Gene Wolfe’s “Book of the New Sun” tetralogy is said to be rife with alchemical symbolism. I have not read it yet, although it has been on my to-read stack for years. Nonetheless, here is a diagram for you, partly because it’s an easy post, but also for me, so that I can add interesting links as I might find them.
The Shadow of the Torturer
The Claw of the Conciliator
The Sword of the Lictor
The Citadel of the Autarch
Of course, there are a few other tetralogies that exist, although they are not as common as trilogies. One already mentioned on this blog is the Aeygpt Tetralogy by John Crowley.
Jung’s diagram of his alchemical tetrameria is supposed to represent the evolving self, and suggests movement, succession, and change and yet stillness, consistency, and renewal. His own diagram is quite different from mine, but I do think that mine has some merit.
What are those elements A, B, C, D, and a, b, c, d, and the subscripts 1, 2, 3, 4, indicating the modification of them? I’m not quite sure that it matters, except that for the relationships between the two, and the relationships between the four squares, and the relationships between the four parts of the four squares.
In Jung’s diagram, A equals a cycle of a, b, c, and d, and likewise B a cycle of a1, b1, c1, and d1, etc., and so we can instead say A is a cycle of Aa, Ab, Ac, and Ad, and likewise B is a cycle of Ba, Bb, Bc, and Bd, etc. In that sense my diagram denotes much the same as Jung’s.
Nevertheless, I’m going to have to cycle through some more thoughts about why one should spend too much time contemplating this diagram.
Professor of Literature Joseph Campbell  popularized the monomyth of the “hero’s journey” , a recurring template for the plot arc or cycle of many heroic characters found in mythologies and even popular modern stories. From his most famous book, “The Hero with a Thousand Faces”:
A hero ventures forth from the world of common day into a region of supernatural wonder: fabulous forces are there encountered and a decisive victory is won: the hero comes back from this mysterious adventure with the power to bestow boons on his fellow man. 
Quite a few diagrams are available showing the generic journey of the hero or heroine; some are more complete than others, and the one I present here is no exception. Campbell’s schema is said to have seventeen basic parts to it, but not all elements need to be present in any specific narrative. I list four basic “acts” (separation, descent, ascent, unification) and twelve basic events, including four thresholds: 1st) crossing into the special world, 2nd) surmounting the supreme ordeal, 3rd) returning to the normal world, and 4th) journey’s end and / or beginning.
Call and Refusal
——–< Separation >
Meet the Mentor
Crossing Over (1st Threshold)
Tests, Allies, Enemies
——–< Into the Abyss / Descent >
Inmost Cave / Whale Belly
Supreme Ordeal (2nd Threshold)
Ultimate Boon / Reward
——–< Magic Flight / Ascent >
Road Back / Refusal
Crossing Back (3rd Threshold)
Return with Elixir / Resurrection
——–< Unification >
Master of Two Worlds
Freedom to Live (or Die) (4th Threshold)
Any hero’s journey must be transformational, and so has associations with alchemical change. It must be of such difficulty that it utterly changes the nature and the mindset of the traveler. Even though many supporting characters may influence, help, and even hinder our hero, it is ultimately about their journey, their sacrifice, and their reward. But what the hero brings back with them is also key to the story, because it is for the benefit of others as well as for themselves.
An interesting dissertation by Richard Warm that I ran across recently proposes that leaders, like heroes, need ordeals and trials in order to bring back the inspiration and wisdom to motivate others. From the abstract:
This dissertation will explore leadership as a mytho-poetic transformational journey toward self-knowledge, authenticity, and ultimately wisdom; the power to make meaning and give something back to the world in which we live; and the necessity of transformation. I view leadership as a transformative process and a transformational responsibility. As leaders we must undergo our own transformation in order to lead change on a larger scale. The dissertation will be both philosophical and theoretical, exploring how the threads of the hero’s journey, transformation, wisdom, and leadership intertwine. …
These ordeals may also be of an intellectual or moral kind, and not just feats of strength or stamina, although those are important too. Warm also has a company  for coaching you on your leadership, life, and legacy.
One of my favorite books that I think of when the hero’s journey comes to mind is “Figures of Earth: a comedy of appearances” by James Branch Cabell. It is a bit of a spoof on fantasy tropes, well before its time. However, I’m not quite sure what the “magic elixir” is that the hero returns with except for his story: that life is what you make of it, or what it appears to be to others, or what you can convince yourself that it is, or that it is what it is and must be sufficient to you in the end.
Full fathom five thy father lies; Of his bones are coral made; Those are pearls that were his eyes: Nothing of him that doth fade But doth suffer a sea-change Into something rich and strange. Sea-nymphs hourly ring his knell Hark! Now I hear them – Ding-dong, bell.
— William Shakespeare, from The Tempest
As a dabbler in Alchemical concepts I was heartened that the American TV show “Lodge 49” was renewed for a second season. The show is mostly set in Long Beach, CA at the current time and revolves around characters who are members of the fictional fraternal social club Lodge 49, a local chapter of a greater fictional organization called the Order of the Lynx. The history of the Order is mysterious and is revealed slowly as it is told to one of the main characters who becomes a new member. There are many Alchemical references in the artwork on the lodge’s walls and in the literature and philosophy of the Order itself (as well as beliefs by a few members) but for the most part the members use the lodge as a gathering place to socialize and to network for personal and business needs.
There is a great sense of ennui and nostalgia in the member’s lives, in the atmosphere of the lodge itself, and the larger world outside. The golden days of yesteryear are past. The economic climate is mostly dire because businesses are shuttering or are corporate nightmares and in general people are not happy in their personal lives and their life’s work. The new member (who could represent our “everyman” but perhaps the Fisher King himself) at first seems to be rather worthless but we soon see has been dealt some rough blows recently. And yet he still seems optimistic and hopeful for a better tomorrow and a return to better days. His sister is more worthwhile but not by much, working a dead end job and living a life that’s going nowhere except trying to help her brother. A sadness and disappointment hangs about in most everyone’s lives.
Our everyman’s enthusiasm and hope soon infects the other lodge members but as we learn more of their backstories and the history of the lodge we feel that a bright future for all is still very much in doubt. Everything is in flux, but there is always a give and take to be considered. Here the idea of “equivalent exchange” comes to mind. To gain something from the world, something else must be given up. To win something, something else must be lost. In the long game, perhaps knowledge is the ultimate prize to be granted, and what we must relinquish is our innocence and naiveté. But not our hope, because without it we are lost and just going through the motions, as many of these characters are.
Alchemy has been seen in modern thought to be an analogy for personal growth and individuation. Carl Jung was a pioneer in this as he explored the meaning of dreams and the unconscious. As the alchemist strived to transmute base substances into gold (the element that was thought to embody both material and spiritual perfection), so a person should work to transform his life and its meaning into the highest forms that they can obtain. This is indeed possible because what constitutes all that is superior, also constitutes all that is inferior. As Above, So Below (from the Emerald Tablet and which is the title of the first episode).
What happens when the fourfold of Noether’s Theorem is spliced together with the fourfold of Pauli-Jung? Both have Space-Time and Matter-Energy. The former has Conservation and Symmetry, and the latter has Causality and Synchronicity.
I had to remind myself that Conservation means consistency (of matter or energy) through time (and space), and Symmetry means consistency (of form) through space (and time), so in some sense they are dualistic.
Combined, one has the three axes of dual concepts, represented above.
What happens if one combines the four classical Greek (Western) elements with the five classical Chinese (Eastern) elements? Air is in the former and not the latter. Wood and metal are in the latter and not the former.
I’ve left out the Aether (the Fifth Element) of the West because I follow Empedocles, and I see that the five classical Japanese elements have those four and Void as well. But, I’m just looking at material and tangible elements.
One might consider Wood and Metal to be derivatives of Earth, but let’s consider them to be distinct for this exercise. So, maybe six elements!
Everything is dual; everything has poles; everything has its pair of opposites; like and unlike are the same; opposites are identical in nature; but different in degree.
— From The Kybalion by The Three Initiates
There are trivial truths and the great truths. The opposite of a trivial truth is plainly false. The opposite of a great truth is also true.
— Niels Bohr
I have mentioned the alchemical notion of the “Marriage of Opposites” several times (here and here). When opposites marry, what happens as a result? Do they cancel one another out, leaving just a boring average as result? Do they explode in a fiery conflagration, like matter and anti-matter releasing energy? Or do they create a new thing, something that is greater than the sum of their parts?
If opposites annihilate each other, what is the result, emptiness or a void? It is often said that nature abhors a vacuum (“horror vacui”), but I think it is far more true that the mind does. In dualistic thinking, everything that is not one thing must be its opposite. Not good is bad, not happy is sad, not black is white.
In classical logic, the Law of the Excluded Middle says that for any proposition “p”, either it is true or its negation “not p” is true. Thus, “p or not p” is necessarily true, a tautology. Similarly, their combination “p and not p”, cannot ever be true, and so is necessarily false. If one can assume “not p” and derive a contradiction, then “p” must be true (reductio ad absurdum).
In intuitionistic logic, one cannot deduce “p” simply from the falsity of “not p” (that is, “not not p”), one must actually prove that “p” is true. So “p or not p” may still be uncertain, if we don’t know how to prove “p”. However, “p and not p” is still false, based on the falsity of “not p”.
In the viewpoint of Dialetheism, it is offered that there are truths whose opposites are also true, called “true contradictions”. Dialetheisms cannot exist in formal logics because if “p and not p” is true, then you can deduce anything you want and your logic breaks down. Nonetheless, much thought through the years has been dedicated to dialetheisms and their ilk. Please see the recent work by philosopher Graham Priest.
When one considers something and its opposite at the same time, how can you reach an agreement between them? In magnetism, opposite charges attract and like charges repel. All too often, opposite viewpoints vigorously repel each other instead of reaching a happy medium. Each viewpoint considers the other “false” and so they push away at each other, instead of meeting halfway in compromise.
If there is empirical evidence supporting one viewpoint and not the other, and both parties can agree to it, then problem solved. But if viewpoints are more like ideologies, and one side shows evidence that the other side dismisses, what then? Are we only left to agree to disagree? That doesn’t seem like a long term solution.
In this blog I have insinuated but not stated explicitly that a marriage of opposites can often be achieved by combining it with another pair of opposites. Rather than meeting in the middle to a void or an annihilation, one can reach the other side by “going around” the danger, by way of intermediates. Much like Winter reaches Summer by passing through Spring and Summer reaches Winter via Fall, this type of structure is found everywhere in human thinking.
In fact, many systems of pluralistic philosophies are built on fourfolds instead of dualities. For example, see the work of Richard McKeon, specifically this paper.