#archetypes  #hero

Intro for ebook of Imaginary Heroes:

I must confess that, 3 decades later, I no longer believe in much of what I wrote for this book, though it still has value for a couple reasons. First, it is a precursor to mythic algebra, showing the sources which developed into it. Also, the analysis of pop culture is still relevant and interesting if we merely relegate archetypes to the status of tropes, not instincts. My current attitude to psycho-dynamics is best summed up in my paper on Wonder Woman, which is part of the other ebook, Mythic Algebra. I quote its statements here:

"Mythic algebra can be used to model stories and show patterns. As a formal system, it may identify tropes for either the writer or reader, and the artist or viewer. While the choices of these tropes occur in a social context, aside from that they still may have a structure. Such formalism does not require determinism, but rather presents the most logical possibilities granted by the language ...

Could the ancient Greeks have ever imagined that their Furies would meet up with Wonder Woman thousands of years later? This hero cycle does not mean that all hero stories have to follow this structure, if only because any storyteller can embellish and improvise the tale to make it different. If hero cycles are universal - whether Campbell's, the tragic Greek, or their combination - they are only so as logical possibilities.

Heroes and villains don't have to change. The basic hero cycle is a kind of template, a starting point for anyone to fill in the blanks or alter the pattern. And part of the joy of humanity is the endless creativity we have to come up with new stories, even if they begin as revisions of myths."

The comments made about hero cycles can also apply to mythic algebra itself: a template of logical possibilities, a formal structure the brain may follow because of its utility to model reality, yet a model to transcend and improvise off of.

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.

First Trio

Comments: Follow-up

            This trio of papers from the Journal of Literary Semantics completes the initial form of mythic algebra as a unitary system. The second trio, from Semiotica, will show various applications of mythic algebra. Before introducing the Semiotica trio, I’d like to pursue some ideas closer to the JLS trio.

            Many literary topics were broached, such as the varieties of ‘figures of text’ in the third paper. Some of the modeled literary concepts also have social uses, like Jungian archetypes. Such variety in the same mythic algebra notation lends support to the claim that all social science constructs are somewhat arbitrary, valid as far as they go perhaps, but only going just so far. For example, the notion of the Hero as analyzed by Campbell and Jung, et al, may have more variation than the theory of archetypes reveals.

            In a 2008 article under my science fiction fan name of M.L. Fringe, I presented a critique of the hero cycle. This article ignores all of the mythic algebra ideas of mythic spacetime, to focus on the aftermath, when all of the action happens back in the real world. Mythic algebra does not enter into the article, showing how limited its relevance can be.

Westercon 57 Notes: The Crime and the Glory of Joseph Campbell

by M.L. Fringe

When Joseph Campbell’s PBS-TV series The Power of Myth debuted in 1988, I was converted to it as much as anyone else. I’d been listening to his lectures on radio for a year by then, so I knew to catch the TV show. Like so many alienated middle class middlebrows, I was filled with the evangelistic fervor that HERE was the crucial insight to bring world peace. Once we told all the religious that they really believed the same thing because religion is a metaphor, then war and hatred would end. It took Native Americans to indirectly convince me of the naivety, 16 years later.

You see, the theme of the 2004 Phoenix Westercon, Conkopelli, was southwest mythology. Kokopelli, the Indian trickster, was a good choice of mascot for Westercon 57, because I could not find any Indians who wanted to participate in the convention. As one of their scholars gently explained to me, Kokopelli, Coyote, et al are not quaint myths to Indians. They are part of their living religion. If you catch a 20-year anniversary broadcast of The Power of Myth, you may notice that there are no Indians in the PBS-TV series, just Bill Moyers talking to Campbell.

The interviews were often on Skywalker Ranch, and praising the Star Wars movies.   Another TV show has a testimonial from George Lucas on how Campbell’s book The Hero With a Thousand Faces guided his Star Wars storytelling. Campbell was famous and influential before Moyers made him more so with PBS-TV. Many knew of his three-stage analysis of the hero cycle: separation-initiation-return to society with a benefit to save it.

What’s wrong with that cycle? What’s wrong is that it’s only one half of the hero’s cycle represented as the complete cycle. If Campbell had written of the full hero cycle, he might never have become as rich and famous as he did.  The full cycle is depressing, and has been told by schoolteachers ever since Greek was translated into English. It includes words like hamartia, hubris, and nemesis. These are the second half of the cycle, the downside when the hero gets too big for his britches and becomes a villain. Hamartia is the fatal character flaw once the hero has done his job and saved society. It leads to hubris, a conceited pride that he should lord it over society or flaunt the rule of the gods. This results in his opponent, nemesis, arising to cut him down to size. If he’s lucky, he survives as a mere commoner, back where he began long ago.

Visually, the cycle looks like this:

Campbell ignored this, as if it wasn't part of the hero’s story. Glossing in his book, he noted “But a deterioration may take place in the character of the representative of the father…The upholding idea of the community is lost. Force is all that binds it. The emperor becomes the tyrant ogre (Herod-Nimrod), the usurper from whom the world is now to be saved.” (Part 2, chap. 3.5) One may apologize for this and claim that the bigger cycle is for the “tragic” hero, not all heroes. But literature teachers bore us with the full cycle of the hero’s tale, and the price those teachers pay is humble obscurity.

We may be less inclined to want to read such complete stories, too, but they are commonly taught in school. Examples include Prometheus (who gave man fire), Oedipus (the incestuous king), and in movies: Darth Vader (George Lucas knows). Apply such interpretations to any religion’s figure of your choice. Just don’t expect to convert any true believers. I’ve learned that much, for I remember Westercon 57.

No new mythic algebra results from this article. If I had used it, the only new uses would have been to show the breakthrough of a nemesis into the real world: M(p,s,t)/M(p)R(s,t) or maybe the banishment of the hero to a mythic land of punishment, a crossover of R(p,s,t)/R(p)M(s,t).

A more clearly dangling thread from the last JLS paper was the mechanism of metaphor, which I kept after until it resolved into part of the first Semiotica paper. The most pressing inspiration for that paper was a new area of application: the semiotic sign. I almost put a final section in the last JLS paper, on how the mythic algebra lineup could be divided into the three kinds of sign: icon, index, and symbol. The treatment would have been too short, and more research on that beckoned.

In the ensuing five years, the question of logic worked into the same paper. It had been implicated in earlier researches, but was the vaguest of dangling threads. Once semiotics was directly addressed, logic became more relevant.

The second Semiotica paper finally addressed the claim that mythic algebra was an ur-mathematics that could develop into mathematics proper. This was more than a dangling thread, as was the topic of association itself, covered in the last paper. While the Semiotica trio makes new uses of mythic algebra to tie up loose ends from the JLS trio, the second trio itself raises some new issues. These will be addressed after, in the epilog.   

            From 1981, we must jump to 1992 when I wrote a properly unpublished book titled Imaginary Heroes in the Age of Science: Archetypes in Popular Culture. There was one good idea in it worthy of publication, which was developed into this collection’s first paper, ‘Mythic Spacetime.’ Once the framework developed in 1992, it took five years of idle contemplation before that set theory insight resulted one night. I now reproduce the few paragraphs, from the 1992 book, which were my first thoughts on and coining of the term mythic spacetime.

            In standard myths, where does a hero commit violence? In the land of adventure, the fantastic other realm outside of normal society. This is part of the constructive social meaning of archetypal models, which modern society tries to erase in its rational models of law and order, but which persists as part of human nature: there is a proper place for violence. In ancient times, it was on the hunt. In modern comics, it’s on the hunt for criminals or super villains. The mythic land is the place where violence is the correct thing to do, and anywhere a superhero is on the job becomes a mythic land for the duration of the fight. This fits in with why most of reality seems to ignore superheroes in the comic book stories.

            It also fits with the history and prehistory of real humanity. The hunting mentality can be thought of as a kind of ‘mythic time’ when men access the archetypes of violence. Coming back to the hearth, they would engage in entertainment to tell of their deeds, thus recalling when they were using their instinctive skills, i.e. accessing archetypes. The original boon that they brought back was the game that they killed. Of course, the women had the superior skill of producing a boon out of childbirth. Either sex has its own version of bloody violence in the mythic space-time.

            The would-be censors of violence on TV probably give less thought to sports. This is the usual mode for people to access the mythic space-time, far more popular than the pop cultures I consider in this book. The socially acceptable channeling of aggression and violent urges into competitive sports is no doubt completely satisfying for the participants. For some spectators, it’s not completely satisfying, and they have to start fights or riot. For other spectators, it may be the equivalent of reading a comic book, with the added experience of getting to shout from the stands. Or in the TV room.

            The notion of a separate space for superheroes to slug it out nagged at me, with its resemblance to Mircea Eliade’s description of making a ritual space. One night in my caregiver years, sitting on a couch by my sleeping mother, looking at a TV screen, the notion to represent the characters as set elements occurred. The consequent idea came that elements were mapping between sets. The further explication of these ideas is presented in the first three papers, all published in the Journal of Literary Semantics, thanks to the instant approval of its founding editor Trevor Eaton.

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.