For the next few years, I will be parsing out the contents of my earlier nonfiction  book attempt: Imaginary Heroes. There will not be a second monthly post to frame these except for this one to introduce the table of contents, prologue and index for the whole book. In the future, if I depart from the book and post something else for the month, it can be distinguished in the Blog Archive list by a second framing post for that month.

Imaginary Heroes book sections: Table of Contents, Prologue, Index

#archetypes  #hero 

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IMAGINARY HEROES IN THE AGE OF SCIENCE: ARCHETYPES IN POPULAR CULTURE by

Michael Griffin

This month's post is the end of the framing material for the book notes. These Epilog comments do presage further research that I did. In the penultimate paragraph I said: "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." This is exactly what was done in the 2nd and 3rd papers of the comic book trilogy. Antivillains and antiheroes were placed on a spectrum scale of good or bad (July 2014 post). The Doom Patrol was compared to the Fantastic Four based on qualitative aspects of individual team members (August 2014 post). Btw, the intended title of the book is simply Mythic Algebra.

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.

These book frame comments would follow the reprinting of the First Trio of papers, and are listed in the table of contents as Comments: Follow-up and Hero Cycle. The hero cycle article in this month's posting was never printed even in scifi fandom (title is from a Cordwainer Smith story btw). It is mildly embarrassing to post it, as an edge of bitterness comes through in some spots.  In 2009 a modified version including the diagram was presented at an undergraduate conference at Arizona State University in Tempe, at the invitation of English major Jenny Brundage.  In 2010 it was presented at the Coppercon 30 science fiction convention in Mesa (thanks to programming director Nyki Robertson). The cycle idea and diagram also was presented  in a Phoenix College class on comic book writing (taught by Hershman John), in a presentation on antivillains by myself and fellow student Sarah Price. Later it was applied to the Wonder Woman graphic novel used as a textbook in the class.  That was also not published immediately but just sat in my notes. Then I saw a panel discussion at the 2011 Phoenix Comicon with Kathleen Dunley promoting the website The Comics Grid. I thought they would be interested in the idea and wrote it up to fit their criteria. They eventually accepted it (2012), and it is the first entry of this blog for June 2014.

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.   

This is the third part of the book framing comments, noted as Imaginary Heroes in the table of contents in the March posting. I may have been too harsh to call that other book attempt unpublishable, except that it had little original thought and was an application of Jungian archetype theory to science fiction and superheroes. I will review it and  consider parsing it up for this blog.