Threesology Research Journal: Static versus Dynamic Equations
"Infinitesimal versus Accordian Calculus"
(Static -vrs- Dynamic)

~ The Study of Threes ~

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With respect to addiction, two types are generally considered to cover all forms being treated since they cause debilitating circumstances, but I shall add a third by correlating the addiction types to the states of matter. Addictions are those activities which cause a person to become a problem to themselves or others who must depend on them for a level of support which a given addiction interferes with, often treated by creating the rationale for adopting a substitution, such as seen in Alcoholics Anonymous Efforts.

  1. Behavioral addiction (Solid): typically those activities revolving around repetitive, if not compulsive, non-chemically related substance scenarios, but can involve solid objects such as gambling, sex, computer/internet, reading, studying, full time student status, as well as those seen in collecting guns, or string, or hats, or comic books, or movies, or newspapers, magazines, webpages, books, etc...
  2. Chemical addiction (Liquid): such as alcohol, ... though this category is used to describe hard forms such as pills, and includes items for a third unnamed category:
  3. Gaseous addictions... involving the sniffing of glue, paint, gasoline, smell of burning items (such as in the case of some fire-starters), and other non-solid chemicals.

Different treatment centers may used different categories, but the point to make, with respect to mathematics, is that the process of mathematics has been established as an appropriate addiction out of which it becomes applied to all forms of human behavior, even when a person is not aware they are engaged in using mathematics. Mathematics is an international addiction just like science, business, religion, cooking, eating, drinking, etc. Repetition on this level is not only difficult to curtail, much less stop, but even the introduction of a new type of mathematics (or any other human activity), typically becomes rejected at first. An old adage for reactions to something new is:

All truth passes through three stages. First, it is ridiculed. Second, it is violently opposed. Third, it is accepted as being self-evident... Arthur Schopenhauer, German philosopher (1788 – 1860)

An example of this can be represented by the research ideas of Lynn Margulis (Her married name at one time was Lynn Sagan... She had been married eight years to Carl Sagan the noted Astronomer and Astrophysicist who would later marry two other women.) Throughout her career, Margulis' work could arouse intense objection (one grant application elicited the response, "Your research is crap. Don't ever bother to apply again.") and her formative paper, "On the Origin of Mitosing Cells", appeared in 1967 after being rejected by about fifteen journals.

While there are variations of the above quote if one broadens one's perspective such as comparing it to a basic representative model of mentality which is similarly seen in basic forms of logic like the And- Or- Not gates of electronics, the Major- Minor- Conclusion premises in Philosophy or the A2 + B2 = C2 in mathematics, etc..., the point might be better understood if I place it into a context of additional ideological breakthroughs that were initially rejected:

  1. Gauss famously discarded Abel's proof that an algebraic equation of degree five or more cannot have a general solution (Abel himself had rejected divergent series as the work of the devil).
  2. Cantor's theory of transfinite numbers was originally regarded as so counter-intuitive—even shocking—that it encountered resistance from mathematical contemporaries such as Leopold Kronecker and Henri Poincaré and later from Hermann Weyl and L. E. J. Brouwer, while Ludwig Wittgenstein raised philosophical objections.
  3. Ramanujan's work on divergent series was rejected by three leading English mathematicians of the time before he was discovered by Hardy.

7 Scientists whose ideas were rejected during their lifetimes By The Doc

Describing a law with three items
  1. Alfred Wegener (1880 to 1930): Continental Drift
  2. Ignaz Semmelweis (Lived 1818 to 1865): Hand Washing Saves Lives
  3. Aristarchus (c. 310 BC to c. 230 BC): Heliocentric Solar System
  4. Gregor Mendel (1822 to 1884): Genetic Inheritance
  5. Nicholas Copernicus (1473 to 1543): Heliocentric Solar System
  6. Johannes Kepler (1571 to 1630): Heliocentric Solar System – Elliptical Orbits
  7. Amedeo Avogadro (1776 – 1856): Avogadro's Law

Rejection with Reason: Of course, many big new scientific ideas are rightly rejected, because most are flawed. Otherwise, today we might accept ideas such as the existence of: Planet Vulcan, N-Rays, Caloric, Pangenesis, an inhabited Sun, and the number of the Universe.

6 World-Changing Ideas That Were Originally Rejected by Damon Isherwood

  1. The Earth is Round – 330 BC: In the 6th Century BC, Pythagoras declared the world was round although other Greek philosophers remained unconvinced until 330BC when Aristotle championed the idea of a round Earth.
  2. The Earth Revolves Around the Sun – 1600s: It probably won't come as a surprise to hear that we originally thought we were at the centre of the universe. The church believed in the idea so much that in the early 1600s they burnt Giordano Bruno at the stake and later sentenced Galileo to house arrest for supporting the Copernican theory that the Earth revolved around the sun. However, the real opposition was from other scientists who held to the view established by Aristotle almost 2000 years before, that the Earth was at the centre of the universe. Today, Galileo is often referred to as the father of modern science.
  3. Darwin's Theory of Natural Selection – 1838: Before Darwin put forward his scientific theory of natural selection in 1838 (he withheld its publication for eight years for fear of opposition), it was generally believed that life on Earth had been unchanging through the millennia.
  4. Pasteurization: Diseases are spread by germs – 1850s: Louis Pasteur thought that disease was spread by germs. He made the discovery after three of his five children died from infectious diseases. When he first put forward his theory in the 1850's he was met with violent resistance from the medical community.
  5. Bacteria Causes Stomach Ulcers – 2005: In 2005 Barry J. Marshall and J. Robin Warren were awarded the Nobel Prize for their discovery that bacteria is responsible for stomach ulcers. However wind the clock back 20 years and Marshall and Warren's idea was being ridiculed by the scientific establishment who maintained that bacteria couldn't live in the acidic environment of the stomach, and that it was just stress or bad diet that was to blame.
  6. Breakthrough Biological Theories on the Human Condition – 1983

4 Scientists That Were Disregarded During Their Time

  1. George Zweig A theoretical physicist: Zweig proposed the theory of quarks right after defending his PhD thesis and at the same time as rival Murray Gell-Mann. However, because Zweig was a young graduate student and not as well established, the journal that both scientists sent their respective papers to, accepted Gell-Mann's after rejecting Zweig's for the same theory. Gell-Mann then went to receive a Nobel Prize in Physics for his work (a real kick in the quarks you could say).
  2. Ludwig Boltzmann: Boltzmann developed equations and formulas which explain the properties of atoms and how they determine the physical nature of matter. Now it transpires that proposing a theory that disproves other laws of physics (and scientists) thought to be correct at the time does not make you particularly popular or appreciated. After years of fighting for atom theory to be accepted, Boltzmann committed suicide. This was only 3 years before Ernest Rutherford discovered the nucleus of an atom, proving Boltzmann's theory.
  3. Gregor Mendel: Genetic inheritance
  4. Ignaz Semmelweis: Hand washing

However, it is simply arrogance for humanity to think that their present form(s) of mathematics is somehow to be labeled a Universal language shared by all sentient beings throughout the Universe simply because we humans think we have somehow reached the pinnacle of cognitive expression which we have uncovered by a close examination of reality; instead of surmising the very real possibility that our forms of mathematics is little more than some imaginative construct like so many other artefacts uncovered as pastimes of large ancient civilizations and lesser nomadic or stationary groups. As such, whether one believes that:

  1. Mathematics is THE WAY of expressing Universally applicable thought processing that humans have uncovered— by a close examination of natural events— because such events, by someone or something for some unknown reason had fashion them to keep such a knowledge hidden from humanity until we had achieved a certain level of mental maturity;... or that,
  2. Mathematics is merely an imaginative artefact akin to some artistic exposition... we need to unravel at least a miniaturized proportionality of mathematic's origins in an attempt to identify if humanity has not mistakenly taken a path at some past crossroads, where another trail, if it had been chosen, would have provided a more prosperous realization of the elusive golden chalice, golden fleece and all things glittering, that many today label as truth... a kind of truth that only pure mathematics is capable of rendering visible, comprehensibly, and applicable to the human condition.

Despite the many histories of mathematics which have been provided in excellent and well-written formulas of expression in an effort to provide different readerships with a valid and authentic recreation of formative steps; those expressions generally do not attempt to step back and view the path we are on... mathematically speaking, as perhaps the result of an impulsively puerile side-ways explorations distracted by chasing after butterflies, catching falling leaves, wistful cloud orientations, fire-fly capturing expeditions... and multiple other scientific, cultural, religious, economic, gender-dominant, political imperialisms, military forays, and gaming types of excursions. Needless to say that those who prefer Pure Mathematics in contrast to those solely interested in the consumerized models of math applications; have met with an instigation of their unsullied realm being thrust into a cave intimated as a cult of old world Conjurers, Mystics, Magi, Sorcerers, and various other transmutation specialists in and out of the Alchemical disposition.

In other worlds, there are many who have come to question the legitimacy of claims being made by mathematicians in regards to mathematics being the penultimate means by which all of life can best be investigated, interpreted and understood. At least not in the present guises it teaches year in and year out to multiple millions who have not provide the supposed great truths which can only be appropriately uncovered, or analyzed, or made comprehensible by way of some mathematical application. Yes, many come to question whether or not mathematics is the so-called Universal language that all sentient beings will be familiar with and thereby provide us with an instant means of understanding one another. Suspicions arise when we see that not all primitive cultures have what might be said to be a mathematical mind, even if they have a rudimentary counting system with categories resembling one, two, three or a few more quantitative word to number associations. Hence, if mathematics is not a supposed instinct (just as some claim that language is an instinct); and requires an increasingly complex social order in which to be generated, then we have to surmise that the present brand(s) of human mathematics is a cultural construct... or cultural artefact of the present models of human civilization just like art, music, acting, dance, architecture, foodstuffs, etc...

Then again, let us make note of the fact that societies practice inequality. While this inequality allows them to spread and prosper... though there typically is widespread inequality, discrimination, bias, slavery... or indentured servitude... or some other social enforcement for people to work under impoverished conditions, this is the currency of social thought under which the present forms of mathematics have arisen. In certain regards so-called modern mathematics arose as a spectral caricature with a backdrop of multiple disparities, and must therefore be looked upon as so many digging, probing, throwing, cutting, stirring, killing, eating, stirring, etc., tools which arise in different contexts in different cultures throughout history, including the tools used by insects ants (for example: Clever ants use grains of sand as 'tools' to reach their food when faced with the risk of drowning, study finds, and another example: Ants craft tiny sponges to dip into honey and carry it home by Kata Karáth, 30 Dec. 2016), birds (for example: New Caledonian crows can use tools like sticks and stones, in a pre-planned fashion, to accomplish a goal. by Douglas Main, Feb 7, 2019), and 10 Animals That Use Tools by Charles Q. Choi, Dec. 14, 2009.

Seeing as how the ever-presently required axioms come from assumptions and beliefs and that assumptions and beliefs are contoured by the environment in which they are born; if we alter the ideological environment with a new philosophical perspective supported by informed rationales of available information and testability, then the production of a new form of mathematics as is being suggested by "Accordian Mathematics" has enough merit for further consideration. Given this implication, the notion that we humans are straddling a 2 and 3-dimensional perspicuity due to the position in time and status of evolutionary development being experienced, a two-patterned versus three-patterned dominant intellectual contention accounts for the many different forms of contrast where multiplicity may come into play such as:

  • 2 versus 3, or 4 versus 6, or 8 versus 12, etc...
  • biad versus triad
  • binary versus ternary
  • dual versus triple
  • dichotomy versus trichotomy
  • dimer versus trimer
  • 2-pronged versus 3-pronged (or 4-pronged versus 3-pronged)
  • double stranded versus triplet code
  • seven plus or minus two versus 5-7-9
  • squared versus cubed (quadralineal versus cubed)
  • stop and go versus stop-wait-go
  • hot and cold versus hot-warm-cold
  • black and white versus black-grey-white
  • etc...

While one may note contrasts, it might be more profitable to view the situation as a reflection of a transitional point in which our consciousness inhabits. Like a bipolar perspective that seeks out patterns-of-two like a mirror image inclination suggesting an active mirror neuron activity seeking a means to communicate perceptions because the more developed counterpart from which language is said to show some approximation, may not yet be fully functional. Analogously, whereas we humans are inclined to think that we have somehow reached our full developmental potential just as the long enduring Homo erectus may have considered themselves to be, if such a thought was possible in their contemplations. The point being is that present humans either have the ability to develop further or will be replaced by some creature with a greater mental faculty; thus indicating that which we think today as being marvelous such as our art, music, language, religion, politics, business, medicine/dentistry, sports, science, mathematics, etc., is exceptionally primitive when future humans will contrast themselves to us. Yet the development of mathematics does not appear to be the result of humans living in a vacuum and the result of which appears to require a complex and competitive society. While Homo erectus is said to have shared a period of direct?/ indirect? "co-habitation" of living alongside Australopithecus and Paranthropus, we cannot at present determine if any of them (alone or in competition with one another)even had a rudimentary form of counting system, much less primitive sense of mathematics. (In Groundbreaking Find, Three Kinds of Early Humans Unearthed Living Together in South Africa by Brian Handwerk, April 2, 2020)

Let me see if this representation will make the situation clearer for some readers: The presence of so many dichotomous ideas occurring in Mathematics is a tale-tell indication of the dominant frame of mind in which the dominant portion of mathematical development occurred. If there had been a dominant cultural habituation of using trichotomies, what we have in the way of mathematics might be expressly different. Another way of looking at this is to take stock of the fact that the three dominant monotheistic (one-god) religions identified as Christianity- Islam and Judaism all came unto their own in desert environments. If the environments had been jungle, ocean-side or other-than-desert regions, these religions might well have developed differently, if at all. However, it should be noted that another monotheistic religion also born in the desert, dislike Christianity, Islam and Judaism:

Abrahamic religions

The Abrahamic religions, also referred to collectively as the world of Abrahamism and Semitic religions, are a group of Semitic-originated religions that claim descent from the Judaism of the ancient Israelites and the worship of the God of Abraham. The Abrahamic religions are monotheistic, with the term deriving from the patriarch Abraham (a major figure described in the Tanakh, the Bible, and the Quran, recognized by Jews, Christians, Muslims, and others). The three major Abrahamic religions trace their origins to the first two sons of Abraham: for Jews and Christians it is his second son Isaac, and for Muslims his elder son Ishmael.

Abrahamic religions spread globally through Christianity being adopted by the Roman Empire in the 4th century and Islam by the Umayyad Empire from the 7th century. Today the Abrahamic religions are one of the major divisions in comparative religion (along with Indian, Iranian, and East Asian religions). The major Abrahamic religions in chronological order of founding are Judaism (the source of the other two religions) in the 6th century BCE, Christianity in the 1st century CE, and Islam in the 7th century CE.

Christianity, Islam, and Judaism are the Abrahamic religions with the greatest numbers of adherents. Abrahamic religions with fewer adherents include the Bahá'í Faith, Druzism (sometimes considered a school of Ismaili Islam), Yazidism, Samaritanism, and Rastafari.


Mandaeism or Mandaeanism (Arabic: Manda'iyah) is a monotheistic Gnostic religion with a strongly dualistic worldview. Its adherents, the Mandaeans, revere Adam, Abel, Seth, Enos, Noah, Shem, Aram, and especially John the Baptist.

The Mandaeans do not worship the God of Abraham and they hate Abraham, considering him, along with Moses, Jesus and Muhammad, to be a false prophet. They regard the Abrahamic religions of Judaism, Christianity and Islam as hostile or enemy religions. Abraham, or Braham, was a priest of the Mandai, who, because he was circumcised, went out into the desert with the lepers and the unclean and began to worship Yurba, one of the powers of Darkness. It was through Yurba's power of Darkness that Abraham and his people became strong. The Mandaeans are Gnostics and worship a supreme God far removed from the malevolent creator god of the material world, who in Mandaean writings, is identified as the Lord of the Old Testament and is associated with the Holy Spirit. Both the Lord and the Holy Spirit are regarded as malevolent figures.[85] While biblically informed, Mandaeanism has been characterized as "not-exactly-Abrahamic-or-Muslim" dualism.


Dualism and Monism

Gnostic systems postulate a dualism between God and the world, varying from the "radical dualist" systems of Manichaeism to the "mitigated dualism" of classic gnostic movements. Radical dualism, or absolute dualism, posits two co-equal divine forces, while in mitigated dualism one of the two principles is in some way inferior to the other. In qualified monism the second entity may be divine or semi-divine. Valentinian Gnosticism is a form of monism, expressed in terms previously used in a dualistic manner.


In many Gnostic systems, God is known as the Monad, the One.[note 18] God is the high source of the pleroma, the region of light. The various emanations of God are called æons. According to Hippolytus, this view was inspired by the Pythagoreans, who called the first thing that came into existence the Monad, which begat the dyad, which begat the numbers, which begat the point, begetting lines, etc.

The Sethian cosmogony as most famously contained in the Apocryphon ("Secret book") of John describes an unknown God, very similar to the orthodox apophatic theology, but different from the orthodox teachings that this God is the creator of heaven and earth. Orthodox theologians often attempt to define God through a series of explicit positive statements: he is omniscient, omnipotent, and truly benevolent. The Sethian hidden transcendent God is, by contrast, defined through negative theology: he is immovable, invisible, intangible, ineffable; commonly, "he" is seen as being hermaphroditic, a potent symbol for being, as it were, "all-containing". In the Apocryphon of John, this god is good in that it bestows goodness. After the apophatic statements, the process of the Divine in action is used to describe the effect of such a god.

Note: we see an underlying mathematical (1-2-3) set-theory arrangement of human cognition disclosed by the words Monad- Dualism- Trinitarianism occupying the fundamental belief systems of several religions... with individual preoccupations enabled to be delineated. Indeed, the concept of an "Unknown" god speaks to the value of zero (0), while the three recurring attributions of a supposed god (Omnipotent- Omniscient- Omnipresent) as reflective of the idea of infinity. If we carry this scenario further, one might indulge in a standard form of Biblical referencing... for example, by looking at the mathematical 3.14 (π) as a representation of one or more biblical passages that one might secure from the three synoptic (Mark, Matthew, Luke) and one idiosyncratic (John) gospels (which is another 3 to 1 ratio example), we have the following to be contrasted with other 3.14 Biblical passages and then unravel the supposed code... if indeed writers of the Bible used the value for a specific purpose:

  1. Mark (3.14): And he ordained twelve, that they should be with him, and that he might send them forth to preach,
  2. Matthew (3.14): "I need to be baptized by you, and do you come to me?"
  3. Luke (3.14): and the soldiers likewise demanded of him, saying, And what shall we do? And he said unto them, Do violence to no man, neither accuse any falsely; and be content with your wages.
    1. John (3.14): And just as Moses lifted up the serpent in the wilderness, so must the Son of Man be lifted up

Then again, one could mix and match any of the 3.14 comments from the different 'books' of the bible to reveal a different account... which could very well lead to some interesting scenarios and interpretations if the bible and other religious texts were subjected to an analysis confronted by an effort to provide an expose' of the development of mathematical concepts in concert with the development of biblical traditions of translation over the centuries since numbers play such a crucial role and that ancient mentalities used cryptic forms of numerical interlacings in which to conceal, transfer, relay, code and otherwise obscure hidden messages and meanings. In order to do so, one would have to have a widely informed grasp of mathematical history and its interrelationship with biblical scholars who took part in the chronicling of biblical materials. It would make for an interesting read if you could correlate the two correctly, which would involve the transference of ideas between different religious scholars involved in the old traditions within a given religious culture.

If what I have been outlining does in fact represent humanity in a transitional development stage, is it possible to push ourselves further out onto the Savannah of enlightenment by presenting a new model of mathematics? Can we use current forms of mathematics as a vehicle for a change in human evolution? Can a new model of mathematical inquiry set the stage for altering human evolution by providing a means for adjusting our perceptions to the existence of a reality better suited to the brain patterns conducive to an advanced species of homonin? Or are we faced with a situation in which even if we could get a monkey to have the brain patterns of present humans with their multiple types of symbolic communication forms, the monkey would essentially not develop into a human with human features, but use the human mindset to rationalize the propriety of the monkey body with its agilities and strengths? Or... could we introduce evolutionary change by adopting a new model of mathematical inquiry which would lead to redesigning society out of which would emerge an improved species? Can improving the purity of pure mathematics provide the necessary vehicle by which humanity can more easily and more quickly reach advanced points of availability, even if those points are not now even on the proverbial radar of present mathematical drawing boards?

Date of Origination: 26 February 2021... 6:59 AM
Initial Posting: June 4th, 2021... 7:04 AM