Second Trio

Epilog: Future Directions in Mythic Algebra Research

            This concludes the published research into mythic algebra, leaving the prospect for further work open. Either the algebra itself could be further refined, or an unending task of new applications could be done. Before new uses are made, I think the algebra itself should be critiqued. This need arises both from the vague generality of the set elements (p,q,x,y,s,t) and the divergent nature of its areas of application.

            As cited in the penultimate paper on numbers, there are three distinct ways mythic algebra could be applied: in pure mathematics, into modeling the natural world, or to explain the workings of the mind. Since mythic algebra was derived from mythology, it immediately serves as a model of mental activity. It makes a structure amenable to describe any symbolic process. No small part of that success is due to the abstract vagueness of the (p,q,x,y,s,t) elements. Also, the association operation itself is so broad as to cover anything, even though the final two papers tried to limit it to a definition of linkage.

            Further research into mental operations may need some more specific operations than just + addition and * association. Again looking at the fifth paper’s chart of number types, it seems a good idea to define comparison and ordering as distinct operations on their own, so * may be truly isolated as just a link. The basic criterion of any operation remains non-reducibility. No operation should be reducible to some form of  +/- additive process, as in a computer language. The point is that the mythic algebra system is not reductionist to nothing-but quantities adding together.  So while a computer may do comparing and ordering of data based on its own +/- logic, that is not the basic reason why mythic algebra does those operations. The operations themselves should be universal to any application, basic parts of any structure. Results of these operations may still be a transform ® or just an unchanged relation of equal = or similar ». We may notate them as the colon : for comparison and > for order, using the math symbol for ‘greater than.’ The ordering is not just quantitative, nor is the comparison. And such qualitative uses of  : and > may have no numerical measure at  all, no scale of 1-to-10 to place judgments upon. These are basic operations not reducible to +/- logic.

            Introduction of : and > into the numbers chart would expand the complexity of it. Instead of trios of  + and * symbols, with 2 X 2 X 2 = 8 possibilities, there would be 4 X 4 X 4 = 64 possible basic trios, including ones not mentioned on the chart. If the chart of number types were used to examine pure mathematics, then further complexity would result. New patterns in any area of mathematics may turn up, possibly leading to new types of math, new mathematical functions, and so to new ways to model the physical world. Even the number trios chart as it presently exists could lead to these results, and caution is needed here, for there is apparently no necessary reason why the three realms of mathematics, nature, and mind should always share the same basic mythic algebra.

            For example, we could argue that while the numbers chart consists of trios of mental origins, these are outside views upon quantity numbers that exist objectively only as cardinals and ordinal qualities. Objectively, there is no mind to compare or order the numbers. They simply exist as they do, and have static structures. Then there is no need to interpose : comparison or > ordering operations until we consider human usage of mathematics. Likewise when modeling nature, who compares and orders? Perhaps nature is reducible to an unknown * linkage, with + addition as a rough approximation to it, a crude surface effect. Yet the unconscious brain mechanisms of the mind do compare and order set elements, so : and > could be introduced into any of the previous mythic algebra results of literary semantics, semiotics, mythology, logic, language, etc.

            Similarly, the (p,q,x,y,s,t) set elements do not have to be the same among mathematics, nature, and mind. All of the number modeling only used the x element. Physical nature would not have to distinguish people from animals, so we may have living things p versus objects x. Can we find any new structures in nature using mythic algebra, though? Do all of the features still occur? P®x could be a living thing dying and so becoming just an object. How helpful are such flexible interpretations of the mythic algebra features? A structural system is considered good the more widely applicable, but it must also be specific. Having six elements for the mind, four for nature, and only one for mathematics may not allow analyses, no matter how many subscripts are used to distinguish individuals.

            Perhaps mythic algebra could become an analytic approach within each field of study, with set elements and functions tailored to that field, with the aims of discovering new * associations within that field. These new *’s may be reducible to classical categories or not, i.e. using + operations of quantities. Chemistry may have each member of the periodic table as a set element. Physics may have each subatomic particle. Biology may have each organism. But why should scientists try such an approach if they are satisfied with the quantitative results that exist? Mythic algebra would only appeal if it could help solve outstanding problems, explain the currently unexplained, or lead to discoveries. All of these activities are beyond me, and I am the only person using mythic algebra.

            Returning to my topic of mental modeling, I suggest using : comparison and > ordering for new operations. To get beyond (p,q,x,y,s,t) elements, one way would be to introduce qualities as their own set elements. In regards to the second JLS paper, we could say if a flower is red, if a person is good. From this, the amount of set elements could grow unlimited. And here we come upon the basic flaw of any structural system. Pushed far enough, it either breaks down or bogs down in complexity. Mythic algebra has avoided this so far by remaining overly simple, covering everything yet nothing precisely.

            For all of this harsh analysis, mythic algebra still seems to have gotten some real results when applied to the mind. Perhaps it is too optimistic to hope that the principles of association could better describe pure mathematics and nature. At least it is a new approach, even if it harkens back to the earliest, mythic times.

Table of Contents

Introduction: Origins

     Singular They

     Imaginary Heroes

First Trio: Journal of Literary Semantics

     Mythic Spacetime
 
     Narrative Algebra

     More Features

Comments: Follow-up

     Hero Cycle

Second Trio: Semiotica

     Mythic Algebra Uses

     Numbers

     Laws of Association

Epilog: Future Directions



Introduction: Origins

     While this book reprints six academic papers and related material, its origins are not in the dry, technical world of academic theory. It started with comic books. Before I went to school, before I learned to read, I ‘read’ comic books at home. Four decades later I was again reading them at home, and developed mythic algebra from them.
     Mythic algebra is a hybrid system of various parts of basic mathematics, sets and algebra cobbled together to describe the symbolic processes of the mind. Originally derived from mythology and superhero comic book stories, the system has been aimed to cover all mental activity, incorporating non-mathematical processes like mental association. This led to the idea that mythic algebra is the ur-mathematics out of which true mathematics, and any other language, evolved.
     This collection of academic papers is based on a radical assumption, that the mind works on symbolic processes which are the same no matter how expressed. Today’s educators speak of different learning styles, which is no doubt true. Beyond this, everyone assumes that each field of thought, each subject area, involves different ways of thinking. How one does mathematics differs from how one understands the arts, stories, language, or any other mental activity. Yet we have one brain for all of this, and while scientists can identify different areas of higher brain activity depending on type of thought, all areas are said to be interconnected. There are also many different types of connection: chemical, electrical, physiological, organelle, and perhaps electromagnetic broadcast. But if all these are considered the building blocks, what structure do they make?
     Notwithstanding the actual variation of brain parts and connections, when they all work together, does it make a single, unified process? Obviously it does, since we are autonomous animals that think and move on our own. While this fact is easily conceded on the level of body motion and physiology, it is rejected at the level of thought. Our personal conflicts, our ambivalent desires, are taken as signs of the competing systems in the triune brain, the reptilian brainstem versus the mammalian midbrain versus the human frontal lobes. Yet the triune brain produces a single person, even if it is only a highly evolved radio box to receive a spirit. Leaving aside spiritual questions, how could any unity of process be recognized? How could this be described in a functional notation system?
     Enter ‘the new math,’ that abandoned approach to teaching grade school mathematics in the 1960s. I am a product of that, for I absorbed the emphasis upon sets as a basis of understanding the world. It has colored my thinking, becoming my natural viewpoint upon anything, long before it inserted itself into my way of thinking about comic books and the first published paper here (from 2000), ‘Mythic Spacetime.’ I get ahead of myself, and must retreat to earlier decades, to give an unpublished example of a worldview colored by sets.