Threesology Research Journal: Static versus Dynamic Equations
What is Mathematics?

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Assisting Mathematics to breathe more deeply by way of Accordian Calculus

My view is that the word "Mathematics" is the label of a box in which is kept various arts and crafts. Some of the items are interesting to look at and others have been adapted to serve more practical uses. Because it is a box, like the titles of so very many other boxes (biology, physics, music, philosophy, architecture, anthropology, archeology, medicine, engineering, toy, shoe, fishing tackle, tool, sewing, computer, etc...), attempting to describe a better model of mathematics requires one to realize they are in fact dealing with a circumstance which can be relegated to the perspective of not only being a box, but those who are adept to using the arts and crafts inside the box, are not necessarily adept at understanding that in order to think or even see outside a given box, we must come to some appreciation of what type of box it is. This is a necessity because the type of box we think we are dealing with will determine how we come to think about cognitive approaches outside the box. If it is a round box one is speaking of, then thinking outside its contours will determine the line of thinking we pursue in accordance with. Likewise if it is a square, tall, cylindrical, abstract or alternatively named box such as a cookie jar, bread box, ice box, shoe box, cigar box, bottle, pack, package, etc... Even though we may attempt to circumvent such an entanglement of considerations by adopting the view that one word or symbol can be used as a generality, such a view is itself yet another type of box. (A cognitive box about one or more boxes.)

Some people are so consumed with maintaining a level of competency for keeping their respective place in a given box, they have little time to even consider thinking outside of it, unless "outside" is a designated allowance such as a short vacation, holiday, or other social activity dependent on one's position within a given box.

If I present you with a Rubik's cube and call it a box, or a chess board and call it a box, or a strand of DNA and call it a box, do we not approach these different boxes in a different way if we so desire to imagine we can begin to think outside them... or beyond their design? Similarly, how does one think of a different color if they are largely immersed in only one or those of the rainbow, if it is the custom not to mix them? How does a mathematician know what I am talking about when I describe a difference between a static and dynamic equation, if their understanding of the words differs appreciably from mine, since they are inclined to use such words in accordance with how they are used in the box of mathematics, while they are busy with one or another art or craft there in?

Typically, equations don't move and are therefore static. The idea of movement when applied to an equation is that it represents a still picture of movement, just like when we take a picture of a soaring bird, jumping fish, falling leaf, etc... While equations found in Calculus are static representations expressing movement, they themselves do not exhibit movement unless we print an equation on a piece of paper and fold it into a paper airplane or carry it around in our pocket. The distinction of what is meant by a dynamic equation and an equation which is dynamic or dynamical, is not typically considered to be a worthwhile topic to ponder in terms of moving mathematics beyond its present state of static-ness. This is due to the fact that we humans, for the most part, do not actually understand what mathematics is in terms of a cognitive activity related to other cognitive activities such as language. Indeed, because it appears that some birds can count without using language... at least not in the sense that we humans do... we are confronted by the issue of whether some sense of enumeration arose before language. If our brain was able to recognize quantity before language was developed (though not necessarily all vocal utterances), then we are confronted with the real possibility that our present mathematics is a precursor to a "higher" cognitive activity either awaiting in some shadow, or attempting to establish some semblance of a fledgling expression, but established mathematical traditions expect the human brain to be trained to carry out its activities in the current shape of the mathematics box.

Let me approach my perspective from another way of illustration. Several decades ago while at a meeting involving numerous teachers, administrators and at least one psychologist, we were collectively asked to participate in a group exercise. Several people were assigned to (masking) tape out a square box onto the carpeted floor in which all of us were asked to get in it. We were then asked to get out of it. Then slowly the taped box was made smaller and everyone was asked to get into it. Again, the process was repeated, and it was generally thought (except for myself it seemed), that we were expected to close quarters in order to keep getting into the decreasing box. Although no one gave us any direction to keep getting in and out of the box each time, several of them assumed this was the case and everyone else followed suit. The square got so small that people were literally standing on one's another toes... except for myself. My immediate supervisor very sternly directed me to get into the box like everyone else, but not everyone was in the box. The administrator directing the exercise was not in it nor his assistants who had done the taping. It was clearly stupid to be like everyone else, but as I looked at the faces of the bunched-up crowd, they were literally vying for the best position in the group, as dictated by the constraints of the box.

If you carve out a niche' for yourself in a given box, you may do well depending on where the box is situated in accordance to the position of other similarly shaped boxes. If there are only so many positions in a given box and you have more people than the box provides positions for, those who don't acquire a spot must seek out some other type of box (social/academic/employment... etc.,) in which to apply themselves; though this does not mean they are actually spending any measurable time away from the 1st, (or 2nd or 3rd) box that they hope at some time to be a part of. While they may not be physically in the box, they mind longs for a plays there in and thus keeps them from applying themselves to thinking outside the box in a genuinely original way.

Is it possible to provide an insight into the development of a dynamic calculus, if that type of calculus expressed a perception which "moves" past the contours of the typically used calculus structure? Let me give an alternative example. Years ago while working with two others, the supervisor presented me with a puzzle that was easily discernable as a dead end syllogism. A type of chicken and egg situation that one need not spend any appreciable time on. When I expressed the problem's solution with a shoulder shrug, the other two employees spent the rest of the morning discussing alternative courses of cognitive approach. Even though I insisted the problem was a dead end, all three of them thought it meant that I was providing an excuse because I couldn't answer it. There was no answer, no matter how hard one wanted to think there was. And this too is calculus. It is an answer to itself. To calculate calculus as a calculable entity unto itself, one must realize it is a craftable art with different applications, but does not render itself readily available to providing and answer of what lays beyond it. This is because it has been contoured to fit within the reality of a box called mathematics. A mathematics which is contoured by a given set(s) of rules and processional order like packages running along a conveyor belt. However, in order for the whole of mathematics instruction to change, the realization that it is an arts and crafts box must become a socialized cognitive reality. In short, mathematics must be taught as an arts and crafts program.

Even though some people take their art and/or their craft seriously, there is too much seriousness being applied to the instruction of mathematics, given the situation it is being taught like a must-have-it-to-graduate course in Latin. Yes, that's right. It is being taught like a language that is not only foreign to the cognitive reality of many people, the application of many mathematics courses to the practicality which most people will be confronted with, is simply worthless... no matter how many academicians claim that it helps people think better, more logically. Such logic as described by mathematics is not routinely translated into a common vernacular used for communication. When there are far too many people achieving high paying positions who do not have a defined "mathematics" background and interact with the young, the so-called useful logic of mathematical reasoning cannot help but fall on deaf ears unless we as a society make it a requirement that all people in all positions exhibit a thorough understanding of basic and higher mathematics or they can not get a job. The problem is, we have too many intellectuals who don't want the entire public to be equal with themselves or they might them be faced with such a level of competition they would not be as employable or as smart as they think they are. There is so much stinkin' arrogance and egotism in so many human endeavours, there exists a concerted effort on the part of how society is fashion (as a box) and maintained to ensure that multiple many people fail. Indeed, all too often one can be confronted with a situation in which a person is set up for failure in order to make another person feel they are superior... like so many on social media who try to entrap someone in a conversation only to provide themselves with the impression they are more intelligent.

If we made basic and advanced mathematics a deliberate criteria for getting a job, most of the work in society wouldn't get done. If everyone had the same mathematics background, we would have a society where everyone might well think themselves too intellectually superior to do any menial task. Along with mathematics and many other academically designed badges is an arrogance that gets more and more difficult to see when everyone in the same room expresses the same unrecognized level of arrogance... including an arrogance of who exhibits the greater humility! So where does this leave us when attempting to convey the idea of an existing type of cognitive orientation involving the difference between a static and dynamic model of calculus? If calculus or any model of mathematics is viewed as the foremost type of craft and to do exhibit something more profound requires the application of yet another block to the conventionalized pile, how can humanity prosper if it is being held back by that which forces it to maintain a given level of functioning around which society revolves and creates multiple positions where individualized forms of arrogance are permitted to be exercised?

Do we await some global plague or catastrophic war to remove the obstacles, whereby a new orientation can come to the fore like a revolution allowing for the introduction of a new form of government that was not enabled to rear its head because the former government aligned itself with those and that which helped to maintain the system of reciprocity? For example, although the U.S. Declaration of Independence clearly states that the people have the right to overthrow the government and create a better one, this is not the case as attested to by the arrests of those who, in 2021, waged a protest at the U.S. Congress but have been cited with those attempting an insurrection. Granted there was no central leader and no actual pronouncement listed grievances against the government avowing to an attempt to change the government, the simply fact that a small portion of the public engaged in such an activity is not viewed in proportion to the allowances made in the Declaration. It is an hypocrisy, just as much as it is an hypocrisy to expect a cognitive view of Mathematics beyond current conventions to exercise itself in a manner equal to that which it is voicing an opinion to step beyond! It is much like stating that if a person survives a dunking (drowning) while tied to a chair they are innocent and if they survive the drowning they are guilty and therefore are in league with the devil. This is how I view the present state of mathematics. Mathematicians allow for a view beyond mathematics so long as mathematics is used to convey it!

I am permitted to describe an unconventionalized view outside the box of mathematics so long as I use conventionalized mathematics to describe the view! This is like permitting someone to be better than a player in a given game so long as the player plays by the same rules of the game... and not allow the creation of a new game where no one inside the conventional game has established a controlling position. Proposing to change the game of mathematics is not permitted. There are too many people, too many positions, and too much money involved with the game of mathematics as it is presently being played..

We have not only fashioned our society around a working model of mathematics, but have fashioned our mathematics around a working model of society. Unfortunately, the social model is faulty and therefore requires that we prepare mathematics for the changes up ahead. A predictive model is warranted.

For example, it is well known that the present so-called "Democracy" of the U.S. is but one flavor of many others. In this sense, all flavors are phony in that the idea of a supposed "Democracy" as a "peoples government" is a false, ideological box. If the U.S. and other so-called democracy flavors were actually "peoples" governments, then the practice of a jury duty model (Peoples Legislative Branch) would be practiced. Since having a jury of one's peers is viewed as a good, if not great feature of a Democracy, then a government fashioned on this ideal state should be written into any and all models of Constitution (whether written or not); which is far superior than the present "Representative" model where the average man and woman are not enabled to run for an electable office because of party, financial or other commercialized restraints. An actual "jury duty" form of representation requires the allowance, nay, the Constitutional provision that any man, woman or worker be permitted to run by way of a process that is not a contrived labyrinthine political structure nor one dedicated to allowing selection to be determined by any selective person or entity wanting to stack a jury with those who promise to be profitable for their views. Hence, while the words "jury duty" are used, this is not to convey the idea that the current jury duty selection process is to be used for creating an actual peoples legislative branch.

Let us refresh the previous point by providing an alternative view that exemplifies the situation about mathematics being contoured by the social structure in which a given mathematics orientation is applied. Social circumstances can alter the types and teaching of mathematics and therefore restructure the box in which mathematics inhabits. A case in point is the "fudging" of numbers on a tax return to achieve a desired result, unless one uses a non-mathematical approach such as refusing to feel out a tax reform and pay taxes. While there are set rules in mathematics, there are those who are likewise set on a course of trying to circumvent the rules, like some lawyers seeking out a loophole if "creative accounting" did not work so well for a client found guilty of a fraudulent return.

Another flaw in the current structure of the mathematic's box is its symbiotic habit of allowing itself to be used by a society in which the claims of its military being part of a democratic process is actually an hypocrisy when one looks at the Military as a stated Socialist and Communistically run enterprise. to give but one example from the following list, we find that whereas it is believed that voting for one's leaders is a distinct quality of a true democracy, the fact that enlisted personnel are not permitted to vote in their leaders is a telling point about the entire organization. Indeed, when does a supposed country like the U.S. with its avowed "Democracy", need the assistance of a non-democratically run institution like the military to support it? The allowance for such an hypocrisy is a tell-tale indication as to the state of our current mathematics and other genres of serious study.


The nmilitary's non-democratic profile (87K)

It is said that history is written by the victor. Let us add that the type of mathematics being permitted is also due to the acceptance of the victor being convinced by mathematicians as to the need for their craft... or at least the innocence and non-threatening activity it poses. Since many a mathematics orientations have been used to qualify a given perspective, right or wrong, it is of need to be routinely suspicious of mathematics and not take it at face value. It goes without saying that we can easily "fudge" equations to fit our predispositions. Yet to claim that this is the case requires more than merely showing correct equations or proposing an advanced equation within the guidelines thought to be second to no other kind of logic. One must correct the perspective from which the particular mathematics is derived by reviewing basic patterns and denoting those patterns as having a similarity to other patterns found in other genres of thinking, so that the translations of ideas into numbers and symbols can be reversed to indicate flaws where they might exist. Using mathematics alone to investigate mathematics is a fool's errand.


Date of Origination: 7th January 2022... 5:30 AM
Initial Posting: 7th January 2022... 10:06 AM