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.

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.

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.

Bridge to nowhere

“The single biggest problem in communication is the illusion
that it has taken place.” ~ George Bernard Shaw

 

A word is a representation. Our language has syntax and grammar, and a lexicon of defined words which are themselves ordered arrangements of representative letters; this is a very flexible representative construct, but we can more generally identify a class of entities which exist not only as things-in-themselves but also as representations of other things. These symbols may exist subjectively or objectively, but they are translatable from the subjective to the objective realms and back again. They therefore have the capacity to transcend subjectivity, to communicate the subjective world of one mind-artist to that of another mind-observer. They are intersubjective.

What I am writing here, with these words, is an expression of my subjective world. Every word I use has an objective existence as pixels on a screen, and you can observe them with your eye; but every word you read and understand generates within your Cartesian theater some subjective entity, and the arrangement of all of the words allows you the freedom to arrange your own subjective version of the world I'm expressing. Your world may not be the same as mine - indeed, I'm about to argue below that it cannot be, and we'll later develop that argument into a powerful teleological principle that I call parasimplicity - but it exists for you the way mine exists for me, and the words we're sharing now are the bridge between those worlds. Intersubjectivity expresses the connection between two subjective realms, and makes explicit the relation between Artist and Observer alluded to before. In this formulation, communication is literally an Art.

The expression that "communication is an art," in ordinary parlance, connotes a certain degree of skill incumbent upon us when we intend to share some aspect of our subjective reality with some other objective being. It draws our attention to the real risk that what we convey when we produce some intersubjective expression is not, after all, what we intended to convey. The old parlor game "Chinese Whispers" demonstrates how this risk arises at both ends of the communicating 'bridge' - indeed, the more people there are intersubjectively sharing an idea, the greater this cumulative risk becomes.

We can posit a maximum number of observers who can effectively share an idea without corrupting it for at least one of the group, but for right now let's leave that to one side - another unconsidered trifle, so to speak. Let's instead consider what is going on when we establish the intersubjective connection: when, for example, you read something I have written.