~ The Study of Threes ~
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As long as this "Natural" phenomena does not change, then the "naturalized twoness" seen in Mathematics will be retained and offer a stable foundation for influencing mental activity aligned with the natural rhythm, unless one can provide evidence of incremental changes taking place in Nature, all the while humans are attempting to solidify the usage of the previous pattern in Nature because the economics of an overall society are based on the old stability's framework. (I am not saying that Mathematics is stable. Being used as a stable foundation only means it is a routinized activity. For example, a person can be routinely angry, upset, jealous, sloppy, crazy, etc...) However, an attempt to analyze mathematics and its usage of presumed stable patterns, requires that we take a closer look at natural events that can be presumed to be linked to the underlying patterns of human behavior (and other life forms according to their respective physiologies).
Though the idea of biological rhythms is well established, this is not the case for rhythms of subjects requiring intense mental activity. The occurrence of "rhythmic mental cadences" I coined as I was writing this as a means of attempting some emblematic portraiture of mental activity which might otherwise be viewed as concentration, creativity, mental focus, or even single-mindedness, pig-headedness, dedication, attentiveness, etc... Nonetheless it is realized (but perhaps not thought extensively about), that if the rhythms of nature change, the old balancing acts of mental, social, and emotional orientations will become unstable. Even though the realization of this would become more acute the more unstable the Natural rhythms took place, incremental occurrences of changes in Natural events from which the underlying patterns of subjects are influenced by, may not be seen and instead create incremental changes in overall social conditions. Incremental occurrences provide for the time needed by living systems to adapt to changes. That is if all life forms change incrementally at the same pace, whereby the whole ecology of interactive life-form behavior remains relatively stable. If one life form such as plants react at a different pace or in a different way as to effect the food chain, those life forms depending on plants will have to play a game of catch-up, such as by trying to force the plants to resume a previous growth activity.
Humans try to be predictable about possible future changes in order to prepare themselves to insure survival. But if they can't see a change coming or are not aware of one taking place on a subtle level, they are left with the possibility they may at some time be faced with a potential crisis involving multiple variables. Having nature as an enemy is not a welcomed proposition, though we humans live with such a circumstance. But Nature is quite seductive in presenting itself as a friend, as a savior, as a mother, father and home. And it is this long-standing seduction which has created a dependency like an infant attached to an umbilical cord. Such is the case for mathematics too. It has been seductively successful in creating a dependency on it to the point it is viewed by some as a queen, if not a god that has no equal and encourages unswerving allegiance in the form of a pre occupational usage.
It is long past due for us to put Mathematics to the test by way of an examination. Yep, we must subject Mathematics to a mathematical test, despite all the types of chess-moving antics it might attempt to circumvent or cheat the process of mental, emotional and physical exams that might be alternatively created along such a trekish sojourn.
If we take into consideration a modernized adaptation of the old three-body problem involving the Sun, Earth and Moon, our model contends that as the Sun decays, the Earth's rotation slows and the Moon continues to recede; then the two-patterned night/day sequence will come to change and along with it, all activities which have established a replication of the sequence, with respect to an accountable ability of a given substrate, be it a life form or otherwise. For example, while it is convincingly accepted that the to and fro movement and bulging of tides is caused by planetary activity, and that plants exhibit behavior in conjunction with planetary behavior, we humans are not ready to accept the view that basic patterns found in the developmental nature of complex life forms had its beginnings in the patterns of planetary phenomena such as linking the recurrence of an anus and mouth as an exhibited (diurnal effected) dichotomy which always has to be shown displaying an opposite direction and opposite position on all life forms, or it is not a "typical" dichotomy and therefore can not be an effect of diurnal planetary activity.
Understanding how basic planetary patterns can affect the basic developmental behavior of primitive developmental scenarios requires us to be able to recognize basic patterns as primitive biological processes would have reactively "seen" them under the conditions and time period when such impressions became established by routines. No doubt the dichotomous events of night and day with warming and cooling trends played a part, just as did the increase in oxygen, though the absence of oxygen as a counter-part to oxygen did not necessarily establish itself as a felt dichotomy except by those events existing at the time of the transition between a non- or reduced oxygen environment and one with an increasing content thereof. However, a one, or two or three-patterned event in Nature may have effected a similar pattern of design by way of a proxy, such as affecting chemical activities which then affected biologically particularized ones. In other words, basic patterns related to biological activity could have been established by one or more go-betweens, thereby obscuring the actual origination of a planetary influence.
In establishing some modicum of understanding the existence of a planetary influencing pattern, it is of need for the reader to visualize the Sun blazing down on Earth as it is spinning much faster in the past the it does today. Visually, the triple-patterned stroboscopic effect of a fast spinning Earth (billions of years ago) coupled to an intense Sun (conjectured as a likely candidate for the production of a triple code in the developmental scenario of DNA and the one-two-three sequence of Germ layer development0, will continue to create the situation where the two-patterned night/day sequence is elongated further into an effectual one-pattern— to the eventual point where the Earth stops spinning and the Sun is thought to have expanded in its White Dwarf stage thus consuming the innermost three planets (Mercury, Venus, Earth).
The Sun has been shining for 4.6 billion years. Considerable hydrogen has been converted to helium in the core, where the burning is most rapid. The helium remains there, where it absorbs radiation more readily than hydrogen. This raises the central temperature and increases the brightness. Model calculations conclude that the Sun becomes 10 percent brighter every billion years; hence it must now be at least 40 percent brighter than at the time of planet formation. This would produce an increase in Earth's temperature, but no such effect appears in the fossil record. There were probably compensating thermostatic effects in the atmosphere of Earth, such as the greenhouse effect and cloudiness. The young Sun may also have been more massive, and thus more luminous, and would have lost its early mass through the solar wind. The increase in solar brightness can be expected to continue as the hydrogen in the core is depleted and the region of nuclear burning moves outward. At least as important for the future of Earth is the fact that tidal friction will slow down Earth's rotation until, in four billion years, its rotation will match that of the Moon, turning once in 30 of our present days.
The evolution of the Sun should continue on the same path as that taken by most stars. As the core hydrogen is used up, the nuclear burning will take place in a growing shell surrounding the exhausted core. The star will continue to grow brighter, and when the burning approaches the surface, the Sun will enter the red giant phase, producing an enormous shell that may extend as far as Venus or even Earth. Fortunately, unlike more massive stars that have already reached this state, the Sun will require billions of years to reach this state.
The process of energy generation results from the enormous pressure and density at the centre of the Sun, which makes it possible for nuclei to overcome electrostatic repulsion. (Nuclei are positive and thus repel each other.) Once in some billions of years a given proton (1H, in which the superscript represents the mass of the isotope) is close enough to another to undergo a process called inverse beta decay, in which one proton becomes a neutron and combines with the second to form a deuteron (2D). This is shown symbolically on the first line of equation 1, in which e- is an electron and V is a subatomic particle known as a neutrino.
While this is a rare event, hydrogen atoms are so numerous that it is the main solar energy source. Subsequent encounters (listed on the second and third lines) proceed much faster: the deuteron encounters one of the ubiquitous protons to produce helium-3 (3He), and these in turn form helium-4 (4He). The net result is that four hydrogen atoms are fused into one helium atom. The energy is carried off by gamma-ray photons (ɣ) and neutrinos, V. Because the nuclei must have enough energy to overcome the electrostatic barrier, the rate of energy production varies as the fourth power of the temperature. ("Sun." Encyclopædia Britannica. )
(The foregoing equation presents us with the deuteron (2), Helium (3), Helium (4). It is a 2-3-4 ensemble that shows up elsewhere: Devil's advocate page 14.
However, the repetitions we are seeing in physical and mental activity to the point of suggesting humanity has reached the outskirts of its abilities may not actually represent human capacity in term of potential, but human possibility because of its confinement to an environment which is incrementally deteriorating. It is the combined (3-body) deteriorations of the Sun- Earth- Moon interactions which are forcing life forms on Earth to adopt a formula of adaptation which permits it to gain and sustain the necessary type of equilibrium for existing in such conditions as a rationalistic survival mechanism. Even while different life forms may come to fully realize that they are on a course of sequential extinction, they hold their chins up... so to speak, and face the eventuality with the unrecognized distinction of a species-specific model of rationalization. In terms of humanity, though it recognizes the eventual distinction to come, it rationalistically creates views, beliefs and practices which provide a model of assumed progress to be gained. For example, on the one hand many humans think in terms of an eventual Nature-driven apocalypse or a man-made disaster, many humans also secure for themselves the rationale that they will then enter into a heaven, a paradise, a transcendence, a nirvana or some-such other model of presumed progressive stage of development. It's as if the stages of development which life forms pass through act as an underlying model from which is garnered the idea that the present existence is yet one stage to develop out of into a next one, much like the evolutionary development which life forms have experienced, such as from a diploblastic (two germ layers) to a triploblastic (three germ layers) state of developmental existence (from which we can presume there at one time existed what may be called a "monoploblasitic" stage, even if it was little more than an aggregation of collected-in-one-spot processes).
Whereas comparative embryology and overall anatomical designs exhibit a routinization of similar patterning, even if the initial deductions were incorrectly interpreted to represent a holistic idea that later became recognized as a fragment of the overall collection as in the case of Ernst Haeckel and his biogenetic law which expressed the view that "ontogeny recapitulates phylogeny—i.e., the development of the animal embryo and young traces the evolutionary development of the species". ("biogenetic law." Encyclopædia Britannica Ultimate Reference Suite, 2013.) It was an interesting holistic view in his era of exploration but later became altered to be describe a much smaller venue of development stated as "embryonic ontogeny recapitulates embryonic phylogeny". Below is an illustration of Haeckel's collection of different animal life forms exhibiting similarities.
While later observers criticized the collection as a fraud, the idea was nonetheless not only unique, but a representation of a cognitive orientation as a recurrence in the human brain. The orientations were similarly dualistic in their basic formulation such as encountered in other subject areas using characterizations such as from left-to-right, top-to-bottom, inside-to-outside, early-to-late, primitive-to-complex, mouth-to-anus, etc., including the reversal of such ideas. The point is, by taking one example from the foregoing list, is it Natural for humans to think (hear, see, taste, feel, write, etc...) in a left to right fashion, or is this an imposed formula of an underlying "two"-based compartmentalization of mental processing?
Similarly, whereas some may say that the drivers of most vehicles are prone to make right-hand turns, is this the case in all situations, most situations, or only some situations? If we view mathematic's as a type of vehicle being driven by billions of people (where different uses of numbers/mathematic's are represented by different types of vehicles from hand held cars to kiddy cars to racing cars, trucks, off-road vehicles, motorcycles, bicycles, etc...), are we to overlook the distinct usage of numerically referenced 1-wheeled vehicles (unicycles, wheelbarrows), 2-wheeled vehicles (bicycles/motorcycles/rickshaws/box-moving dollys, roller cabinets, etc...), 3-wheeled vehicles (tricycles, 3-wheelers, etc...), 4-wheeled vehicles (most motor vehicles/farm tractors/skates, skateboards, etc...), "5-wheeled" vehicles (5th wheel, steering wheel), 6-wheeled vehicles (buses, semi-truck tractors), etc..., and those vehicles with multiple, but a limited array of wheels (Tractor and trailer semi-trucks...18 wheelers..., tanks... multiple wheels encased in chain tracks, half-tracks, machinery, mechanical watches, etc...)?
While the different types of vehicles (mathematics/counting) have differentiated utility, the different applications need not be used to obscure basic patterns such as stop/go, up/down, from here to there, inside/outside. In other words, the complexity to which we humans apply mathematics to different configurations of underlying simple patterns need not obscure that a lack of progress is being made in the usage of the types of basic patterns. Mathematics is not moving humanity ahead despite all the external types of makes and models that are being fabricated and sold as a "new math":. We most often describe a vehicles power in terms of horse power. An old idea adapted to a different setting which helped the public find a meaningful comparison between flesh and bone (horse) transportation and mechanized transportation. Mathematicians use a similar tactic to sale the idea for the necessity of using mathematics, whereby no one is looking to step beyond this type of thinking to envision a new model which can transport human abilities into a new age. Similarly, Nature itself is not redesigning itself. It still uses the old tool called evolution, and its triplet-code pattern in DNA/RNA appears to be exempt from Evolution expressed in what could be counted such as a quadruplet, quintuplet, sextuplet, etc... codon system. Like politicians erecting laws which permit them to either circumvent them by claiming a specialized "National Security" provision, structure them with some loophole to take advantage of, or have some other stay-out-of-jail card such as a diplomatic immunity, both Nature and Mathematic's appear to work off of a similar premise of plausible deniability when things go wrong.
If we say that the recurring dichotomies to be found in mathematics is as natural as the pairing of amino acids is, does this automatically excuse mathematic's from likewise using this presumed natural order of processing as a reflection of an origin on a path towards obsolescence? Whereas a sail, oar, and life sustaining provisions accompanying you on a raft/boat in the middle of an ocean may provide comfort and hope of reaching some body of land, there is no guarantee that all will go well. Neither can the stable staples provided for by the underlying patterns in DNA and Mathematics... regardless of one's obsessional belief in such Natural provisions. If mathematic's is but an echo of Natural processes which come to change to the extent of creating an extinction of humanity, then the spider webs called human civilization (seen in the left-over monuments of past cultures), can well present any future being with a sticky mess of distraction, such as sentimental advocacies of claimed historical value.
Granted there are incremental changes in one subject area or activity from some former representation, but most often what we see is merely a swapping of placements, practices, and (typically)... people involved. Add to this that human individual and collective memory can be very short indeed, we are presented with a situation that it is frequently difficult for some people to recognize either a repetition or advancement. Change by way of simple substitution is sometimes described as a change (for the better or worse); even while the change does not in fact represent an advancement... however one might come to define what is meant by an advancement other than the mere adoption of one or more substitutions. Take for example the case in which one person replaces another as a political leader. While some may claim this as an advancement, the advancement in this case may mean little more than getting rid of corruption, and not that the underlying form of government has actually been altered to prevent any future corruption by one or more leaders from ever being elected to office again.
The same sort of changes can take place in any academic field. In the present case of examining Mathematics, we are confronted with a situation which I am claiming to be representative of a field that has reached a cognitive limitation due to an underlying repetition of a basic structure which is preventing it from advancing except by way of substitution. There is no new field of mathematics which has been developed to significantly alter the life framework of humanity. Mathematics, like all other genres of intellectual pursuit, has reached an impasse and is currently spinning it wheels... though the current drivers of the subject are too focused looking out their windshields to take a look sideways or rearward. It is like a circle of trucks bogged down a muddied ravine who can't actually see in front of themselves because the windshields are muddied by others attempting to race ahead in hopes of discovering some hitherto unexplored realm where some golden fleece, golden chalice or other golden opportunity awaits those who are willing to make not only the necessary amount of sacrifices, but the correct ones as well.
While different analogies exist to be used in the present essay, the present one will suffice as a means of introducing a recurring dependence by current mathematical models, on what I perceive to be an over-reliance upon the usage of dichotomization— as is found in psychology as well, and has been referred to as a condition of Persistent Dichotomies. In order to understand what I am talking about, it is of need to realize there is a large presence of dichotomization in Mathematics. While some readers may already be aware of this, they may not have placed their observation into the context of an enlarged set of examples found in other genres of research. Let me first provide a few examples from Mathematics (Dualities in Mathematics), and then some from psychology, though dichotomies from other subjects might well be included. And it should be noted that the word "dichotomy" is being illustrated in the present context with a multiplicity of intellectual garments such as opposition, complimentary, complementary, juxtapositioning, etc., and in general, as a pattern-of-two that may alternatively be represented by various labels within the context of a given subject's adopted vernacular, such as for example, duality, duo, bilayer, dimer, bifurcation, bipolar, fork, twice, two, one and one, three minus one, biad, couple, handedness, radius, etc..., some of which may indirectly point to a "two" but only a single and/or multiplicity are conventionally expressed.
Dualities in Mathematics
- add/subtract
- whole numbers/fractions
- real numbers/imaginary numbers
- positive/negative (a "neutral" is cognitively available for inclusion)
- geometric/non-geometric
- multiply/divide
- X axis/y axis
- greater than/less than (equal to is centralized position)
- subscript/superscript ("middlescript" exists but is not characteristically labeled)
- (integer but no "outeger" nor "midteger"?)
- probability/improbability
- possibility/impossibility
- finite/infinitesimal
- Constructive (standard-traditional) analysis/Non-standard analysis
- decidability and undecidability (as part of the two incompleteness theorems found in a discussion on meta-logic; from which the notion that axioms present us with a mechanistic adherence to problem solving. "metalogic." Encyclopædia Britannica. Article by Hao Wang, Professor of Logic, Rockefeller University, New York City, 1967–91. Author of Logic, Computers and Sets and others. And Morton L. Schagrin, Professor of Philosophy, State University of New York College at Fredonia. Author of The Language of Logic.)
Dualities in Psychology
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And let us not forget to include such well-known dualities as spiritual/material, body/soul, and the Nature/Nurture controversy, the Chicken/Egg dilemma, inner space/outer space, Micro-/Macro-, Black/White (raciality), rich/poor (upper/lower social classes), Major/Minor musical cords, singularity/multiplicity, slow/fast, in the red/in the black (accounting), forward/about face, etc... In fact, let us take any subject and we can find some representative expressions of two-based ideas illustrated with a given subject's working vernacular. And yes, it is fully recognized that there are other patterns but the point to be made is that there appear to be only certain patterns which repeat themselves in multiple subjects. If one creates a makeshift graph simply to introduce the idea without intending to provide any real representative occurrence, we can imaginatively design a graph for the purposes of a philosophical conversation piece, which quickly advances to the notion we may be dealing with a diagrammatic puzzle akin to a Hamiltonian circuit occurring in three dimensions instead of a singularity, that a simple illustration such as the following is a simplistic beginning of a path similarly reviewed in other puzzles such as the three wells and the 7 bridges ideas.
If we view the frequency that certain number patterns occur in different subjects both individually and collectively, as well as in different combinations, the frequencies (as well as lack thereof suggested by the word "infrequency" and the notion of intermittent frequency), a researcher might think in terms of starts, stops, and jerking movements... all of which can have different durations. Nonetheless, it presents us with a model of information that traditional numerologists have tried to supply us with, but owning to the widespread disinterest in an activity that is most often off-handedly dismissed as being irrelevant, a larger study of a larger sampling from a larger subject base has not been undertaken. Commonly, there are those who frequently react to a "collection of threes" (which involves more than just patterns-of-three though it may be the originating dominant theme of a given task); as a rather quixotic pursuit of information consistent with a hobby of collecting some odd occurrence of a (typically) manufactured good/item, though there are those who collect only items to be found that have been manufactured by nature such as diamonds, shells, flat stones, triangular stones, fossils, butterflies, plants, leaves, etc...
Date of Origination: 19th March 2022... 5:23 AM
Initial Posting: 24th March 2022... 3:24 AM
Updated Posting: 2nd January 2023... 11:00 AM