair Major and Augmented to the Minor and Diminshed forms.
Page initially created: Friday, 17th August 2018... 4:36 AM
Page initially posted: Thursday, 13th September 2018... 8:33 AM
Updated posting: Thursday, 20th September 2018... 8:07 AM
Herb O. Buckland
herbobuckland@hotmail.com