Threesology Research Journal: Perspectives on Mathematics
Perspectives on Mathematics

~ The Study of Threes ~
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Here is a list of pages I have been working on regarding a different perspective of Mthematics. I will add more as soon as I finalize the 15 or so I have already written but need to verify spelling and HTML formatting:

Language of Mathematics Predictive Mathematical Models Favorite Equations - and - Favorite Numbers Mathematics' Unreasonable Effectiveness
Simple Dualities in Mathematics 1 Simple Dualities in Mathematics 2 Simple Dualities in Mathematics 3 Simple Dualities in Mathematics 4

Infinitesimal versus Accordian Calculus series
((Static -vrs- Dynamic Equations)

This is a philosophical exercise without the use of equations. I do not know how to write an equation for a type of mathematics that has never before existed. Whereas mathematics in both simple (such as counting) and complex forms (such as Algebra, Geometry, Trigonometry, etc...) have been used to analyze different subjects, it has been a rarely used tool applied to mathematics itself.


Accordian Calculus 1 Accordian Calculus 2 Accordian Calculus 3 Accordian Calculus 4
Accordian Calculus 9a Accordian Calculus 9b Accordian Calculus 10a Accordian Calculus 10b
Accordian Calculus 10c Accordian Calculus 11a Accordian Calculus 11b  
Accordian Calculus 12b      
       
       

While I have subjected other subject areas to an analysis of attempting to illustrate the existence of basic patterns by using numbers, it seems only fitting that I eventually turn my attentiong towards the very subject which claims a dominion over numbers. While mathematics, with respect to its usage of numbers does not typically use a basic formula of math to analyze its own content with an attempt to identify the basic patterns of ideas being used based on a simple measurement; it is of value for those interested in identifying the existing patterns of this cognitive dimension.

To me, mathematics is a much a philosophy as it is an art, though other labels and ideas can be applied such as viewing mathematics as a type of expression similar to the nest building of some birds, the web building of some spiders, the huts of beavers, the mounds of some termites, the burrows of various animals as well as the inverted conical/triangular burrow-traps used by antlions. It is with some amusement when I encounter someone referring to the mathematics of humanity as a language which all sentient beings in the Universe will no doubt use, and yet not claim other activities as being a universal language such as a spider web if we should encouter a spider on a distant world who displays the same type of behavior as do some spiders on Earth. No doubt we might well find numerous similarities of expressions with different life forms on distant planets yet never think to claim such behavior as a Universality nor as having any significance other than being a curiousity for some later consideration.

It is rather self-centered, egotistical and an expressed self-absorbtion for humans to think that their mathematical behavior is somehow a basic truth that all sentient beings in the Universe would most likely be able to understand and communicate with humans by way of a Vernacular called Mathematics, as if human mathematics is a Lingua Franca (Universal Language) suggested as the governing medium by which all forms of bartering and exchange can take place as was the case in the early history of humanity... a humanity which shared an interest in possessing certain goods once their value was realized for a given context. Surely then, one might suppose, that sentient beings in the Universe would have an interest in something in the possession of humanity that can be used to barter with. And yet, what if no other sentient being has any interest in any resource humanity has to offer or would prefer to not deal with the primivity of humanity since it would be easier to introduce some virus to kill them off instead of having to waste time in negotiations.

While mathematics has shown its value to humanity and mathematicians have insisted on describing mathematics as being a precious commodity to be dependent on, it is a tool existing amongst other tools which are valuable in their own context. For example, you can't fix an over-flowing toilet with a math equation, you need a different tool (such as a plunger or "sewage snake") that humanity has devised for such an occasion. Likewise, a math equation will not make you breakfast in the morning, though some might argue that mathematics is used when we navigate a vehicle to go to and from a destination... we simply have devised a means of obscuring the recognized involvement of mathematics from our perceptions of everyday tasks... though there are some who make a concerted effort to make a comment thereof. However, mathematics might well be used in designing a tool to unclog a toilet as well as be used in some fashion by which the food-stuffs and eating/food preparation tools are acquired. While simple forms of mathematical measurement are use to gauge the level of toilet water and the quantity of food to be prepared, we have used a reductionist methodology to assign some importance to keeping the presence of mathematics in view. Indeed, by claiming that mathematics exists in all things, we have engaged the notion of creating mathematics into a type of symbiotic organism, if not some more basic biological characterization similar to describing the ubiquitous presence of DNA in different life forms.

Mathematics is not typically used to analyze mathematics... that is, to elucidate the basic patterns of mathematical thinking expressed in the many ideas used to describe the parts and processes of mathematics. Thus far, in my initial efforts to uncover the patterns by subjecting the various ideas of mathematics to a basid formula of enumeration similar to that used on other subjects, what I have encountered is the presence of a dominant usage of two-patterned ideas, as well as the presence of an underlying usage of geometric forms which conceal the absence of quantity and quality of thought processing. For example, we do not find ideas in mathematics which routinely practice the usage of large quantities, and that in using equations, the dominant style is a linear form that is used to describe circles, triangles and other geometric forms, but equations themselves to do not exhibit these geometric models. Whereas we can note the presence of linear, circular and triangular configurations as an ensemble of constructive usage in other subject areas, we don't find it with regularity in mathematics.

While it is true we find a diverse array of geometric forms, we do not find these forms being used in the construction of formulaic equations. Whereas one might want to argue that a quadratic equation can be visualized as a square and that the notion of "squared" and "cubed" appear to reference a similar type of illustration though they are viewed as different functionalities; such notions have not been assigned such a representation of cognitive usage. In other words, there is no established criteria for viewing such ideas in a framework of analyzing mathematics as a type of cognitive activity which can be viewed to illustrate its patterns set side by side the patterns being used in other subject areas that rely more on words than numbers. There are mathematical dimensions to words just as there is a language and grammar to mathematics. Using a system of numbering to analyze numbers...so to speak, is a task to map out the cognitive dot-to-dot terrain of mathematics... thus revealing its similarity to other ideas and its limitations.

Despite all the embellishments being used by mathematicians in their productions of equations and applications, very simple patterns can be detected and analyzed as an expression of human brain activity, and formulated without bias, discrimination, or prejudice next to the patterns found in other subject areas. Reducing mathematics to its cognitve nakedness reveals its framework below all the different types of symbolic frills and trappings, mix and match as mathematicians do in an effort to express some originality of conceptualization and get their name associated with an equation to be referenced by others sharing their interest.



Page Origination: May 30th, 2021...1:53 AM
Initial Posting: June 1st, 2021...3:24 AM
Updated Posting: July 21st, 2021...2:15 PM