Threesology Research Journal: Linear, Circular, Triangular examples
Linear, Circular, Triangular configurations
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~ The Study of Threes ~

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Note: Whereas The triangle is commonly viewed as a 3-point object, of which in this section I will be providing numerous examples from a variety of areas (though I am sure readers could provide additional examples); it is necessary to point out that the three geometric forms "line- circle- triangle" appear to be a type of 3-patterned interconnected transitional developmental sequence that sometimes occurs.

As a general rule-of-thumb, the higher up in elevation one ascends, the more pronounced is the presence of Triangular- shaped trees, all of which are colloquially referred to as Pine Trees; and that many people give special reverence to by decorating during Christmas, and most people overlook the symbolic similarity to the "flashing/blinking" lights on a triangular Christmas tree and the "flashing/blinking" lights of the Sun (and Moon) along their triangular paths as the Earth rotates; an event that would have been more pronounced when the Earth was spinning much faster in centuries past.

However, the lower one descends in elevation, the more pronounced is the presence of Linear- shaped trees. And in between the high and low elevations can be found a more pronounced presence of Circular- shaped trees. Hence, here is an example of a naturally occurring indication of life proceeding in a Linear~ Circular~ Triangular fashion, even though we can find examples of trees that we might want to offer as a counter-argument to this generalization. However, it is clear that we go up in elevation to cut down a triangle-shaped tree for Christmas and do not look for one in the desert or on the beach. The following illustration gives a generalized portrayal of this Linear~ Circular~ Triangular tree-shape circumstance:

Three Trees

Auxin and Apical Dominance: Auxin produced in the dominant growing tip (usually uppermost) inhibits growth in lateral branches (those below it). This results in the typical triangular shape of conifers.

--- Plant Regulation and Response ---

While many people can see these three forms, they have difficulty in seeing distinct divisions due to the presence of overlapping circumstances of growth. This is further complicated by the fact that many species of trees (and plants) are successfully transplanted by humans (and other means) into different terrains than the trees initially developed. Additionally, the human definitions of Low~ Medium~ High with regards to the Linear~ Circular~ Triangular generalization, may be better expressed with respect to variations of growth in a single locality instead of a global assessment. This idea may help us take into account climatic variations with respect to altitude and geological processes which has its own type of variable mixing and matching of Earth-terrain formations. In an abstract sense, one must wonder whether the label "altitude" is a type of geophysical "species" which undergoes its own forms of Slow~ Medium~ Fast evolutionary processes, that must be taken into account in selecting an area of comparison for purposes of judging the validity of a Linear- Circular- Triangular formula.

The following image is a generalized representation of the Linear~ Circular~ Triangular formula as it relates to differences in terrain:

3 terrain divisions

There are everyday expressions which suggest these three divisions, though in each circumstance we can find examples of the other characteristics:

  • Linear:

    Flat plains, Calm (flat) lake, Desert "flats," Mesa (is Spanish for reference to a hill flat surface such as a table top, which is the middle reference between plateau~ mesa~ butte), etc...
  • Circular:

    Rolling hills, Rolling waves, Rolling prairies, etc.,
  • Triangular:

    Reach the summit/peak, white "tipped" waves, High desert dunes, etc...

The point is, we humans generally use labels which refer to a linear, circular, or triangular form, and do not customarily use such expressions as:

Don't the hexagonal hills, the star-shaped mountains, the pentagonal waves, etc..., look pretty this morning?

Linear Circular Triangular
Hot Climates Warm Climates Cold Climates
Tropical Fruits Deciduous Fruits Pinon Nuts, etc...
Primitive Peoples Modern Peoples Future Peoples?
Linear/Lean Diet Circular/"Robust" Diet Triangular Diet?

Along with fruits, we could also show vegetables growing in a Linear~ Circular ~ (or) Triangular shape... both with and without applying too much imagination.

The list above gives a rough outline of comparing occurrences relative to one another in contexts that we are well aware of as having overlaps, but the respective delineations can not be dismissed as "fruitless" approximations of inquiry. It can be recognized that in a generalized comparative way, there is indeed a Linear~ Circular~ Triangular pathway of development that we humans take.

But what are we to make of the notion of a "Triangular Diet?" Does this merely mean we develop triangular-shaped diagrams such as the Food Pyramid present in the United States that some think is a useful tool to teach a healthful dietary regime, while others consider to be a form of Agriculture- Industry propaganda supported by the government to insure the sell of certain products cultivated in the United States? (Ask any woman on a diet about the "suggested" amounts of bread to be consumed according to the U.S.D.A. {United States Department of Agriculture} recommended food servings, and she will heartily disagree because such amounts put weight on you... unless you are someone who, after getting their gallbladder removed you don't eat anything with fat in it and will consume no-fat bread as a main stable.)

Is such a diet more preferable to an other-than-Earth circumstance such as in the (cold of) space or another planet in some other galaxy? Surely the correlation of a colder climate to a triangular reference doesn't mean we humans are more advanced if we eat whale, walrus, and seal meat, as do the Eskimos living in a cold climate.

But the transition into a cold way of life may be interpreted to be a triangular peak of human growth in the sense that an ice age eliminates the weaker individuals of a species. In a survival context where a species intermittently experiences climatic changes ranging from hot to warm to cold in which they must survive for extended periods of time, the survivors of a cold climate are indeed at the peak of dominance in terms of such circumstances that may or may not be valuable if applied elsewhere in the Universe.

Slowing Earth Rotation A One-Patterned "total" illumination is an interpretation of a regularly occurring event that can be represented as a linear expression even though it is produced by an accelerated circular rotation.

The Two- Patterned Night/Day illumination clearly is a representation of a circular event with little need for further explanation.

The Three-Patterned strobe-light effect of the Sun's three "moments" dawn- noon- dusk, is a triangular image even though we of today need to use time-lapsed photography in order to more readily see what the pristine elements of biology were subjected to.

The following list of Linear- Circular- Triangular examples is for those who can easily visualize geometric forms from the printed word:

"3" Basics Formula Linear (flat) Circular Triangular
3 Galaxy/Universe items Our galaxy through space Motion of galaxy Expansion/Contraction  {<>,X}
3 Earth motions Earth+Moon+Sun Rotation of Earth Precession of Earth's axis
3 forms of matter Liquid Solid Gas
3 fundamental Forces Electro-magnetism
(N/S polarity)
Gravity Nuclear (+)(-)(+/-)
3 conceptual models Primitive NSEW Native American Indo-European
3 cross-sections of hair African: ribbon-like Asian: circular Caucasian: ellipsoid
3 Earth shapes Earth is flat Earth is round Earth is a triaxial ellipsoid
3 Universe theories Universe is flat Spherical Saddle (triangular)-shaped
3 stone tool shapes Mono-facial Bi-facial Tri-facial (arrow heads, etc...)
3 engineering tools Lever Pulley/Wheel Fulcrum
3 engine shapes In-line, Slanted, etc... Radial, Rotary V-shaped
3 shapes game Paper Rock Scissors
3 human face items Eyebrows Eyes Nose
3 playground items Monkey bars/See-saw Merry-go-round Slide/Swing-set support
3 in-vehicle views Road, Stick shift, etc... Steering wheel Perceptual view of distance
3 early industry tools Staff, Poker Pottery wheel, Kiln Fire (flame), Bellows
3 pre-industry tools Stick Rock Fire (flame)
3 Cyanobacteria shapes Filamentous
3 Stromatolite shapes Flat-layered Domical/Columnar Conical
3 bird-flight formations Diagonal, Horiz., Vertical "Bunched up together" V-shaped (also J/L variations)

Note: I used the symbols {><} and {X} in the triangular column of the Galaxy/Universe category in the above table, to portray a triangular-like perception of expansion and contraction.; Did the Universe expand like a bursting ball in all directions or a selected direction? It is not certain if the "Big Bang" occurred at a single point and then expanded in all directions. Unless we care to consider that our Universe is the result of an implosion, which is 1 idea, then there are 3 other theories we can consider, which brings our overall formula to a 3:1 ratio. The other three being a Linear- Circular- Triangular expansion after the Big Bang. Also, if the expansion is slowing down, is there to be an eventual "Big Crunch?"

For those of you who are unfamiliar with the passage of the Sun traveling along a triangular solar path, here are a few images from the google images search option using the word "solargraph". The images clearly show a triangular profile. You need only attempt to visualize what this might have been when the Earth was traveling at an acclerated rate in the distant past. Surely the rate of the Earth's rotation has played a part in the onset of different life forms, particularly when it is noted that the human form of life did not arise until the Earth was traveling in the late 22 hour to early 23 hour rate of rotation. Humanity and many life forms did not exist when the Earth was spinning faster cause the lenght of day to be shortened. An approximate attempt to look at the different rates of rotatrion and the onset of the different human-like characters is addressed on this page: Are Humans Rotation-Rate Specific?.

Several images of the Sun's path called a solargraph

Because the 3rd born Caucasian/Indo-European hair as seen in cross-section is not exactly what many might refer to as a "true" triangle, this suggests more is needed in terms of evolutionary development for the human species. In other words, we are evolving towards the "three" whatever this may mean in the final analysis.

Types of Stromatolites

Note: The Domical and Columnar forms are said to grade into one another. Not only does this present us with the image of overlapping considerations, but also the possibility of a 3-part grouping: (1) Flat~ (2) Domical/Columnar~ (3) Conical

In a more immediate application of the Linear~ Circular~ Triangular idea, the idea of human origins Out of Africa, places the Africans as having came first, Asians having come second, and Indo-Europeans/Caucasians having come third.  When we look at a cross-section of a hair shaft from each of these groups, you find the hair of Africans exhibiting a Linear (flat, ribbon-like) appearance; the hair of Asians as exhibiting a Circular appearance; and Caucasians as exhibiting an ellipsoid appearance. In other words, the last group is closest to a triangular configuration but it clearly has room to grow before reaching what may be termed a "true" triangular appearance. And once again, with respect to the occurrences of overlapping growth we find in tree groves as well as geological formations, in the human sphere, there are circumstances of overlap due to inter-breeding, rape, as well as incest.

When we look at the development of the human species with respect to brain growth in general and brain cells in particular, the neurons of the cortex fall into three predominant types:

(1) Granule
(2) Stellate/Martinotti
(3) Pyramidal

These form a three staged construction of:

Granule >>> Stellate >>> Pyramidal

Here once again we can see a three-stage development process from a simple to more complex structure that results in a triangular (pyramidal) design. While the triangular shape of the pyramidal cell can easily be seen in the following image, the linear and circular designs are inferred:

3 principal types of neurons
--- AND Corporation ---

A different representation of the Linear- Circular- Triangular formula can be found on pages 145-146 of the book "The Long Trip" (A prehistory of Psychedelia) by Paul Devereux ©1997, ISBN 01401.95408 (paperback).

...He (Heinrich Klüver) accepted a more general stage progression (with respect to the narcotic experience of Mescaline) in which "very elementary visions are followed by visions of a more complex character," and identified four essential types of the elementary hallucinations, which he called "form constants."

  1. [Linear] One of these he refers to using terms like "grating... lattice... fretwork... filigree... honecomb, orchessboard-design."
  2. [Circular] Closely associated with this was the "cobweb" form constant.
  3. [Triangular] A third form constant that Klüver felt deserved special mention was the "tunnel, funnel, alley, cone or vessel."

  4. Today, we particularly recognize the "tunnel" image from the accounts of those who undergo near-death and "out-of-body" experiences. A very important property of this form constant is that it often heralds the moment when the subject stops merely observing the geometric and patterned motifs, and begins to enter into the hallucinatory or visionary world. The subject is engulfed by the imagery and begins to participate in it. The person's consciousness slips down the tunnel into the otherworldly realm. Klüver saw the "spiral" image as the fourth basic type of form constant, but this is essentially the same as the tunnel or funnel effect...

    From the perspective of Punctuated Equilibrium which argues that some species may evolve very quickly in what may be termed an evolutionary "jump," most paleontologists judge an evolved form by size and functional morphology.  But as can be seen in the following paragraph taken from pages 49-50 of the book "The Monkey Puzzle" by John Gribbin & Jeremy Cherfas, there may still be readers who will not make the connection with respect to an overall design change in one area of study and another (evolutionary) change taking place elsewhere.

    "But the theory of punctuated equilibrium does give a very good idea of how to go about searching for a missing link, even though it might have existed for only a short time. You need to look at an animal that existed in vast populations for a relatively long time and which was very likely to become fossilized. Molluscs inside their shells provide an extremely good candidate, and Peter Williamson, a colleague of Stephen J. Gould's, spent a lot of time searching the fossil beds around Lake Turkana, where Richard Leakey's team looks for ancient man, examining the fossilized snails there. He found one species that had the usual rounded edge to its shell, and another that was very similar except that the edge of its shell was more angular, like a helter-skelter. The rounded shell occupied the fossil beds in huge numbers and persisted, unchanged, for millions of years. Then, quite suddenly, it gave way to the shell with the triangular edge, in the same vast quantities. Williamson examined the geological boundary between the two species, and there, among the normal shell, he found a population of snails that were clearly in a state of transition, part rounded and part triangular."

    3 forms of pelvis
    --- Early Hominid Evolution ---

    In short, from a round form to a triangular form. It may have been that a type of linear form preceded the circular form but no clear example is as yet identified or been preserved in some fossilized form, and after the triangular form, if a species lives long enough to evolve, a type of fusion takes place.

    In the human sphere of events, one might consider that early Native Americans who sat in a circle within a triangular-shaped tee-pee as a form of transitional stage of development from one design to another. We might even see evolution in action in the story of King Arthur. He chose to use a Round Table to settle the disputes of the Knights who fought over specific seating arrangements produced by the circumstances of using a Linear (rectangular or square) form. The Knights were vying for the honor to sit at the "head" end of the table as an indication of superiority.

    The point to be made is that some people think of evolution solely in terms of biological life forms with respect to physical structure and not activities of those organisms. They fail to consider that more complex organisms may continue an evolutionary trend in a different sphere of behavior. For example, a person having developed a (linear) spear may or may not use an attached triangular-shaped spearhead, yet they may exhibit circular behavior in conversation and then exhibit a type of triangular behavior in non-verbalized day dreams. A more advanced individual may show more overt forms of a circular design with the linear and triangular forms unconsciously disguised with garments, superstition, foliage, etc., and yet an even more advanced individual may design an overt example of a triangular form of thought processing with linear and circular forms of behavior expressed as intermittent internalized minor attributes of functional design with respect to organs, fluid composition, etc...

    Evolution can take place by small graded steps as well as by what have been termed "evolutionary jumps" to somewhat describe the idea of Punctuated Equilibrium. But evolution may also use a third method which is a variation of these two forms. Why limit the idea of Evolution to but one form of type ("species")? Since we humans have developed an idea exhibiting the existence of three basic domains of life (Archaea~ Bacteria~ Eucaryota), let us also consider the possibility that there are three types of Evolution. There is no reason for us not to consider that language development doesn't have its own variety of Evolution as well as genetics, physiology, cognition, physics, music, dance, philosophy, consciousness, etc... While this remark may appear a given that is taken for granted by some as an actual reality, there are those who scorn any suggestion of the word "evolution" being applied to any consideration.

    In other words, it is a straight forward remark suggesting that even if someone doesn't believe that evolution has any value when applied to humanity as a whole, this does not mean that they can not consider the possibility that evolution does take place in other circumstances. Sometimes something that is found to be distasteful to chew on because of such a big bite, may not be found to be so distasteful if they take small portions in which to nibble on. It is incredibly stupid for any person not to consider the possibility that a so-called Creator would not, on occasion, use evolution as a tool for one or more circumstances.

    When we look at the next example, it would appear that an idea of a Linear® Circular® Triangular maturational transition is false when we compare the rib cages of primates considered more primitive, with the human rib cage:

    human & chimp rib cages cone and triangle overlapped

    primitve hominoid rib cage
    Primitive hominoid ribcage
    ---The ribs of Homo erectus---

      skeleton of human
    Human skeleton
    skeleton of ape
    Ape skeleton
    skeleton of chimp
    Chimpanzee skeleton

    ---Skeletons for Sale---

    Lineup of Skeletons
    --- Skeletal Comparisons---

    Linear Circular Triangle

    When someone thinks of a Linear® Circular® Triangular maturational transition, the way such is written in a sentence in a linear form can give a misleading interpretation that one sequence always follows another without variation. Whereas a maturational transition need not follow a linear formula, but may in fact be in a circular or triangular pattern of reciprocity in order to explain some circumstances of overlap that appear to exclude one of the patterns that are expected to be present as an intermediary.

    Linear « Circular « Triangular

    As you can see in the following table, a 3 X 3 alignment leads us into a sort of tic tac toe assemblage that, in an abstract formulation, renders us a simplistic model of different species variations by simply exchanging the terms "linear, circular, triangular" with different hominid species and thereby encounter a small incite into the different interplays of dominance, intermediary, and inferior. While we could further abstract this into the placement of amino acids in the boxes for a generalized representation of sequencing parameters, which bodes well with such a model because of the triplet codon system, the basic point I want to make in the present discussion is that there is a maturational overlap that has taken place in hominid development, and that this overlap does not necessarily have to proceed along a path that we of the present feel is a "start to finish" perspective, much in the same way as there is an overlap of the sequences in the following table, regardless of how you play this version of tic tac toe.

    Circular Linear Circular
    Linear Circular Triangular
    Triangular Triangular Linear

    However, it must be considered that the suggested "higher" triangle rib cage form of "lower" primates is a distinction that is separate from the evolution of the larger hominid line since it is well known that humanity did not evolve from chimpanzees or apes, but that all the primates are considered to have arisen from a similar ancestral stock. And let us not forget to consider the rib cage designs of other animals, for example, in this case another mammal familiarly known as the bat. As can be seen in this X-ray exposure, we have another view of a triangular-shaped rib cage.

    triangular bat ribcage
    --- Bat Bits ---

    In simpler terms, the triangle ribcage design of "lower" primates and "lower" life forms that are frequently interpreted to be part of the hominid line, are a characteristic that marks the pinnacle of development for the species. In other words, the ape is not evolving a chest form that is a design beyond that of a triangle, and the human circular "barrel-shaped" rib cage is an indication of an "immature" design. While I am using the word "immature" as a metaphorical reference to the circular design (whereby the triangle would be the mature form and the linear model a type of infant form), the connection may be more representative than a metaphor when we consider the possibility that the modern human species has lasted as long as it has because it retains features of an immature state which enables it to more malleable, susceptible, and "suggestible" to changing environmental circumstances. It is through the retention of immature features that enables present modern humans to more readily adapt to environmental conditions that may have changed more quickly in past centuries, and may do so again, if the current "weird" weather changes are any indication thereof.

    Date of initial creation: Sunday, July 23, 2017, 4:05:32 AM
    Latest update: Wednesday, March 17th, 2021... 2:51 PM

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