Threesology Research Journal: Math Perspective page 13
Mathematics Perspective: page 13

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(Continued from previous page.)

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.

This is not to say that the day/night sequence of the Sun and Earth interaction directly or indirectly influenced all existing pattern-of-two being observed taking place in biology such as the double-helix strandedness in DNA, or the Yin/Yang configured dichotomies, or the multiple dichotomies seen in Mathematics, etc..., but let us not overlook it either by claiming such a notion as being comparable to the (disparaged) idea of planetary influences of human behavior described by Astrology. This is neither to totally discredit the idea that planetary behavior can affect biological behavior, nor totally agree with it. Some examples of dichotomies (and all other enumerated patterns) may well have multiple types and degrees/durations of influences. Some influences may be static (remaining in a relative state of non-movement as described in human terms), others dynamic (moving), and/or constant or intermittent.

Those who argue for a "two-patterned" dominance occurring in Nature need to address the absence of "twos" from multiple references such as the Earth being on the Third planet near a Sun, a Triplet code in Genetics, patterns-of-three in atomic physics, etc...

If we take for example the configured dualities of the Yin and Yang idea as illustrated below, let us not overlook the usage of the word "trigram" to describe the three-line configurations in the I-Ching, nor that the configurations only feature one and two-line composites. There is no actual three-line configuration. The one-line representation can be analogously paired with the male penis and the two-line representation with the female vagina (or "split tail" label used by some older men).


Yin, Yang and I-Ching examples

The "True Trigram" idea was mentioned on the 1st page in this series.

When we describe the presence of dualities so as to be as forthcoming as possible about the apparent wide-spread prevalence, we might well want to include the idea of rivalries such as between the corporations Coca Cola and Pepsi, Puma and Adidas, McDonald's versus Burger King, Microsoft versus Apple, Ferrari versus Lamborghini; and is a listed culled from this youtube presentation: How Ferrari Motivated This Former Prisoner To Invent Lamborghini. Another type of duality is that seen in the theme of Rags to Riches, typically describing a person or person's developing a financially successful company from impoverished conditions which are highlighted and emphasized in a historical retelling of the business' beginnings, as if in doing so is somehow to be equated with a greater level of supremacy as opposed to someone or group that is born in wealth and becomes wealthier. In (a dualistic) contrast to this, we find that in some cases we find a wealthy or privileged or famous person turning away from such social accoutrements to seek out a believed greater position, person or advantage. An example of this is the story of The Buddha who gave up the luxury and prestige of being a prince to endure poverty and privation in order to follow a presumed more enlightened path. A third example is that found in the story of Walden, in which the values of "austerity, simplicity, and solitude," were endorsed, though upon reading the account we see in many ways that this philosophy was not followed to the degree one might expect when one advocates a type of "returning to nature" theme of life.

It is a curious thing to see a person or multiple people focusing on a single number pattern, but do not pursue a focus on other patterns, even if their presence overlaps with a pattern one has spent time and energy on in collecting examples thereof. Whereas I have indicated on several occasions due to the exercise of the research I do that a pattern-of-three is preferenced, I can not help but notice those occasions where patterns-of-three are absent or occur with other patterns such as in the case of a 1-2-3 sequence as found not only in developmental biology, but various cultural expressions such as a parent may say they are going to count to three to entice (or otherwise threaten some confrontation) a child to engage in or stop some activity. Whereas one can encounter a person interested in Numerology engaging in the practice of highlighting different examples of different numbers, they do not also speak of the limitations of number patterns which they encounter. Indeed, one would think that out of all the infinity of numbers at our human disposal there would be hundreds, thousands, millions of enumerated patterns to make up a standard collection similar to having a dictionary of words except in the form of a dictionary of numbers. In short, the "vocabulary" of number usage is very small. And the usage of the same small quantities of numbers being used in different subjects is the same type of activity we see when we look at the frequency of which letters are used most often and those which are used less.

With respect to overlapping number patterns, it is necessary to note that we need to view patterns as assemblages or composites which may not exhibit a conventional sequentiality such as the 1-2-3. For example, I have come across composites of three items exhibiting a 2-3-4 pattern as illustrated on this page: Devils's Advocate page 14A. No doubt other combinations exist, including truncated variations such as a singular value, a dual value, etc., where occasions of reversal can occur as well as a presumptive higher (or lower) value such as in the case of Embellished Dichotomies, where a set-of-two can masquerade as a set-of-three either in form or function. Language very often is used to exhibit some intended higher expression by mimicking a lower expression which otherwise reveals the presence of a duality or 1-1 or 1-2 configuration presented as a 1-2-3 portrait to give the impression of being something more, greater, higher, in addition to, etc...

It is of need to recognize the dominant presence of dualities in the structure of Mathematics in order to think in terms that present day Mathematics may well be an expression of a primitive form of thinking that attempts to display itself as having no equal, but is in fact a philosophy quagmired in the pattern-of-two quicksand where the dynamics of it is seen in the intellectualized antics of Mathematicians. In other to understand what I mean about Mathematic's dominant usage of patterns-of-two as an indication of primivity, it is necessary to make analogies with the developmental sequences exhibited in the idea of Evolutionary biology involving genetics. Whereas we can see Mathematics as an evolving expression of cognitive behavior and cognitive behavior development as an expression of an evolving biology subjected to the stresses of the environment; we do not often take into consideration how the effects of an incrementally deteriorating environment has on the overall sequence and how this can be manifested in the patterns of enumeration which repeat, become deleted or diminished from usage, and the increased usage of one or more over time. Such patterns no doubt play a role similar to a barometer or even tree rings to provide an insight as to the course of human history... its past, present and future. If in fact human biology is or can be as dramatically changed by way of adaptation to the alteration of environmental conditions because biology must adapt to those conditions, then a recurrent behavior such as the usage of given number patterns can play a role in the understanding not only of human cognition but to what degree the environment is changing to influence such changes.

Mathematics has become so pervasive around the world and applied as a tool for so many tasks, it is easy to understand how its recurring patterns are both overlooked, dismissed or otherwise rationalized into some respectable portrait by those who favor such a tool (or alternatively described as an instrument), by those who would be confronted by someone wanting to point out a perspective which implies a manipulatively duplicitous side to Mathematics. As a tool or instrument it has become idealized by some as a "true" gift from some purported god-entity, and others consider it so useful in so many subjects that it could be viewed as being equivalent to a undeclared Natural law. Yet, Mathematics is a tool created by humans, no matter how often or serious, or intensified would be the proclamations of those whose egos are so very deeply invested in the usage of such a tool, they take great pains to present Mathematics as being no less than some purported Queen of all subjects... and not itself a subject, slave or indentured servant whose life-span has a shelf life.

Mathematics is not accepted by everyone as the purported "Queen" of all sciences and subjects; even though multiple subjects have appropriated its mannerisms, gestures, garments and use the word "Mathematics" like someone who engages in dropping the name of an important person during a conversation as a means of heightening their own social status. Indeed, despite the fact that several course subjects require students to have an in-depth grasp of a given mathematics model because it is presented as a measure by which one's own thinking can be judged as being more rational and logical, many people might well describe mathematics as a type of Art form, soundless music, or some literary avenue akin to poetry. In other words, they view Mathematics as the actions of a creature similar to the activities seen in the construction of a (bird's) nest, (and) colony, (spider) web, burrow, or other construct used by Nature or a product of nature in terms of a life form's survival efforts and skills. Being able to "do" advanced mathematics is seen similar to the activity of aligning the colored squares of a Rubik's cube into a given arrangement, or performing well at a given board task with certain rules employed as if they were akin to axioms used in Mathematics. Clearly, some people view mathematics being played out like the rules of a political arena for a given type of government observance and practice, that are held up to be viewed as a rigged system like that seen in casinos and State or National Lotteries (there is no International lottery as yet).

It is well understood that the brains of different people are colloquially described as being "wired" differently to account for some desirable or undesirable quality. Some behaviors are termed skills and become accepted as having a wide-spread desirability, while other abilities are useful only in a given community or situation. Yet, this brings us to directing our attention to formerly addressing the issue of what then is better or more desirable than the present model(s) of Mathematics? Is it something that is easily acquired, takes years to develop, has an everyday practicality or serves only limited but some highly useful effect? Does the present brain construction of humans have an ability to acquire such a behavior or does it require not only a change in the human brain but human genetics as well, or some other physiological feature awaiting to be born through a mutation of blood serum, plasma, or gut microbes?

Yet, if we do not attempt to establish some workable criteria for analyzing mathematics by using mathematics as its own investigative tool (if it is possible and not contradictory or irrational); then the idea that present Mathematics is a primitive mental task may not come to mind and nor that there is a need to pursue a type of thinking which succeeds Mathematics as a higher model of conceptualization which can be usefully applied with both great practicability but as a tool for exceeding conventional parameters of consideration not routinely present as a point of personal or inter-personal conjectural philosophy. Analogously, whereas the ability to make and use stone tools and hunter's tools (weapons) in a given past era were most likely behavior that others were in awe of, and that many of us today would not be able to easily adapt ourselves to learning if we were somehow transported back in time to some very distant age; such skills would conversely be out of touch with the reality of living in today's social scheme of marketable job and survival skills. In other words, at least some of us should be thinking in terms of how thinking might evolve (in practical terms) if and when the conventional wisdom of implying mathematics is no longer a useful viability. Nor should we be quick to turn to rationalizations to protect one's ego from the assault of considerations which come about to plague us if we can not remove ourselves from the quagmire of routinized conventionalities of thought which our present survivability requires us to comfort ourselves by introducing excuses which accept present mathematics as the highest rung achievable by the human exercise of brain activity.

One mathematical framework after another is created, providing niche's for the interest of a given person for a given orientation using what they may believe as bare and essentially accurate expressions of that which express or can uncover a traditional view or a view which can be embellished to the point of being presented as something altogether new and not merely some alternative perspective of a traditional grasp of a given intellectually-trained terrain of perception. Such frameworks, such axioms, such proofs are akin to the rules developed by game-board manufacturers who may "tweak' them in accordance with a change in the color or shape of a given game piece of proscribed parameters in which or upon which to conduct a particular type of activity otherwise known as a game or sometimes preferentially egotized into a model of supposed seriousness so as to imply a greatness to that which can otherwise be diminished and harnessed by lesser minds, so long as they are not persuaded to believe they are incapable of participating in a task. Labels and titles can have an effect on behavior, as well as requiring one to "dress up" (intellectually or otherwise) for a given situation. In other words, if one is tasked with having to "think in a right (expected) way" or "act in a right (expected" way in order to be thought of as engaging in a given task in a proper way or otherwise commit some foul of demeanor whether or not a given task is accomplished; we have what amounts to is an activity called Mathematics... though the word "Mathematics" can be substituted with any subject heading.

Yet even if one is not actually a good mathematician, if their presence and demeanor can be used to support the exercises of those who are good or great mathematicians as defined by those who support such a subject, they are used as either body guards or means of creating obstacles and detours who would attempt to discredit Mathematics by calling it an Art form or primitive mental exercise. Without being able to provide a useful substitute, the question of whether present day mathematics is already in its antiquity close to its shelf-life ending date, is rendered moot. How does one go about showing that present day Mathematics is in a static form if no recognizable alternative dynamic model can be shown or even grasped?

If in fact Mathematics is static as I am claiming, I need also to address those claims by others who would say that it is dynamic. Mathematics itself has no movement as one might be inclined to view it in biological terms. The assumed dynamic nature of Mathematics rests on its application to ideas or actual constructs which do move, including the movement of ideas. With this said, let us ask if Mathematics can evolve to a form of self-movement like an organism. However, if Mathematics is not alive in the biological sense, is it only "alive" in an analogical sense connected with actual activities be they biological, mechanical, fluid or atomic? Is math like the phenomena we describe as time... but in the sense of time (as an actual entity), we do not see it just as we do not see the wind... only effects there of. Just as we say a Chess game doesn't move, yet many claim it to be a dynamic game. In most, if not all instances, we view movement from the perspective of a contrast of multiple perceptions (such as objects), or at the very least two objects, giving us a pattern-of-two as a basic standard of reliance. Patterns-of-two, just like other patterns are quite pervasive, but are not routinely being counted as an occurrence which can be enumerated along with other patterns to show us that only a few patterns of number are routinely used, while others less so due to infrequency brought about by one condition or another.

Just as most people apparently overlook the repetitious occurrence of one number pattern or another, there is cause for consideration (if not alarm) if changes or constants of number patterns do or do not change over time and from place to place. Usage of number patterns as a tell-tale sign of cognitive behavior might well be used as an indication of either changes in culture and/or physiology and/or the larger environment. Tree rings as indicators of environmental conditions largely remains as an "out-of-sight... out-of-mind" measuring tape of change, unless one is reminded of such a convention upon seeing a tree having been cut down and a log with its tree rings are looked at more closely. So too is the usage (presence) of number patterns, if I may be permitted to offer such an idea though most people have a tough mental "bark" (due to cultural desensitization) which prevents them from recognizing the presence of one or more number patterns. Most of us take number patterns for granted, since we are "so used to" using them as a day-to-day exercise routine of interacting with others and other worldly events.

A short while ago while perusing youtube lists of different movies and coming across one entitled Three Desperate Men (1951), I began watching it and all of a sudden the realization that I was being routinely subjected (while watching different movies) to a list of credits that more often than not were presented in a pattern-of-two profile. I see the pattern in different movies but had never made a conscious realization of it just as I had not realized (when very young) that movies routinely begin after the Director is named. This latter instance was pointed out to me by overhearing another boy make the comment while a bunch of kids were sitting in the old Garden Theater in Columbus, Ohio, where the entrance fee was a dime. When the fee was increased to a quarter later on, I was shocked, just as I was shocked that my favorite nearby hamburger joint (Burger Chef) had raised the price to 15 cents. Another movie Theater which cost a quarter at the time, raised their price to fifty cents. All of these costs were enormous sums of money for those kids who hunted for pop bottles and (glass) milk jugs to turn into a grocery store for money. It was a day and age when the cost of most candy was in the penny range.


Old movie showing two-patterned credits

Just as many people have overlooked the dominant recurrence of patterns-of-two in movie credits, despite the multiple movies they've seen over their life-time, the same is occurring for those who have a repeated observation of mathematics. For me to suggest they might be engaging in a Westernized model of the Yin/Yang profile which became subjected to an (I-Ching labeled/associated) orientation equivalent in its time to the development of a "higher" (more complex) mathematical framework, may not sit well for those whose ego of presumed superiority or personal exultancy use mathematics as a portrait of themselves. However, this being said, how does one convey the number 3 (used as an analogy to describe a different model of mathematics) when the extant culture is invested so heavily in a mathematical construct that is dependent on the number 2 (patterns-of-two)? How does one use a formal system of mathematics with an underlying foundation resting on patterns-of-two, to portray that which has a different foundation, if the former over-shadows the fledgling beginnings of the latter?

Whereas there are multiple people who view mathematics from a skeptics observational platform, they no doubt also admit to its viability, just as one does any tool that may give the appearance of being strange or crude, though in the hands of a partitioner, can perform various feats akin to magic. Call it sleight -of- hand, sleight -of- mind, or whatever, most of us might well agree that mathematics is a useful tool, but that it does not necessarily mean it is a universal tool that all (presumed) intelligent beings in the Universe use Mathematics— as illustrated by humans... irrespective of symbols being employed. Numbers are numbers some might say, and therefore have a Universal application though it may differ in appearance and application. While it is a survival tool, is it a tool that is human specific, despite humans attempting to see some measure of mathematical or number or counting behavior in non-human life forms. Indeed, an attempt to establish the universality of number usage as a reverse attempt to portray that the number usage of humans is of a universal quality shared by multiple life forms and is therefore pervasive in the universe... whereby humanity's invention of mathematics is simply an extension of a Universal truth which humanity has a unique ability and position to be impressed upon with and make use of. In other words, for those who claim that Mathematics is a different model of "the word of (a) god" and humans can make use of such a word... this thus means humans are close to god... at least Mathematicians are anyway.

If Mathematics is a behavior of humanity just as one might assign specious-specific behaviors, mannerisms, garments, socialization, etc., to other life forms, then the assumed Universality of Mathematics being used by all sentient beings (that is, sentience defined in human terms), is an illusion, no matter how often a movie script writer might try to incorporate such an idea into a character's dialogue to suggest the person is intelligent. Script writers, like police officers, are only as intelligent according to the context the either want to create for themselves or find themselves in.

Plimpton 322 tablet

After a long history of trial and error, one might expect Mathematics having eventually been able to be developed (fine-tuned, tweaked) into a useful ( practical) tool... of if need be, a weapon. However, like the projectile points of old (arrows, knives, spears) which have come to be replaced by other types of projectile points which go faster, further and cause more damage due to being combined with the chemistry of propulsion; this may be the case we are confronted with in regards to mathematics. If current mathematics is (for example) a bow and quiver of arrows which has been subjected to refinements by different people in different cultures over vast expanses of time, then it is not without precedent to speak of replacing mathematics with a different implement... even though some find interest in playing with, hunting with, or competing with a bow and arrow in the present day era.

For those not having much previous encounter with the idea of Mathematic's historical trek:


Excerpt of Mathematics' development


Development of Mathematics excerpt

In an effort to describe the development of mathematics from its crude and primitive implementations by different people in different eras such as for commerce/accounting, prediction/fortune telling, gambling, art/geometry, music, religion, astronomy, etc., multiple types of analogies might well be employed to convey the idea of progress... even if that progress retains an esoteric application within a given subject. Whereas a subject may have been refined over the centuries with numbers and a specific mathematics application, it may not have exceeded itself to be developed into what one might otherwise denote as a higher mathematics. Instead, one might see an elaborate form of basic arithmetic which is interpreted by its users as a calculus, but it has no widespread applicability to other concerns of life. For example, the numbers used in Astrology are not necessarily applicable as a mathematics to build a bridge over which people travel in their vehicles, though some readers might be imaginatively inclined to say that the words "bridge" and "vehicles" can be interpreted in a personal, if not metaphysical way... whereby the idea of a bridge to a higher consciousness can be built by way of the particular "mathematics" used by one or another esoteric field of interest (astrology, numerology, palmistry, etc...), and that a person's 'vehicle' can be interpreted as a soul.

However, regardless of the verbal gymnastics and contoured semantics the partitioner of a given esoteric ideology may employ to circumvent any perceived threat to their interest; the fact remains one can see a developmental course of number usage that one might also view as a sequence. From this perspective it is much easier to describe present day mathematics, despite all of its "unreasonable effectiveness in the natural sciences", as a functionality of human thinking processes which might well be improved upon, and multiple mathematicians are attempting to expand from their particular orientations. Yet, is there then multiple evolutionary treks that Mathematics can take like offshoots of a given species adapting to different terrains, or should we instead focus on the development of one dominant species of mathematics by examining the underlying two-patterned code, thereby possibly affording us a means to create a new foundation out of which develops a different species of mathematics which forces the cognitive abilities of humanity to develop further in order to take advantage of its presumed superior ability?

Again, let me ask if it is at all possible to use our present mathematics to describe a new model of mathematics or will the use of the present mathematics set up a system for confirming the viability of the present mathematics instead of offering even the hint of a mathematics structure superseding it? How is it possible to display igloos, tepees, mud huts, thatched roofs, etc., and think that these offer insight into modern forms of architecture if such architectural forms have not crossed the mental terrain of such everyday dwelling builders?

We need to look at the development of Architecture as an expression of cognitive development, and in particular accept the view that many different types of construction can occur off of a blueprint in an individual's mind, where measurements and calculations occur away from any written document. Since many a tinkerer, butcher, baker, candlestick maker, cook, housewife, inventor, scientist, etc., have a personalized calculator within their mind (whether providing correct answers each and every time or not); there is some level and type of calculation taking place as a functionality of the human brain, just as one might consider that plants, insects, and animals (all life forms) have their own type of born-with calculus with which they navigate a given terrain and may or may not construct a spiraling attachment, termite mound, ant lion burrow, spider web, beaver hut, bird's nest, etc., with... there is an identifiable pattern we can enumerate, even if such an idea is not commonly thought of. It needs to be identified and measured over time to see if there are any discernible changes and whether or not the presence of a recurrence foretells the presence of an inflexibility, despite those who would claim a great diversity and use this to excuse themselves from recognizing the presence of any recurrence with the same underlying pattern cloaked by the usage of languages which act as camouflage to disguise the presence of a recurrence being used by multiple life-forms engaged with an environment which impresses such a pattern on life processes and can thus cause life forms to perish when the billions-of-years exercise dwindles to obsolescence, and since life forms are so habituated to it, they do not know how to make adjustments for survival using a different pattern. Such is the habituated usage of present day mathematics.

If we organize the idea of developmental mathematics in terms of habited or potentially habitable dwellings, one might refer to caves and other Natural non-man made structures such as being beneath a branch, brush, and cliff as examples, though the word "structure" does not necessarily mean stability. Intermittent or a "one-off" usage of a given place might well be used as a temporary housing since any number of occasions may arise to displace a person or group of people such as a bear entering a cave, a mountain lion climbing a tree, a wild boar inviting themselves to enter into a clump of bushes, etc...

Nonetheless, let me attempt some loosely bound associations as a means to convey the idea of Mathematics development over time, by employing the analogy of dwelling development... many of which in the present day era are not structures in which people customarily sleep in, such as places of work, museums, art galleries, concert venues, courtrooms, etc... Granted your personal opinions may vary and bring to light exceptions where structures built by ancient peoples give the impression of exceeding the capabilities of modern building techniques (such as cutting and moving heavy stones to build pyramids); the associations are generally permissible for the present analogy (which includes overlapping, back-sliding, mutational and ahead-of-its-time developmental scenarios):

Proto-/Primitive/PRE-history Mathematics:
(individuals or small groups)
Caves, Trees, Bushes, Cliffs, Holes in ground/Tunnels Fledgling number counting
(i.e. "one...-two...-many")
POST- Proto/Primitive Mathematics:
(Large clans, large tribes)
Stone huts, Mud huts, Tepees, Igloos, Lean-tos, etc... Formation of Number accounting
Pre-Formative Mathematics:
(Denoted as early "civilizations")
Large stone dwellings for Royalty, often occupied by beginnings of organized religious orientations relying on superstitious beliefs Geometry, Trigonometry, application to pre-scientific method

Yes, I realize many readers might want to create their own versions of this analogy, but the point is that we can use an analogical referencing model from different subjects to create the view that Mathematics has evolved from primitive beginnings and thus, much like a biological species, is subject to the vagaries of environmental influences which influence behavioral outcomes that may follow a course that results in extinction because a life form can become so dependent on a given way of life (food stuff, terrain, weather), that an earlier flexibility for adaptation is lost and they are forced into extinction... though at the time (much like the reign of the dinosaurs), such a consideration would never enter anyone's mind. Such is the case for Mathematics. It is so pervasive, owing to the fact it has different species inhabiting different cognitive domains of humanity, no one stops to think that the orientation of present day humanity may be leading Mathematics into a cul-de-sac which will force it to become so inflexible its only means of escaping a change in the cognitive terrain of human conceptualization (which boxes it in because human physiology is forced to accommodate the incremental changes in the overall environment); is to die out, like so many languages have done so.

The very real possibility that the evolutionary development of Mathematics is obliged to render itself in perpetual servitude to the closed-in looping of human consciousness adopting the methods of adaptation to fulfill a life orientation in concert with the incremental deterioration of the planet and planetary system having used a night/day sequencing for billions of years; behooves us to look at the real origin of Mathematical reason by unveiling its basic structure such as the recurring presence of patterns-of-two, which apparently has a direct affinity with the development of the dichotomous yin/yang model which associates pairs found in nature as observed by the two eyes of humanity.

No less, let us not forget that as humanity supposedly evolves— and with this change comes a greater complexity in the construction of dwellings, we find that there is an increase in the artificiality of human dwellings, which might thus also be extended to the development of Mathematics as an increase in the complexity of artificiality. For example, constructed homes are not nature edifices such as caves. The electric lighting takes the place of a Sun and Moon's light, though the light of the Moon is an artificiality of light from the Sun. Likewise the artficiality of running water, plumbing, heating, cooking, and air conditioning. Indeed, most people living in the conditions of artificiality are actually out-of-touch with real Nature. This includes the wearing of clothes, using toilet paper and other toiletries as well. No matter how one may argue about the benefits derived from the large range of artificialities humanity lives with; how can we be assured of a flexibility in our capacity to adapt to a change in Nature, if the conditions of Nature are defined in accordance with a Mathematics that is itself an accumulation of artificial contours of thought? Whereas we make up mathematics to suit circumstances, yet so many of those circumstances are products and/or processes of artificialization.

Let us also ask if the term "Proto" or Primitive mathematics suffices as an intellectual heading which appreciably helps us to uncover the foundation(s) of cognitive behavior expressed in what can be described as mathematical terms. Since neither "Proto" nor "Primitive" are illustrated in numerical terms, how are we to construct a evolutionary line of descent in direct mathematical terms which thus uses mathematics to analyze itself? If one does not equate some enumeration with the terms Proto or Primitive, how do we mathematically assess the cognitive development of mathematical thinking as a sequence, much less determine whether or not there exists an early orientation towards the development of thinking in sets, groups, or chunking... as one might analogously align with the idea of chunking used in the (linguistic) babbling of infants and later activities of memorization... bringing us to grappling with the linguistics of mathematical behavior and yet not witnessing an effort by researchers to include the sets of ideas presented in the construction of hearing and grammar?

While the labeled trigrams of the I-Ching are an elaboration of the yin/yang (binary configuration), and the labeled trigrams are a misnomer in the sense they do not actually portray a three-patterned configuration because simple lines are used to portray the male and female generative models (one line for penis and two lines for the vagina), the idea of a three-line configuration is absolutely ridiculous given the constraints of the underlying orientation. This too is the case for mathematics. Its structure is base so firmly on the usage of dichotomies that the idea of introducing a new model of mathematics which no longer uses a dominant dichotomous orientation might well be viewed as an absurdity. But, since the fact remains we find most humans not adept at using mathematics as a rigorous tool; this tells us that Mathematics may well be an artificiality... that is... an art form that has been promoted to prosper and be fine-tuned just like many a product used for everyday tasks. Nonetheless, how much can a toilet paper product be improved? Such is the case for Mathematics. It has both everyday and specialized brands of application but can not be improved upon past a certain point... a physiological change in humanity would have to take place for additional changes to take place.

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: 20th August 2022... 4:17 AM