An article of faith

"Doubt is a pain too lonely
to know faith is his brother."
~ Khalil Gibran

 

 

 

 

 

The Fifth Key of the Tarot, known variously as the Pope or, more commonly, the Hierophant (the word literally means 'teacher of holy things'), is the sixth card along the journey of the Fool. The Law of Fives, that false teacher, suggests it should be significant (not only is it the fifth key, but the prime factors of six sum to... five).

 

We've intimated previously that knowledge is bound by unsurmountable limitations, and that transcendental truth cannot be gained through the application of reason alone. What is left is what necessarily underpins any edifice of reason: faith.

 

Faith is what the Hierophant offers - faith, the "substance of things hoped for, the evidence of things not seen," as the Book of Hebrews relates. Faith is often derided in our materialist culture; but the truth is revealed when we consider the foundation of that culture - for it rests on certain axioms of ontology, of epistemology, which in their nature are not and cannot be proven from earlier principles. Faith is the bedrock of rational consciousness: faith, which appears to admit none of the character of reason, turns out to be essential to reason; just as reason, appearing to ridicule faith, depends upon it. This is an intimate paradox, whose nature I shall leave it to the reader to decide.

 

It is tempting to assert that enlightenment, that cannot be accomplished through Reason alone, can be accomplished through Faith. There are even examples that seem to corroborate this assertion; but, in truth, Faith alone fails too. The reason for this is in fact rather subtle; it has to do with the relative plasticity of Reason.

 

Suppose you hold some view derived logically from certain agreed axioms - as a trivial example, suppose you are of the opinion that there are no black swans, based on the empirical observation that you have never seen anything but white swans and the meta-empirical observation that empirical observations are reliable arbiters of actual fact. Suppose you then encounter a black swan. This new datum contradicts a predicate of your hypothesis, and, as a rational thinker, you revise your hypothesis: you accept the existence of black swans (this possibility is why Hume had a Problem with Induction).

 

Now, suppose your belief that all swans were white stemmed from a pure faith, unsullied by Reason. Suppose you encountered a black swan: your faith would not admit its existence. You would rationalize that it was not a swan, or that it was a white swan painted black, or that you imagined it, or any of a hundred other counterfactuals to avoid having to assail your article of faith.

 

Faith in the transcendent is a precursor to enlightenment; faith in the merely subjective is a barrier to enlightenment. And neither Faith, nor Reason, will enable us to tell the difference...

 

This then, is both the power and the peril of the Heirophant: that he offers a reality more permanent than the one we can apprehend through Reason, yet less certainly true.

Clothes maketh the man

"When the power of love overcomes the love of power,
the world will know peace." ~ Jimi Hendrix

 

 

 

 

 

 

Hans Christian Andersen gives us a tale, among many, that concerns a certain Emperor. This Emperor desired clothes suitable for his noble standing and prodigious authority; two wily tailors claimed that they had such garments, possessed of this property - that only persons of the wit and nobility of the Emperor would be able to see them. Accepting the Emperor's gold, they proceeded to drape him in entirely imaginary raiment, before leading His Imperial Majesty to a mirror. Unable to admit that he saw himself naked - mindful that only a mean and ignoble mind would see him thus - the Emperor confessed himself delighted, and went forth among his courtiers. They, like their Emperor, were unwilling to admit what was right before their eyes; bound by convention, by fear, by orthodoxy, they all gathered round and praised the wholly fictitious new clothes. A parade was arranged, the better to display the Emperor's wonderful new clothes to his subjects; as it happened, one of these was a small boy, too foolish to have accepted the conventional wisdom, who cried out "the Emperor is naked!" Horror turned to hilarity as the crowd accepted the boy was right; the power of the Emperor was broken, and he was humiliated.

 

There is a lesson here when we consider the Fourth Key of the Major Arcana, also The Emperor. Where the Empress denotes the natural energy of qi, the Emperor represents the shaping and harnessing of energy, the imposition of will upon the world, the establishment of order. Malaclypse the Younger might remark that the Empress reflects upon the Eristic Illusion, while the Emperor reflects upon the Aneristic Illusion. The truth, as we might guess, is neither of these illusions, and also both.

 

Although the Emperor is the Fourth Key, he is the fifth card in the Major Arcana. The Law of Fives tells us that he should have some significance as a result, but we should be alerted by the presence of the Zeroeth Key that the significance here can be misleading. Parasimplicity necessarily entails doubt, which is another restatement of Godel's Incompleteness Theorem. All the same, the stability - the permanence - of The Emperor is another characteristic of the transcendent, and it is interesting to note that the card, self-similarly perhaps, has undergone rather less transformation down the ages than other members of the Arcana. The hidden weakness beneath the apparent strength of The Emperor is the one alluded to in that Andersen fairy tale: namely, that his belief in his own power blinds him to the existence of anything beyond it. Being merely puissant, the Emperor believes himself to be, in King James' memorable phrasing, a "little God on Earth." His inflexibility in a world of flux renders him susceptible to obsolescence.

 

The Emperor is a cautionary tale; emblematic of structure, he carries the implicit reminder that all that can be made, can be unmade. As Solomon's ring reminded him: Gam Zeh Ya'avor.

The Elan Vital

"Vitality shows in not only the ability to persist
but the ability to start over."

~ F. Scott Fitzgerald

 

 

 

 

 

Where the Popess is identified with the intuitive Virgin, the feminine yet unsullied by the masculine, the fourth Tarot card - the Empress - is identified with the fecund Mother; her association is with Isis, where the Popess is with Hathor. The second aspect of the Triple Goddess, she is the Queen of Heaven; she is the vessel of the lifeforce, the elan vital.

 

Numbered 3, the Empress represents the common energy between the One and the Two, the energy of increase, the parasimplistic urge to be more than one's mere being-in-the-moment. In Rider-Waite, she is seated with crown and scepter, and her throne is carved with a heart-shaped design: because love can be understood as this energy of increase, the motivating force that makes an individual seek to become part of something more. The Empress is both a signifier of love and of fertility.

 

Although she restores balance to the first four cards of the Tarot, being a second female after the first two males, the Empress is not a union of the energies, a divine androgyne; she is not a parasimplex. She does, however, embody the parasimplicity principle: her presence in a drawing indicates a desire for increase, and generally the gratification of that desire. 'Increase' here could be material, although usually a somewhat more spiritual development is implied.

 

The energy of the Empress is universal; it is undirected, but it flows inevitably between living things. It is identifiable with qi in Chinese belief: the acupuncturist places needles at key meridians in the human body to identify and redirect the flow of qi, just as the feng shui practitioner orients the furnishing of a room to promote harmonious flow through the building (qi, accordingly, is self-similar and so partakes of the character of transcendence). Although these examples indicate that the energy can be controlled, it would be a mistake to think of it as something that ought to be harnessed. The principle of wei wuwei recognizes this implicitly.

 

 

 



Pope Joan

"I am more afraid of my own heart than the Pope
and all his Cardinals. I have within me the great pope, Self."
~ Martin Luther

 

 

 

 

The Pope is the spiritual leader of Roman Catholicism, the 'Vicar of Christ,' God's right hand on Earth. According to orthodox Roman Catholic doctrine, the Pope is infallible - his word is divinely inspired, and so cannot be in error (the Muslim prophet Mohammed, in what you may see as an echo or evolution or reflection of this, remarked in the Hadith that "my people cannot agree on error;" as a result, ijma, or 'consensus,' is considered in scholarly Islamic circles to be a basis of religious authority. Authority, and fallibility, have not been explicitly discussed as yet, but of course they are centrally important to a parasimplistic worldview). One might expect that in the spiritually symbolic Major Arcana, one would find a Pope, and one does (his number, as Malaclypse the Younger could tell you, is 5, and we'll come to a discussion of his import later); but first, one finds a Popess.

 

The reason for this is tied in with the numerology we talked about a while ago, the arithmetic underpinning of the Law of Fives. The Magician, numbered 1, represents the apotheosis of the Self in this moment (allegorically, the Self in the moment of satori, the Self in the moment of awareness of itself qua self) - but this Sein-in-der-Welt is, of course, not the parasimplistic self, which is both itself and something more than itself. The Magician is identity, and Identity is an illusion.

 

The Popess, numbered 2, is duality; this is represented most clearly by her obvious femininity, by contrast with the foregoing two cards (respectively showing Man in the folly of ignorance, and Man in the folly of self-knowledge). In Rider-Waite, she is shown with a crescent Moon at her feet - this is also the iconographic depiction of the Virgin in Roman Catholicism, in reference to the Book of Revelations (and, intriguingly, according to one theory, in reference to Catholicism itself, and what came before it) - and wears the diadem of Hathor, the Egyptian "Mistress of the West." Both allusions identify the Popess with motherhood, with the divine, and with the yin energy of the taijitu. In Rider-Waite, she is depicted holding the Torah and seated between the pillars of the Temple of Solomon, reinforcing the syncretism of the imagery.

 

(The Popess also has a historical imagery to it, a very early and subversive element of proto-feminism, but despite her appearance in the title, Pope Joan is not a subject for discussion in this metanow.)

 

The Popess can be understood as the apotheosis of the female, which is more than mere Identity because the female can nurture and birth new beings. The female explicitly has something of the divine energy of Creation in her, which the male can merely ape with construction of unliving devices. The symbolism of the Virgin is significant here; the Popess powerfully alludes to the Pagan Triple Goddess of Maiden, Mother, and Crone, and the biologically necessary role of the male in conception is not to be understood here as part of the Divine Mystery of creation. Where the Fool represented blind faith, and the Magician self-knowledge, the Popess betokens intuition - a sense of things unseen, complementary to and cumulative with the Magician's arid knowledge of what is clearly before him. The Popess makes the connections between things without needing to know what those things-in-themselves are; the Magician understands things in their nature without appreciating the wholeness of the world. Thus the necessity of union between the energies for balance, and for enlightenment.

Magical thinking

"Has the world ever been changed by anything
save by thought and its magic vehicle the Word?"
~ Thomas Mann

 

 

 

 

The Fool is numbered 0; he is nothing, a blank slate, a tabula rasa, ignorant even of his own ignorance. The Magician, second of the Major Arcana, and numbered 1, is the Fool within the Abyss, knowing himself and his ignorance and the transformative power of that ignorance. The Magician is the Fool enabled, energized, created; he is the Trickster God made manifest.

 

Where the Fool represents the seeker after wisdom, the Magician represents the awareness of things unseen. He is not the apotheosis of wisdom - that comes later - but he is on the path, because he is no longer seeking. What we are seeking, we cannot have found, or else we would not be seeking it. The Magician understands that it is more efficient to stop looking and instead focus on seeing. In Rider-Waite, the Magician is crowned with infinity, and girdled with Ourobouros: all things begin and end in this moment of awareness, this consciousness, this satori. The staff of the Fool has transformed into the wand of the Magician; the wand is raised to the heavens, while his other hand points to the earth.

 

The Magician is the bridge between the subjectively real and the transcendentally surreal; he is the Gateless Gate. He is the potential in Man, the aptitude, the capacity. Self-aware, self-possessed, self-sufficient, he is the catalyst: unchanging himself, he changes all. This is the mystery beyond reason. This is the maker and unmaker of mountains and rivers. This is the beguiler of the senses, the deceiver of the mind, the keyholder to the doors of perception. Should we trust him? That doubt is the manifestation of the Unknown; fear of the Abyss keeps us from him, but acceptance of the Abyss - Foolishness - encourages us to take the leap of faith. We take nothing in there with us; we are only ourselves, but fortunately ourselves are more than our selves, since we are parasimplices. The Magician knows this, knows us, intimately; the Magician is us, any of us, when we accept all of what we are - fearlessly, foolishly, fully.

 

The Magician represents, above all, the mystical process by which the unknowable objective is transcended to become subjectively real. This most crucial mystery is the beginning of all magic: it is the creatio ex nihilo, the divine spark without which the world remains meaningless and void.

Fooling about

"A fool thinks himself to be wise,
but a wise man knows himself to be a fool."

~ William Shakespeare

 

 

 

 

The Fool is the first of the Major Arcana - the twenty-two trump cards of the Tarot deck - that we will consider: fittingly, because it is the first, and so, of course, numbered... zero. The twenty-two cards represent what some call "the Fool's journey," which can be represented as the evolution from folly to wisdom (although in the truer transcendental sense, it's the evolution from seeing the folly in the Fool to seeing the wisdom in the Fool).

 

There are a number of illustrations used to depict the Fool; perhaps the most famous sequence is the Rider-Waite deck which dates back to the early 20th century. It shows a medieval "fool," a court-jester-type, strolling unconcerned, head back, a staff slung over his shoulder with his meager possessions in a bag on the end, a dog trotting along by his side. He carries an innocent white rose. He is walking blindly towards the lip of a precipice.

 

Earlier versions from the Italian Trionfi (which was a popular card game; Tarot cards are still used for playing as well as divination) depict a beggar or a wild man, in some cases chased by the dog that accompanies him in Rider-Waite. In some French versions, the Fool becomes a more stylized analogue to the traditional Joker of conventional playing cards.

 

Symbolically, the Fool represents a rich mythological tradition of tricksters, from Kokopelli to Anansi to Loki to Shaitan to Rumpelstiltskin. Like Lucifer - the light-bearer - the Fool is about to plunge into the darkness of the Abyss, which is only implicated in Rider-Waite but represents the Unknown, the darkness of ignorance. Reason recoils from ignorance as the alert man shies away from the abyss; but the Fool is without fear. He accepts the Abyss without needing to interrogate it. He plunges into the Unknown neither willingly nor unwillingly; he plunges into it because it is before him, and for no other reason.

 

Just as zero produces all numbers - creatio ex nihilo - so the Fool produces all the other possibilities through his interaction with the Void. The Fool seeks wisdom, but he does not seek it consciously: he seeks wisdom because he is a Fool. In emptying his mind, he enters the void; in entering the void, he loses material things [his pack], beauty [the rose], and the world [the dog], and finds what the void has for him.

 

Nietzsche said: when you stare into the Abyss, the Abyss stares back.

 

The Fool is mankind subjected to that pitiless reflected stare; Mankind at his core, Mankind compelled by his basest instincts toward acquisition, toward beauty, toward companionship, and toward transcendence. He is both a beginning and an end; a reliquary for wisdom and a dispenser of wisdom; an origin and a goal. There's a reason his number is zero, and there's a reason that zero is represented by a circle. But we'll get around to that.



Poker face

"Creativity is the ability to introduce order
into the randomness of nature." ~ Eric Hoffer

 

 

 

 

Quantum theory concerns the very smallest particles in the universe; particles so very small that they form the building blocks of subatomic particles like the electron. At the quantum level, matter behaves very strangely - what we think of as particles act more like waves, and what we think of as immutable physical properties become much more mutable. Heisenberg's famous Uncertainty Principle tells us that the more precisely we measure one property at this level, the more imprecise other properties become - for example, we might be able to exactly determine a particle's position at a moment in time, but only at the cost of being entirely unable to divine anything about its velocity. This result is commonly conflated with the 'observer effect,' but is distinct from it - randomness, it turns out, is 'baked in' to the observed world. The validity of scientific laws, that make the world around us a relatively predictable and orderly place, depend upon a substrate which is fundamentally unpredictable and chaotic. This is an iteration of the Paradox of Self-Reference, of course.

 

If we think of the subjective realm as being infinitesimally close to, and yet inevitably distant from, the transcendental, it makes a degree of sense for the subjective, at the limits of measurable perception, to approach closest to the transcendental. If we think of the transcendental as the fundament from which all possible energy-states spring, it makes sense for randomness - probability; potential - to be the recognizable characteristic of transcendence as it immanesces upon the subjective.

 

Happily, we don't have to supercool an atom and bombard it with radiation countless times to identify this kind of randomness in operation. At the macro level we have plenty of analogues to choose from: rolling dice, shuffling decks of cards, throwing yarrow stalks into the air and seeing how they land (incidentally, one of the fundamental constants, pi, emerges from the latter if you look at it right). The first of these is not well-known as a form of divination, although Luke Rhinehart can attest to its power; the latter two, however, certainly are. My knowledge of the I Ching is very limited in this metanow; but I know a thing or two about cartomancy, and my own experiences with the Tarot deck have reinforced my belief in a parasimplistic universe. In essence, all forms of divination have this character: that they combine a certain degree of conscious analysis with a certain degree of deliberate randomness. Successful diviners demonstrate the ability to associate elements freely, without imposing a pattern on what they see - the better to clarify the pattern that exists within them already. FIAT applies: everything is connected, because everything is everything. The Tarot cards can tell us anything we want to know about anything at all, because they embody the characteristic randomness of the transcendental. Insofar as we can avoid rationalizing and pre-empting the judgement of the cards, we can access the transcendental in our own consciousness and let the cards speak through us. It is to the cards of the Major Arcana, and their symbolic significance, that we turn next.

The whole world in His hands

"In some sense man is a microcosm of the universe;
therefore what man is, is a clue to the universe." ~ David Bohm

 

 

 

 

So yesterday we talked, not especially transparently, about how one goes about deconstructing oneself in order to mirror the world around one. We didn't really get into the why of it - curiosity about the transcendental seems both an incongruously casual aim for such an all-encompassing task, and to some extent a mismatch of concepts (how can one be curious about a subject one cannot intellectually grasp?) - and we aren't going to today, either. Why is a very important question; in fact, it may be the only question, but it's off-topic (is it?).

 

We're going to dodge 'why' for the moment because the transcendent doesn't truck with why. The question denotes purpose - which can have meaning only in the context of an outcome state different from the present state (that's actually too simple; conservatism is a legitimate purpose if its viewed as opposing an organic trend in the current metastate towards transformation, although the subtle difference between the two may only be apparent to a sufficiently Zenoic examination). The transcendental, which is always everywhere equally immanent upon the subjective, has no purpose - all possibilities are equally within and beyond the transcendental.

 

We're instead going to look at what, which is to say we're going to consider identity again. Specifically, we're going to consider identity from the perspective of the transcendental, which means we're going to indulge again in vague analogies. We'd mentioned the Aleph, the point that contains the whole universe; that represents one extreme of the possibility space (if we suspend for a moment our bourgeois notions about particles sharing space and time coordinates - think of it as a Paulian conversion). But for a probability space to exist, it has to contain all the possibilities. The mirrors we talked about yesterday clearly lie some way along a continuum from the universally accessible max-local Aleph to the locally accessible universal mirror (the parasimplex). There should, indeed, be a far limit to that continuum: the point which doesn't partake of the universe at all, the transcendent immanent upon the void. We call this singularity, and it's another terrifically useful and important concept that we'll hit up in another metanow.

 

We could advance the hypothesis that every entity in the apparently objective universe around us lies somewhere upon this continuum - but then the transcendental would be immanent upon the objective as well as the subjective, which would mean that objective and subjective map perfectly across the transcendental (it has to be across the transcendental, because objective and subjective are necessarily estranged). It is certainly possible that such a perfect mapping exists, but there is no reason why it must; accordingly, the transcendental may indeed be immanent upon such perfectly-mapped objectives and subjectives, but should also be immanent upon the conceivable subjective which maps to nothing objectively real - to rephrase, the transcendent immanesces upon impression and idea alike.

 

And this means that there can conceivably exist in the world objects which are merely objective; objects which are merely subjective; and objects which partake of the character of the Aleph, and in some fashion bridge the divide between the two. And that means that what we talked about before, about making ourselves a mirror, might really be overcomplicating things. It might be simpler to find a thing, or a system of things, that offer us a different sort of mirror. And the reason it might be simpler is that the transcendental is right there in all of us, in the process by which we interrogate the world.

 

But we'll get to that, in the next cycle. 23, skidoo!

 



Reflections

"The whole purpose of education is
to turn mirrors into windows." ~ Sidney J. Harris

 

 

 

 

I tapped myself on the shoulder before I wrote this, the better to remind myself that I need to talk about Shannon sometime and why information and entropy are linked; but this is not the time for that discussion.

 

This is the time to talk about mirrors. Mirrors are a form of parasimplex: you can look into any mirror in the world, and see the same face you would see in any other mirror (although that face would not be your own, exactly - not least because of its lateral inversion) - and yet any other person could look into that same mirror and see a different same face in each one. There is an echo of both the paradox of identity and the paradox of persistency here, if you're listening for it (remember Lord Ravenhurst's warning on that, though).

 

The transcendental mirror, though - what would that show you when you looked into it? One way of answering this question is by considering the transcendental mirror to be simultaneously immanent upon all subjective mirrors. The transcendent is not bound by limitations of time or space; it is omnipresent (if only in a surreal fashion) and eternal (if only because it is untouched by Time, which after all dates from a mere Planck second after the Big Bang - and is destined to be extinguished along with everything else in the maximum-entropy state). Thus, this transcendental mirror would show you, not only your face when you looked in it, but also your face when you looked into any other mirror, and also any other face when it looked into this mirror, and also any other face when it looked into any other mirror. It would show you the perfectibilized relation of mirror and observer; it would show you the observed universe of mirrors in a single mirror. It would show you the All-in-One: the Aleph. Both Borges and Leibniz have worthy reflections upon the Aleph, which in turn naturally reflects upon them in their full manifestations; within the Aleph, as all things must be, we are already discussing these aspects.

 

Insofar as parasimplicity makes a virtue of anything, it is this ethical principle: speculum ego; I am a mirror. According to the parasimplicity principle, we should strive to be all that we can be - everything exists in order to exist more. More than this (remember: the Parasimplicity Principle is itself a parasimplex, so there is always more), we should strive to be all that we have been - the parasimplex does not abandon past instars, because it is no more itself at one time than at another. Neither does it recoil from contradictions: indeed, these are the spoor of paradox, within which we glimpse the transcendental in the unresolved processes of Reason. Thus we should accept all that we have been, and all that we might be, as equally essential reflections of what we truly are. To be a parasimplex is to embrace identity in the abandonment of identity - to become a Gateless Gate.

 

This seemingly impossible task, as with all tasks, begins with a self-similar task - for all action is self-similar to the transcendental action of wei wuwei. In this case, we seek to become mirrors of mirrors by first becoming mirrors of our world: this is why the enlightened man goes to eat rice when the bell sounds, and goes to his bedchamber when the bell sounds again, and rises from his slumber when the bell sounds the third time. The enlightened man recognizes himself in every stranger, and he accepts the stranger as he accepts himself. We say of those renowned for conviviality - "he never meets a stranger." Verily I say unto you: the enlightened man never meets anybody but strangers.

 

Borges, again, that invaluable vademecum, describes this process in a lovely fable entitled "Pierre Menard, Author of the Quixote." In it, the fictional Menard embarks upon an appropriately Quixotic quest: to rewrite Cervantes' classic. Not satisfied with merely translating it, and abhorring the notion that he might improve upon it, Menard sets about experiencing the Quixote as Cervantes himself did - after an abortive attempt which he himself bitterly rejects before completion, he immerses himself in the lifestyle of the 17th century Spaniard and eventually succeeds in reproducing a Quixote that is line for line identical with the original - but, as Borges' abstracted fictitious reviewer of Menard's Quixote notes, so much richer than the original for having been written by a 20th century Parisian. This should not be understood as presenting Menard as a parasimplex; however, in the illustrated shortcomings of Menard from that perspective, it provides a template for the initiate to follow.

 

 



Taking stock

"Deconstruction insists not that truth is illusory
but that it is institutional." ~ Terry Eagleton


On its face, "parasimplicity" looks a lot like an excuse to make things that are really simple a lot more complex. But, as I hope you've picked up by now, what parasimplicity - or anything else - looks like isn't close to being what it really is. For instance - and this is just a 'for instance' - it also serves as a handy tool for making things that are really complex a lot more simple. The Law of Fives is extremely simple, and as good a shorthand for the very complex things it actually references (which this collection of blogs to date has similarly referenced but at more length, including the obligatory self-similar discussions of the Law of Fives itself). The reduction of all paradoxes to the twin paradigms of All-in-One and One-in-All is another parasimplistic operation (actually the final operation in a chain that begins with the appreciation of all statements as interactions of paradoxes, but we'll get to that).

So, how do we apply parasimplicity? How do mountains become not-mountains, and then not-rivers become rivers? If you've been paying attention, you may already know. What you know may even be what I was trying to say; equally, what you know may be more than what I know. We can't know what we don't know, but we'll get to that, too.

Let's tie in the koan to our five-layer reality cake.

Mountains are mountains and rivers are rivers - this we can consider to be referring to the objective mountains and rivers. Bear in mind that these are not mountains and rivers we can ever directly know: we form subjective impressions of the relations of properties we intuit as belonging to the objective realm, and that is as close as we can get to knowing them.

Mountains are not-mountains and rivers are not-rivers - these not-mountains and not-rivers are not, as you might be forgiven for thinking, equivalent in our model to the subjective mountain- and river-impressions. The not-mountain is the intersubjective mountain: the mountain that emerges from discourse, from interrogation of our subjective mountain-impressions. IF the objective mountain is real, and IF our impressions of it are accurate, and IF we share our impressions truthfully, and IF we don't later edit or filter our consensus to fit some concept of 'truth' - and those are all very big 'ifs' indeed, which we'll review when we turn to Baconian Idols in the near future - then the not-mountain may be apparently identical with the mountain (this is one of the cruder approaches to paradox resolution, in fact - the rejection of the paradox as presented on the grounds that the presentation is corrupted by one or more of these factors). But not-mountains are, well, not mountains..

Mountains are again mountains and rivers are again rivers - these 'again' mountains and rivers are the transcendental mountains and rivers, which we have said are immanent upon the subjective (we might, with a sly wink at Dali, say they are immanent upon the objective as well; in fact Dali's paranoiac-critical method is another rewarding subject for study). We have already said that we can't directly know the objectively real mountain - so how can we possibly hope to know the transcendental mountain beyond? We cannot cross the same river twice (so claims Heraclitus), so how can we know the transcendental river that is beyond all those once-crossed iterations?

The answer is that we need to work against our brilliant knowledge-building engines, our glorious rational Big Brains. We are hardwired to recognize patterns, and we are hardwired to filter and sort the data our brains receive to make it a coherent conscious experience (a trivial example with which you're probably familiar: optics being what it is, the visual data we receive on our retinae is inverted; our brains flip the image over during processing to restore it to its putative objective orientation). However, if we seek the transcendental, that which is equally remote from all things, that in which mountains are again mountains is equivalent to mountains are not mountains or even mountains are rivers - we won't find it after our brains are through processing the data.

Recall that objective entities are entirely separate from subjective ones. Yet our brains, in processing the data from the objective, produce impressions that are subjective and are qualitatively the same as Humean ideas that have no relation to empirical data whatsoever. What this tells us is that the process of rational cognition is capable of bridging the divide that separates objective and subjective - and what that is really telling us is that, somewhere in there, we are working in the transcendental. Each and every one of us, it turns out, is also a Gateless Gate.

The transcendental Universe is self-similar, not only with the objective, but with the myriad subjective Universe-impressions. We could, perhaps, approach some rational understanding of the transcendental if we could somehow simultaneously apperceive all of those possible subjective information-states; but the self-similarity of the Universe, embodied in the Gateless Gate of each self-aware consciousness, makes this unnecessary.

How do you pass through a Gateless Gate? Begin with a gate, and take the gate away so it becomes gateless. Then pass through. 'Get OUT,' as Crowley had it.

Six Blind Men and an Elephant

"We have to remember that what we observe is not nature in itself,
but nature exposed to our method of questioning."
~ Werner Heisenberg

 

 

 

 

There is a famous parable that comes down to us from India, the land that birthed the zero, that concerns six blind men and an elephant. I shall repeat it here, after my fashion, because among its many facets this parable is a fine illustration of parasimplicity - and parasimplicity thrives on repeated illustration, as Lord Ravenhurst observed.

 

So: there were in a certain village six blind men, whose lack of sight they were determined not to keep them from knowledge (this is an illustration-within-the-illustration of the difference between knowledge and wisdom). They hear that a merchant has brought an elephant to the village, and they are very eager to learn what an elephant is like. None of them wishes to miss the opportunity to experience the elephant directly; all of them hurry out to greet the beast.

 

The first approaches the elephant, reaches out and touches it upon its leg. "Lo!" he cries. "An elephant is like a tree!"

 

The second, grasping its tusk, disagrees. "An elephant," he sagely observes, "is like a spear."

 

"No," says the third, feeling its ear," an elephant is like a sheet."

 

"You mean a rope," says the fourth, feeling its tail.

 

"What are you talking about?" demands the fifth, feeling its side. "An elephant is like a wall!"

 

"Aaaaiiieeee!" screams the sixth, feeling its trunk. "The elephant - it is just like a snake!"

 

And the six blind men fall into squabbling, while the elephant goes on its way.

 

***

 

An alternative version of this story features six blind elephants and a man... the first elephant feels the man, and determines that men are flat. The other five blind elephants agree.

 

Whether that's just a joke (only just, at that) or a reflection of the aphorism that elephants never forget is something you'll need to decide for yourself. The parable is another parasimplex: it becomes something different as your understanding of it grows, without ever changing from what it always was. Elephants are again elephants.

Parasimplicity

"Nothing is itself alone."
~ Oscar Wilde

 

 

 

 

And so we come, by a commodius Vicus, to parasimplicity.

 

The first formulation of parasimplicity that visited me was this:

 

"Everything that exists, exists in order to exist more."

 

This is what I now call the teleological principle of Parasimplicity, which later evolved into the ontological "everything is itself and something else" and the epistemological "transcendental truth is the whole greater than the sum of subjective truths." All of these say the same thing in different paradigms, but the teleological principle is going to be my focus today.

 

The closest thing orthodox science has to a teleological principle is probably the Second Law of Thermodynamics. This essentially states that, in any system, heat energy is transferred from a hotter to a cooler system; in the limit, the thermodynamic system of the whole universe tends towards maximal entropy - what is sometimes referred to as 'heat death.' Entropy is the property of thermodynamic equilibrium; maximal entropy occurs when that equilibrium is at zero. Since temperature is an indirect measure of mean particle velocity, maximal entropy correlates to the system in which all its particles are entirely without energy. Among other important consequences, the Second Law of Thermodynamics disproves the possibility of the perpetuum mobile - but we'll come back to that later.

 

An entropic system is arguably the simplest possible arrangement of elements in a system. In a system of maximal entropy, nothing changes. It simply is what it is, and cannot be anything else. There is no way in which any element of this system can have any knowledge of any other element, or of itself - there can be no information transfer within such a system as information transfer is impossible without energy transfer, and energy does not transfer in a maximal-entropy system. Max-entropy is not only the death of heat: it is the death of Consciousness; and it is the death of Time (there's room here for an interesting speculation as to whether Consciousness and Time are somehow functions of one another, or whether this is mere coincidence; another time, we might turn our consciousness to that question).

 

In any system short of max-entropy, energy causes particles to interact with one another. Energy transfers between particles; information passes between them too. A thermodynamic system short of max-entropy exists in several states - we can view these states as occupying successive instants of Time, or we can view them as superimposed probabilities, or we can view them as notional sectors of a putative Block Time - but what matters is that its existence (its transcendent existence) is not the unitary existence of max-entropy (of Nothingness) but the plural existence of thermodynamic systems. This is what we mean by the ontological assertion of parasimplicity - because each state, while representing a real systemic entity, also represents only a part of the whole system of possible thermodynamic states (and each state is a necessary part of that system, requiring itself and every other possible state - a very important consequence of quantum theory). Only the ground state of max-entropy exists on its own, separate from all other states. One can present the analogy of a system permutating through every possible energy state on the course towards max-entropy; equivalently, one can speak of a system summing all its possible energy states to achieve max-entropy, which is merely to consider every successive instant as itself a necessary element in a whole. It also, of course, provides another paradigm of the All-in-None (which is the transcendent: the formless void, the fundament from which all matter and energy springs).

 

Equating this to the teleological principle is somewhat counterintuitive; it helps if we take our existing view of a thermodynamic system evolving through all its possible energy states towards the simplest, most elegant, max-entropic Nirvana "one step beyond." Let us postulate that the max-entropic state is not, after all, entirely devoid of energy: let us postulate that, as a perfect summation of all possible energy-state dispositions of the thermodynamic system, it incorporates a perfect balance of opposed energies acting on every particle (this isn't so far-fetched as it might seem; the apparent stability of macroscopic matter is revealed at the quantum level to be the result of a perfect summation of quantum probabilities in which 'quantum interference' mitigates against the seeming instability of a system in which every particle has a positive probability of existing in every place). We can now consider each of those summed energy states in isolation, and say that in the max-entropic system that state has no discernible existence but nevertheless exists. It exists both to sustain max-entropy and to negate it; in its existence, it necessarily gives rise to the existence of counterbalancing energy states. Everything that exists, exists in order to exist more.

 

We'll be coming back to this, because in this exploration we are not bound by the monodirectional river of Time - and because this discursion is itself a parasimplex, but that should by now be apparent.

Zenophilia

"Never confuse motion with action."

~ Benjamin Franklin

 

 

 

 

Zeno of Elea anticipated many of the points I've touched upon over the preceding few posts in formulating what Bertrand Russell described as "immeasurably subtle and profound" paradoxes. Zeno was a Parmenidean philosopher, who shared Parmenides' belief that "All is One;" his paradoxes challenge the notions of Time and Space and the existence of entitites within them.

 

His 'Paradox of Place,' for example, is both a Platonic Form of the self-reference paradox and, paradoxically enough, a refutation of the Platonic Theory of Forms:

 

"If everything has a place, then place itself has a place, and so on ad infinitum."

 

He similarly challenges Time in the Fletcher's Paradox:

 

"If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless."

 

In fact, elsewhere in his writings, Zeno demonstrates that not only is it impossible to move, it is impossible to start a journey or to reach a destination. Yet it is even more clearly demonstrable that motion occurs and that physical entities undergo motion travelling from place to place.

 

Intriguingly, advances in quantum physics suggest that apparent motion - and even more importantly, apparent lack of motion - are both not as straightforward as they seem. A famous experimental result, Young's Double-Slit Experiment, proves that light operates as a wave; Einstein's Nobel-Prizewinning verification of the photoelectric effect proves that it operates as a particle. The fundamentally paradoxical notion of wave-particle duality, which follows from these two results and leads to a bizarre conception of matter as a measure of quantum interference patterns and mass as a byproduct of collisions with Higgs bosons - all of this is just another paradigmatic way of representing the Parasimplicity Principle.

Time travel

"Change alone is eternal, perpetual, immortal."

~ Arthur Schopenhauer

 

 

We'd talked yesterday about identity, and how fractured a thing that is. We considered primarily the intersubjective entity - the word, the symbol, the representation of the objective in discourse. Today we're going to look more at the objective entity itself, the Dasein, as we move from a consideration of self-referentiality to infinite recursion.

 

What do we mean by Dasein? The term comes to us from Martin Heidegger, and it literally means "being there." As opposed to simply "being," it denotes being in a particular place - which, for a dynamic entity in a dynamic universe, entails being also at a particular time. A "being," particularly the abstract "being" that we draw upon in discourse, does not have a necessary relation to any other being; the Dasein exists in the context of other entities in time and space. It has coordinates. In an important sense, the Dasein gives meaning to Time and Space - we understand both indirectly by the changes entities undergo through dimensions of time and space. Our consciousness of space is perhaps more direct: our proprioceptive sense tells us how our physical body is oriented in space, and gives us some idea of its relative propinquity to other physical bodies. Our sense of time passing is not as direct, and in fact the naive view of Time as a river flowing from past through present into future can limit our worldview in important ways despite being the most straightforward way to interpret our impressions of the empirical world.

 

Borges, in Funes el memorioso, describes a remarkable character blessed (or cursed) with absolutely perfect recall. This individual's unique worldview creates for him a difficulty with identity - his recall is so perfect that he can recall every single instant of his subjective existence with crystal clarity. He does not need to reference an abstract intersubjective as a placeholder for the vague recollection that must suffice for most of us. He remembers every single instant of perception as its own unique set of entities - the bed or the book or the tree that he saw this morning is, for him, isolated from every other perception of what we would see as "the same" bed or book or tree. Number has no meaning for him; defying arithmetic, he invents his own number system in which each number has its own idiosyncratic name (the number five hundred in his system is known as nine, for example). It may seem that Borges invents Funes merely as a device to investigate the assumptions that underlie our perception of the world; in fact, the neuropsychologist Alexander Luria describes a real-life case with striking similarities, and there are perhaps a dozen such cases in the literature of brain science.

 

There are obviously good reasons to assume that Time does indeed flow in a linear fashion from Past to Future; that our naive impressions are accurate depictions of an empirically real world in which physical entities interact in predictable and measurable ways. Centuries of scientific experiment support this view; but it's worth remembering that the assumptions underpinning science, the axioms of science, predispose us to accept certain sorts of evidence. Inductive reasoning - the scientific habit of extrapolating from known patterns exhibited in the past to predicted patterns expected in the future - suffers from this problem, as David Hume noted: there is no good reason to believe that some relation which has been demonstrated between entities in the past will continue to be demonstrated in the future. One pithy formulation of this is the observation that we can't know that the Sun will rise tomorrow, just because it did today and yesterday and every day before. We can produce all sorts of scientific arguments why it should, but all of those arguments rest on inductive reasoning as well. We must accept axioms on faith, in science as in any system of thought. In fact, an axiom is necessarily not provable within the logic it supports (this isn't Godelian Incompleteness, however; this is a fundamental question of knowability, and one we'll look at later in the company of Fitch and Gettier, among others).

 

If Time is somehow other than linear; if it is, for example, a continuous dimension in which all events we perceive as consecutive are actually simultaneous - if, going one step further, it is a fractal dimension in which all possible events, perceived and unperceived, are simultaneous - then our assumptions about its passing and our motion through it are flawed. The limits of our experience of Time are revealed as precisely that: limits of our experience, and not of Time itself. Paradoxes of infinite recursion encourage us to visualize alternative models of Time that resolve or obviate the paradox - but that we are discussing in another metanow...

The Great I AM

"Reality is merely an illusion, albeit a very persistent one."

~ Albert Einstein

 

 

 

I had said earlier that all paradoxes are either paradoxes of the All-in-One, or of the One-in-All. I will restate that here: Identity and Persistency are the twin illusions that shape our world. It may not be clear how that is a restatement; today's discussion will begin an attempt to build that bridge.

 

We talked at some length a while back about what being means. We had said that something is in several senses, potentially several senses at once. The implication of this is that identity can mean several things simultaneously, as well.

 

Let's consider something with a fairly stable identity, as we'd naively consider it: Mount Rushmore. Chances are pretty good that you recognize that name, and that as you read it, your Cartesian Theater obligingly summoned up an image of it. You probably thought about the Presidents' heads carved into it. You probably feel pretty confident that you know how many Presidents there are up there... which ones... how they're arranged... what the rest of the mountain looks like...

 

Getting less confident, right? In fact, even people who've seen Mount Rushmore with their own eyes would probably be less than certain about those details. Even though most of the people who read this understand what 'Mount Rushmore' is, I'd venture a guess that every one of you has a subtly distinct, individual, subjective impression of 'Mount Rushmore.' So, while we can maybe agree that there exists an objective Mount Rushmore, it isn't as real to us as our subjective version. And the intersubjective Mount Rushmore is a strange beast indeed - it encompasses all these subjective versions, and the objective Mount Rushmore, under an umbrella that lets all of us recognize the same mountain (even though it's not the same mountain). What's more, without summoning that shorthand, I could offer you a vague description that nevertheless incorporated the necessary details for you to recognize the idealized Mount Rushmore. And that's before we get into Mount Rushmore as a symbol or an association for each of you personally.

 

The point is that, even with something that all of us think we know as an objectively real entity, it exists in many different ways, as many different things. Everything is both itself, and other than itself: this is the Parasimplicity Principle. The self-similarity Mandelbrot described in Nature's curves is another aspect of this: identity as a pattern of infinite recursion, Self as both self and self-concept and concepts of Self beyond the self, as many unique iterations as there are possible perspectives. Paradoxes of self-reference arise because of the essential dichotomy between the Self we are being and the Self of which we are aware in the process of Being. Russell's famous paradox - "this sentence is false" - arises because we erroneously view it as equivalent to "the sentence 'this sentence is false' is true." Truth, in this context, denotes positive Being - Being in a state of awareness. The truth that Self alters itself in the course of becoming aware of itself qua self makes it paradoxically impossible for Self ever to be truly self-aware; despite the inescapable truth that self-awareness is the hallmark, the necessary condition, of Self-being or Sein-in-der-Welt.

 

Persistency, it turns out, is just Identity viewed from another dimension - the dimension of Time - and that will be the subject of our next discussion.

The womb of truth

“Every experience is a paradox in that it means to be absolute,
and yet is relative; in that it somehow always goes beyond itself
and yet never escapes itself.” ~ T. S. Eliot

 

Over the last couple of posts, we’ve looked at paradoxes – statements that seem to be understandable in our representative system, but produce confounding results. Mandelbrot’s statement that a coastline gets longer the shorter the scale of measurement becomes is an example of a paradox of infinite recursion; Godel’s statement that any logical system must be inconsistent or incomplete exemplifies a paradox of self-referentiality. I will hereby gift you another of my unsubstantiated assertions: all paradoxes are either paradoxes of infinite recursion, and so statements about the One-in-All; or they are paradoxes of self-referentiality, and so statements about the All-in-One.

These concepts of One-in-All and All-in-One, to which we briefly alluded some time ago in a discussion of the Phoenix, are important in theology, where they provide analogies for the Divine. Within the pentapartite model of reality outlined early in the life of this blog, these concepts are transcendental – they derive meaning only as relations with ideals, or metarelations.

Systems constructed by our rational faculty cannot grasp these metarelations, because they are bound to the objective and subjective realms. Even though I am providing you the raw material for a scheme that describes metarelations, it necessarily falls short of being properly descriptive – my assertion that there exists something beyond our understanding is not at all the same thing as an assertion that this specific entity here is understandable as being beyond our understanding (in fact, you might be able to recognize this second construction as a restatement of the paradox of self-referentiality). Nevertheless, an examination of paradoxes has value – not only as an intellectual exercise, but also as a spiritual one.

Nicolas of Cusa, known also as Cusanus, elaborated a sophisticated philosophy around this notion of paradox as a womb of truth in the transcendental sense. He posited a cosmology in which God was both within and beyond the All of Creation and the Nothingness of Void; he described God as the non aliud, the ‘not-other,’ that is, the thing which is neither One nor the Other (this can be seen as a challenge to the Aristotelian Law of the Excluded Middle, an anticipation of Godel’s Incompleteness Theorem, or yet another restatement of the paradox of self-referentiality). For Cusanus, God was the unimaginable union of All and Nothing in One.

(A quick aside: note that Cusanus here introduces a third element to our earlier picture of One-in-All and All-in-One. In fact, we can now talk of One-in-Nothing, All-in-Nothing, One-in-All, Nothing-in-All, and All-in-One. We could talk of Nothing-in-One, but that would actually be Two, harking back to our earlier discussion of essential numerology. The cosmology of One, Nothing, and All is another restatement of the Law of Fives.)

Cusanus accepted that God was unknowable, in accordance with Church teaching (he was a Bishop of Rome in the Catholic Church). He nevertheless felt that we could understand something of the Divine, seeing perhaps “as through a glass darkly” but seeing nonetheless. Cusanus believed this could be accomplished by meditation upon the coincidentia oppositorum, the “marriage of opposites” – in the sense that paradoxes simultaneously defy and unify the opposites of True and False in a bivalent logic, they are ripe for Cusanian study.

The asymptote of reason

“Science may set limits to knowledge, but should not
set limits to imagination” ~ Bertrand Russell

 

Another important mathematician, who produced another important and paradoxical result, was the Austrian Kurt Godel. Where Mandelbrot considered the objective realm, and applied mathematical models to understanding it, Godel’s focus was on the subjective – he was a logician, and he was investigating how we form an understanding of the world rather than what that world might objectively be like.

We could argue that Godel and Mandelbrot were considering the same substance from opposite sides – that Mandelbrot was actually modeling subjective representations and Godel in truth modeling objective realities; we tend to assume that there is a high degree of concordance between subjective representations we can all intersubjectively communicate and objective entities we can all subjectively observe. This is not necessarily the case, as Descartes found to his dismay, and that is why I draw the distinction here between the logical models of Godel and the applied mathematics of Mandelbrot.

When we talk about a logic, we are talking about a framework in which statements represent either properties or relations of entities – this is why I say a logician deals with the subjective realm, because of course the Cartesian theater is constructed out of these same substrates. A logic consists of axioms, and rules for deriving statements from these axioms, and for assigning these statements some truth value. The most commonly understood forms of logic are bivalent, taking truth values of True or False – and, commonly, what we understand to be true is really just that which we observe to be agreed upon. This is not a particularly logical way of considering truth, as it happens, and we’ll come back to talk some more about the consequences of that later.

For right now, we’re going to follow Godel in the examination of a particular question about logic: how far can a logic go? Is it possible for us to conceive of a logic which allows us to examine every possible statement and assign it a truth value?

Godel was looking at logics that could describe arithmetical properties and relations; Mandelbrot’s work indicates that such properties and relations are sufficient to describe very complex processes in the natural world (indeed, Mandelbrot’s work has applications in many fields including sociology and econometrics). Accordingly, his conclusion that in fact no logical system could completely and consistently describe the natural numbers – and, by extension, the world, although Godel himself didn’t go that far with it – says something very important about the limits of human knowledge.

Godel actually devised a whole new numbering system in pursuing his complex proof of the undecidability of certain formal mathematical propositions, but we don’t need to in order to grasp the central idea. We can use a thought experiment to produce the same result.

Consider the case where we actually can design a thorough logic for assigning a valid truth value to any statement – such a logic is programmable into a computer, and allows us then to build a Universal Truth Machine. Any question we put to the Universal Truth Machine can be parsed by it, analyzed with its powerful logic, and identified as True or False.

Suppose now that we test our Universal Truth Machine, and give it this statement to chew on: “the Universal Truth Machine will find this statement to be false.” The Universal Truth Machine can understand this statement, but it can only find it to be false if the statement is in fact true, and its programming defines True and False as exclusive opposites. By the same token, the Universal Truth Machine cannot find the statement true unless it is in fact false. Therefore, our machine cannot give an answer – cannot prove the statement – and so cannot, in fact, be universal.

Godel’s genius was in formalizing a statement that can be represented in any sufficiently developed logic, and that proves for any logic that it somewhere hits this problem. It must, therefore, be either incomplete – being unable to prove the Godel statement – or inconsistent – being able to prove that it is simultaneously true and false without crashing. This fascinating result leads to the peculiar conclusion that our own brains, which encode sufficiently developed logic to model the world, are themselves subject to Godel’s Incompleteness Theorem. That’s a rabbit-hole for another day, however.

Wheels within wheels

“Clouds are not spheres, mountains are not cones, coastlines are not circles,
and bark is not smooth, nor does lightning travel in a straight line.”
~ Benoit Mandelbrot

 

Of course, there’s more to mathematics than numbers. Mathematics is a way of modeling reality, and there are a range of approaches to that modeling. One of these is to simply interrogate some aspect of reality, and attempt to devise a representation that models the result.

The French mathematician Benoit Mandelbrot took on the formidable challenge of modeling the physical contours of things in the objective realm. He pursued a method of modelling the shapes of clouds and mountains and coastlines, which were not immediately apparent as obeying any coherent mathematical principle. In 1967, he published a paper that asked the innocuous question “How Long is the Coast of Britain?” – it was to prove revolutionary, and would give rise to the concept of fractals. This concept is very important to my own parasimplistic worldview, but of course it has far more important implications than that.

Coastlines, it turns out, are tricky things to measure. If one attempted to measure the coastline in units of, say, 10-meter lengths – approximating the actual contours of the coastline – one would find a shorter result than if one used 1-meter lengths. The 1-meter lengths would give a better approximation, and would be longer as a result. In fact, as Mandelbrot’s paper illustrated, the shorter the unit of measurement becomes, the longer the overall measurement becomes. In the limit of an infinitesimally small unit of measure, the coastline of Britain becomes infinite.

This might seem at first blush to be absurd, but Mandelbrot expanded on this result to show its consistency with a whole family of known mathematical relationships that exhibit the property of self-similarity – that is, the curve viewed at a large scale resembles the same curve at successively smaller scales. With a self-similar curve modeling variable x against variable y, the appearance of the curve between, say, 1 and 2 will be the same as the appearance of the curve between 1.0 and 1.1, or between 1.00 and 1.01, or at any smaller scale of measure. Such curves are said to have a Hausdorff dimension between 1 and 2 – the upper bound, curves of Hausdorff dimension 2, are known as Peano curves and have the property on successive iteration of completely filling the space over which they are measured, after the fashion of a ‘Greek key’ motif. Moreover, Mandelbrot listed several examples of naturally occuring self-similar relations – famously including the leaf fronds of ferns.

Mandelbrot was, like most mathematicians, building on the work of predecessors (including in this case Lewis Fry Richardson, who had tackled the coastline paradox himself and posited a mathematical law governing coastlines that foreshadowed Mandelbrot’s result that coastlines were self-similar). The focus of his 1967 paper, which was to form the basis of his work until his death of pancreatic cancer in 2010, was actually a modern application of a very ancient paradox proposed by the Greek philosopher Zeno of Elea – the dichotomy paradox, famously elaborated in his paradigm of a race between Achilles and the tortoise. Zeno’s paradoxes give us a useful structure for considering parasimplicity and being-in-time (what Heidegger refers to as Sein-in-der-Welt), and we will be returning to them.

Creatio ex nihilo

“Abstraction is everybody’s zero but nobody’s nought.”
~ Robert Smithson

 

Zero is believed to have been invented as a number like other numbers by the Indians, somewhere between the fifth and ninth centuries. The idea of ‘null space’ or the ‘void’ was known and used by earlier cultures, but the Indians were the first to produce a symbol that could be utilized in mathematical calculations to represent the void. When we consider numbers today, it is appropriate for us to begin with zero as the unique numerical symbol for nothingness – indeed, when we derive mathematical operations from set theory this is exactly how we do start, with zero as the symbol for the empty set.

If the first number is zero, denoting nothingness, then the second number – one – denotes identity. In set-theoretic terms, it is the set which can have only one possible element (the set of the empty set, in fact). This set-theoretic interrelation between nothingness and oneness is mirrored in the symbolism of the taijitu, and the doctrine of creatio ex nihilo – something out of nothing.

The existence of zero and of one as numbers generates the concept of category; a unitary entity having more than one component subentities. The simplest structure of category is duality – the category that has exactly two elements, as ‘one and zero.’ The numerical symbol for duality is two.

Three elaborates this concept of category further into the more general plurality. Where twoness denotes a paradigm of either/or, a binary system within which ‘one’ may acceptably and completely be defined as ‘not-zero,’ threeness opens a doorway – a Gateless Gate, indeed – onto countable infinities of paradigm in which each element is uniquely itself and cannot be defined in terms of any other element (although it can be defined in terms of all other elements, with reference to the established concepts of nothingness, identity, and duality).

Four, being both the sum and the product and the power of two twos, embodies divisibility. This is a further elaboration upon plurality – with the addition of fourness, we now find that there exist some plural entities which are both entities in themselves and unions of lesser entities. We can, of course, derive numbers along the real number line by defining mathematical operators that utilize this principle more generally – indeed, we could do that when we had only zeros and ones to play with – but fourness is the philosophical symbol that uniquely develops this concept.

These, then, are the numbers which symbolize the essential concepts of being: nothingness, identity, duality, plurality, and divisibility. You probably already realized this, but we have just derived another expression for the Law of Fives.

The unforgettable fire

“Unity can only be manifested by the Binary.
Unity and the idea of Unity are already two.”
 ~ Siddharta Gautama

 

A word, before we delve into the very simplest sort of numerology, about my avatar. I fell in love with this design many years ago because of its symbolism. It may not be immediately apparent, but the avatar depicts a fiery phoenix, wings outspread, against a backdrop of flame. To me, at least, with the eye of faith, it also depicts the taijitu of the Taoists. These are both symbols of unity and opposition; Cusanus would recognize his coincidentia oppositorum and be glad. That the symbols are themselves the products of wholly different cultures, using wholly different representations, yet conveying the same meaning, makes this synthesis of the phoenix and the taijitu especially pleasing to me: a coincidence of coincidences, and therefore a Gateless Gate.

For me, the expression ‘Gateless Gate’ has a particular meaning associated with transcendence as I defined it before. I’d suggested that the subjective realm is essentially ‘walled off’ from the objective realm, but that two subjectives can be connected by an intersubjective ‘bridge’ – it follows, although this was not stated, that the intersubjective entity makes not only a bridge but a doorway at both ends: it opens the mind it reaches, but only in a limited fashion and only into the objective realm. Nevertheless, such doorways in this model afford us an analogy to the qualitatively different doorways that must connect all realms within the transcendent, which relates to the ideal in the same way as the objective relates to the subjective. The Gateless Gate is the opening of the ideal – of the extrapolation of the intersubjective appreciation of the property-relation matrix – upon the transcendent.

It is very important to understand that Gateless Gates, in this model, are the only links to the transcendent. It is impossible to pass into transcendence save through a Gateless Gate. We should also note that the Gateless Gate is strictly abstracted from either property or relation – our idea of the Gateless Gate, necessarily tethered to property and relation and so to the world, cannot be the Gateless Gate itself. Indeed, the Gateless Gate cannot in any way partake of any property of Gate as we understand that term, neither can it bear any relation to Gate as we understand it: this is why the Gate is Gateless, and why we cannot approach it from within the edifice of our Reason. Nevertheless, the Gateless Gate is universal: the transcendent is perpetually immanent upon the subjective.

The Phoenix recounted in legends by Herodotus and Ovid was a mythical firebird: a creature born in flames that lived 500 years and then immolated itself only to re-emerge from the flame. Herodotus tells us that the newborn Phoenix conveyed the ashes of its father to Heliopolis; Ovid remarks that the newborn Phoenix, uniquely among all the Earth’s creatures, is its father remade. It can be seen from these expressions of the Phoenix that it represents both the unity of Life and Death, and the unity of Self with Other.

The Taijitu (which, roughly translated into English, means “diagram of ultimate power”) originated in China, and represents the twin forces of Yin and Yang. Formed by the exact division of a circle into equal parts black and white, entwined around one another like two fishes, the taijitu shows us that there is light in darkness; and, in darkness, light. The complementary elements are necessary and essential to the whole, but inviolate. Yin is never yang, and never without yang; yin without yang would be a mirror without reflection. From the interactions of yin and yang emerge the Five Phases of qi: fire, earth, water, wood, and metal.

Within the context of a symbol that unites the Phoenix and the Taijitu, it may or may not be interesting to observe that there exists within Chinese mythology a bird analogous to the Phoenix: the Fenghuang is itself a unity of the male Feng bird, and the female Huang bird. Moreover, it Is a union of all birds in one bird, and so a representative restatement of Borges’ Argumentum Ornithologicum. It is considered the feminine counterpart to the masculine Dragon in Chinese mythology: the All-in-One, as opposed to the One-in-All.