Science of Mathematics

The Science of Mathematics

Historically mathematics is the science of structure, order, and relation that evolved from counting, measuring, and describing the shapes of objects. Consequently at the reasons for its etymological root are daily practical (e.g. metaphysical) application. There exists a philosophical problem which presents something of a challenge herein with these traditional views of mathematics. That's the bad news. The good news is that Elegant Reasonism is specifically designed to segregate the various issues so that we might address, reconcile and cope with them using science and industry standard approaches. How do those problems and challenges manifest themselves? Susanne K Langer was the first philosopher we are aware of which quantified and codified 'the problem' when she essentially stated that: mistaking an abstraction for actual reality is a fatal epistemological error. Such errors are now called herein: "Langer Epistemology Errors or (LEEs)". During his lectures noted theoretical physicist Richard P Feynman danced around this very issue:

Consider regarding the above video:

  • Contemplate exactly how to go about determining "which theory looks more natural" when human physiology is predisposed to LEE commissions...
  • Are both theories in the same or different EIMs?
  • Are EIM established rules holistically enforced throughout the encapsulation manifesting that interpretative instance?
    • For example: If 'c' is the speed of light, and nothing can exceed that value then why is any equation allowed to employ any multiple of that value?
      • Does such an action constitute an incongruity? Why or why not? Does that constitute "moving goal posts"?
      • Does such an action constitute a Sigma Defect to any given investigation in full systemic context of Six Sigma?
      • What implications does such an action mean for employed ISO 9001 QMS standards?
      • How does taking that action in any investigation impact or influence the Systems Engineering contemplation involved?
      • How does taking that action change or influence treatment of the fundamental foundations of the EIM manifesting that interpretation?
      • Realizing that something can be logically correct yet remain physically different , does that action philosophically influence in any way how science is approached for the holistic investigation or discussion being undertaken?
      • Are 'the ends' justifying 'the means'?
  • Does the EIM manifesting the various theories under discussion close to unification?
  • What standards and rules are employed when constituent elements are changed within a given theory and what systemic impact does that have relative to and respective of interpretation?
    • Where and how are such changes quantified and codified relative to the abstractions employed in context of systemic commission of LEEs?

The problem and challenge then and which we all currently face is that human physiology does not present us with the reality which manifests those objects. What our physiology does present to our brains via our central nervous systems (CNS) are abstractions which allow us to perceive (at scale) objects so we may practically engage them. Those abstractions do not naturally conspire to present the unified Universe, rather only a small window on to all that is. Philosophy is the mother master field of study. The original philosophy of nature as it was historically known is what became modern science. Elegant Reasonism addresses these issues through its rules requiring the use of a plurality of Encapsulated Interpretive Models (EIMs) be employed by any given investigation noting that at least one of them must close to unification. If at some point in the future a large number of such EIMs exist then they may all be employed in order to better reflect the unified Universe.

The problem faced by traditional (status quo) thinking is that EIMs establish fundamental foundational interpretive context. The implication of that cold fact is that if you change EIMs then everything else changes subtly also and that includes all of philosophy and all of science. Consequently the requirements and criteria of unification must be considered as a predicate priority consideration, otherwise anyone (including Albert Einstein) will set up a model of the universe which may be completely logically correct, but it potentially will never close to unification exactly for these reasons. On that point and specific to Albert Einstein what he created through his body of work, especially that in 1905 and again in 1916 when he created Special and General Relativity is absolutely 100% logically correct, but therein lay the strategic clue required in gaining the precipice allowing perception and engagement of the unified Universe.

Elegant Reasonism, as filed with the USPTO (See Press Release entitled: Unification Accomplished), is two types of IP; a utility process and a net new epistemology. To understand the path to epistemology we must understand how to wield Elegant Reasonism as a utility process in order to see how it was able to produce the first fully compliant Encapsulated Interpretive Model (EIM) which closes to unification: The Emergence Model. This is all parsed into a single sentence on the front page of the white paper for Elegant Reasonism. As filed, Elegant Reasonism includes three elements: the utility process, the epistemology, and the first EIM to close to unification: The Emergence Model.

At that level, herein major branches of philosophy relevant to Elegant Reasonism (in alphabetical order) are:

Science itself is a philosophy, and herein it is important to realize the Elegant Reasonism constitutes a net new epistemology. There is a point here relative to the science of mathematics and it is the methodology employed to recognize the distinctions between context made manifest by encapsulated interpretive models of the Universe and the mechanics of mathematics studied for many millennia. The mechanics of mathematics does not change because of Elegant Reasonism, nor does the philosophy governing its rules. What does change are the various variables and constants employed by other sciences, their definitions and use all of which conspire to manifest context of the various models.

There is an implication from this insight however and it concerns the long lived metaphorical war between physicists and mathematicians. The issue is best illustrated by Langer Epistemology Errors in context of what it takes to manifest context by the various models, the requirement for their 'encapsulation' and subsequent treatment of them within Elegant Reasonism holistically. When we use phrases like "the math works", the reality of that statement is that herein (e.g. Elegant Reasonism) it means that the mathematics conforms to the realm of the c's within a given model AND it survives ISO 9001 QMS standards, AND Six Sigma as it is holistically applied across the phase steps Recognition, Illumination, and Analysis, (especially Development of Treatise), ultimately culminating in a final Treatise aligned with the actual real unified Universe.

In Unification's Wake, Part 02: Mathematical Proofs

Historically the approach mathematical sciences took did not delineate whether or not Langer Epistemology Errors (LEEs) were being committed, nor did it segregate different simultaneous truths across a plurality of Encapsulated Interpretive Models (EIMs) where each presented a potentially different evidence chain path to the relationship patterns manifesting that truth.

You may click the above paragraph title to review these charts or listen to McGowen give an informal talk using them as a presentation right here, right now.

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Available Online Education

The intent of this area is ultimately to provide a comprehensive set of actual courses which enable or augment the Elegant Reasonism Syllabus currently under development. Ultimately we would like to provide a comprehensive online course delivering Elegant Reasonism skills across all skill and age levels.

Auburn University Online

MDPI Open Source Journals: Mathematics

Mises Institute for Economics

MIT Open Courseware: Mathematics


Operations Imply WorkFlow

Working to understand Severance in the original systems review it was something of a revelation that if it had been know by McGowen, it had been forgotten and it is that every small mathematical operation must be accompanied by tangible WorkFlow in the real world's processes (usually described by some branch of science). In the case of Severance it was found deep in the mathematics used to solve for Einstein's Coefficients of Emissions. There, there is an equation where we all perform 'canceling operations' on paper all the time. Here though the insight was the cancellation of the variable 'c' out of the equation leading to the final coefficient. C cancels out of that equation exactly because the photon left the system and that was the first time we saw evidence of Severance in action, albeit from an M1 point of view.

Engineering Reasoning

"It is only a few rare and exceptional men who have that kind of love toward mankind ... that makes them unable to endure patiently the general mass of evil and suffering, regardless of any relation it may have to their own lives. These few, driven by sympathetic pain, will seek, ...some new system of society by which life may become richer, more full of joy and less full of preventable evils..."   — BERTRAND RUSSELL. I9I9- Proposed Roads to Freedom

Elegant Reasonism needs to be the framework which forms the basis of a comprehensive engineering based systems review across all disciplines.


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