Threesology Research Journal
The Devil's Advocate and 3's Research
~ page 14A ~
~ The Study of Threes ~

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Devil's Advocate Series:
1 2 3 4 5 6 7 8 9
10 11 12 13 14A
15 16 17 18
19 20 21 22A
23 24 25 26 27
28 29 30 A 30 B 31 32 33a 33b 33c
34 35 36 37 38 39 40 41 A 41 B

Please note that while this page is focused on providing examples of the "2-3-4" formula of patterns-of-three, there are other "unconventional" sequences that can provide separate listings such as the 32- + 42- + 52- + of the Pythagorean theorem; or the ABC of alphabet teaching; or the XYZ of co-ordinate graphing layouts; or a bi-symmetrical exposition to produced six (as in insect legs), or the two eyes, two antenna, two front legs/ hands combined with 3 pairs of legs; or the dash- space- dot of Morse code; or the usage of a three-part Boolean logic used to "embellish" the dichotomy of zeros and ones for computing based on the on/off switching of an electrical circuit; or the many other varieties of three-patterned ensembles that come to overlooked because a person in seeking some specifically desired sequence of sequenced sequences which may or may not involve periodic substitutions, delays, distractions, digressions, intermittancies, overlays, subdivision, exclusion, inclusion periodicity in a short, medium or long term appearance, operation, structure, etc...

Examples of the {2-3-4} pattern-of-three model

2, 3, anf 4 of a kind poker hands 2, 3, 4  muscle origins

(card and muscle images added to page: 4/21/2020; 3:25 AM)

Entry for VSEPR image: March 26th, 2023

Electron pair arrangements yielding a 2, 3, 4 configuration

2, 3, 4-bladed boomerangs
(boomerang examples added to page: 10/13/2021)

Here is one example of a 2-3-4 pattern that many of us has seen but not compartmentalized into a list with other examples of the same pattern. I place it here as an add-on at this date: 6/6/2020, because it is another example of a common idea that I previously overlooked when first compiling examples for this page.

2, 3, and 4-wheeled off-road vehicles

Whereas many of us readily accept complexity as an "emergent property" exhibited by some simple configurations, we don't readily accept such a sequence to occur outside the formula we become accustomed to. It "throws us for a loop" so-to-speak when we encounter some pattern which we think is incongruous instead of altering our initial design which allows for what may at first appear to be some disparity. We want the observed patterns to fit our mental schemas instead of the other way around. Our brains sometimes works like a conveyor belt system that churns our mental products in a given way and given time, and think it odd or that something is wrong if the product or time of production becomes altered. We get used to a time schedule and product quantity as well as quality to be produced, and think it is somehow "disturbed" if the process is altered "to the beat of a different drummer"... unless a person is allowed to walk, skip, crawl, dance, march, etc. to the beat of a different drummer because those in their social purview make allowance for it.

An example of the 2-3-4 grouping can be found in the form of deaths of family members occurring on (usually small) aircraft. Whereas it is reported that 4 generations of family members died or 3 generations of family members died in an aircraft crash, there typically is no comparable numerical "2" generations reference. Instead, for example, reports may speak of a mother and daughter or father and son. I have not come across anyone making mention of 5 generations of a family dying nor referencing a single person as a "1" generation loss. Whereas a 2-3-4 pattern can be identified, a strict requirement for its presence with a standard format will not reveal it. (Entry: 7:32 AM, Arizona time, 11/2/2021, Tuesday)

Another example can be seen in a study of Astrology. While many who are casual readers of their own horoscope may be aware of the 12 Zodiac signs, those who dive below the common recognition and understanding may come across additional patterns such as a 2- 3- 4 ensemble. However, all the patterns may not be compared with other subjects as part of a project at listing basic patterns of ideas in order to establish a working blueprint of human cognitive activity over time and contexts. If one deals merely with cataloguing ideas without subjecting them to a further analysis intent on describing some number (quantity) related association, words alone might keep one from listing ideas other than as emotional content or literary content or musical content, etc., all of which enable multiple interpretations to be derived if one so chooses not to engage in anything more definitive than word-related generalities. The Zodiac, at least from the following account, describes a 2- 3- 4 ensemble. This paragraph and image are added at 4:03 AM, 8/31/2022:

2, 3, 4 ensemble pattern in Astrology

Does the 2-3-4 pattern (like others), portray a sequence of developmental organization of what actually exists within that being observed, or is it a projection of human mentality seeking some metaphor for representing a recurring internalized cognitive pattern that symbolically recreates a physiological characterization that may be a selectively-oriented (and) biologically-directed manifestation of an environmental influence that can.... at times, be reflected in a mirror-image portrayal which is opposite to a perceived reality; that is, in "opposition" (a reversed order and not necessarily in a combative sense... but perhaps seemingly in a bi-symmetrical sense with our observation thereof as a third point of reference) to that being proposed? Like the property of vision which flip-flops images on the back of the brain (visual cortex) and which may account for the recurring "flip-flopping" of ideas such as instead of the Sun revolving around the Earth, this (two-patterned) idea was flip-flopped to illustrate a reality where the Earth rotates around the Sun.

Flip flopped vision related to flip flopped ideas

Whereas we humans egotistically want to think that our brain is this magically marvelous erudite computing device that does so many wonderful things, we are not inclined to think that it was developed with flaws despite the acknowledgement that it grows and develops and accommodates itself to whatever conditions prevail. Instead of thinking that the brain is born in a well state, perhaps we should flip-flop this consideration and think that it is developed in a sick, diseased, misaligned, mistaken, etc... state of development and must be cured through experience... which typically involves some formal and/or informal education.

Another example of flip-flopping is the notion of phlogiston upon the discovery of oxygen:

(Phlogiston) in early chemical theory, (was a) hypothetical principle of fire, of which every combustible substance was in part composed. In this view, the phenomena of burning, now called oxidation, was caused by the liberation of phlogiston, with the dephlogisticated substance left as an ash or residue.

Johann Joachim Becher in 1669 set forth his view that substances contained three kinds of earth, which he called:

  1. the vitrifiable
  2. the mercurial
  3. the combustible

He supposed that, when a substance burned, combustible earth (Latin terra pinguis, meaning "fat earth") was liberated. Thus, wood was a combination of phlogiston and wood ashes. To this hypothetical substance Georg Ernst Stahl, at about the beginning of the 18th century, applied the name phlogiston (from Greek, meaning "burned"). Stahl believed that the corrosion of metals in air (e.g., the rusting of iron) was also a form of combustion, so that when a metal was converted to its calx, or metallic ash (its oxide, in modern terms), phlogiston was lost. Therefore, metals were composed of calx and phlogiston. The function of air was merely to carry away the liberated phlogiston.

The major objection to the theory, that the ash of organic substances weighed less than the original while the calx was heavier than the metal, was of little significance to Stahl, who thought of phlogiston as an immaterial "principle" rather than as an actual substance. As chemistry advanced, phlogiston was considered a true substance, and much effort was expended in accounting for the weight changes observed. When hydrogen, very light in weight and extremely flammable, was discovered, some thought it was pure phlogiston.

The phlogiston theory was discredited by Antoine Lavoisier between 1770 and 1790. He studied the gain or loss of weight when tin, lead, phosphorus, and sulfur underwent reactions of oxidation or reduction (deoxidation); and he showed that the newly discovered element oxygen was always involved. Although a number of chemists—notably Joseph Priestley, one of the discoverers of oxygen—tried to retain some form of the phlogiston theory, by 1800 practically every chemist recognized the correctness of Lavoisier's oxygen theory. "phlogiston." Encyclopædia Britannica Ultimate Reference Suite, 2013.

Another example of "flip-flopping" (though some readers may prefer to use a word such as "substitution" instead), was the miasma (bad air) theory verses germ theory:

Broad Street pump and the "Grand Experiment."

Many British physicians investigated the epidemiology of cholera.

  1. The first cholera epidemic in London occurred in 1831–32, when (John) Snow was still learning his craft.
  2. When the second cholera epidemic occurred, in 1848–49, he and others founded the London Epidemiological Society, intending to advise the government on ways to combat the disease.

Snow reasoned that cholera was caused by a microbe-like agent, or germ, that was spread through direct fecal contact, contaminated water, and soiled clothing. However, his theory was at odds with the then prevailing theory that cholera was spread by bad air, or miasma, arising from decayed organic matter. The two etiologic hypotheses—germ theory and miasma—were widely debated, with available clinical and population-based evidence serving as the basis for arguments from both sides. The etiologic debate raged for many years. It was not until the causative organism, Vibrio cholerae (initially discovered in 1854), was well characterized in the 1880s that the debate was decided in favour of germ theory.

  1. Snow's respected reputation in epidemiology arose from two classic studies of the third epidemic to reach England, which began in 1853 and lasted until 1855.

The first study concerned the Broad Street pump outbreak of 1854, which killed many persons in the Soho neighbourhood. He used skilled reasoning, graphs, and maps to demonstrate the impact of the contaminated water coming from the Broad Street pump. The second study was the "Grand Experiment," also of 1854, which compared London neighbourhoods receiving water from two different companies. One company relied on inlets coming from the upper River Thames, located away from urban pollution, and the other company relied on inlets in the heart of London, where the contamination of water with sewage was common. Snow showed the harmful effect of contaminated water in two nearly equivalent populations, and he suggested intervention strategies to control the epidemic. His ideas and observations, including innovative disease maps, were published in his book On the Mode of Communication of Cholera (1855). Later, in the 1930s, Snow's work was republished as a classic work in epidemiology, resulting in lasting recognition of his work. ("Snow, John." Encyclopædia Britannica, 2013.)

Ralph Frerichs: Professor in the Department of Epidemiology at University of California, Los Angeles.

John Snow and removal of the pump handle

A third example of "flip-flopping" can be seen in the idea of the Heisenberg uncertainty principle. It is particularly easy to note that if the uncertainty principle is a certainty, then it can not be an uncertainty principle, unless we are to conclude the human mind engages in routinization of conveying reality in a dichotomous (flip-flopping) articulation where we say one thing but view another, sometimes called "double-speak" in politics and "legal doubles" in the legal profession... as if the human mind is stuttering and/or babbling. If the Uncertainty Principle is a Certainty, then the following definition needs to be flip-flopped to indicate that the concepts of exact position and exact velocity (together or apart) do have meaning in nature. It is merely our human flip-flopping faultiness which inclines us to see the world upside down, inside/out, right versus left (such as in the different directions of writing)... so-to-speak. The idea that humans once thought the world was flat as opposed to round is yet another variation on this theme, as well as the other multiple other dichotomies, with or without a third entity taking place is perhaps a more encompassing articulation of this overall idea.

The (Uncertainty Principle) statement, articulated (1927) by the German physicist Werner Heisenberg, that the position and the velocity of an object cannot both be measured exactly, at the same time, even in theory. The very concepts of exact position and exact velocity together, in fact, have no meaning in nature.

"uncertainty principle." Encyclopædia Britannica, 2013.

Yet another example of flip-flopping came to mind after being reminded of the water torture used in Medieval Europe with respect to a psychotic reverence to the Devil, by way of the testing of individuals who were claimed by one or another religious authority to be possessed by or in league with Satan. Ironically, instead of what is presumed to be barbaric and illogical methods of torture being used to determine guilt or innocence, the people of today are thought to be subjected to a legal process that is more humane and just, as words which replace the old religious terms of being righteous. Unfortunately, the financial, social and personal (psychological/emotional) costs are akin to a modern day form of torture resembling a gauntlet one must navigate safely through while being subjected to the sometimes horrific barrage of accusations, suppositions and innuendoes thrust at them by the various forms of media in use. Let us take a look at the topic of torture to see how the views of humanity have "flip-flopped" from the religious to the secular in an effort to bring about a condition of truth, though the supposed secular (non-religious) perspective still remains alive and well below the surface of accusation and outcome, otherwise there would be no need to swear on a bible and say (3 times! like a magical, mystical incantation) that they will affirm to Tell the truth- Whole Truth- Nothing but the Truth... so help them god... The news media very often plays the part of a vociferous bloodthirsty audience (or antagonist against authority) at a medieval inquisition, "trial" or execution.

(Torture refers to) the infliction of severe physical or mental pain or suffering for a purpose, such as extracting information, coercing a confession, or inflicting punishment. It is normally committed by a public official or other person exercising comparable power and authority. Although the effectiveness of torture has been defended by many throughout history, notably Aristotle and Sir Francis Bacon, it was attacked as early as Roman times for encouraging its victims to lie.

In ancient Greece and Rome, physical torture was lawfully used, usually on non-citizens or slaves, as a means of obtaining information or confessions. Later, in early medieval Europe, torture was used as the trial itself in the ordeal, wherein the suspect's response to extreme physical pain served as the basis for establishing guilt or innocence. In the later Middle Ages, torture was again used to secure confessions in cases of serious crime (confession was known by the term “the queen of proofs”), though it was nominally subject to strict conditions. ("torture." Encyclopædia Britannica, 2013.)

(An ordeal is) a trial or judgment of the truth of some claim or accusation by various means based on the belief that the outcome will reflect the judgment of supernatural powers and that these powers will ensure the triumph of right. Although fatal consequences often attend an ordeal, its purpose is not punitive.

(H.O.B. note: imagine people thinking torture... because it is labeled "ordeal" or in the context of an authoritatively designed activity seeking some supposed valuation described as "truth", is not itself a type of incarceration which consequentially is punitive, but is claimed to be otherwise, by those who do not have to be subjected to it, and everyone is thought to somehow have the same sensibilities!)

The main types of ordeal are ordeals by:

  1. Divination: A Burmese ordeal by divination involves two parties being furnished with candles of equal size and lighted simultaneously; the owner of the candle that outlasts the other is adjudged to have won his cause. Another form of ordeal by divination is the appeal to the corpse for the discovery of its murderer. The ordeal of the bier in medieval Europe was founded on the belief that a sympathetic action of the blood causes it to flow at the touch or nearness of the murderer.
  2. Physical test: The ordeal by physical test, particularly by fire or water, is the most common. In Hindu codes a wife may be required to pass through fire to prove her fidelity to a jealous husband; traces of burning would be regarded as proof of guilt. The practice of dunking suspected witches was based on the notion that water, as the medium of baptism, would “accept,” or receive, the innocent and “reject,” or buoy, the guilty. (H.O.B. note: In other words, if a person drowned then they were found to be innocent, but if they survived they were guilty and subject to execution.))
  3. Battle: In ordeal by combat, or ritual combat, the victor is said to win not by his own strength but because supernatural powers have intervened on the side of the right, as in the duel in the European Middle Ages in which the “judgment of God” was thought to determine the winner. If still alive after the combat, the loser might be hanged or burned for a criminal offense or have a hand cut off and property confiscated in civil actions.

Source: "ordeal." Encyclopædia Britannica, 2013.

Inserted: 4/16/2021, Friday: A 2-3-4 pattern arises when we follow the succession of square roots. We find √4 = 2, √9 = 3, √16 = 4... the progression continues, but the first three "rational squares" result in the 2-3-4 pattern. The others are irrational.

Inserted: 5/26/2021: a 234 ensemble related to atomic Nuclei:

2, 3, 4, atomic nuclei ensemble

In giving an account of the "2-3-4" ensemble of a three-pattern example, it was not until I reached page 24 in this series did I realize that the double, triple and quadruple systems of accounting needs to be included. In other words, I didn't think of it until I was working on some other task in the series. Whereas the double-entry formula of accounting deals with the personalized commercial end of the profit and loss dichotomy which superseded the singular accounting method of one's personal holdings (and not typically an account of one's losses whose tabulation was conventionally kept in one's mental ledger and not "on the books" so-to-speak, a triple-entry model of accounting keeps track of external parties transactions to oneself, so as to have identical accounts), though it should be noted that several different interpretations of triple-accoutring are available and may be termed "triple book" accounting, which can "creatively adjust" the definition just like "creative accounting" methods are sometimes used to circumvent tax laws. A quadruple-entry accounting system often involves a basically contrived interaction between two or more agencies or departments who may service a third party, such as separate government agencies or inter-departmental activities of intentionally "complexified bureaucracies" providing one or more direct services to a citizen or publicly-private citizen-entity or to a person or entity that is doing the servicing to citizens. In other words, "guadruplification" of typical double-entry systems becomes interactively compounded to give the impression of exceeding a double-entry system where in fact the double is being replicated or "reduplicated" (like that seen in infant babbling).

At this (interjected) moment (1:52 AM, 11/6/2019, Wednesday), I am currently on page 37 in this series. A couple of days ago I took apart a mountain bike that was purchased at a Goodwill store for $39.95, in order to re-grease the bearings. This morning as I lay in bed I was recounting the re-grease job to a proposed email to my brother Charlie who is an avid cyclist. As I went over the scenario I realized I had greased the wheel bearings, the crank bearings and the fork bearings. A further contemplation on this "three", evoked the realization that there were two sets of bearings for these three different areas and that overall I re-greased two sets of wheel bearings, one set of crank bearings and one set of fork bearings. Hence, we have 2 bearings for 3 items totaling 4 overall areas. Thus, I encountered another 2-3-4 sequence.

While working on the "Embellished Dichotomies" pages at this date: 12/15/2019, I was reminded of the Duplex- Triplex- Fourplex housing arrangements.

As is often the case in my encounters with the "two", it is like a primitive person whose mind is conscious of the possibility of exceeding itself in complexity, but does not have the actual evolutionary established developmental criteria in their brain structure for the transition to take form (or is exhibiting a moment in time where evolution is caused to make a detour by returning to an earlier stage of development... a sort of retreat to catch one's breath and regroup... because our biology is designed as a tactic of survival, though other tactics no doubt may exist); whereby various types of substitutions are created to give the impression that a development beyond the "two" has been achieved, like labeling and illustrating a system of a thought as a "trigram" but it is merely an extension of a bigram, whereby a "two" is repeated and placed into a third position, but it is not an actual third symbol to reference the presence of an evolutionary step into a third realm of developmental achievement... even though one may be particularly aware that a transition of where they presently are is undergoing a developmental change into something other than where their mind presently is (perhaps seen as a shadow, flicker, whisper, sensation, scent, the "something there" phenomena, as an skewed corner-eye phenomena, pause, intermittence, vagrant aperture, mirrored reflections of mirrored reflections, etc...). Foreshortened, Trigrams are actually Bigrams in disguise. The human mind is using a camouflaging technique to give itself the impression of being that which it is not... like the raven in Edgar Allen Poe's poem:

In there stepped a stately Raven of the saintly days of yore;
Not the least obeisance made he; not a minute stopped or stayed he;
but, with mien of lord or lady, perched above my chamber door—
Perched upon a bust of Pallas just above my chamber door—
Perched, and sat, and nothing more.

Pallas, ancient Greek god of War and Warcraft Note: although you might find the word "Pallas" denoting a reference the ancient Greek goddess Athena, it also references the ancient Greek Titan (a second generation deity) who was the god of battle and warcraft featured in statues with a spear. By way of being guilty by association, so-to-speak, the word pallas also denotes brandishing a spear, which is a symbol of the male penis that can be further linked to ancient customs of phallic worship and is said to be designed like a penis, just as are swords with a hilt. Primitive brains had peculiar-to-us interpretations of nature and the human place within the world where there often-times existed multiple gods, multiple demons... mixed with disease, malnutrition, lousy water and sewage, homelessness, widespread ignorance, greedy business people engaging in monopolies, self-serving medical professionals, unhygienic practices, war-mongering entities, double-standardly crooked politicians, superstitions, multiple medical issues, various cults, exploitive religious leaders and entities exploiting people by way of the knowledge gained from different models of confession, racism, discrimination, inequality, etc... Hmmm, sounds just like today. I must have taken a trip back in time to a very primitive past that keeps repeating itself because established institutions are "two-focused" and try to conceal this by trying to appear to be "three-focused" when those in the system do not have the brain development to step forward into an actual third formula of consciousness whatever this may mean in terms of a functional social order of humanity.

And as part of the above digression from the topic of the 2-3-4 ensemble, with respect to the state of humanity, let me include a poem I jotted down after it "popped" into mind and woke me up at 12:46 yesterday evening:

It is a well known fact
yet I need to remind
diseases often come back-to-back,
just as nature designed.

Thus it should be no surprise
to see waned diseases on the wax
tis one of Global Warming's facts,
more diseases like (Donald) Trump will arise.

Both singularly and in groups
in isolated scourges and pandemics
sported by religious militant troupes,
or the military's many-styled fanatics.

The LGBTQ is an example no doubt
as is the anti-vaxers campaign
but let's not leave business out,
with its rooted evil to disdain.

More pain and suffering are to come
since global warming is not done
social diseases linked to population growth,
as Charon begins singing in his boat.

Let me interject two examples of the 2-3-4 ensemble which appeared to me this morning 5 Jan 2020 as I lay in bed and fought myself to get up to venture into the cold room. After which having decided to get up for good, I noticed the time as 1:58 AM. The two examples are:

  • I noticed that shaving razors come packaged as having 2 blades, 3 blades and 4-bladed versions. While I am aware of the straight razor still used by some barbers and the single blades used by my father and grandfather, these are not conventional items to be purchased in most stores. And while there may be versions with more than the 2- or 3- or 4 variants, I have not come across them.
  • The riddle of the Sphinx: What is the creature that walks on four legs in the morning, two legs at noon and three in the evening? The answer is that a child crawls on four limbs, later on the child matures and walks on two legs, followed by old age in which the person uses a cane. Hence, we have a 4- 2- 3 representation.

While working this morning: 5 Jan 2020 on the "A New Communism" pages, I came across a Britannica reference dealing with a biblical verse suggesting a simple type of Communism. The Verse comes from Acts 4:23. I then altered the numbers and made references to them as well, from Acts. The entries come from this site: Bible hub

  • Acts 4:32- All the believers were one in heart and mind. No one claimed that any of their possessions was their own, but they shared everything they had.
  • Acts 4:23- On their release, Peter and John went back to their own people and reported all that the chief priests and the elders had said to them.
  • Acts 3:42- (doesn't exist)
  • Acts 3:24- Indeed, beginning with Samuel, all the prophets who have spoken have foretold these days.
  • Acts 2:34- For David did not ascend to heaven, and yet he said, The Lord said to my Lord: Sit at my right hand.
  • Acts 2:43- Everyone was filled with awe at the many wonders and signs performed by the apostles.

It would be interesting to see what narrative could be unraveled by looking at the other parts of the bible in this regard.

I now interject another 2-3-4 ensemble example (3:57 AM, 11/9/2020), though I had thought of it years before. It was not until I was sitting near three bananas set into a bowl that the recall occurred. It appears that many people typically peel a banana with three peels, while others "flower" the fruit by peeling back four "petals" of the skin. However, on some occasions I have encountered a two-peel variation. Only if extremely ripe have I found that a banana peels back in several (more than four) "slices" of the skin. And while it is readily easy to find images of three and four-peel variations, I could not find a two-peel example. I had to buy a small bunch of bananas and peel them one at a time on separate days. It was the third banana (no I am not kidding) that gave me such an example. And no, I did not intentionally strive to create such a version. I actually wasn't expecting to get one since memory told me that previous examples came when I attempted to peel a rather green one. Let me also include that many of us might well describe the state of a banana's ripening as from a green stage to a yellow stage and then to a brown or black stage, though variations of the brown and black might well be included such as by pointing out brown spots or speckles, unless the fruit itself is brought to bear in the examination... such as from hard to soft to mushy.

3 general banana variations

Banana with two peels image 1 Banana with two peels image 2 Banana with two peels image 3 Banana with two peels image 4
Banana with three  peels image 1 Banana with three  peels image 2 Banana with four peels 4 peels banana

Here are two more examples of the "234" ensemble: (Date: March 18th, 2021, 1:53 PM. I came across them yesterday while researching material for the upcoming paper "Infinitesimal versus Accordian Calculus".)

What a tangled web we weave... so goes the saying when compounding more and more to more and more and then some.

Look at how enumeration can take on a geometric form

Origination date (of page heading: Friday, September 6th, 2019... 3:54 AM
Initial Posting: Saturday, September 7th, 2019... 12:47PM
Latest Updated Posting: Wednesday, August 31st, 2022... 4:35 AM
This section split into two pages at: 7:56 AM, 2/11/21, Thursday
Updated Posting:Tuesday, March 28th, 2023... 11:26 AM

Your Questions, Comments or Additional Information are welcomed:
Herb O. Buckland