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What I am trying to accomplish is to show that not only is there an over-riding reliance of patterns-of-two in mathematics, but provide examples of patterns-of-three as a contrast. If you are not firmly conscious of how frequent patterns-of-three crop up in different subjects in different guises, the presence of patterns-of-two may not likewise be firmly acknowledge and represent a primivity of conceptualization as does the over-riding reliance of "twos" in economics which brings humanity recurring problems. This statement needs to be restated on each of the dualities pages because they do not explicitly focus on patterns-of-two alone.
Here is a short list of Anatomical directional terms which can otherwise refer to geometrical orientations or quantitatively... to one, two, or three (sometimes referred to as "Many" or "Much" or "Bunch" or "All"). It is helpful to identify the meaning of a word or phrase which can represent a quantity. Since words are used in mathematics, the underlying numerical or quantitative symbolism needs to be acknowledged in order to grasp what I mean by the abundant usage of dualities or dichotomies as opposed to other quantities. If someone does not explicitly point out a recurrence of "threes" in anatomy, you might not come to make the connection yourself in any forceful recognition to be used in other settings. Here is an example of A list of threes in Anatomy.
- Anterior: In front of, front
- Posterior: After, behind, following, toward the rear
- Distal: Away from, farther from the origin
- Proximal: Near, closer to the origin
- Dorsal: Near the upper surface, toward the back
- Ventral: Toward the bottom, toward the belly
- Superior: Above, over
- Inferior: Below, under
- Lateral: Toward the side, away from the mid-line
- Medial: Toward the mid-line, middle, away from the side
- Rostral: Toward the front
- Caudal: Toward the back, toward the tail
- Bilateral: Involving both sides of the body
- Unilateral: Involving one side of the body
- Ipsilateral: On the same side of the body
- Contralateral: On opposite sides of the body
- Parietal: Relating to a body cavity wall
- Visceral: Relating to organs within body cavities
- Axial: Around a central axis
- Intermediate: Between two structures
In short, Mathematics can not get past the third counting element. Its abundant usage of dichotomous references reeks of the same mentality found in the dual expressions of the Yin/Yang idea, as well as the 0/1 language found in computers. While the patterns are indeed useful, they also describe a redundancy of thought processing whose origin is necessary to understand in order to plot its course over time as the resources of the planet Earth continue to depreciate. Equations are the language of expression which have taken on the role which conceals the presence of a primitive cognitive base being used in mathematics, and the global teaching methods being used are assisting— in fact demanding that the public continue in its usage of this primitive thinking pattern. Just because we have devised a symbol for the concept of "one" as well as a word shared by millions, does not mean this is appreciably different from a primitive's sage of "ugh" and a scratch mark.
Similarly, looking at the real Mona Lisa as opposed to a painting or picture thereof, does not provide for an appreciable difference in the behavior of viewing in the first place. While alternative words and symbols can be used to describe a situation which assists someone in creating an equation that others have failed to may be interpreted as a feat of genius, the standard level of perceptual capacity of the human species remains the same ... in some sense, but in another sense, camouflages the presence of a wide-spread deterioration taking place. A genius equation is of little value if others do not grasp its utility beyond the claims of a few describing it as an expression of superior thinking. A painting and picture are embellishments of the same activity. However, this is a situation that others are aware of, as if they are a Cro-magnon attempting to teach Neanderthals to count higher. Current mathematics, all of it, is a Neanderthal model of conceptualization. Since so many religions, governments, and businesses are run by a similarity of Neanderthal thinking, it is difficult to introduce a new way of thinking when so many rely on the primivity of their mathematical Neanderthalism. A Neanderthalistic Mathematicalization is present everywhere, having produced a religion-like following amongst those who assist in the culture perpetuating the same orientations of thought.
Though not explicitly stated as a routinely-used mathematical expression, in some mathematics symbols and operations, the opposite of an idea is frequently inferred. The situation for the recurrence of dualities or dichotomies or opposites... as they may be called from one person to the next, is of need to be reviewed to some extent in order that the presence of a simplistic way of thinking is identified. For example, let us look at Infinity and its proposed opposite:
- Infinitesimal/ Infinity:
- Infinity is the largest number there is, so the opposite of infinity would be the smallest number there is.] ( What Is The Opposite Of Infinity?)
- There is no specific math symbol stating the word "opposite", though the − (minus sign) comes close. It is used for the absent html: ["&neg;") (negative) symbol as well. Hence, one for two.
- The usage of mathematics is not language rich. Many of the dualities of word groups (right/wrong, night/day, white/black, etc... ) found in language do not occur in mathematics... per sey. Mathematics attempts to cover all instances of oppositional with a few symbols as if to condense, symbolize and abbreviate language so that we will arrive at some supposed basic cognitive structure of human thinking; but mathematics also is an unrecognized longhand that needs further development, though many might argue it is the definitive shorthand approach to logical thinking. In other words, despite its brevity and usage of stripped-down symbols to achieve some sought-after purity (without embellished frills, lace, etc. found in language), mathematics remains a primitive model of human thinking whose potential has not yet been surveyed, much less tapped. Mathematicians are keeping math in its present primitive state of expression.
In an effort to expose the underlying basic patterns being used in the "cognitive stream" of mathematical activity. A list of at least a few of the many symbol-related ideas should be provided. However, please understand I am not trying to be exhaustive, just representative, so that this recurrence of pattern can be seen as a similar currency of mental activity being used in all other subjects as well, whereby we can assess a larger scope of basic cognitive activity as a similarity of functionality. By itemizing the patterns of mental activity occurring on a basic level, we can come to realize that the state of human thinking is in a very primitive form of expression. In other words, the brain activity of humans is on a level similar to the simplistic counting method used by primitive peoples. Despite all the elaborations and symbols employed to illustrate human thinking, what we can see is a very primitive exercise... as if the human mind will not evolve into a more complex mode of thinking... The reason(s) for this may be diet, may be culture, and/or related to what I believe is an environmentally enforced conservation as an adaptation against three incrementally occurring environmental deteriorations that humanity does not have the intelligence nor capability to alter... and the only thing humanity can do is leave the planet, leave the solar system and leave the galaxy. All resources and all energies and all forms of education, business, religion and politics need to be focused on the same task of getting humanity away from the environmental enslavement of a form of conservation which is dragging humanity towards the same fate of deterioration. Humanity can not persist in its foolishness of comparing species-related time intervals with those intervals of time related to geological and astronomical events. It is both silly and rather stupid to equate the life span of humans in an individual or collective sense to geological and astronomical processes of time displacement. Human life span is miniscule, and must be factored in accordingly, with a new model of calculus that present day biologists, physicists, philosophers, and mathematicians are not using because they are invested too deeply into a model of mathematics is akin to notching marks on a stone, bone, or some visualized unknown which is never shown.
The three incremental deteriorations are:
- The Sun is burning out. It's incremental deterioration is affecting all of biology. It is difficult to appreciate the level of conservation we are adopting in response, because we formulate rationalizations which keep us tide to the Earth, such as by referring to a piece of land as "the father land" or "Mother land" (notice no son, daughter or relative is assigned recognition); or labeling it as "mother earth", when we should be thinking in terms of forcing humanity to grow up and severe the umbilical cord by getting humanity away from the Earth, and not be dependent on NASA or any government, business, or religious run space agency or endeavor whose ulterior motives are governed by selfishness, short-sightedness, and self-serving strategies which create philosophies and policies that are meant to cage, chain and otherwise restrain human development beyond their egocentricity.
- The Earth's rotation is slowing. The electro-magnetic dynamo is undergoing incremental deteriorations. They are not recognized in the necessary context because researchers are using the wrong philosophy of detection and 'resultation'. Their equations are incorrectly focused onto blueprints which were drawn up by antiquated idealisms being perpetuated by a system of mathematics that is detrimental to the continued existence of the species. The once more accelerated rate of the Sun's effects on biology due to an increased rate of rotation can be correlated with the emergence of humanity and other life forms. In other words, the length of day at the time of humanity's emergence may signal that there is a dependence upon how fast the Earth must be spinning in order for there to be a viable environment for humanity to prosper in. Too slow or too fast a rotation is not good for certain life forms, if all of life as well. The human ability to adapt has a limitation... a limitation that can otherwise be labeled a conservation... or an environmentally forced-on-us requirement to create rationalizations both as a defense mechanism and survival mechanism in relation to the incremental deteriorations.
- The Moon is receding. The Moon in the distant past once loomed much larger in the sky. It is well known that the position of the Moon to the Earth alters the flow of ocean tides. As the Moon recedes further, the tides one day will stop. The (what I call) "washing machine effect" will be no more. The current rate at which the Moon is receding nonetheless sets us up with making incremental adjustments in our lives that we are not accustomed to monitoring in any significant way with respect to the type and level of changes taking place. We have not designed instrumentation for this because their has been no compressive philosophical perspective guiding us along such a path of accepting the existence of such.
In an effort to show the current state of primitive mathematics humanity is practicing and the need for a new formula of calculation... a new calculus that I am amusingly labeling "accordion calculus" as a means of expressing the need to teach Calculus to breathe deeper— in order that its closed (infinitesimal) state can be taken out of its box so that it truly can play a greater "music of the spheres" range of accomplishment; it is of value to review some mathematical concepts in order to grasp the prevailency of dichotomies and to show where basic counting expressions are being made, as well as those concepts advancing a triple pattern of thinking, not to mention the absence of what we might think would be logical exercises to be used in mathematics reflecting three-part syllogisms. In the case of quadratics (supposed "4" expressions), and other supposed "higher" enumerations that may or may not reference such by the usage of the word "polynomial", the paucity of references needs also to be noted. In other words, we find most expressions beginning with single-digit referencing or otherwise low number expressions, where the primitive three-patterned counting sequence of "1-2-Many" is being exhibited symbolically. It matters not that one may express the sequence such as 1, 2... ∞, the fact that this statement references the usage of a three-patterned formula is a tell- tale indication that the human mind is referencing the usage of a conservation of thought. Whether one says 1, 2... infinity, or 1,2,3, or X,Y,Z, or 1,22... polynomial, or some other words and symbols doesn't change the fact that a three-patterned expression is a mental currency like using nickels, dimes.... quarters for a vending machine. It is similar to the recurrent models of syllogisms in philosophical brands of logic such as expressed with "all A is B, all B is C, therefore all A is C". This argument is a formalization that is fundamental to all logic (page 744, American Desk Encyclopedia, 1989), and is exercised in the proofing of mathematics, even though some believe that Logic is not Math.
In the old listing of the liberal arts, there were two basic classes of subjects: the three language arts (the trivium) and the four math arts (the quadrivium). Logic was always considered to be the second of the language subjects, after grammar and before rhetoric.
Grammar is the prerequisite for logic, since the ability to argue and reason rightly assumes the ability to communicate competently. And logic is the prerequisite for rhetoric, since logic is one of the three persuasive appeals: to the will (ethos—the appeal to the speaker’s character), to the imagination (pathos—the appeal to the audience’s emotions), and to the intellect (logos—the appeal to truth). Logic is not Math
With respect to the syllogism styled as "all A is B, all B is C, therefore all A is C", we find other constructs of three items which do not appear to represent a similarity of design, but need to be examined as a curious illustration of an expressed cognitive display. For example, we use the term "Panther" to describe a big black jungle cat, but there is in fact no such animal. What is being referred to is either a jaguar or leopard. Hence, we have the word equation of jaguar + leopard = panther. Or using characteristic terms found in philosophy: Major premise + Minor premise = conclusion. The underlying mathematics pattern is the same. Viewing jaguars and leopards as a singular item called "black cat" and then relabeling this phrase with the word "panther", is the same sentence of A's relationship to B's relationship to C's relationship with A. Or, similarly, as seen in the child's Fuzzy Wuzzy expression: Fuzzy Wuzzy was a bear, Fuzzy Wuzzy had no hair, Fuzzy Wuzzy wasn't fuzzy was he? Each of these three examples is representing an underlying cognitive pattern where 1- 2- 3 signifiers are being illustrated. Irrespective of the type of interpretation we may want to attach to them, the same pattern exists... even if someone wants to argue content meaning or if an actual third item is being addressed as a separate entity with its own identity.
Underlying all mathematics is a basic accounting behavior involving a conserved set of enumerations (such as one- two- three patterned formulas), as if to suggest that mathematics, despite all its embellishments, is a system of accounting-for this or that before the advent of double-entry accounting out of which other forms of number manipulation arose that we call algebra, geometry, calculus etc..., when accounting gets intertwined with other interest such as Chemistry, Astronomy/Astrology, biology, gaming, etc... Underlying all the models of mathematics and their individualized embellishments and elaborations, is the presence of a simplistic formula of accounting based on perceptions of reality and our reactions to those perceptions. In order to give Mathematics a swift kick in the rear to get it to remove itself from its many sedentary forms of intellectual activity, we need to use a different perception of reality in order to change the focus of our efforts to account for different phenomena.
At present, mathematics is simply a recreational exercise of simplistic number and symbol manipulations that are embellished and elaborated into contours which are then reapplied to the perceptions being used to influence them, whereby a reverberating echo is sustained and misinterpreted as providing both a source and trail for a greater truth to be exposed. The basic tools of arithmetic have become like a medieval scythe that had a set of floral emblazoned Renaissance wheels attached to it which was then known as a mechanical mower... upon which was later added a 18th/19th century steam engine followed by a 19th/20th century gas motor that in the 21st century has had an electric motor applied in some cases; after which more elaborated math influences called electronics was applied upon which a starting button was attached... but the basic usage of the once hand-held blade has remained the same.
Our mathematics is dependent on our perceptions that use mathematics to support those perceptions which provide for a particular type of world-view survival to be sustained and supported with embellished arguments from different subject areas using the same type of mathematics logic. We need a new survival requirement perception so as to punch Mathematics in the stomach, slap it in the face, and kick it in the shins in order to remove it from its self-perception (illusion) of being Queen of all the subjects... and forced to look into a mirror which sobers it up from its stuck-on-itself delusions.
 Nova presentation: Mathematics is the queen of Sciences |
 Number Theory: Queen of Mathematics by Gresham College |
The global institution of mathematics has created a University level psychiatric ward for itself, with wards in the military, business, law, religion, sports, gaming, etc... where it performs all staff functions and patient oddities as well; while conducting group therapy sessions called (European) "maths" classes and (American) mathematics lectures-with-labs... as if the usage of the word "lab" increases the validity of activity through enculturated socially accepted forms of arrogance because the mathematics' activities of expected repetition routinely show themselves to be no different than dogs chasing their own tails, or dogs chasing the tires of a moving vehicle, or humans taking photographic selfies of themselves while falling off an abyss which becomes an addiction indicated by a mathematics' degree... and is a realization that frequently comes to the threshold of consciousness of those pursuing an advanced degree who come to question their role as a person rowing an oar in unison with others because their ability to memorize affords them to keep pace and rhythm of institutional requirements, while often sacrificing other interests that may well be more satisfying as an individualized creative effort if they would only give such efforts a chance to assert themselves in their initial fledgling exercises. Many who pursue advanced degrees are not just accountants, they have untapped creativity that needs only to find an outlet and be self-encouraged. Sometimes it is necessary for a person to be their own cheerleading squad and let their creative inclinations take whatever baby steps it needs to learn how to walk on its own.
The pristinely simplistic and primitive mode of thinking underlying mathematics needs to be brought out into the daylight in order to expose its crudeness and past-due need for an evolutionary development to occur. Mathematics is like a person striving to excel, but is being forced to toe-the-line of accepted standards which interfere with its potential. Mathematicians are forcing mathematics to "stay the course" or else lose its reputation and position in society. As a person, mathematics is not allowed to throw up its hands and quit. It can not walk off of a job nor play hokey, unless mathematicians allow it to do so. To take a day off from the normal routine (so to speak), and see the world from a different perspective. Like any good commanding officer knows, it is sometimes necessary for a soldier to deliberately go Awol as a means of getting their bearings. Such is the case for Mathematicians. They need to miss roll call. They need to miss a troop movement... just long enough for them to gain the very perspective from which will emerge a New Calculus in their respective genre of mathematical inquiry. We have got to force the entire global community of Mathematicians to Jump ship. Mathematics is in need of a very long overdue vacation from itself, so that it can return refreshed, reinvigorated and re-inventive. Society needs to do whatever is necessary to mathematics: force it to walk a plank, tar and feather it, etc., in order to get it to free itself from its current chain-gang mentality that is being repeated by millions to the extent it has become a monotonous din through which actually reality is no longer thought to exist unless it can be proved with an equation that someone has made up!
There is the curious thing however, that while both math and logic share certain expressions, both claim to be separate entities. Logic, as expressed with words is said to be a language "arts" phenomena, and yet some mathematicians claim that they are engaged in artistic exercises. Thus, are there two forms of logic or three... that is, if we then consider physics to be its own brand of logic as well? If the word "logic" has multiple meanings, this may mean that no subject has yet come to the realization of what it is actually trying to explicitly describe when it labels an activity as being "logical". Physics, Mathematics and Philosophy all claim to be in the possession of something they refer to as "logic", but in this perspective, each of them is a blind person trying to describe an elephant. Hence, each of them can claim they possess the superior form of logic so long as you accept blindness as a valid axiom with which to work from. And if we include all other subjects with their respective brands of so-called "logic", we increase the retinue of blind men competing in a labyrinthine structure which their opinions have created, and force civilization to live within.
From the mid-19th century, when it became increasingly unusual for scientists to contribute to both physics and chemistry, "natural philosophy" came to mean just physics, and the word is still used in that sense in degree titles at the University of Oxford. In general, chairs of Natural Philosophy established long ago at the oldest universities are nowadays occupied mainly by physics professors. Isaac Newton's book Philosophiae Naturalis Principia Mathematica (1687), whose title translates to "Mathematical Principles of Natural Philosophy", reflects the then-current use of the words "natural philosophy", akin to "systematic study of nature". Even in the 19th century, a treatise by Lord Kelvin and Peter Guthrie Tait, which helped define much of modern physics, was titled Treatise on Natural Philosophy (1867). Natural Philosophy
Physics seeks to be grounded in observation and reality. Predictions are made and tested against reality; if the theory fails to match reality, the theory is discarded and a new theory sought. Logic does not; it is purely an abstract exercise that depends on axioms and reasoning based thereon. So while physics is clearly dependent on logical and mathematical reasoning, I would say that it is not limited to "logical science" (whatever that may mean).— Edward Sherry Is Physics Logical Science?
Yet, if we are going to use the idea of "logic" to establish what we think is the paramount level or at least most direct path to arrive at the penultimate "Truth", though this word may in fact be a fallacy wrapped up in what is/are the best survivalist strategy(s), let us ask whether the study of Logic in its original Greek Trivium offering using language, is of greater value to humanity than the form of logic being stressed by mathematics using its application of symbolic logic... not to say that words themselves are not symbolic etchings of behavioral expressions using the corridor of speech by way of the mouth. Let us further ask:
Is the "logic-al" seen in 'psychological' actually logic in the sense of the Trivium model or mathematics model? Is it better or worse? This is where the term "Pschologism" may be of value for consideration:
Psychologism is a philosophical position, according to which psychology plays a central role in grounding or explaining some other, non-psychological type of fact or law. The word was coined by Johann Eduard Erdmann as Psychologismus, being translated into English as psychologism.
The Oxford English Dictionary defines psychologism as: "The view or doctrine that a theory of psychology or ideas forms the basis of an account of metaphysics, epistemology, or meaning; (sometimes) spec. the explanation or derivation of mathematical or logical laws in terms of psychological facts." Psychologism in epistemology, the idea that its problems "can be solved satisfactorily by the psychological study of the development of mental processes", was argued in John Locke's An Essay Concerning Human Understanding (1690).
Other forms of psychologism are logical psychologism and mathematical psychologism. Logical psychologism is a position in logic (or the philosophy of logic) according to which logical laws and mathematical laws are grounded in, derived from, explained or exhausted by psychological facts or laws. Psychologism in the philosophy of mathematics is the position that mathematical concepts and/or truths are grounded in, derived from or explained by psychological facts or laws.
Psychologism
Intro to the Philosophy of Mathematics (Ray Monk)
Is any subject to be defined as incorporating its own valuation of logic based upon its own rules, observations, principles... and what have you, mix or match as you will according to a shared system of value by all those participating in the culture of a given subject?
Dualities, dichotomies and therefore... examples of limited expressions used sometimes to quantify/qualify larger ideas... just like a primitive mind using the word "Many" to represent more than two, or three, or four... Sometimes we see a singular symbol. Most often we can pay witness to the usage of two symbols which are frequently expressed in a turned around opposite way to present a dichotomy, much in the manner as the list of yin/yang polarities are illustrated and had been designed with primitive mentalities using a pairing methodology for assaying reality as it was perceived in a given time and place. Next in line are examples representing a 1-2-3 progression, but no further. Then we come to even fewer examples where a "4"-patterned construct is put into usage. Afterwards, there may or may not exist symbols directly related to any higher number value, even though equations can be used to express larger considerations. In such a case, let me again state that present day humans have learned how to embellish the concept of "many" or much, or a lot, or a heap, by using such words as infinity, Universe, multi-dimension, polynomial, etc... Yet these elaborations of language are but substitutions for the primitive groupings and conceal the continuing presence of a primitive mindset that mathematicians are forcing the world to perpetuate and not reach human cognitive potentiality.
Page initially created: Wednesday, March 3rd, 2021... 1:19:25 PM
Page initially posted: Saturday, May 22nd, 2021... 7:15 AM
Updated page: Monday, December 6th, 2021... 6:24 AM
Herb O. Buckland
herbobuckland@hotmail.com