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.

 

 



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 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.

To be or not to be, that is the question

“Quantum theory also tells us that the world is not simply objective;
somehow it’s something more subtle than that.” ~ John Polkinghorne

 

Although it is the beginning, it's not the sense in which we ordinarily - naively - think of things existing. We think of a thing existing in a measurable way; we think of it having physical properties like weight and dimension and color. This is objective existence, and it is different in important ways from subjective existence. One of these is that an objectively real entity is directly accessible to multiple observers. A mountain is, objectively, a mountain which can be observed independently by many people. Furthermore, an objectively real entity does not exist because it is observed (Berkeley is coughing pointedly, but let us ignore him for now); indeed, it exists even when it is not observed. Unlike a subjective entity, the objective entity has an independent existence of its own. It is the independence of objectivity, and the empirical evidence of our physical selves as such independent objective entities, that gives rise to the awareness of self qua self without which subjective existence were impossible.

If you accept that, you can also accept that objectivity exists a priori to subjectivity; the subjective analogue to an objective entity arises out of the process of observing that objective entity with a physical sensorium. There is a very interesting problem in empiricism, encapsulated by the philosopher David Hume when he posed the question: can we imagine a shade of blue we have never directly perceived? Hume differentiated between 'impressions' that are subjective entities triggered by or derived from the objective world around us, and 'ideas' that are subjective entities generated without reference to the objective reality in which we physically exist. Whether we can apprehend an idea of blue that is sui generis, and not merely an impression unconsciously remembered, remains a dilemma for empiricists. For our purposes right now, it is sufficient to state that all of us can readily understand both subjective and objective existence, and further that we can understand they are qualitatively different kinds of existence.

Because of the fuzzy skepticism of Descartes, it is not always possible to state definitively of any particular entity of which we are consciously aware that it is either subjective or objective; and this is another sort of problem, addressed by Borges in his Argumentum Ornithologicum. Nevertheless, we have at this point identified two ways in which a thing may be; and, at least theoretically, we have established that these ways of being are not necessarily universal - that is, some entity may 'be' only subjectively, or only objectively, although it may well exist in both ways and it can exist in both ways so homogenously as to blur the line between the two.

That is already quite some philosophical ground we've covered, but this is the point where we return to Korzybski and the metanow (which is not a Korzybskian construct, but which relates to his time-binding notion very handily). We do so by considering an entirely different kind of existence. We do so by considering words.