Notes On Reality Before The Artist [part 3]

18 June 2014

I compose these notes to fit the mind of the student for whom I intend them.This is part 3; you may find parts 1 and 2 here and here, respectively. I include the introduction from part 1 again below.

For those more or less advanced, there may seem much that digresses or states things too succinctly. I believe one may still find value in reading these notes, even for those not the student in question. In those places where things seem too much elaborated, I apologise that my student’s frame of mind overtaxes yours. And where things move too quickly, I can only suggest immersing yourself in the more elemental or basic texts that address the matters at hand.

Also, I use past and present conjugations of the verb “to be” under protest. You should imagine every occurrence in quotation marks; typographical preciousness prevents me from indulging this visually.


No system, however imperfect, contains errors.

Therefore, we must come to terms with the fact—ourselves each being omniscient—that the errors of omniscience must lie not in ourselves but instead in the nature[1] of omniscience.

However, given that adding manpower to a late project makes it later, we may understand then not only:

  • that the reproduction of the world—understood in its broadest and narrowest senses—puts off the end of the world, but also
  • that the elaboration of a trinary (or greater) logic can only paper over, sometimes very cleverly or intriguingly, the abyss that binary logic (or dichotomous thinking generally) opens up.

Let us take some steps to move beyond this.

The Artistic Act

In what follows, I make no claim to historical accuracy. In fact, whether we should even desire historical accuracy leaps to mind as a question. To generalise about the Artistic act from the single example of one Artist may well lead into more cul-de-sacs than open roadways. So, all apologies to the specific experience of the Artist, and those whose egos rest on admirations or loathings for those specifics, but if we would find a way out of that which too much determines us, then it will almost certainly not come by following his example.

If in the previous section I kept dubiously veering toward implying a necessary commitment to a given form of metaphysics (one where Existence precedes Being), here we remain on more pleasingly abstract ground—we may, therefore, proceed more as dilettantes.

Let us understand that the Artist did his thing by developing an explanatory model, i.e., focus on “he invented physics” in its sense as providing “an explanatory model of Reality”. Mathematicians would, out of their vanity, attempt to insist that this explanatory model must necessarily in mathematics, but I will show this does not hold water.

Mathematics, in its ultimate sense, exists as a purely aesthetic creation. I will defend the use of the word “aesthetic” here later, but it connects to Schiller’s sense ultimately as well.

Mathematics, in its purest sense, has nothing to do with Reality, and never does or will, thank goodness. Of course, engineers (and scientists and alchemists) regularly sully this purity in applications—the (pure) explanatory model of Mathematics gets water down, tinkered with, adjusted, used, harnessed, &c, to achieve a particular desired outcome in Reality. This implies no critique; rarely, if ever, do the Ideal and the Actual coincide perfectly.

Presumably some might object to this framing. Imagine a screwdriver turning a screw, then. This works marvellously reliably even though (1) we know that at a quantum level neither the screwdriver nor screw “exist” in any sense we would agree warrants the term; (2) we know, if we bother to admit it, that the very fact of our observation has utterly skewed our vision of “whatever is really going on”; and (3) all of this must necessarily comprise an objectivist illusion anyway.

So mote it be. But these heady and weighty epistemological facts aside, on we go tightening the screw quite contentedly, like a bumblebee flying despite the “laws” of aerodynamics or the existence of planets that “contradict everything we know about planetogenesis”.

And what happens here: we take the fact that the tool works as evidence that our explanation of what is going on “is true”. Therein lies the ultimate error and conceit.

So, of course, where mathematics similarly “works” it offers the same illegitimate “proof” as offered by the screwdriver and screw. Again, we may ignore the heady and weighty issues lurking all around why it works, but only because we are pragmatically out to screw screws and don’t really ultimately care how it gets done. It seems a 50/50 likelihood anyway that our explanation must “be true” (or “be false”), so why not just flip a coin and proceed accordingly. Nonetheless, the fact that mathematics works (like a screwdriver) does not provide evidence that our explanation for that working has been justified.

Continuing the metaphor, just as we see that the screwdriver was made to fit (some attributable characteristics of the) screw, so we see that mathematics (in its practical application) was made to fit (some attributable characteristic) of Reality. In the absence of a screwdriver, for instance, one might use a wrench to turn the screw, or one might use a knife or claw, or one might simply twist the screw with a hand or tentacle, or one might hold the screw and turn the Reality one wants to screw down, &c. So also do the qualities of Reality (the encoding of Reality) permit all kinds of (mathematical) ways to “grapple” with it.

Meanwhile, one finds countless ways that mathematics remains absolutely daft about Reality. Mammalian reproduction demonstrates the impotence of mathematics as an explanatory principle, whether we fancy it as 1 + 1 = 1, or 1 + 1 = 3. Self-evidently, we can’t do everything with mathematics (and by mathematics, one might as well say “science” as well, especially to the extent it represents applied mathematics), contrary to what its proponents insist, largely because they want to increase their salaries, institutional vanity, or whatnot. Mathematics (and science) must necessarily encroach into domains where it doesn’t belong, just as “humanities” encroach into science and mathematics, &c.

But when we say mathematics was made to fit the Encoding of Reality, we cannot ignore the historical fact that someone Encoded that Reality. More precisely, we might proceed in this mathematical manner without bothering to figure out whether the Encoding of Reality is deliberate or accidental—and from a pragmatic standpoint, it doesn’t matter—but in terms of finding our ultimate freedom from determination, we cannot be so narrow-minded.

We might ask, therefore, what determined the Artist—was his work “made to fit” the Encoding of Reality as he found it? I think not, but that must be addressed in later sections (if at all).

What makes the Artist’s offering non-mathematical principally involves what I will call for now its “wilfully chosen character”. To put this one way, mathematics (and thus science), at least by intention, claims to be internally non-contradictory, i.e., self-consistent. In point of fact, mathematics contains no end of discontinuities, logical contradictions, bad decisions, and the like, but these remain visibly papered over (1) because several of such anomalies comprise more or less harmless or negligible problems, (2) the problems do not make their presence felt because mathematical application limits itself to the problems focussed upon, and (3) because mathematics explicitly fails in application in those areas mathematicians tend to avoid utilising it in.[2]

What mathematics shares in common with the Artist’s offering derives from its aesthetic character, i.e., mathematics requires (at least by declaration) a closed, interpretive loop—hence the often noted likeness between mathematics and language itself (or the insistence that mathematics comprises a language). By contrast, the Artist’s offering does not stand as constrained in this way, just as no artistic offering does. One may therefore object, on aesthetic grounds, to the introduction of Zeus into a romantic comedy, but this objection rests on criteria different from the sort of objection the appearance of Zeus—as a literal deus ex machina—would represent in a formal geometric proof.[3]

In direct contradiction to the mathematical way, error and contradiction form two of the most essential—or at least recurrent—tropes in the Artist’s palette, and all artists. These things are anathema for mathematics (and by extension, science). Less frequent, but in some ways with even more dire consequences, are the narrative or artistic floutings of “logical deduction”, which in the physical universe appears in the form of causality. In science, one never hears an end to the cry “correlation is not causality,” whereas in the Artist’s Work, mere sequence alone (as also with karma) seems enough to indicate “causality”. When one follows the word “the” with the word “sun” the very motion of language itself generates “the sun” in a way that seems definitionally contrary to the sort of empirical verification science especially relies upon.

Of course, in a formal geometric proof, as one goes from one line to the next, you construct a similar kind of sequence to “the” and “sun”, except that the linking between step A and step B follows with a kind of inevitable automaticity. To tell you “the” implies nothing about “sun,” except in retrospect, whereas to say that tall four sides of a parallelogram are the same length already strongly suggests we are in the presence of a square—or, even more clearly, not in the presence of a rectangle, a triangle, &c., &c. All that “the” tells us is we are likely to have a noun (or an adjective) to follow, but which one, we can hardly say. But even here, weird as it would be to have “the” be followed by a third-person past conjugation of a verb, only mere convention rules out this likelihood; an artist interested in messing with established norms might adopt this trope as a master strategy. And certainly after the fact—after we see “the ran”—then we might insist, “Ah, but that too was as fated as the content of a mathematical proof.” But with the geometric proof, such fatedness was long since been completed (certainly before we ever reflected on it; in fact, it didn’t need our reflection to “exist”); in such a proof, to “invent” really does comprise “to discover,” if only you have enough cleverness.

So, while the introduction of Zeus into a romantic comedy might amount to a fatal, aesthetic misstep, different in kind from a mathematical error during a geometric proof, nonetheless one might also find a way in the artistic work in question to make such an introduction work. I do not mean simply by this that some fans of the piece will adore the appearance of Zeus while others will find it absurd and off-putting. I mean, rather, that on an objective analysis of the piece, which many might insist is impossible in the first place,[4] we may judge the introduction of Zeus as a success or an error.

One cannot emphasise enough this difference. Mathematically speaking, once one says “point, line, plane,” then all that follows from those premises has already been stipulated even if not yet spelled out or made apparent, e.g., the qualitative features of parallel lines, rules about triangles, &c. And as soon as someone with clever enough eyes comes along, they will note that the claim about the universal qualitative characteristics of parallel lines (e.g., of infinite duration without ever touching) actually contains an ambiguity, so that spherical and hyperbolic geometries then suggest themselves. But even these later observations were already stipulated by “point, line, plane”—they only wanted invention, i.e., discovery. And just as (at least) three branchings of geometry came to light with the fullness of time at the point of the axiom about parallel lines, one might similarly uncover “invisible assumptions” in the characteristics of “plane” or “line” or “point” as well (no doubt some already have been). And as each of these bifurcates at their respective points, branching out into still further and stranger geometries, we will say that those too were simply awaiting their discovery.

Mathematics, as an aesthetic enterprise (particularly when it disavows the conceit of corresponding with Reality), has this “inductive” character: one states an axiom (or axioms) and then hunts down the consequences of those stipulations. Not so with artistic offerings.

Many critics (though rarely The Critic, so far as I can tell) like to expatiate breathlessly about the “inevitability” of a piece. In a poem, we might sometimes marvel at the aptness of a word or choice of metaphor, &c. But even here, a typically crucial aspect of the experience of encountering the work involves the surprise of that moment. Everything churns around in the narrative, and suddenly the word “seagull” or whatever drops like an albatross in front of us, and we find ourselves stunned, illuminated, gasping, or whatnot—marvelling at how perfectly “seagull” sums everything up, &c. We did not see it coming—or only suspected it as an unconfirmed possibility—but its arrival seems nothing more (or less) than the working out of a Fate we had not hitherto completely anticipated.

We should not mistake this experience for the sort of “inductive predestination” involved in mathematics, and even less so in language, which mathematics sometimes gets likened to. The sort of “inductive” pull we might identify in language involves those expectations learned from syntax, grammar, and conventional usage. If step 1 of a proof—like Aristotle’s oak in the acorn—implies all that follows from it, then syntax, grammar, and conventional usage offers something like this “inevitability”.[5]

More precisely, language does not have the theoretical perfect closure that mathematics does, principally because mathematics declares “meanings” (aesthetics) while language provides a “means” of expression. We frequently conflate these two things, understandably enough, but one may actually make additions to the (wholly self-referential) enclosure of language as one may not in mathematics, i.e., one may invent new tools (new words) but once those tools are made they afford a limited number of things they can do (applied meanings). This does not mean mathematics (and science) cannot increase in its quantity of knowledge, of course, but only that it cannot enlarge the terms of meanings it can generate.

This sounds like an overstatement and inaccurate, for this reason: because language generates the possibility of and capacity to embody new meaning, then the operation of mathematics itself can only find expression for that new meaning within the (closed) context it already inhabits. Or to put this another way: when mathematics (or science) experiences a paradigm shift, it does so because of an articulation and modification within the domain of language itself. In other words, someone draws a distinction (in language) and that distinction permits the expression of new meanings within the domain of mathematics. See the footnote.[6]

I say “language” for the sake of clarity, but I mean “expression” in its broad sense. Body language, dance, the honeybee’s movements to indicate the location of flowers, all of these rest in the domain of expression. The distinguishing trait of language arises in its conventionally shared set of meanings—or to put it tendentiously, “word” and “meaning” collapse into one another as identical; more accurately, the function of language permits an essentially seamless elision, however illegitimate, between “word” and “meaning”.

This (usually unconscious) collapse of “word” and “meaning” permits “language” to do a communicative kind of work that “dance” or “body language” or “theatre” often has trouble doing communicatively. I mean, of course, that if I wave my hand in a certain dance-like way, the chances that anyone understands this as “My name is Iridium” remain extremely low, unless of course I make this gesture toward people who understand this gesture in a conventional sense. To say the phrase “My name is Iridium” (or any of the virtually limitless other variations I might concoct (“My name is—that is to say, if I am going to go to the store later, I might as well pick up some kittens—Iridium”) still manages to “convey” my “meaning” almost regardless of the words.

The ambiguity of the pictorial arts, of sculpture, of dance—of those means of expression that do not include words—of course opens a vast area of play for artists who work in those media. Many have stared at the blotch of paint on the wall in perplexity and then found the title card, “The Soul of Hiroshima” beside it and felt a thrill of horror or whatnot—a clever, maybe merely clever, use of words to augment “visual only” sense data. But it shows the communicative power of language.

In the case of the Artist, part of his Work (or perhaps its thematics) consists of Language itself. That is, he not only “invented time and space” but he also invented (or redefined) “time” and “space”.

In any case, however, however much we feel the “genius” of an artist, the sense of “inevitability” when the word “seagull” drops in our lap has the force less of some sort of “inductive” characteristic that artistic work has in common with mathematics (and science) but points more to (1) the skill of the Artist in manipulating his or her audience, or (2) the acculturation of the audience to expected or conventional cultural forms. Here again, grammar, syntax, and the rules of linguistic construction all play an important part of that expectation. It provides a trap, in fact. If the peril of non-verbal art involves the attempt to bracket off the image so only the intended “meaning” comes across (assuming that is what you want), then the peril of verbal art involves the attempt not to isolate the word so deeply in its own hermetically closed saying/meaning that one’s intention, as an artist, becomes unsayable.

Much ink gets spilled about “where” the generation of meaning occurs vis-à-vis language. Does the reader construct the meaning out of the Author’s arranged words or does the Author impinge her meaning on the Reader? Or do neither, because language occludes both sides of that equation while simultaneously enabling something else. Or does even Language itself, like the Reader and Author, stand “in” Chaos, because Chaos itself provides the actual shared commonality amongst all four involved in artistic reception?

The point rather seems to concern rather the elemental differences between mathematics (as an aesthetic gesture) and the Artist’s work (as an aesthetic gesture). And the primary distinction concerns the endlessly interlocking “logical necessity” that mathematics claims above all else, whereas the artistic object requires no such explicit commitment. Thus, if Mathematics decries Art as worthless because it can mean anything, then Art decries Mathematics as tragic since it can only mean one thing.

In Art, expression follows expression (word follows word), one upon the next, like lines of a geometric proof, but nothing along the way makes the same kind of predictive or inductive claim for the artistic work. And precisely that lack of necessity permits—sometimes validly, sometimes not, often with depressingly pointless results—the Reader’s aberrant reading of even the most straightforward text.[7]

And so, the work of the Artist makes no claim of correspondence between the Work and Reality. This by no means means that “fiction” cannot express the facts and conditions of experience, of course; it simply means that the aesthetic object usually (and wisely when it does so) does not claim it “is true” in a logical senes. Thus, in general, the aesthetic object rarely loses sight of the fact that what it represents “isn’t” any truth (especially not in an autobiography), but primarily represents truths intead. Mathematics, by contrast (and science) proceeds more disingenuously.

This clear separation of Fiction and Reality (or Work and Reality) makes clear that what the Artist overlays over Reality has no necessity in and of itself. Like mathematics, it ideally remains self-consistent, but it has no obligation (and no ability) to make itself identical with Reality. Mathematics (and science) pretend otherwise, even as they fall over themselves denying it.

But in this first gesture of Art, then, we see already a window of possibility for freedom, freewill, and liberation—the Artist’s narrative remains just that, a narrative. In a kind of sense, it represents an only one, but not a necessary one, and thus not the only one in absolute terms. The simplicity of the solution here—simply tell another narrative—masks the difficulty involved in doing so, for the principal reason that the Artist’s narrative has defined the most elemental aspects of narrative: time and space. Or at least that’s the narrative we’ve encountered.

To approach this from another angle, while the Artist’s Work has no correspondence whatsoever with Reality (i.e., the substrate of Encoding it draws upon to construct its narrative remains untouched, even to this day) those who have been subsequently created within that Reality have inherited as a matter of their Being and Existence the Artist’s narrative. Just as Nonexistence called forth something different than itself (Existence), the narrative that the Artist inhabited called forth something different than itself (the Narrated, as well as the narrative in which we have all subsequently laboured, lived, loved, died, and been born again, and so forth).

More problematically than being unable to dismantle the Master’s house with the Master’s tools, we find as we build any alternative tool that it already belonged to the Master.

Still, against this difficulty, we see in the non-necessity of the Artist’s narrative—it didn’t have to be that way—that other ways, however hypothetical, remain hypothetically possible.


[1] My aversion to the use of the word “nature” borders on reasonable, but here needn’t occur a variation on the origins of my aversion. What I would note, rather: I would much sooner have written “Therefore, we must come to terms with the fact—ourselves each being omniscient—that the errors of omniscience must lie not in ourselves but rather in the qualities (or perhaps the quiddity) of omniscience itself”—but had I done so, not only would the sense of the claim have become unfamiliar (largely due to the word “quiddity”) but also because a certain kind of intellectual “work” or “symbolism” gets carried by the word “nature” that fails to come across with the word “qualities”. This suggests that the word “nature” (rhetorically speaking) performs a sleight-of-hand—perhaps even a bait-and-switch—that, I suspect, lies at the root of how sapient consciousness in particular get deceived about the most fundamental things. Perhaps later in these notes I will return to this.

[2] This doesn’t stop them from endlessly promising mathematics (or science) will finally one day penetrate the veil of these difficulties. Thus, the third point above is the claim, for instance, that mathematics fails to analyse Art, but this does not stop pseudoaestheticians from trying again and again sporadically from coming up with some dopey nonsense about mathematically modelled aesthetic meaning. The premises and conceits of this, in its various attempts, are too silly for examination in this context, but I simply refer to them by allusion. The second point above hinges on the pragmatism involved. Because, in the screwdriver and screw example for example, the “frame” of the application isn’t concerned with the micro-level of atomic clouds (in either the screw or the screwdriver), then the “mathematics” works here precisely because it has been fitted to work; its justification is entirely tautological.

[3] However compelling his “because I say so!” would be as a “proof”.

[4] The naïve and the poorly informed alike plentifully say much in error all the time.

[5] It is not uninteresting to consider this more closely. In the phrase, “you can lead a” we see how conventional usage dictates what comes next, so that when it continues, “you can lead a battalion, if you are an officer” surprises us. Similarly, the pull of subject-object agreement, or the linking of the definite article and a noun (or intervening modifier) also points to this “inevitably,” though linguistic production (or at least literature) makes a great deal of warping and breaking these things, much to our delight. And even at the level of the word: if I tell you I am thinking of a five-letter non-nonsense word in English that begins “KNOC” then there is only one possible letter that comes next. In terms of information, this means the terminal K is completely redundant; it serves a function only and strictly to confirm what one already knew with “KNOC”. At the same time, obviously, if we lift the stipulation that the word may not be a nonsense word or that it must be English, then other possibilities enter the aesthetic field that artists might draw upon, quite contrary to all grammar, conventional usage, or syntax. Mathematics has nothing like this freedom.

[6] I don’t wish to get into the wrong sort of hairsplitting, and so I banish this point to this footnote. At some point, to distinguish language from meaning becomes a reductio ad infinitum if not an ad absurdum. Earlier, I proposed that following its emergence from Nonexistence, Existence then declared the characteristics of Being. So too here, after arising out of Nonmeaning, Meaning then declared the characteristics of Language. Or again, only after we possess Existence may we declare the substrate of Existence (as Being). So just as Existence precedes Being, then Meaning necessarily precedes Language, and it is only after we dwell in Meaning that we declare the substrate of Meaning (as Language). Of course, there are manifold non-temporal and non-ontological creatures for whom these generalities fail to apply. Amongst “typical sapient Beings” (if the phrase makes any kind of sense), then the main objection to what I wrote above centres around that kind of experience as when one “has an idea” (a Meaning) and then tries to find a way to embody it in Language (e.g., by adapting an old word, or by a neologism) and so it will seem that Meaning generates Language (science generates the world) not the other way around. In the first place, some will point out that that “meaning” already dwells (necessarily) in “language” (or, more properly, some variety of embodied expression, whether verbal, linguistic, visual, kinesthetic, &c). If by “language,” then we understand “embodiment” in the broadest sense of the word, and we understand by “meaning” to be the “import” we ascribe to our activity or activities, then once again we see that only after we emerge from “meaningless” will Import declare the substrate of Import (as Embodiment). Insofar as we do not have “bodies” until we say we do—to invoke a privileged third-party point of observation only defers this question indefinitely—then once we have entered into this loop, of Existence declaring Being, of Meaning declaring Language, of Import declaring Embodiment, then we are always already forever “one step behind” it will seem. From our first moment of Meaning, we declare (as a kind of seemingly necessary hypothesis) Language as the substrate of Meaning, presupposing as we do that Language must have preexisted it. And from our first moment of Existence, we declare (as a kind of seemingly necessary hypothesis) Being as the substrate of Existence, presupposing as we do that Being must have preceded us ontologically. This does not follow. What preceded (as a hypothesis) Existence is Nonexistence; what precedes Meaning (as a hypothesis) is Nonmeaning. Or more precisely still, what preceded Existence is neither Existence nor not Existence, is neither Being nor not Being. &c. And so, to return to the point that prompted this footnote, because we assert that Language precedes Meaning (even as it is the other way around), then all possibility of meaning originates in Language—at least, that’s where we give the originating potential too. And so Meaning, thereby defers of shifts responsibility to Language, and it is in that sense that I insist that Language provides any and all ground for Meaning (and mathematics or science) to further articulate itself. At this point, to imagine a counter-factual to this would involve the emergence of Meaning not encoded in language—or, more generally—meaning that emerges as nonembodied expression, which is most assuredly difficult to imagine. Anticipating the end of this essay, I will say the most fruitful avenue from tracking down this weird idea arises when think of meaning that emerges in multiple states at once, e.g., as meaning that is simultaneously true and false, as a thought that is simultaneously not a thought (so to speak). More later.

[7] I should add, this brittle insistence on the non-entailment of word to word, sentence to sentence, paragraph to paragraph (or, most generally, expression to expression) in Art takes no account of the artist’s desire to build up a cumulative meaning (generally). But if a mathematician desires to build up a meaning (a proof), mathematics in itself (by design) requires not just absolutely elemental rules of operation but even very large macroscale operations that lock together definitionally and obligatorily. It is as if mathematics could do itself, in the absence of help from any sapience. Not so with Art. No sonnet will ever “compose itself” (however wu-wu and mystical an oracular-type artist asserts). Artists must explicitly build up the entailments of their compositions, even as they may also rely heavily and explicitly upon ready-made materials. Put a man and woman on a stage and most will anticipate a romance; let the author have one call the other “brother” or “sister” and that correction “resets” the meaning-building structure of the piece. &c

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