Threesology Research Journal
Threes Poster Column 3

(The Study of Threes)

BTR emblem Buckland's Third Revolution Poster,
3rd column
BTR emblem

~ The Study of Threes ~

3 Types of Languages (Isadore of Seville, 7th Century A.D.):

(1) All the Oriental nations jam tongue and words together in the throat, like Hebrews and Syrians.
(2) All the Mediterranean peoples push their enunciation forward to the palate, like the Greeks and the Asians.
(3) All the Occidentals break their words on the teeth, like the Italians and Spaniards.

3 rulers are noted for carrying out experiments (by isolating children from all spoken language influences) to determine which language would be spoken first, and hence, identify the first language:

1. Egyptian Pharaoh Psammetichus (664 - 610 B.C.)
2. James IV of Scotland (A.D.1473 - 1513)
3. Roman Emperor Fredrick II of Hohenstaufen (A.D. 1200's).


The "Three Languages" story occurring in Fairy tales is said to be very old and exist in various versions in different cultures.

3 allophone (phonemic derivative) environments:

(1) At the end of a word (only oral vowels; no nasal vowels)
(2) Before nasal consonants (only nasalized vowels; no oral vowels)
(3) Before nonnasal consonants (only oral vowels; no nasalized vowels)

3 types of alphabet in use characterized by 3 different methods of indicating vowels:

1. Greek, Latin, and so on - vowels indicated by separate signs
2. Aramaic, Hebrew - Arabic, and so on - vowels indicated by separate diacritic marks
3. Ethiopic, Indic - vowels indicated by diacritic marks attached to the sign or, very rarely, by internal modification.

3 subtle parts to one expression by the historian Francis Parkman (1823-1893):

(1) He who would do some great things in this short life must apply himself to work with such a concentration of force as,
(2) to idle spectators who live only to amuse themselves,
(3) looks like insanity.

3 subtle parts to analogy: Back to the Crib & Bottle though you call it Bar & Booze, get Drunk so you can Toddle and the unknowing will excuse.

3-part emphasis by Samuel Taylor Coleridge: I believe that the process of thought might be carried on independent and apart from spoken or written language. I do not in the least doubt that if language had been denied or withheld from man, thought would have been a process more simple, more easy, and more perfect than at present.

3-part expressions:
Cool- Calm- Collected;

Lean- Mean- Fighting Machine;

Oh-My-God! (or Gosh!);
(Between you- me- and the fence post);
(1st the worst- 2nd the same- Last the best of all the game);

(Those who can, do - Those who can't, teach - Those who can't teach, teach teachers);
Past the lips- Through the gums- Look out stomach cause here it comes);
Love- Honor- Obey (weddings),
(A minute in your mouth- An hour in your stomach- A lifetime on your hips);
Beg- Borrow- Steal;
Men- Women- Children;
Bell- Book- Candle;
Ready- Willing- Able;
Blood- Sweat- Tears;
Fat- Dumb- Happy;
Hither- Thither- Yon;
Hook- Line- Sinker;
Hop- Skip- Jump;
Lock- Stock- Barrel;
Me- Myself- I;
Jeepers- Creepers- Where did you get those Peepers;
By Jiminy- Jingo- Gee;
Ninety-Days Wonder;
Butter-Bar Lieutenant;
Dog-Day Afternoon;
Preserve- Protect- Defend (Presidential Oath);
Turn on- Tune in- Drop out (Timothy Leary);
Duty Before Pleasure (Work Before Play);
Age Breeds Aches;
Seeing Is Believing;
Art Imitates Nature;
Hang In There;
Keep On Truckin';
Borrowing Brings Sorrowing;
Walls Have Ears;
Never Say Never;
Never Give Up (In);
Never Say Die;
Forewarned Is Forearmed;
Vipers Breed Vipers;
Keep the Faith;
See You Later;
I Love You;
In The Beginning...;
Be A Man;
Get A Job;
Count Me In/Out;
So Be It;
It Is Done;
Wanna Get Lucky?;
No Retreat- No Surrender- No Hostages;
Go for it,

*** Note: The predominant world view of criminals is a pattern-of-two. They see the world as Black/White, Right/Wrong, Good/Bad, Good/Evil, Win/Lose, Convict/Cop, etc... In the prison environment is the division of Convict/Inmate. Inmates will involve themselves in programs while Convicts won't participate in the "system." We encourage this grouping-into-twos perspective by forcing many prisoners to sleep in two-man cells though there are three overall sleeping arrangements: One man cell - Two man cell - Dormitory style (open bay). There is no middle ground for the criminal. No Win-Win alternative. They see only a Win/Lose or Lose/Lose situation. There is no gray area, no compromise, no middle, only extremes. For those of you who need to be slapped in the face in order to recognize the hysterical ludicrous idiocy occurring with our Education system ideology, Political social self-governance philosophy and our pathetic prison/youth "correction" rehabilitative measures , let me also step on your toe and punch you in the stomach:

If a child, for whatever reason (poverty, abuse, malnutrition, retardation, etc...) has a predominant world-view that is 2-patterned oriented and is required to do class work/homework and participate in a class/home/job whose teacher/parent/boss is (for the most part) unaware of their own 3-patterned preferences because (as will be seen in the following examples) a pattern-of-three is an inherent structure of the material being taught, there will be CONFLICT expressed in a variety of ways such as delinquency, criminality, pregnancy, suicide, truancy, etc... And in spite of the notions of 'gangs' (large groups) committing crimes the reality is that most juveniles commit crimes/delinquency in groups of 3, in groups of 2, or alone. Sociologists call these groups Triads, Dyads and the Loner.

(There are typically three number "words" of primitive peoples: One for the quantity 1, Two for the quantity 2, Many for any quantity beyond two. When a person has had too much alcohol to drink, we say they had one too many. The sleeping arrangements of prisoners are: One man cell - Two man cell - Many men 'cell.' Unfortunately, most of those who will read this page will not be conscious of the correlation just made, much less recognize the sociological implications of the intoned linguistic paradigm.)

Table 2.4 Examples of imposed recall structures. Most frequent grouping for each class with frequency given in parentheses. (From Wilkes, A.L., P and Simpson, I., Quarterly Journal of Experimental Psychology, 24, 48-54.)

Doublet Triplet Quartet Other
5 Adult (9) 2:3(5) 3:2(6) -  
10 (5) 2:3(10) 3:2(5)    
8 (6) 2:3(9) 3:2(5) - -
6 Adult (4) 2:4(4) 3:3(9) 4:2(3)  
10 (2) 2:2:2(2) 3:3(12) 4:2(3) -
8 (1) 2:4(4) 3:3(10) 4:2(2)  
7 Adult (3) 2:5(2) 3:4(5) 4:3(3) 5:2(3)
10 - 2:2:3(1)
3:2:2(6) 4:3(5) 5:2(3)
8 - 2:2:3(6) 3:4(7) 4:3(2) -
8 Adult (1) 2:2:2:2(3) 3:3:2(3) 4:4(4) 6:2(1)
10 - 2:3:3(5) 3:3:2(4)
4:4(2) 5:3(1)
8 - 2:2:4(2)
3:3:2(3) 4:2:2(5) 5:3(1)
Percent incidence
of group structure
All lists and Subjects
Adult 29.0 46.8 17.7 6.4
10 yrs 30.1 49.3 15.0 5.4
8 yrs 41.1 39.7 17.8 1.3

In a further study a partial replication was carried out using random samples of children of 10 and 8 years. Each child started with a consonant list of three items which was read and recalled to the usual criterion. Thereafter list lengths of four, five, six, seven and eight consonants were tackled in ascending order, the list at all lengths being randomly chosen for each subject. Tape recordings of the criterion reading and recall trials for each list were pause analyzed and imposed groupings identified from the presence of inflection pauses. There were 20 subjects at each age level with equal numbers of male and female children. As with the adult subjects the classification of imposed structure is based upon the size of the first-imposed group and included in Table 2.4 are the mast popular groupings observed during the recall at these age levels. The numbers in parentheses refer to the number of subjects choosing a given structure.

Taking adult performance over list length as a reference point a triplet preference is clearly shown. For all list lengths except list 8, the most frequent adult pattern is built around an initial triplet grouping. As Ryan (1969) has observed where symmetrical grouping is possible this tends to be preferred, serving to emphasize a 3:3 grouping for list 6 and to attenuate a 3:3:2 grouping for list B. If grouping type is expressed as a percentage of all grouping occurrences then strict comparisons are only possible for the doublet and triplet types since list 5 could be divided as 2:3 or 3:2 but not as 4:1 given the dependence on an inflection pause measure for identifying group boundaries. It follows that the incidence of doublet and triplet groupings can be meaningfully compared over list lengths but not groupings in excess of three items. For adults the incidence of doublet structures was 29 percent and, of triplet, 46.8 percent.

For the 8-year-old sample no predominance of triplet groupings was found, the percent incidences being equivalent, 41.1 and 39.7 percent. In the 10-year-old sample the distribution was close to the adult form, 30.1 and 49.3 percent. The grouping structures given in Table 2.4 apply to recall during criterion trials and it is possible to compare them with the grouping structures imposed during reading. It should be noted, however, that structural alterations from reading to recall can take different forms which need to be distinguished. Suppose for example that list 8 was read as 2:2:4. During recall the grouping pattern could again be 2:2:4 (Duplication), 4:4 (Omission), 2:2:2:2 (Addition) or 3:3:2 (Change). Of these possibilities Omission and Addition retain features of the original structure whereas change need not do so. Of the adults, two subjects introduced a change in their recall of list 5 and four subjects did so for list 8. The 8-year-olds showed a greater tendency to change from reading to recall than the adults but not to the extent found for the 10-year-olds of whom 12 out of 20 changed for the eight-item list. It seems plausible that the age difference is due to a developmental shift in the grouping base-tending to three items for older subjects. The established increase in memory span over this age range would appear to support this interpretation (McLaughlin, 1963).

Wilkes, Lloyd and Simpson (1972) argued that for adult subjects a single repeated rhythm based upon triplet groups was underlying the observed results. Subjects repeatedly imposed groups of three items leaving a terminal group of either two or four items. Assuming Broadbent's estimate of a register capacity to be correct at three items the present results couple the maximum use of that capacity with a single repetitive rhythm. The children's data did not permit a similar conclusion for the repetitive use of a single base but strongly implied a developmental progression in this direction. In general, therefore, the use of inflection pauses to identify spontaneous grouping structures provides an account consistent with other independent descriptions of similar learning tasks.

3 forms of memory: Sensory - Short-term (working) - Long-term
3 forms of long-term memory: Procedural - Semantic - Episodic

*** The foregoing article by A.L. Wilkes from chapter 2 of "Studies in Long Term Memory," 1975, is one of many experiments by researchers who conclude that best memorization results from "chunking" in groups-of-three, (and above normal memory obviously results from using a hierarchal (triangular) structure as opposed to a linear, circular, or non-specific arrangement... for particular types of information.) The recurrent usage of three-patterned chunks by adults and older children is distinct from the usage of two-patterned chunks by some younger children. This two-patterned preference is further elaborated on in the studies of Bruno Bettelheim by his analysis of children and Fairy Tales as is indicated in the following excerpt from his "The Uses of Enchantment" on pages 74 & 75. As a corollary to this let me mention that criminal psychologists have profiled a tendency of criminals to portray a child's perception of the world with adult labels. It has been said that criminals are like two year olds because they harbor an attitude described (in a three-patterned way) as "I want what I want when I want it," which is clearly characteristic of the criminal's typical two-patterned "All or Nothing" approach illustrated by the phrase "I want it all or I want no part of it (but neither ran you if I can't have it").

The three-patterned repetition "I want what I want when I want it" that is used as an imposed description upon two-patterned oriented individuals, serves to camouflage the difference in thinking processes between the criminal and non-criminal. By imposing three-patterned (unconsciously) preferred descriptions on individuals with a two-patterned preferred orientation, such a three-patterned preferred cognitive grouping perspective obscures confirmation of what our common-sense notions about criminals say, namely, that they think differently from non-criminals. It is a necessary distinction that we continually trip over like some branch in a forest that we step on and cause ourselves to stumble, thus distracting us from recognizing that we need to adapt a whole new spectrum of rehabilitation measures based upon a 1-2-3 maturational development sequence. Like-wise, our Educators must become sensitive to the realization that a student may be subtly exhibiting a preference for two-patterned groupings in an academic environment whose instructor and/or subject matter is fundamentally three-patterned organized and necessarily requires the same of the individual.

If an individual's 2-patterned grouping preference persists in such an environment, there is the very real potential risk of conflict, confusion, or criminality if such a student is not offered an effective 2 into 3 transitional-grouping-preference learning skills curriculum attended with an appropriate teaching methodology. For whatever reason, be it poverty, abuse, malnutrition, retardation, etc., we must acknowledge that same students do not make the same "normal" 2 into 3 cognitive-grouping-preference transition as do their peers. (Some are slower while others are accelerated.) Convincingly, this is why mast delinquents turn away from criminal activities while a minority continue to commit offenses through adulthood.

As a final example of the aforementioned "3 imposed on 2" circumstance, another three-patterned perspective prison administrations impose on inmates is the basic security measure of Minimum - Medium - Maximum which indicate a prisoner's level of escape risk. We should acknowledge that at this point in time, society is a little bit late at trying to teach many of these individuals that they live in a world that is becoming all the more increasingly three-patterned oriented, particularly if they have a predominant two-patterned perspective. It is a pattern that most of us, for the most part, grow out of using as the foremost means of orienting ourselves in the world, society, job, family and various other social or non-social circumstances.


To "see both sides" of a problem is the surest way to prevent its complete solution.
Because there are always more than two sides.
-Idries Shad, from his Reflections

By Bruno Bettelheim

Before and well into the Oedipal period (roughly ages three to six or seven), the child's experience of the world is chaotic, but only as seen from an adult point of view, because chaos implies an awareness of this state of affairs. If this "chaotic" fashion of experiencing the world is all one knows, then it is accepted as the way the world is. In the language of the Bible, which expresses the deepest feelings and insights of man, in the beginning the world was "without form." The way to overcome chaos is also told in the Bible: "God divided the light from darkness." During and because of the Oedipal struggles, the outside world comes to hold more meaning for the child and he begins to try to make sense of it. He no longer takes for granted that the confused way he sees the world is the only possible and appropriate one. The manner in which the child can bring some order into his world view is by dividing everything into opposites. In the later Oedipal and post-Oedipal ages, this splitting extends to the child himself. The child, like all of us, is at any moment in a welter of contradictory feelings. But while adults have learned to integrate these, the child is overwhelmed by these ambivalences within himself. He experiences the mixture of love and hate, desire and fear within himself as an incomprehensible chaos. He cannot manage feeling at one and the same moment both good and obedient, yet bad and rebellious, although he is. Since he cannot comprehend intermediate stages of degree and intensity, things are either all light or all darkness. One is either all courage or all fear; the happiest or the most miserable; the most beautiful or the ugliest; the smartest or the dumbest; one either loves or hates, never anything in between. This is also how the fairy tale depicts the world: figures are ferocity incarnate or unselfish benevolence. An animal is either all-devouring or all-helpful. Every figure is essentially one-dimensional, enabling the child to comprehend its actions and reactions easily. Through simple and direct images the fairy story helps the child sort out his complex and ambivalent feelings, so that these begin to fall each one into a separate place, rather than being all one big muddle.

As he listens to the fairy tale, the child gets ideas about how he may create order out of the chaos which is his inner life. The fairy tale suggests not only isolating and separating the disparate and confusing aspects of the child's experience into opposites, but projecting these onto different figures. Even Freud found no better way to help make sense out of the incredible mixture of contradictions which coexist in our mind and inner life than by creating symbols for isolated aspects of the personality. He named these id, ego and superego. If we, as adults, must take recourse to the creation of separate entities to bring some sensible order into the chaos of our inner experiences, haw much greater is the child's need for this! Today adults use such concepts as id, ego, superego and ego-ideal to separate out internal experiences and get a better grasp on what they are all about. Unfortunately, in doing so we have lost something which is inherent in the fairy tale: the realization that these externalizations are fictions, useful only for sorting out and comprehending menial processes. Giving the inner processes separate names-id, ego, superego--made them entities, each with its own propensities.

When we consider the emotional connotations these abstract terms of psychoanalysis have for most people using them, then we begin to see that these abstractions are not all that different from the personifications of the fairy tale. When we speak of the asocial and unreasonable id pushing the weak ego around or the ego doing the superego's bidding, these scientific similes are not much different from the allegories of the fairy tale. In the latter, the poor and weak child is confronted by the powerful witch that knows only its own desires and acts on them, without regard to any consequences. When the meek tailor in the Brothers Grimm's "The Valiant Little Tailor" manages to subdue two huge giants by making them fight each other, is he not acting as the weak ego does when it plays id against superego and, by neutralizing their opposite energies, gains rational control over these irrational forces?

Many errors in understanding how our minds work could be avoided if modern man would at all times remain aware that these abstract concepts are nothing but convenient handles for manipulating ideas which, without such externalization, would be too difficult to comprehend. There is in actuality, of course, no separation between them, just as there is no real separation between mind and body.

When the hero of a fairy tale is the youngest child, or is specifically called "the dummy" or "Simpleton" at the start of the story, this is the fairy tale's rendering of the original debilitated state of the ego as it begins its struggle to cope with the inner world of drives and with the difficult problems which the outer world presents. The id, not unlike how psychoanalysis views it, is frequently depicted in the form of some animal, standing for our animal nature. Fairy tale animals come in two forms...

Note: The above comments about Fairy Tales are from pages 74 - 75 of "The Uses of Enchantment: The meaning and importance of Fairy Tales" ©1975 ISBN 0-394-72265-5.

3 ("powered") "arbitrarily chosen" Electronics math tool: 10-15 10-12 10-9 10-6 10-3 ... 103 106 109 1012 1015 ...etc.

3-patterned formulas:

C = pi x D (Circumference of a Circle) E = H x V (Planck's Constant)
A = L x W (Area of a Rectangle) P = I x E (Watt's "Law")
A = 1/2B x H (Area of a Triangle) E = I x R (Ohm's "Law")
A = pi x R (Area of a Circle) E = V1 + V2 (Kirchhoffs Voltage Law)
E = M x C2 (Einstein's formula) P = R x B (Percentage formulas)
Z = Eg รท Ig (Thevenin impedance formula) A2 + B2 = C2 (Pythagorean theorem)

1,2,3-patterned symbols

*** Thales of Miletus; "Thales Proposition" (Triangles over the diameter of a circle are right-angled), is oldest theory of occidental mathematics. (Think of this in terms of a Triangle/Earth impression.)

3 patterned: 6 zeros (million); 9 zeros (billion);12 zeros (trillion); 15 zeros (quadrillion); 18 zeros (quintillion); 21 zeros (sextillion); 27 zeros (octillion); 30 zeros (nonillion); 33 zeros (decillion); etc...

*** Same Sum---Every Time: Take any three-digit number in which the first digit is larger than the last digit. Reverse the number and subtract the smaller number from the larger one. Reverse the result and add this number to the result. For example, use the number 725. The reverse is 577. Subtract 527 from 725 to get 198. The reverse is 891. Add 891 to 198 to get 1,089 every time. If the result from step 2 is a two-digit number, such as 99, put a 0 in front of the 99 before reversing it. (For the numerologically inclined, the result is 9, the perfect multiple of 3.)


GCD (Greatest Common Divisor);
HCF (Highest Common Factor);
LCM (Lowest Common Multiple;
LCD (Lowest Common Denominator)

3 laws of Addition & Multiplication: Associative - Commutative - Distributive
3 common set of unite to indicate angular measure: Degrees - Radians - Grads
3 laws of indices (Algebra): Multiplication - Division - Powers

Common set theory expression: (1, 2, 3...)

3 Quadratic equation constants: Coefficient of x2 - Coefficient of x - Term of x
3 functions of angles in Trigonometry: Sine - Cosine - Tangent
3 basic triangles: Obtuse - Right - Acute
3 ideal geometric entities are the synthesis of all forms: Point - Line - Plane
3 letters used to name an angle with the vertex as the center letter: ABC, CDE, EFG, etc.
3 labels for mathematical term quantity: Binomial - Trinomial - Polynomial
3 fundamental math problems: Add - Subtract - Multiply (Division is a form of Multiplication)
3 Addition/Multiplication parts: Addend - Addend - Sum/Multiplicand - Multiplier - Product
3 Subtraction/Division parts: Minuend - Subtrahend - Remainder/Divisor - Dividend - Quotient
3 divisions (ones - tens - hundreds) are grouped by a comma: ones-tens-hundreds, thousands

***From an Elizabethan Manuscript (1570: Multiplication is vexation, Division is as bad; The rule-of-three doth puzzle me, And practice drives me mad.

("Rule-of 3" arithmetic, found in Chinese textbook dating 1000-900 B.C.)

3 basic movement types for most resistance meters: d'Arsanval - Iron-vane - Electrodynamometer
3 electrical circuit types: Series - Parallel - Series/Parallel (combination)
3-phase systems used in most electric generators
3 basic transistor layers: Emitter - Base - Collector
3 patterned Power "Law": Power equals Watt divided by Time
3 laws of Indices (Algebra): Multiplication - Division - Powers
3 patterned current-in-amperes equation: (I)amperes equals Q(coulombs) divided by T(seconds)

3-patterned general formula of the Scientific Method:

(1) The observation of the phenomena and the recording of facts.
(2) The formulation of physical laws from the generalization of the phenomena.
(3) The development of a theory that is used to predict new phenomena.

3-colored flag: Children are taught to pledge allegiance to the U.S. Flag

Maintenance update posted: Friday, 16-June-2017... 11:35 AM

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