Strange loops
Self-reference
There was a popular column in Scientific American magazine during the early 1980’s named Metamagical Themas, authored by Douglas Hofstadter, winner of the Pulitzer Prize for his 1979 book Gödel, Escher, Bach: an Eternal Golden Braid. His column alternated with Martin Gardner’s long-running column Mathematical Games, of which Metamagical Themas1 is an anagram. When I read Gödel, Escher, Bach I was mesmerized, having already been fascinated by the works of the logician Kurt Gödel and the artist MC Escher; and who doesn’t love JS Bach? Hofstadter’s insight into the abstract commonality between the trio was thrilling; a thrill that has not subsided 45 years later. He taught me to look for abstract patterns in places I would not have thought to look.
The abstraction self-reference was of great personal interest at the time. Escher with his paradoxical drawings and Bach with his fugues2 gave it visual and audible form. Gödel formulated it into his profound incompleteness theorem, which I consider to be one of the greatest intellectual achievements of the 20th century along with Einstein’s relativity theory and quantum theory (Planck, Einstein, Dirac, Schrodinger, Heisenberg, Born, Feynman3 among others).
Gödel’s incompleteness theorems, published in 1931, can be stated as:
No consistent system of axioms whose theorems can be listed by an algorithm is capable of proving all truths about the arithmetic of natural numbers. For any such system, there will always be statements about natural numbers that are true, but that are unprovable within the system.
Such a system cannot demonstrate its own consistency.
Gödel’s first theorem is a consequence of the fact that in axiomatic systems of the kind the theorem applies to, there are more true statements than there are proofs so there must be some true statements that cannot be proved.
Gödel’s second theorem is an extension of the first and is explicitly self-referential. Self-reference requires a way to represent the whole by part of the whole. For example, the statement:
This sentence is composed of seven words.
is self-referential (and also happens to be true). The word sentence is the part that represents the whole. Axiomatic systems of the kind to which the theorem applies are incomplete in that they cannot internally prove that they are internally consistent, i.e., that they are not self-contradictory, even if in fact they are not. Internal consistency can only be demonstrated externally.
Gödel’s incompleteness theorems reveal an inherent limitation about what we can know with our rational minds, suggesting that rationality itself is incomplete as a means of knowing. That Gödel was able to logically prove the limitations of logic using logic, is a testament to the self-honesty of logic. Sincere truth-seekers eventually realize that logic and rationality serve their highest purpose by bringing them to the threshold of expanded consciousness. Crossing the threshold requires a calming of mental turbulence that preoccupies our attention in the Construct, the realm of cause-and-effect and linear-time. This is easier to do after one has felt the full impact of Gödel’s work. Having put full trust in the honesty of pure logic and mathematics, and having trained one’s mind to hold itself to that high standard, the realization that logic itself declares its own incompleteness can have the effect of silencing the mind. The rational mind, in its hard won dedication to truth, is then willing to step down from the throne of consciousness, to yield to something beyond its understanding.
Only a few know, how much one must know to know how little one knows. — Heisenberg
In 1937, Werner Heisenberg4 recognized that our knowledge of physical reality as perceived by our physical senses or measured by our physical instruments can never be complete, in principle. There will always be uncertainty in a particle’s position and/or velocity if an attempt is made to measure them both at the same time, regardless of the precision of the measuring instruments. We, as inhabitants of physical reality, are limited in what we can know about physical reality from within physical reality.
Alan Turing5 realized the same abstract truth in the context of computation. In a 1937 paper he proved that no computer program exists which can determine whether an arbitrary computer program will ever complete its computation; the halting problem is undecidable. There is a limit to what computer programs can compute about general computer programs, in principle.
The problem reduces to the inherent futility of attempting to reduce the whole to a part, to create a symbolic reference to be used to rationally understand that whole, whether in reference to the physical universe (physical laws purport to apply everywhere and at all times — they are essentially statements about the whole), the infinity of computer programs, the infinity of natural numbers or the infinite Self, for that matter. On the scale of Creation, completeness is an attribute of the whole which in truth is holographically contained in each of its parts, contrary to all rational understanding. It cannot be compressed into an image or symbol in some deductive proof in some axiomatic system existing in some rational mind; it can only be experienced by being.
Awareness of this limitation does not invalidate the usefulness of self-reference in the context of rationality, in the realm where it applies. Indeed, mastery of rationality is a great achievement and one of the prizes that this Construct we call reality offers to those who come here to learn. Rationality is a projection of Abstract Truth into the Plane of Duality which, like a trail of breadcrumbs, can lead us out of this plane to a transcendent reality if we are able to break free of its paradoxical strange loops of the kind sketched by Escher:
Paradoxical self-referential statements like the following, if contemplated upon, have the potential to silence our rational minds and thereby liberate us:
This sentence is false.
Zen Koans
Zen koans likewise have such potential. My personal favorite was written at the end of her life in 1711 by Ryōnen Gensō, a Zen Buddhist nun6:
Sixty-six times have these eyes beheld the changing scene of autumn. I have said enough about moonlight. Ask no more. Only listen to the quiet voice of pines and cedars when no wind stirs.
And the following koan help me realize the non-linear nature of time7:
A gosling was placed in a bottle and fed until it grew into a goose. How could you get it out without breaking the bottle or killing the goose?
For those inclined to contemplate Zen koans, I recommend these collections: 101 Zen Koans and The Gateless Gate, the latter being resonant with The Door of Everything8 :
The Great Way is gateless, Approached in a thousand ways. Once past this checkpoint You stride through the universe.
Jnana Yoga
The development of the rational mind is not a step to be avoided, if one has any predisposition in that direction. Part of why we are here experiencing the Construct is to use its unique environment to further our development. Those who do not develop their rational minds miss out on a valuable tool for navigating the Construct and, not being able to think clearly for themselves, are more likely to have blind faith in authorities, religions, science, etc.; they must find another path to the threshold of expanded consciousness. In Hinduism, there are three classical paths to liberation: jnana (knowledge), karma (service) and bhakti (devotion) yoga. Those who follow path of knowledge or self-realization return to the spirit realm with the trophy of understanding.
We return victorious to the spirit, having descended into hell. And from hell we bring trophies. Understanding is one of our trophies. — Don Juan Matus
Being trapped in one’s rational mind and obsessed with the artificial self-image that it constructs using faulty reasoning based on the axioms that linear-time and cause-and-effect are real, are what cuts one off from spirit — and this is the very definition of hell to those like Don Juan, who confessed that his motive for travelling the straight and narrow warrior’s path was fear and what he feared the most was to lose the nagual, the abstract, the spirit.
Compared with losing the nagual, death is nothing. My fear of losing the nagual is the only real thing I have, because without it I would be worse than dead. — Don Juan Matus
Jnana yoga is a simple and direct path to liberation from hell, albeit a challenging one. It amounts to simply realizing who we really are, which is not our rational mind or its idealized self-image9; therefore, we must silence our rational minds and break the mirror of self-reflection, thus dispelling the Illusion. It is the path of truth at any cost; the will to stop living a lie even if it means exposing one’s artificial persona for what it actually is: a mere facsimile of self propped up as a mask intended to deceive — to fake it until we make it, to go along to get along — but which only deceives other masks along with itself in its journey through Inferno. Having silenced our rational mind and having disidentified with the image it constructed, we can restore our connecting link to spirit and tap into silent knowledge, as Don Juan Matus described it.
Rationality: a shamanic path of liberation
The shamanic10 tradition of Don Juan Matus as described by Carlos Castaneda followed a command of Spirit to pass on its traditions to successive generations of shamans by forming parties of apprentices according to specific rules, as selected by Spirit. Carlos’ party was composed of himself and three women: Carol Tiggs, Taisha Abelar and Florinda Donner Grau. Carlos was pointed out by Spirit to Don Juan as the leader of the next generation. At the time he was a graduate student of anthropology at UCLA; it was during the course of his field work that he encountered Don Juan. Later, after his party was formed, all three of his female cohorts also completed doctorates in anthropology, or so I gather. I know at least that Florinda11 wrote a book about her field work in Venezuela. This, perhaps surprising, emphasis on mental development was the result of their belief that the rational mind must be fully developed to the highest level so that it willingly yields dominance having truthfully recognized its own limitations.
Rationality among humans is actually very rare — even among those with advanced degrees from universities. Those who acquire it are only a step away from liberation, but the vast majority instead become self-absorbed. Don Juan stated that only humans among all organic beings turn their full attention inward, away from spirit. All other creatures naturally align their internal filaments of awareness, or threads of consciousness, with external filaments of awareness that compose existence-at-large. Some of them actually merge with those filaments and move with them. Humans focus their full attention on their own internal filaments; i.e., the filaments reflect upon themselves, disregarding existence-at-large.
The difference between a rational person and a self-absorbed person is that a rational person ignores impulses from the existence-at-large. Such impulses are experienced as feelings and to the hyper-rational person, feelings are irrational and therefore are to be devalued, discredited and suppressed, even including the feeling of love.
A self-absorbed person, on the other hand, without being consciously aware of it, allows the external impulses to stir up internal agitation. Since internal filaments can only be intentionally aligned after they are first quieted down, a self-absorbed person has little hope of connecting with spirit. A rational person, although ignoring spirit in favor of his self-image, at least can attain inner calm. He will probably live longer, his energy not being consumed by endless petty dramas centered on the self (actually, the self-image). At best, he is in a position to intend alignment, open the door of everything and leave his personal hell behind — if he becomes aware of the possibility, if he seizes his cubic centimeter of chance when it appears. The moral of this story is: if one takes the path of reason, then go all the way. Make it rather a path of truth, even at the expense of reason. Such a path inevitably leads to unreasonable Love.
When one is dedicated to truth rather than rationality, one begins to pay attention to paradoxes rather than to gloss them over in attempt to defend one’s house of cards, one’s rational construct. Indeed, one actively seeks paradoxes to contemplate. This is what true scientists do: they look for contradictions, inconsistencies, flaws. They scrutinize and invite scrutiny; they rejoice when a discrepancy or flaw is discovered because it represents an opportunity to advance knowledge, to take a step closer to truth. In Don Juan’s world, abstract truths always seem like paradoxes to the rational mind and so they are used as teaching devices to expose its limitations.
One such paradox is that as the truth-seeker approaches the door of everything, they must become paragons of rationality and sobriety, and at the same time they must shy away from those qualities in order to be completely free and open to the wonders and mysteries of existence. The resolution to all such contradictions is to dynamically balance opposites, and then to find a transcendent third point of reference from which the two opposites are perceived as two sides of the same coin.
The third point of reference is freedom of perception; it is intent; it is the spirit; the somersault of thought into the miraculous; the act of reaching beyond our boundaries and touching the inconceivable. — Don Juan Matus
Self-absorption: a hellish trap
The self-absorbed are trapped in a construct of their own creation, cut off from spirit. How did this state of affairs come about? According to Don Juan:
Then he talked about ancient man. He said that ancient man knew, in the most direct fashion, what to do and how best to do it. But, because he performed so well, he started to develop a sense of selfness, which gave him the feeling that he could predict and plan the actions he was used to performing. And thus the idea of an individual self appeared; an individual self which began to dictate the nature and scope of man's actions. As the feeling of the individual self became stronger, man lost his natural connection to silent knowledge. Modern man, being heir to that development, therefore finds himself so hopelessly removed from the source of everything that all he can do is express his despair in violent and cynical acts of self-destruction. Don Juan asserted that the reason for man's cynicism and despair is the bit of silent knowledge left in him, which does two things: one, it gives man an inkling of his ancient connection to the source of everything; and two, it makes man feel that without this connection, he has no hope of peace, of satisfaction, of attainment.
Don Juan explained that excessive concern with the individual self is the mark of modern man and makes him a homicidal egoist, a being totally involved with his self-image. Having lost hope of ever returning to the source of everything, man sought solace in his selfness. He accomplished a magical maneuver: he found a focus point of awareness that is unique in that it perpetuates his self-image. The soul sickness of modern man is no more or less than a self-reinforcing fixation on a particular point of awareness out of the infinity of such points: a hellish trap. Continual reflection of the self-image back to itself generates the force behind the fixation. The mirrors of self-reflection are the walls of the trap.12 Anything that can break this fixation, this obsession, this trance, this stupor, brings liberation. Thus, the shamans’ program for their apprentices is to repeatedly jolt their awarenesses so as to dethrone self-importance13. Any explanations given to their rational minds are primarily intended to trap their attention and set them up for a jolt.
Perhaps the most important understanding for the rational mind is that self-importance is self-pity masquerading as something else.
Self-pity is the real enemy and the source of man's misery. Without a degree of pity for himself, man could not afford to be as self-important as he is. However, once the force of self-importance is engaged, it develops its own momentum. And it is this seemingly independent nature of self-importance which gives it its fake sense of worth. — Don Juan Matus
Victimhood is concomitant to self-pity. It is more or less the opposite of sovereignty. Man is reduced to the status of a needy beggar or scrounger, deploying his meager resources to snatch whatever he can from his surroundings in order to survive, when all along he already had everything he could ever need within. To have any chance of claiming our sovereignty and reconnecting with spirit, we must vanquish self-pity.
I never saw a wild thing sorry for itself. A small bird will drop frozen dead from a bough without ever having felt sorry for itself. — D.H. Lawrence
Your inner work will reveal to your awareness the extent to which your compassion for others is actually pity, and that when you feel sorry for others you are actually projecting your self-pity onto them, which tends to reinforce their victimhood. Instead, lead them sovereignty, if you are guided to do so as an agent of Spirit:
Give a man a fish and you feed him for a day; teach a man to fish and you feed him for a lifetime.
When we wallow in self-pity we are easy targets for the Dark Elite, whose diabolical agendas are often disguised as compassion for the poor, the disadvantaged, the oppressed — they are great virtue signallers. Absent self-pity, we can instantly recognize their scams for what they are, see the root of the problem, and act with true compassion and without self-importance. We act only upon command of the Spirit and do so with power and abandon, confident in the designs of the Spirit and humbly grateful for the part we are given to play in those designs. Only the Spirit knows when someone is ready for their cubic centimeter of chance:
Chance, good luck, personal power, or whatever you may call it, is a peculiar state of affairs. It is like a very small stick that comes out in front of us and invites us to pluck it. Usually we are too busy, or too preoccupied, or just too stupid and lazy to realize that that is our cubic centimeter of luck. A warrior, on the other hand, is always alert and tight and has the spring, the gumption necessary to grab it. — Don Juan Matus
The burden of existence
What is the point of the Construct? I have written that it is a school for the development of awareness. But I have also written that it is a furnace for the forging of sovereign beings capable of standing alone and intact in the presence of divinity. A strength and internal cohesion is required to withstand the full force of the Supreme Being’s presence, but equally important is the strength and internal cohesion needed to withstand being alone, a state we must accept and endure as heirs of the One. A requirement of full self-realization is the willingness to bear our share of cosmic sadness:
Something is finally getting through to you. You're right. There is nothing more lonely than eternity. And nothing is more cozy for us than to be a human being. This indeed is another contradiction — how can man keep the bonds of his humanness and still venture gladly and purposefully into the absolute loneliness of eternity? Whenever you resolve this riddle, you'll be ready for the definitive journey. — Don Juan Matus
Don Juan was moved by this poem by the Spanish poet Juan Ramón Jiménez:
The Definitive Journey
…and I will leave. But the birds will stay, singing:
and my garden will stay, with its green tree,
with its water well.
Many afternoons the skies will be blue and placid,
and the bells in the belfry will chime,
as they are chiming this very afternoon.
The people who have loved me will pass away,
and the town will burst anew every year.
But my spirit will always wander nostalgic
in the same recondite corner of my flowery garden
Perhaps the greatest trophy we take with us on our definitive journey into eternity/infinity is our humanness, and by that I mean our capacity for genuine rapport, which gives us solace in the face of eternity/infinity. Perhaps that is why the Supreme Being fractalized into us, so that it may find solace through us. It chose to fractalize in such proportion that the ratio of self to other is the same as self to whole, setting up a rapport between self, other and whole. This is the Golden Ratio, which is ubiquitous in Nature. It is also called the Divine Proportion and the Golden Mean, the latter also identified with a philosophy of dynamic balance. It is no accident that the mathematical concept of mean is the root of the word meaning, for it is the rapport inherent in the Golden Mean that gives our existence meaning. And it is no accident that ratio is the root of rational.
Perhaps our self-pity is ultimately a reaction to our personal loneliness which is an echo of cosmic sadness, and our fear of death is really a fear that when the coziness of the illusory Construct dissolves we will find ourselves alone again. (Isn’t our greatest sorrow the loss of a loved one?) Perhaps what we really fear most is that we cannot not exist. Perhaps the greatest gesture we can make is to willingly accept our share of the burden of existence by becoming sovereign. Our consolation is that the burden is lightened by the meaning we accrue from that gesture, and the love for our greater being that motivates such a gesture: Self-Love.
Making love…out of nothing at all. — Air Supply
Hence the name of this book: Metamagical Musings, with an indirect homage to my scientist persona which enjoys mathematical games. I intend to share my own Metamagical Themas in a subsequent chapter.
A musical form consisting of a theme repeated a fifth above or a fourth below its first statement. Also, a dreamlike state of altered consciousness that may last for hours or days.
My academic great uncle.
I knew Werner’s son Jochen; he once attended my seminar.
I referred to Turing machines in my dissertation.
I was a Zen priest during my most recent lifetime.
See The Door of Everything: …you will glance backward and discover that the "Door" never did exist at all.
Recommended inner work: The Idealized Self-Image.
Carlos uses the word sorcerer instead of shaman in his books. I avoid the former word because of its negative connotations. In my own mind I spell it sourcerer.
I briefly met Florinda at a workshop at UCLA.
Not unlike the way some lasers work. Light Amplification via Stimulated Emission of Radiation — LASER. The material (such as ruby) of a cylindrical rod is stimulated to emit photons by a high-intensity flashing light source wrapped around it. The emitted photons bounce back and forth between the mirrored ends of the rod, resonating. Some leak through the end that is partially transparent, but by that time they are aligned and so form a coherent beam. The partially transparent mirror is like the door of everything. We will cross into infinity/eternity when we have become resonantly powerful, aligned and internally coherent sovereign being, forged into that state while trapped between the mirrors of self-reflection — but only if we manage to break through the mirrors.
I prefer the term self-centered to self-important. When Don Juan uses the term self-important, I believe he intends the specific meaning: takes oneself too seriously. We are important; but we tend to take ourselves (actually, our self-images) too seriously when are cut off from spirit.