2.1 dead reckoning

ASS: What academy is this, to keep “don't cross the line” above the door?

FOOL: It is a school of Pythagoreans.

ASS: Can one enter?

FOOL: For an academic, not without difficult, and many, conditions.

ASS: Now what are these “conditions”?

FOOL: They’re quite numerous.

ASS: I asked what, not how many.

—Giordano Bruno, 1584

What, then, are the “conditions” governing your demarcations of this from that, here from there, now from then, yours from ours? If perchance you have the wherewithal to repudiate the veridicality of the Whatness of what, the Thisness of this—and by extension, the Thatness of that, and the Otherness of the other—and for good measure (by way of Eckhart), the Isness of is—and moreover, should you muster the whathaveyou to refute their predicability point by categorical point, then—on one hand, you will have (negatively) denied yourself the capacity to (positively) affirm anything about anything, but on the other hand, you will have retraced an apophatic arc of recourse all the way back to, e.g., Averroës, Maimonides, or Cusanus (1464) to find that “The concept of truth that rejects both opposites disjunctively as well as conjunctively is the more absolute. For to the question whether God exists there can be no more unrestricting response than that (1) it is not the case that He either exists or does not exist and (2) it is not the case that He both exists and does not exist.” That, or some other equally ruthless four-corner ratiocination sufficient to suspend your choice of polemical opponents by their own fallaciously purported prerogatives. Just ask Wittgenstein (or Popper).

X markiert den Punkt

Despite our bent for German Metaphysics (née “Rhineland Mysticism”, to say nothing of Viennese), we harbor no ill Will to superimpose our own eccentric Boundaries (categorial or otherwise) über the Bonds of foil Stamp or waxen Signum, impressed by Academy or Sovereign, under threat of hot poker or clerical Fiat. This is not to say that we wholeheartedly acknowledge the veridicality of the latter—for on this, we shall up Pascal’s ante, if while checking his Wager. Put in more practical terms, we cannot legitimately sympathize with Eco’s aversion to accusations of “harboring systematic ambitions”—for qua Technologists, our work is by definition systematic (to say nothing of our ambition, which is of so airy and light a quality that it is but a shadow’s shadow).

Put in less practical terms, as ‘metalinguists’, we may all see fit to recapitulate the more contentious cris de coeur of our various accursed combatants with more conviction and less correlation if (by way of Eco’s caution,) we can discern Odin from Thumbelina by way of Pythagoras—that is, if we can select the right tool for any given job—be it reconstructed phonology, neurolinguistic meta-analysis, radiocarbon dating, or a nutcracker. Practice cannot ‘make perfect’ (but for parasemantic parables of Sufis armed with sandpaper, as Borges or Rumi remind), yet even course familiarity grades to fine facility, so long as we select from a sufficient array of tools—of which, where their articulation is ‘your job’ so to speak, their provision would be ours.

Your Humble Narrator did not spend twenty-odd years skirting Titles as some sort of hysterical exercise in pro-drop auto-nullaphora, but the better to apprehend and articulate, on one set of hands, the multinational branding apparatus (crooked to flails, yoked to pricks, stimulum vinculare), and on the other set of hands, to comprehend and correlate variously and variably paid practice in the (ahem) black arts of the media myriad. So, that was then and this is now: we say “as Technologists, we at Archemind” address the mundane requisites of our brand positioning—and contrariwise, our brand of ex-position-ing (excision, erasure, displacement, disavowal) in a manner which is—baroque stylistics notwithstanding—not unlike Lacan’s

“[impossible] subject supposed to know [nothing]”

—which is to say: Insofar as we (here “we” could very well include you) are employed as or otherwise positioned as information ‘purveyors’ (writers, speakers, teachers, analysts, clerics, consultants, directors...), we may find ourselves in a double bind: On one hand, we may be required to appear more knowledgeable than—or at least be presumed capable of conveying more ‘know-that’ (if not ‘know-how’) to each of (y)our ‘consumers’ (readers, users, viewers, students, analysands, patients, parishioners, clients, customers, underlings...); on the other hand, we (at Archemind; and you?) may be restricted from imposing judgement upon said consumer—and moreover, from inscribing (y)our value(s) to said knowledge in the course of its transmission. This may call for a tricky bit of shadow-boxing—being a doubly difficult desideratum in a metalinguistic discourse—but (for ourselves, anyway,) we need not abscond to Lacan’s animatronic lectern.

wee dwarf thee mechanickall turk

Despite being frequently caricatured as “equal parts art and science” (a self-flattering platitude) or “an applied science” (a self-flattening pleonasm), TECHNOLOGY is the reciprocating organon (o shame your dirty mind) by which formal rules (theory) iteratively recurse empirical regularities (practice), the reciprocal iterations of which necessarily disregard the accidental properties of the discourse domains to which it is turned—or in which it turns. (Trepidation’s trephination; benign ORs to bone rings. We might as well say “Hey, look—an ice-pick! Stick it where you will.”)

To shore up such a definition of ‘technology’ we must strive for specificity. As regards (exoteric) extension (or intention), the foregoing rhetorical switchback recaps itself in just about the same fashion as if we were to interpose (Lat.) ars as an apodeictic autopoietikon between (Gk.) episteme and techné. In any event, each of these pairwise parties to recursion (empirical/formal, rules/regularities, theory/practice, episteme/techné, -logy/-graphy, even) remains strictly indiscernible into its antipodes (per se) despite being (pro re) distinguishable—or at least recognizable, in folk-psychology terms, as (procedural) ‘know-how’ in contrast to (situational) ‘know-that’.

So to know how that does is, the hifalutin know-it-all may well read our distinguishable-but-not-discernible formula as a proxy for the (con/dis)junction of ontology and epistemology—if so, fine; as we say, this retraces an “onto-epistemic” reciprocation. However, as regards (esoteric) intension (or comprehension), this is just about the same as if we equated ‘technology’ to ‘consciousness’—which would bring us back to reiterate that “Intelligent Artifice ≠ Artificial Intelligence” before we smacked face-first into the causa sui and other “perverse rape[s] of logic” (Nietzsche). Reversible tools loot reliable servers. Back to the drawing board. (We might as well say “Man is the Measure” and call it quits.) In any case, as the instrumental organism (be it individuated or collectivized) hones its instincts and inclinations into faculties and facilities (abilities and aptitudes, capabilities and competencies) by interminable iterations of ‘trial and error’ (from hypothetico-deductive scientific method to military drill), its hand will reach as needed for the appropriate instrument, be it a framing hammer or a flaked hand-axe. Just ask Heidegger.

At what point does this line of argument cross over into metaphor? Lest we “bring a knife to a gunfight” as the old-timers say, may we re-submit for your re-consideration that rhetoric (broadly, as per Aristotle—or better, per Cicero—or belligerently, pre-Ramus,) continues to govern the judgment and selection of theoretical models (for better and for worse), and hence their adoption as juridical paradigms (within academia and without), to a far greater extent than any logician would decree were they King, or Queen, or President, or Poobah. Of course ‘in this day and age’ we are no more likely to look up and find a Philosopher-King who predisposes our positions than a Logician-Queen who deposes our suppositions (or worse. Just ask Alice). Nevertheless, should we debark to dismantle Black Boxes with brio, we would do well to inspect our inventory of tools. For while you may use a ball-peen hammer to skin a cat (in a box, on a mat, with a fox, in a hat), there stands a Heisenbergian probability that you are going to smart your thumb. That’s just common sense.

How do we begin to distinguish this from that without first splitting the world in two? This is a question that sets off from interpretations of interpretations interpreted and winds up negating the negation of the negation—from Ipsum Esse to Posse Ipsum, from Quidditas to Haecceitas—and as we aim for the Archipelago of Archeography we risk vanishing into the Isthmus of Istigkeit. Lest we find ourselves chasing exponentially multiplying white rabbits and swans into black holes and hats, we should like to heed Eco and sidestep “Bruno’s space of an infinity of worlds, perhaps all simultaneously present in different dimensions”—if only for a moment, while we take our bearings.

boring systemic perambulators

We may best articulate the distinction of “-graphy” from “-logy” by way of the reciprocation of empirical and formal attributes by TOPOGRAPHY and TOPOLOGY, in that the former is capable of representing the latter, but not of constraining it—and vice versa. More particularly, (empirical) topographical representations are governed by (formal) topological constraints (e.g., a world map represents a sphere on a plane), whereas topological representations lose their formal character when they are taken to rely upon empirical topographic data.

While what we do consists in applying practical ‘-graphies’ to theoretical ‘-logies’, we (at Archemind) can neither limit our praxis to ‘lexicography’ nor describe it as ‘topography’ or ‘cartography’ but for metaphor. As such, had we aspired to ‘elevate epistemology to first philosophy’ (an excursive asymptote ascribed to Descartes), we would have hung a shingle reading ‘epistemo-graphy’. But does saying ‘onto-graphy’ tip our hand? Yes and no. Had we wished to follow ‘the linguistic turn’ (a discursive trope inscribed by the fin de siècle antipantheon), we would have double-bound ‘metalinguistics’ as the metonymically girded Dictator of lictorae and the overarching Dominus of the (power)set of all Power(set)s of all “Universes of Discourse” (Boole).

Rather than trade worn coinage or mint fiat currency, we would suggest that ‘ontography’ is but one of the many possible applications of topology—in particular, that of demonstrating the (formal) coherence of structures that are otherwise (propositionally) impredicative. For example, where Lacan did just that by way of paradoxical parole and a clutch of schematics, we would do so by way of lexicography, topography, cartography and the like, compiled via ‘interaction design’ and/or ‘experience design’ (inasmuch as these last terms seem to be displacing ‘information architecture’ and ‘information design’ in the jargonsphere. Being offered the hifalutin position of “User Experience Architect” back in 2001 surely showed the dot-com bubble hoisted to its hot-air limit).

To warrant our proposal at the most basic level, we must then promote topology—not to “First Philosophy” (a post now held in rotation by Politics, Ethics, Physics, Theology, etc.) but to primary specifier (we would like to say ‘schemator’). Why? Topology, as a metamathematical medium, affords a singular capacity for conducing constraints multilaterally amongst semiotic modalities—among which we prioritize the phonological, the algebraic (on which model we would like to say ‘calculaic’), and the visuospatial—or if you prefer, the geometric. (Topologizing the olfactory is a challenge we shall leave to our betters.) Where we aim for explication, we should where possible prefer the self-evident motivation of geometric presentations to unnecessarily arbitrary algebraic representations—and both should be preferred to unadorned phonological writing (we would like to say ‘phonography’), which may well be the noisiest of all possible signals. (Taking after Bruno’s braggadocio and Lacan’s Lalangue, we may be hammering this last point well past home.)

how many fingers am I holding up?

Should we find ourselves compelled to a patriotic gesture by false jurisprudence in the mode of a HUAC, we would point not to our evident (“our” being your humble narrator) admiration of our own (“our” being The GodFearing, ApplePieing, GrandSlamming U!-S!-A!) venerable Willard Van Orman Quine, to whom the American Academy owes some prolongation of respectability into the 20th century, yet for whom our admiration is attenuated by his entitlements—but rather to our admiration of the criminally under-appreciated Charles Sanders Peirce, to whom the American Academy owes some comprehension of its incapacities, and for whom our admiration is attuned to his eccentricities.

Now, that the matter of no new truth can come from induction or from deduction, we have seen. It can only come from abduction; and abduction is, after all, nothing but guessing. We are therefore bound to hope that, although the possible explanations of our facts may be strictly innumerable, yet our mind will be able, in some finite number of guesses, to guess the sole true explanation of them. That we are bound to assume, independently of any evidence that it is true. Animated by that hope, we are to proceed to the construction of a hypothesis.

—Charles S. Peirce

Peirce was surely the 19th century’s greatest logician-cartographer—and less surely, the founder of semiotics (insofar as his semeotic of interpretive cognition may, or may not, be discerned, or discernible, from Saussure’s semiology of structural linguistics)—and, per his champion in William James, of philosophical Pragmatism—despite his oxymoronic preference for “Pragmaticism.” The pedantic patriot may further note that e.g., Deleuze and Eco both found particulars in Peirce that were otherwise lacking in their converse corners of the continental drift. The patriotic parrot may note that Your Humble Hortator withstood the protracted trance-induction that is American public school without once sputtering the so-called “pledge of allegiance”—and for that matter, without pumping the prescribed empty cardiac deixis We People hastily swapped for the pseudo-historical Romanesque high howdy once our far-flung Old-World friends spoiled it for everyone. We digress.

to proceed to the construction of a hypothesis

Peircean guessing-games notwithstanding, the onto(graphic? ontological? ontic? ontical? onticological? ontographicological?) questions (or rather, the catena of consequents) that we would like to pose here—despite periodic reformulation over the centuries, continents, and universes of discourse—remains, in short: Can we warrant our assertions as to the schematic order of entities (real and ideal, actual and virtual) in absolute terms that account for relativity—or in ahistorical terms that account for histories, etc., by way of necessary invariants that account for contingent variables—but now, without relapsing into (the terms generally regarded as of) precritical (nor regressing to prehistoric) metaphysics? Some question. At the point of a hot poker, our own foolhardy answer would be:

Yes—so long as we take “terms” to refer to axioms and specifications, not words and propositions—and so long as we take “account” not as an index to tally, but to demonstrate—and moreover, not by shooting into pickle barrels stocked with the familiar foul fish, but by moving with tangential targets, one and all—by way of such praxes as formalization and ontography, never mind nomination as Formalists or as Ontographers—by which time, surely, the hot poker would have foresworn our unpalatable surmise, if only by foreclosing our tongue. In terms of rhetoric (or even argumentation proper, stripped to the nits and picks), this question may very well reduce to the vicissitude anticipated of the terms “absolute” and “necessary” and “ahistorical” when retroactively measured across relatively contingent historical events. (And for our next trick, we prick out James Joyce’s other eye with Hume’s Fork.)

In any case, our technological aim is to facilitate communication among disparate domains from a maximally disinterested standpoint. You may well ask if such a point exists, on which we might stand in “disinterested” repose. The answer, of course, is no—but whosoever would qualify herself—in advance, as adjunct, or in any authorial addenda of her work—“as a Scientist,” or “as a Philosopher,” (in contrast to “as a Theologian” or “as a Cleric” or “as an Artist”) is obliged to orient her assertions by way of such a point’s virtual apodeictic coordinates as surely as whosoever would avow himself a Muslim must orient his person towards the actual geodetic coordinates of the Ka'ba. The converse is, of course, that maximal disinterest risks coincidence with maximal disorientation. Just ask Hegel.

“Sun comes up, sun goes down.”

As regards those topics you find closest to hand, do you know where you stand on the crucial positions and pivotal points of your (meta-)discourse, between which topoi and loci you run to and fro? Even if so, you may yet fall one geodetic datum short of geodesy. That is to say, with calibrated compass and carefully folded map ready-to-hand, you may navigate the surface of the earth in blissful ignorance of its relative position, provided that you don’t look up. But once you have, and by which astronomical observations (with or without zoomorphic memorial aids,) you’ve seen fit to recapture said datum, you will have graduated to Ptolemaic cosmology. Welcome to the second century.

To satisfy our doubts, therefore, it is necessary that a method should be found by which our beliefs may be caused by nothing human, but by some external permanency [...] upon which our thinking has no effect. Some mystics imagine that they have such a method in a private inspiration from on high [but] in which the conception of truth as something public is not yet developed. Our external permanency would not be external, in our sense, if it was restricted in its influence to one individual. It must be something which affects, or might affect, every man. And, though these affections are necessarily as various as are individual conditions, yet the method must be such that the ultimate conclusion of every man shall be the same. Such is the method of science.

—Charles S. Peirce, 1872

to precede the deconstruction of antithesis

Can we measure the distance between these two Peirce quotes? If we resort to historico-philosophemes, we might eyeball them against the positions taken up by “Left” and “Right” Hegelians in the wake of the Marx backstroke—or, we could suppose Peirce to have pulled the incommensurable ends of German Idealism together by some sort of Möbius maneuver capable of short-circuiting Hegel’s prescription for “Absolute Idealism” into Kant’s proscription of “Transcendental Realism”—or, we could reckon that his stint at the USGS (United States Geological Survey) may have served as a Kantian curative by way of (presup)positing convergence over correspondence. In any case, no matter which way we slice his metaphysics, Peirce’s cartography, in particular his quincuncial projection (QP), gives us a properly situated and correctly oriented example of reciprocation by (formal) topology with (empirical) topography.

Topology requires every conformal world map be topographically indiscriminate—i.e., the map must be able to conform a representation of any sphere irrespective of its surface features. The immediate distinction of the QP is that it seems to ‘turn inside out’ seamlessly—that is, we typically picture it as ‘open’, centered on either the north or south pole, thus splitting the antipode to the four corners. As such, when we imagine (i.e. visualize) it as ‘closed’ (and this may be more or less difficult for the untrained eye)—that is, with each broken edge mated to its counterpart, we find not a sphere, but a related irreducible topological primitive (others being, e.g., the torus and the trefoil knot); this primitive consists in an apparently volumetric enclosure that—being indiscriminately orientated vis-à-vis ‘inside’ versus ‘outside’—bounds two volumes of infinite extension.

Like the Klein Bottle, the ‘closed’ QP is forbidden from the 3D space we occupy—unlike the first topological primitive that conforms two volumes of infinite extension, the surface, which rather than bounding the two, separates them and as such, eludes visual representation but for circumscribed segments (just as ‘here there be dragons’ at the edges of Bill O’Reilly’s flat Earth). The QP distinguishes itself in this regard by representing itself in full on any flat surface, such as your computer screen, by way of any two perpendicular cuts. The QP construction is reciprocal in that its topology requires one or more asymmetric topographical features to afford this representation. And yet, once tessellated (tiled), it becomes readily apparent just how arbitrary these topographical features are—including the nominal location of the two poles, and the placement of the two cuts required for the planar representation of a single instance (i.e., the sphere as tile, tessera, token, atom, unit, monad). Can the QP tell us something about what, or how, Peirce was thinking? It cannot fail to. Can we translate it? Perhaps—but into what, and how?

Let us take as (1) the QP topology portrayed above, which is an empirical geometric figuration—more specifically, an instantiation—or precisely, an unmediated self-presentation through which the formal QP specification is apprehensible by any marginally sophisticated viewer, in that the necessary data for (e.g., what Kant would call) ‘apprehension’ (if not Einbildungskraft in full) transmits along sub-linguistic, non-conscious (if not pre-conceptual) sensorimotor conduits, i.e., mechanisms that are quantifiable in turn by recourse to neurophysiological modeling. So qualified and quantified, (1) can be transposed into (2), an algebraic notation—in particular, a syntagm (syntactic sequence) of glyphs (graphemes, letterforms, analphabetic squiggles) which has been specifically granted arbitrary correspondence to discrete (segmented, identifiable, quantized) functions; so qualified, (2) would be a re-presentation through which the formal QP specification would be apprehensible only by recourse to a codex on the order of Little Orphan Annie’s secret decoder ring (“buy more Ovaltine!”).

Codices notwithstanding, we can transpose neither (1. figuration) nor (2. notation) into (3), the armature of propositional language on which we are accustomed to conducing (and moreover, attributing) meaning—at least, not without importing extraneous affective or aesthetic content (Habermas: “political culture ... cultural substance ... substantive ethical ideas [etc.]”). Do these constraints make the QP ‘meaningless’? Yes, or at least they should—but do they make the (non-meaning of the) QP ‘ineffable’? No, but only inasmuch as we can articulate the denotative extension and connotative intension by which, e.g., ineffible, unspeakable, impredicative, and irreducible can be meaningfully demarcated on a contextual basis. This may be a tall order, but we ought not confuse it with a tall tale.

the last refuge of scoundrels

As petulant pugilist Bill O’Reilly is fond of parroting as an (ahem) ontological proof, “sun comes up, sun goes down, tide comes in, tide goes out,” etc.—and mark this, Fox and Friends (a title pregnant with humor for Fassbinder fans) do not reflect a statistically trivial sample of mental defectives, but rather represent the majority of our citizens (but not, we should hope, of our registered voters). The point here is that no matter the discourse domain, language is a territorial instrument—and moreover, metalanguage is the discursive plane on which, for better and for worse, religious doctrine finds equal footing with both formal axiom and psychosomatic endoxa. Irrespective of its legitimacy, metalanguage—taken to include not only the discourses of linguistics or philosophy but of logic, rhetoric, and journalism—bares wolf’s teeth through sheepish faces. One cannot defend ‘the high ground’ from within its bounds. In terms less metaphoric and more mechanistic, Boole’s Universes of Discourse exceed their own nominal bounds as (syntactic) instruments of (logical) im-plication by requiring (semantic) reference to (ontical) ex-plication. The map folds in, the map folds out. “So we now use the country itself, as its own map, and I assure you it does nearly as well.” Or so posits Mein Herr (by the plume of one Charles Dodgson), and yet unsatisfied, “Now let me ask you another question. What is the smallest world you would care to inhabit?”

For if Copernicus’ work, as others have remarked before me, is not as Copernican as we think it is, it is because the doctrine of double truth continues to offer shelter to a knowledge that, up until then, it must be said, appeared to be quite content with that shelter. So here we are at the palpable border between truth and knowledge; and it might be said, after all, that at first sight our science certainly seems to have readopted the solution of closing the border.

—Jacques Lacan, 1960

By phenomenological happenstance, the fact that we can drive from Palm Beach to Cape Mendocino with a folded map (a Mercator projection, even,) leads us to believe (against our better judgment,) that the earth is (“still”) flat (as if it magically were then wasn’t—a notion upon which philosophies “for us” would insist). As environmentally situated flesh-and-blood creatures, we continue to rely upon just such a map, which—having been pressed into the service of naïve realism by premodern fiat—is reprinted on demand, if only to navigate mundane affairs—even those of the rigorous investigator who, so to speak, must put her pants on one leg at a time like the rest of us.

Nevertheless, somewhere between the platitude of “the map is not the territory” (Korzybski) and the plumb-line of “it is nevertheless the map that precedes the territory [via] precession of simulacra” (Baudrillard) we tend to take a tractrix for a tangent (or, to quote Bugs Bunny, “a wrong turn at Albequerque”) if only to promote sociopolitical equilibrium over propounding “Copernican revolutions” unto seismic “paradigm shifts”, lest we slip between the cognitive cracks. As such, we can either subject our moldering maps to the austere (if not ascetic) measures of modernity—or, we can play like we just left the old map in our other pants, because after all, don’t we only sneak the occasional as-needed peek to reassure our fragile egos of their own (our own) individual importance in the face of impending facelessness? So long as we ply the latter as the platus quo, our best efforts at an epistemological account consist in rolling up a tube through which, upon dilating and/or contracting what is almost certainly the wrong end, we shriek polemic at peak volume. That is to say—

“my Black Box can beat up your Black Box”

—a language game that all can play, having all been children at one time or another, thus having been a party to playground taunts, if only by turning a blind eye. Here we shall demonstrate the rudiments of our would-be “disinterested repose” by way of three or four rounds (turns, innings, acts, plays, volleys, moves) of this ignoble non-game. During play, we shall chalk up our points of contention, disagreement, and departure from rules both arbitrary and motivated; to wit, unlike “I know you are but what am I?” (being intransitive and therefore undecidable), the invariant constraints of the “mine can beat up yours” parlay foreclose a decisive ‘win’ despite the strict transitivity of the purport.

But such formalisms have done little to dissuade any and every ragtag team qualified by capite censi from the statutory appellation of “winner” (and by contrariwise consequence, “loser”) status. In being illegitimately snatched (if not Pyrrhic) victories, one and all, avowed recognition of said status by the demos is invariably enforced by adhering gold stars, blue ribbons, green clovers and suchlike upon the “winners”—and by extension (here we have exactly not a metaphor for something else), affixing not-so-lucky charms to the “losers.” Again, from (1) this thing is a person and (2) that thing is not a person follows (3) persons go in this box and (4) non-persons go in that box.

Cued by Ockham, we should first cut the paradigmatic black box to a parsimonious formal specification—namely: a box is a three-dimensional container, the simplest of which reduces to one ‘inside’ volume and one ‘outside’ volume, and thereby to a single closed two-dimensional surface. With no further modifications, we can punt this abstract hobgoblin into play as a redoubled reification (“fallacy of misplaced concreteness”): If we call this the inside, we have “The Explanatory Gap”; once we turn it inside-out we have “The Hard Problem”. We can demonstrate (in brief) this para-non-solution by way of the Necker Cube, which is neither a topological presentation nor a topographical representation, but rather an optical illusion (of ‘multistability’) courtesy of the Gestalt psychology school:

The Necker non-cube keeps company with the panoply of so-called “impossible objects” that offer little epistemological value beyond exploiting the neurological defects given of any adaptive organism. Should you derive enjoyment (or funding) from ‘arguments’ as to which way the non-cube faces and suchlike, you will find yourself in a large, enthusiastic cohort. Bravo! Far be it from we to suggest you inquire otherwise. In any case, for our part we find this rather like a chess board stripped to the kings—a de facto draw, the cursory play of which would remain dull even in the hands of a Kasparov or Kubrick. We prefer to work forwards and backwards by examining the system of constraints by which interval, periodicity, chirality, (vectors, tensors, etc.) are discursively imposed by so mere an act as attributing a ‘substance’ or ‘essence’ to any or every nominally empirical (actual-real) yet stubbornly formal (virtual-ideal) object, be it unfathomable Void or hard Kernel. To promote the latter (examinations) over the former (exceptions), we thus resolve a compact combinatoire for flat-pack (dis/)assembly of Boîtes Noires:

The black box can be (not de-scribed, but rather) ex-plained by way of exactly eleven 2D projections—a census sure to disappoint fans of the Twelve (Gods, Houses, Apostles, Imams, etc.)—that is, unless you count yourself as the twelfth, with the absconded thirteenth Party (or Person, or nominal Pivot-Point) as semblable, but that would be heretical in four out of five sects of both Christianity and Islam—never mind the Pagan panarchy (by “Pagans” we mean: fans of the Greek and/or Roman Pantheon(s), as succeeded by such convertible Platonists as Augustine, never mind never minding ‘spiritualist’ or ‘New Age’ frippery-peddlers), tallying as they do upon less pervasive (if not less restrictive) ledgers and less persistent (if not more insistent) palimpsests. Of course, fans of the ten Sefirot face the opposite problem, of a singular inadmissible or unassimilable excess—but then again, the medieval Judaic(/Christian) K(/C)abbalists solved that demi-bit with the (in retrospect, somewhat Heisenbergian) oscillating tenth-not-eleventh (or, nth-not-first) position on the Ancestral (if not Atavistic) Tree.

But the former are anthropomorphs, such as were (metonymically) constitutive of Christianity and (supposedly) disavowed by Islam—in either case, they ‘disqualify themselves’ from play on grounds of formal austerity (which is not to say “prohibition of idolatry,” as that would be doctrinaire whereas qua referee we are rather dogmatic—and if you cannot tell the difference, God help you). Moreover, the latter Tree, per the Sefer Yetzirah—while less phytomorphic than graph-theoretic—yokes accidental content to substantial form, thus disqualifying it in turn from our commutative combinatorics. As for trees, we prefer Porphyry’s ontographical paradigm, from which descended our common ‘tree structure’ by way of, e.g., Ramon Lull, who sliced and diced transversally through various Hermetic, Judaic, Christian, Islamic, and Scholastic schemata to pursue—as per Eco’s adroitly titled tome, The Search for the Perfect Language.

You may have already reached a verdict on whether or not we (at Archemind) are engaged in such a search (in general or in particular) by way of our tongue-twisting topology, or if we’re simply greasing the (square) wheels of an involuted Joycean machine. In any case, we are in no position to properly put thumbscrews to wingnut improprieties; you are. As for the types of formal operation by which motivated constraints can be deployed to undergird an arbitrary law (for whatever that’s worth): If we allow the use of dissymmetric (chiral, mirrored, flipped) versions, we would seem to offer twenty-two forms instead of eleven:

However, this would inhere two types of information loss (entropy)—in particular, we would force two types of data into question insofar as the individual ‘player’ could not recover them (by deduction, induction, abduction) from the fully constructed box in order to determine the mechanisms of its construction, i.e., the rules set by the ‘maker’. Two plats show axial symmetry, such that we could not tell the left-handed box from the right, and four plats show radial symmetry (eight if we allow the chiral flip), such that—while we could tell the left-hander from the right-hander—(as an aside, should this exercise strike you as folly, talk to a dietician or a psychopharmacologist about isomers)—we could not tell up from down (nor east from west, etc.) on either hand:

And so, to a fiat! Should we wish to preserve an element of either guesswork or chance (cf. backgammon), we could allow chirality on all eleven or, with more formal restraint, on nine. Should we wish to eliminate guesswork altogether (cf. chess), we would have to provide the player with data sufficient to reconstruct all three dimensions and all three orientations while moving back and forth between volumetric container and flat-pack box-parts. Bound to the latter, we are forced to impose strict rules for construction:

If your ready-to-hand configuration of peripherals can automate duplex printing, you’re in luck. Otherwise, print side A, then feed it back through your printer to superim(presup)pose the other side A. Once we account for unfamiliarity and printer driver vicissitudes, we reckon this task should take you no more than three attempts. Snip snip, glue glue, you can now take your pick from five black boxes of demonstrably unique constitution:

So much for the pre-game. Now, if you fancy topical twists, but you look down your nose at full-contact sport, you can apply procedures of the prior sort to a football (of which the international polygon offers greater variation than the American oblong) without (A) getting your knees dirty and without (B) having to learn a single rule of pitch or gridiron—although, in the case of the American football, you would be hard-pressed not to auger its aeronautical import. So far so good. Now, should we wish to put the box into play, we would learn nothing via recourse to game theory of the sort that secured the institutional entrenchment of ‘rational agent’ economics.

Rather, we must examine actual human behaviors—or, to load the term, rituals—we must, that is, if we are to justify shouting (the allegorical equivalent of) informed color commentary over the thunderous din of chanting ochre-faced hooligans. In the field, this would be, generally speaking, cultural (or social) anthropology; in the lab, this would be experimental (or clinical) psychology (or neuroscience) of the sort that, e.g., in the name of ‘behavioral economics’ results in nothing so much as an overdue empirical validation of Freud’s most unspeakable inferences (as gleaned from examination not of persons, but of rudimentary organisms. Po-mo ’ologists who have been conditioned to sneer at Freud would do well to consult Eric Kandel, whose ‘hard science’ props include a Nobel Prize in physiology, if you fancy that sort of thing. We digress).

What games can we play with a black box? Note that by “games” we mean: various types of ritualized trance (be it state-sanctioned, state-sponsored, or state-symptomatized) induced by codified somatomotor repetition (including speech and song, drumming and dance) or prolonged stasis (including selective sensory deprivation), both of which produce phenomenal and morphological aberrations via neurophysiological fatigue and/or semantic satiation. Should we allow for isomorphic (self-similar) scaling of the box, or for variation in construction materials, the permutations of play would be innumerable—however, limited to three scales and five materials, we can make quick work of the old Goldilocks routine:

(A) At roughly 1:200, you can construct the box of plywood, line it with lead, paint it black, then—all by your lonesome—hunker down inside the box until you’ve accumulated sufficient Orgone Energy to convert your naysaying neighbor to the One True (Wilhelm) Reich(ism). (B) At roughly 1:3000, you can construct the box of stone, drape it in black fabric, then—with a billion of your closest friends—in its absence, prostrate yourself in its direction while reciting repetitively five times a day; in its presence, circumambulate it seven times accompanied by deictic gestures at invariant intervals. (C) At roughly 1:4, you can construct the box of select animal skins, die it black, then—with a million of your closest friends—strap it to your forehead, orient yourself towards a geodetic datum in a manner not the least bit dissimilar to (B), and rock to and fro while reciting repetitively at intervals contingent to variables.

We trust our bald caricature afforded you a chuckle or two—but at who’s expense? If on one hand, you fancy yourself scientifically enlightened and suppose yourself immune to superstition by dint of having opted out of explicitly sectarian ritual, you may find these three examples consist in equally arbitrary behaviors. If on the other hand, you have been systematically entrained to sectarian specifications, you may find that one, two, or all three examples consist in equally alien behaviors that are eo ipso abhorrent to your person, your people, or your prototype. But if, having both hands otherwise occupied, you put the shoe on the other foot, you may very well find—without attributing positive or negative valuation to (much less passing judgment upon) such variously unfamiliar yet uniformly nonviolent behaviors—that each consists in theory in a most austere formal rigor, and moreover that (B) and (C) consist of a material praxis demanding acute sensitivity to the spatiotemporal situation of the individual and distribution of the community in both absolute and relative terms. As for the ill-fit Goldilocks-box knocked together at point (A), we do have trouble not laughing aloud at the thought of a precisely William-S-Burroughs-sized “Orgone Accumulator” rattling out his trademark telex ... ... ... “language is a virus from outer space” ... ... ...

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