Threesology Research Journal
The Devil's Advocate and 3's Research
~ 31 ~

~ The Study of Threes ~

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

Since I have several hundred images that need to be collated into some amalgamated comprehensibility that for the moment I am merely presenting in a collage which may appear to have little sequentiality to some readers expecting to be presented with a start-to-finish threesological type of textbook, let me reiterate that I am still gathering information which at times needs to be interjected here and there. In other words, what I am attempting to do I am at present describing as a time-line, let us not overlook that the timeline is part of the multiple pattern-of-three ensembles I am identifying. An ensemble, if the reader is not sure of what I am referring to is a sequence of three items which may or may not exhibit a conventional ordering of familiarity. While the familiar ones are often seen, they are not typically being described as a "pattern-of-three ensemble". For example:

  • ABC or 123 (We sometimes describe the teaching of the alphabet and numbers with these three groupings).
  • 2-3-4 (and example of the heart chamber quantities of fishes- reptiles- mammals, which also displays an evolutionary sequence).
  • 3-4-5 (Pythagorean theorem).
  • 4-5-6 (reference being used here to designate multiple sequences of three-patterned numbers used on combination locks).
  • 5- 7- 9 Stanley Miller's Magical number 7 plus or minus two.
  • 24- 7- 365 (twenty fours hours a day- seven days a week- 365 days a year).
  • 10- 2- 4 (an old advertising insignia used by those connected with the Dr. Pepper soda drink).
  • Date of birth, social security number, telephone number (all three have three-patterned numerical sequences in the U.S.).
  • Mono- Bi/Di- Tri
  • Primary- Secondary- Tertiary
  • (Ones- Tens- Hundreds)... (Thousands, Ten thousands, Hundred thousands)...
  • (Primary- Secondary- Tertiary)... quaternary
  • 3 stop and 1 start codons
  • Single stranded RNA- Double stranded DNA (absence of triple stranded model)
  • ATP (adenosine 3 phosphate), ADP (adenosine 2 phosphate), AMP (adenosine 1 phosphate)
  • primary... (Secondary- Tertiary- Quaternary)
  • etc...

In many instances there is an absence of a third item or any direct reference to a "3". Such instances need to be note. We need to identify sequences of one and two and four and five, etc... In so doing, those who... for example, like the number 7, will be introduced to the notion of being able to accept and assist in identifying when a seven occurs and when a reference to the seven is absent. The same goes for threes, twos, fours, fives, sixes, etc... If we are going to suggest that some number like a 1, or a 2, or a 3, or a 4, or a 5, 6, 7, 8, 9, etc., or a grouping thereof is important, we need to identify under what circumstance(s) they are absent as well as when they make an appearance in different contexts in different subjects.

The different patterns represent different frames of reference. Such an idea has been fortuitously described in the description of bicycle frames that I drew up yesterday morning after finding a reference to the design of the bicycle frame which was described as the development of the "triple A" frame. Necessarily so, since I am thinking in terms of evolutionary development, I wondered if and when a double and single A frame occurred, and whether there was a design which exceeded the "3". Interestingly, there is a double A frame, but from my perspective it was simply a perception of looking at the triple A frame from a different vantage point. A point of contention to which I have encountered in the survey of different ideas being offered for the same information, illustrated by the following cartoon figure I have previously presented as an example on page 19 and page 22 about the difference of opinion being rendered for the same information:

Two versus three opinion

Now let's take a look at the bicycle frame philosophical analogy I had created for the Tour De France 2019 page:

Two versus Three frame of reference

Clearly, what some claim as a "Two", others claim as a "Three", leading to needless controversy, except that the human ego gets in the way and the "2" or the "3", or some other value becomes aligned with a person's self-image that they want to project and protect as a uniqueness.

What came to mind this early morning concerning the difference of opinion aligned with the barking of dogs that would not quiet down no matter what was said because some of the dogs where at a distance one did not have ready access to, nor could see what or if anything they were barking at or for; the image of the world as a rural community filled with mongrel dogs presented itself as an image. Along with the idea of most people being analogous to mongrel dogs, I viewed... with some humor, the idea that so-called professionals where those vying for some position of being seen (and heard) as a special breed (with a prominent bark). I openly laughed at the metaphor since it presented me with the situation that I am in a position of trying to bark (speak my piece) during a moment when other dogs are trying to bark as well. Unless something occurs to make all the dogs stop barking, which they do after awhile, I will not have enough silence to voice my opinion. Then again, the other dogs (researchers) may have retreated indoors or become occupied with some other task of their more natural inclinations and are thereby distracted from paying any attention to what I have to say or not. Honestly, at a conference filled with purported professionals of one or another preferred orientation, one is confronted by the presence of an enclosure where multiple dogs are barking at once. HA! If one has ever tried to get a kennel of dogs to be quiet at the same time, only T well-known presence of a defined Alpha-dog whose voice acts like a megaphone or microphone may have any affect... but not in all circumstances to keep all the dogs quiet.

Those reading this page may or may not find it humorous to view themselves as a mongrel dog, or even a special breed (of "mongrelity") typically labeled a pure breed of dog. The idea that their opinion is like that of a dog baying at the moon may not be an image that strikes a cord of welcomed reflection, whether or not it is defined in terms of a group of professionals or pack of wild dogs barking in concert at some perceived shadow on the wall of the cave in which all of them share as members of a tribal subject matter in which ceremony of language and dress are routinized expressions of experience. However, in so many instances, we find differences of opinion about the same subject matter being barked about from the vantage point of where one is standing and with whom one is standing nearby... at least in their mind's eye, since it is not only misery which likes company... but also religious, political, business, academic, scientific, sports, entertainment, criminal, etc., beliefs as well. They all have their own intoxications. So, let us ask, which moon, or sun, or stars, or lightning, or stranger, or shadow are you inclined to bark against or about or for... noting that even the dogs of owners will sometimes bark at them, if not bite at them, pee on them, chew their shoes, furniture, etc., or attempt to hump them in their excitement or supposed resentment?

While my analogy is not very flattering to those accustomed to looking at everything as a mirror image telling them that they are a special breed of person assumed to being interpreted through a lens of humility that others witness as well, the overall point to be made is that a "Threesological" approach to observing and cataloguing different perceptions is a means by which the different perceptions can be categorized to develop an overall perspective of the different perspectives we might alternatively describe as cognitive patterns. Cataloguing them in their many colors, flavors, languages, symbols, (presence) and absence(s) will assist us in determining if they are attached to a cyclicity, short-term appearance, length of existence, deterioration rate, breadth, etc...

This needs to be done in order to identify whether there are actual changes in human cognition in terms of either progress or deterioration. For example, is it helpful for us to use the analogy of ideas as if they are species which have life spans, half-lifes, and extinction rates of existence? Is it helpful to use a timeline configuration with or without viewing the timeline as part of the overall cognitive scenario? How do we get others to move beyond the typical inclination to resort to using the notion of several or multiple or many or much or some enumerated value suggesting too many examples, and therefore provide them with an excuse not to expend any energy and effort in the development of a timeline? In other words, in describing a list of threes, I sometimes encounter those who reach a point in the discussion which they resort to thinking and thus claiming that there are... in their guesstimation... multiple examples, and leave this expression as the final say-so in any further attention being given to the topic. However, the same goes for all subjects. Those who are interested in topic and sustain an interest do not actually reach a point where they make a claim for a multiplicity that is too exhausting... or they persist in a subject in so far as their knowledge exceeds everyone else they encounter... or they deliberately try to profess ownership of a subject by presenting information in a manner to distract or detour another's efforts in the same subject. By an effort of reducing the quantity of people in their subject field, they presume some personalized speciality of dominance and can claim ownership of the terrain.

For some, a given pattern viewed in a given way affords them all the ownership they desire, like a single bladed pocket knife they imagine has some sort of especial attribute that no one else or no other knife has. However, from my perspective, a multi-tool knife is better, but not the only tool. And neither do tools need to be made of metal. Tools can be ideas, whether explicitly voiced or not. Such is with the "threes" idea. The "3" is not the only kid on the block of numbers. The "3" kid is not always around the cognitive neighborhood one ventures onto. Sometimes the kid likes to play hide-n-seek or jump out of bushes, and at other times it is doing chores. Sometimes the scholar, other times the detective or neighborhood buffoon. Sometimes the philosopher whittling a stick while sitting on a porch swing, other times the absent minded professor lost deep in thought to the point of forgetting to eat. This and more is the "3" for me. The "3" has many experiences, many acquaintances, many friends and relatives. But not every encounter with others is fruitful nor without mishap. Indeed, the "3" is a life form just as other numbers represent life forms as well. They can be anthropomorphized or not. They can be serious, funny, or any emotion... or lack thereof to any degree one might be enabled to image. Such is the nature of numbers. With color, with voice, with nakedness and fully clothed in a variety of apparel and appearance, like kids playing dress up or dress down... with or without makeup accustomed to a given era or not. Hence, the reason we see so much of "higher" mathematics noted as an artistic adventure that may or may not find a place amongst a serious application.

Let us take for example the pursuit of a three ensemble in the following youtube presentation whose title "The 10,958 Problem", does not give an immediate "three" reference unless the title itself is viewed as a (patterns-of-three expression):

The 10,958 Problem

However, neither does the "single digit" title of the following imaged paper from the above presentation suggest a "three" reference though it is filled with them:

Three digits in Single digit representations

In the following Youtube presentation, we are presented with the notion that the number 3 is everywhere (mathematically speaking), but the comment at the end of the presentation provides an alternative sentiment... even though the presentation uses the value "3" and the explanation for doing so comes out like a rationalization more than a reason:

3 is everywhere

The next youtube presentation is about the representation of Pi (roughly designated as 3.14... or Einstein's birth month and day), as being 3.2. The point being for the present case is the reference to the "3" and "2" as a generalization:

How Pi was nearly changed to 3.2

This next youtube presentation on "squaring the circle" as a follow-up to the previous presentation, is provided here to make the comparison with human cognition and the repetition of patterns underlying ideas which are being used as if the mental activity of humans is prominently attached to the usage of a straight edge ("ruler" that is not ruled) and compass, giving us a system of beliefs analogous to "constructible numbers".

Squaring the Circle

In short, the presence of constraints or conservation is described by the limitation imposed by using two devices (straight edge and compass), but by the addition of a third "tool" called algebra (which thus becomes an aforementioned non-tool or "transcendental" tool), we are able to figure out that idea forced onto consciousness. In other words, the idea of "squaring the circle" was the appearance of a cognitive development beyond the cognitive development of a "two" orientation that could not be appropriately addressed by the tools constructed by a two-patterned orientation. The development of a three-patterned orientation was needed. However, one should not thus think that from a three-patterned cognitive orientation that we are being presented with images representing some as yet to achieve development in cognition that some might want to reference as a 4, or 5, or 6, etc... While we can see the development of cognition in the 1-2-3 scenario, I am not willing to accept the idea that human cognition, under the present (incrementally deteriorating) environmental conditions, is developing a "higher" stage of cognitive development as it has done previously. The effect of the noted conservation may well be in charge to create a limitation that we come to rationalize as being non-existent or does not otherwise affect us.

Just because we have had problems in the past that eventually came to be solved, does not mean this is an eventuality for all problems. The apparent presence of a conservation effect may well constrain us, though we rationalize otherwise.

The third installment in this series deals with "Zeno's Paradoxs", involving the philosophical concepts "one" and "many", the two of which should bring to mind the development of a sense of number in human thinking, which for the sake of discussion, can be labeled with the pattern-of-three previously noted as "1-2-Many".

Zeno's paradoxes are a set of philosophical problems generally thought to have been devised by Greek philosopher Zeno of Elea (c. 490–430 BC) to support Parmenides' doctrine that contrary to the evidence of one's senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion. It is usually assumed, based on Plato's Parmenides (128a–d), that Zeno took on the project of creating these paradoxes because other philosophers had created paradoxes against Parmenides' view. Thus Plato has Zeno say the purpose of the paradoxes "is to show that their hypothesis that existences are many, if properly followed up, leads to still more absurd results than the hypothesis that they are one." Plato has Socrates claim that Zeno and Parmenides were essentially arguing exactly the same point.

Indeed, like the arguments dealing with the frame of reference dealing with the "2" and "3" opinions.

Zeno's Paradox

In the idea of "halving the distance", let us compare the notion of "half life" found in the reference to atomic particle decay:

Half-life, in radioactivity, the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay (change spontaneously into other nuclear species by emitting particles and energy), or, equivalently, the time interval required for the number of disintegrations per second of a radioactive material to decrease by one-half.

For example: The radioactive isotope cobalt-60, which is used for radiotherapy, has, for example, a half-life of 5.26 years. Thus after that interval, a sample originally containing 8 g of cobalt-60 would contain only 4 g of cobalt-60 and would emit only half as much radiation. After another interval of 5.26 years, the sample would contain only 2 g of cobalt-60. Neither the volume nor the mass of the original sample visibly decreases, however, because the unstable cobalt-60 nuclei decay into stable nickel-60 nuclei, which remain with the still-undecayed cobalt.

If the reader hasn't notice it, let me make it evident that patterns-of-two are being referenced in ways that for the common intuition might seem paradoxical. It is a type of thinking that needs to be identified as a pattern-of-two solved by applying a pattern-of-three orientation, though the person may not be aware of the application of both types of cognitive patterning being applied. Hence, the presence of a 2 and 3 pattern for looking at the same context from different vantage points.

While it can be suggested that mathematics is a type of three-patterned cognition, we often find that it gets embroiled in dealing with two-patterned problems so as to appear to be able to solve them using the tool of mathematics, when actually the assumed tool called mathematics is a refashioned pattern-of-two applied from a different vantage point, and is not a representation of an evolved consciousness as some might want to consider. Calling a change in perspective by the name of "mathematics" with its own language, does not mean we are actually dealing with a different ("evolved") animal of human conscious. Like the different perspectives of the bicycle frame, this is what we see occurring in mathematics and many sciences... and attempted means of explication by the language being used by theologians. They are looking at the same thing from different vantage points, applying a particular language and/or symbolism, and inferring it as some type of "higher" thinking or consciousness. Much of the problem is the problem of communicating simple ideas (involving multiple patterns-of-two) in convoluted ways to create a complexity (or paradox) so as to give oneself and/or others the impression of an assumed "higher" intelligence that can be understood by using one particular language and/or symbolism (such as mathematics) over another model... where the "models" can be interpreted as types of cognitive tools that have been altered by color, positioning, context, etc., but have not actually changed at all in the basic underlying structure.

A pattern-of-two described as a difference between two distances can be added onto by the concept of time, or context, or actors (game pieces, actors, speed, structure, etc...), but this does not alter the basic underlying construction of a singular pattern-of-two that has become compounded or multiplied by the addition of another variable. Hence, the two-pattern does not become an actual three-pattern (like calling a Biad a Triad, around which a philosophy is created and participated in by others with pomp and ceremony). In much of mathematics we see the involvement of only pattern-of-two being addressed in elaborate ways and labeled as being complex, when they are actually little more that "complexified" patterns-of-two around which social organization gravitates and devises its systems of interaction in accordance with.

Wrestling with the paradox of one or another "patterns-of-two", however it is constructed, can not be solved so long as a two-patterned rule-of-thumb is used as the defining cognitive pattern being applied in attempting to solve it. Like Einstein is quoted as saying:

Quote attributed to Einstein

Without recognizing the presence of different cognitive patterns being repeated and how they interact, we can not actually "know thyself" in order to become better than ourselves, if we are at all able to while subjected to an incrementally deteriorating environment. Mathematics is one type of cognition that is being defined by some as the penultimate type of cognition and that only through it or some future variation thereof can all problems be solved. However, if mathematics is just an elaborated pattern-of-two model out of which lesser patterns-of-two forms can be solved by placing an individual at a different vantage point around the same in-focused orientation as others, then an out-facing form of cognition may well have to come into play in order to get humanity to step beyond the parameter of concerns and considerations it is presently quagmired in. To use a comparison with the "well-behaved sum" comment exercised in the foregoing presentation, the idea of having paradoxes (as unrecognized patterns-of-two) is part of a mathematical and philosophical system that is "well-behaved", since normal behavior is often defined by the presence of "recalcitrance', "revolution", and "retributive retaliation".

Origination date: Friday, October 18th, 2019... 3:01 AM
Initial Posting: Friday, October 18th, 2019... 10:14 AM
Updated Posting: Friday, January 20th, 2023... 12:25 PM

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