Lucretian Geometry (a speculation)

Is an hoop just a dot by other means?

A dot and an enclosed circle are certainly more dissimilar than a dot and a connected line in space (i.e. a hoop). A circle is an outline, a trace, history’s most pragmatic abstraction, whereas hoops, loops, Möbius strips – these more closely resemble the paradox of the dot.

If you think about it, dots are simply impossible: they’re either tiny (thick) lines or filled-in circles (i.e.:“a hair or a hairball”). Dots are uncanny.

Dots are not the same as points.

In Euclidean geometry, points are the beginning realities (so called one-dimensional space), but in fact they are complex abstractions of the imagination. If you think about how lines are defined as the shortest distance between two points, this is phenomenologically incorrect since in fact the lines include – or subsume – the points themselves. In this formulation, “point” – or dot – means “end,” an intangible concept denoting the place where a thing ceases to be a thing and instead becomes a not-thing, separated, void. Following Lucretius, who posits that the world is made up only of “bodies” and “void” (and no “third things”), an end is not an abstraction but the observation of void. Consecutively, points (vis-à-vis Euclid) are ill-defined abstractions that seek to make sense of impossible dots, and in turn, impossible realities.

In three-dimensional space, ends become edges, giving further shape to the Lucretian geometry of void and furthering the groundlessness of points.

But knives do cut, you may say.

Importantly knifes do not cut on their own, independently; they cut into other things. We say a knife cuts because we see an apple or a cheese wedge bisection at the point of contact with the knife’s edge. [Furthermore, there is no knife that is not a tool (or a consumer product), hence a further abstraction.] A cut is equal parts cutting-thing and cuttable-thing.

Though it possesses more verisimilitude, the Euclidean third-dimension is in a way the most problematic because it gives body to shapes but leaves out the energy, the vitality, the presence of thing-ness. Disappointingly, three-dimensional space is less-than inert. If you think about a stationary wheel (the one on your bike in the shed), it is not a circle in the third dimension (albeit with the accidental imperfections necessarily added to bring abstract shapes into actuality, through welded metal and molded rubber, etc.). What do wheels do but spin? Balls but roll? Blocks but impede? Pyramids but erode? Three-dimensional space is still abstracted “space” and does not represent “live” space. Motion – kinematics, not time – is the fourth dimension because movement necessarily resembles living bodies – living bodies in active relationships with other living bodies. [It is Lucretius not Augustine who first insists that time is insubstantial: “Time also exists not of itself, but from things themselves is derived the sense of what has been done in the past, then what thing is present with us, further what is to follow after. Nor may we admit that anyone has a sense of time by itself separated from the movement of things and their quiet calm” (On the Nature of Things, 1. 459-463, Rouse & Smith).] The Euclidean spectrum of x, y, z, t is both abstract (as opposed to descriptive) and ideological (as opposed to universal) as it attempts to present the sense of things as a heap of sensible things extra-dependent of nothing, where in fact objects are extra dependent of precisely nothing, of void, that allow for the presence and interactivity of other objects.

A hoop then has two conceptions, one in the third-dimension and the other in the fourth-dimension. A hoop, like a circle, has no beginning or end, except when we remember that a circle does indeed have a beginning (the abstract x center) and an end (the circumference dictated by d distance from x in all directions). Hoops in the third dimension have this same finite quality to them, only with added complexities of gauge and further demarcations shaped by their bloated edgings with void.

In the fourth dimension of kinematic geometry, however, hoops begin to assemble their symbolic association with infinity and no longer resemble the Gordian knot whose complexity is merely a complicit illusion. This is because a moving hoop, a loop looping, a shaping of objects into a material blur of non-beginning and non-ending, mirrors the velocity of experience. [A model Mobius strip then is really just a three-dimensional representation of the fourth-dimensional hoop.]

When a bus darts past your field of vision, it moves away in a linear vector defined in essence by the surface of the earth’s crust. If you are on a bus darting past Overland Avenue, the earth is transformed into blurring lines of light and matter. The bus stops and the experiential hooping of earth-things comes to an end. Just as waking and sleeping are not fixed points of experience but only definite matters in the abstract (a fact also mirrored in our entire existence of being here and then eventually not), these liminal continuums mirror the experience of being hooped.

Returning to the failures of three-dimensional geometry versus actual “live” geometries, all three-dimensional objects imply a spectral dissection dictated by their coming into contact with experience (i.e. with sense and reflection) and perhaps none so illustratively as a hoop. The are two ways a subject can be presented to a hoop: as a thing-that-hoops and as a hooping-thing. As a thing-that-hoops, it is a child’s hula-hoop or a metal bracelets – but a hooping thing can be any encapsulating space of varying thickness: a belt, a car, a department store floor, the woods, etc. Life cocoons experience, but observers – others – are finite, specifically our widths, even just the space of a brain synapse, or an atom. A loop is a tube in the moment. A moment in a tube is a container. In life, the wild is counterintuitively a confined space. Our conceptions are always-already limited, yet simultaneously more complex than their abstraction attempts to conceal.

Back to the original question: Is a hoop just a dot by other means?

If you go fast enough, all shapes turn to lines, and if you are constantly moving then what’s the difference between the continual line connected in space (a hoop) and a dot? At top speeds, dots become indistinguishable from hoops, not to mention other dots. Dots – not points – are live space when they are blots, spots, smudges, spills, drops – all synonyms of human accident. The information age devalues uncanny dots and their vicissitudes because they avert the binary codes of mobility.

Quote #9: Timothy Morton (2013)

I start the engine of my car. Liquefied dinosaur bones burst into flame. I walk up a chalky hill. Billions of ancient pulverized undersea creatures grip my shoes. I breathe. Bacterial pollution from some Archean cataclysm fills my alveoli—we call it oxygen. I type this sentence. Mitochondria, anaerobic bacteria hiding in my cells from the Oxygen Catastrophe, spur me with energy. They have their own DNA. I hammer a nail. In consistent layers of ore, bacteria deposited the iron in Earth’s crust. I turn on the TV and see snow. A sliver of the snow is a trace of the Cosmic Microwave Background left over from the Big Bang. I walk on top of lifeforms. The oxygen in our lungs is bacterial outgassing. Oil is the result of some dark, secret collusion between rocks and algae and plankton millions and millions of years in the past. When you look at oil you’re looking at the past. Hyperobjects are time-stretched to such a vast extent that they become almost impossible to hold in mind. (58)

From Hyperobjects: Philosophy and Ecology after the End of the World.

Word #8: “phyllotaxis” (n.)

noun. [Botany]

  1. The arrangement of leaves or other lateral members (e.g. the scales of a pine cone, the florets of a flower of the family Asteraceae ( Compositae), etc.) on an axis or stem; the geometrical principles of such arrangement.

Below are mathematical functions for variant phyllotaxis shapes found in organic structures, and, even more fantastically, their nomenclature.


Quote #6: Alexander von Humboldt (1808)

New forms, too, enter the common treasury of language. The speech of humans is enlivened by everything indicative of natural truth, be it in the representation of sensory impressions from the outer world or of profoundly stirred thought and inner feelings.

From the 2014 edition of Views of Nature translated by Mark W. Person and published by University of Chicago Press. See this week’s earlier post for more on von Humboldt’s radical ecosemiotics written more than three decades after this passage.

Humboldt contra Saussure

On the advice of Andrea Wulf, whose The Invention of Nature: Alexander von Humboldt’s New World makes for stellar reading, I’ve been pouring over the German polymath’s seminal texts, namely Cosmos, Views of Nature, and Essay on the Geography of Plants. Wulf wonderfully weaves not just a kind of “Greatest Hits” of the once-infamous, since-obscured writer/thinker but delves deeply into his dense works (it helps that they are evocative and poetic to begin with) – including mentioning his theories on language. Besides Simon Winchester, who turned the history of the OED first into a British caper film a la The League of Gentlemen or X-men and then a Gothic murder mystery, I don’t know other bestsellers who openly discuss semiotics for pages and pages. More to the point: I’ve read a great many of those 20th century theories of language in vogue after the second World War, and I can’t recall a single mention of von Humboldt (even from the French, who happily hosted him even while Bonaparte was lobbing cannons at his Austro-Hungarian Empire!).

Something Wulf fails to mention explicitly (though perhaps it is the reason why she couldn’t just fail to drop the subject altogether) is that von Humboldt’s theories of language appear throughout his works; they are sporadic, but consistently sporadic.

Here are some of the heaviest sections from the introduction of Volume II of Cosmos (representing his later work from 1844, but which I randomly read first; cool fact from Wulf: he debated naming the book Gaia, especially ironic considering Wulf and other Humboldt scholars have indicated that the “pre-Darwinian Darwinist” suggested the Gaia theory of a living Earth a full +125 years before it caused a rage amongst environmentalists in the 1970s, where it is still customary to direct attribution):

Exploded errors may survive partially among the uneducated, aided in some instances by an obscure and mystic phraseology: they have also left behind them many expressions by which our nomenclature is more or less disfigured; while a few of happier, though figurative origin, have gradually received more accurate definition, and have been found worthy of preservation in our scientific language.

In a far more interesting way that I am accustomed to reading – and, importantly I think, without using the terms – he is talking about dialects, regionalisms, and slang. He continues:

That which sense grasps but imperfectly offers a free field to creative fancy; the outward impressions change with the changing phases of the mind; and this without destroying the illusion, by which we imagine ourselves to receive from external nature? that with which we have ourselves unconsciously invested her.

This is, to my recollection, a much more dynamic dialectical observation than Ferdinand de Saussure. The Swiss structuralist simply argued (and much later) that there’s no internal logic to a word referring to a thing; signifiers are relational to other signifiers in a linguistic system and not to the external world of contingencies (remember: from de Saussure we get the surrealistic, anarchical interplay of signifier and signifier à la Duchamp). Humboldt, too, is no essentialist, however he sees language not akin to a priori reason or something mechanical that ultimately has no meaningful interplay with the natural world (after all, he writes further on in the introduction, “[t]he impression produced by the grandest scenes of nature does not depend exclusively on height;” here, like Saussure he severs the external world from its cultural overdeterminacy). Rather, the functionality of language ignores (or has amnesia about) just how intimately connected it is to the signified (but not in positivist or predetermined ways). What he is articulating is very delicate and even circuitous and sounds kind of mystical (he even uses the term), but I think he’s trying to say, building on Kant and The Critique of Pure Reason, that human language has a role in natural world: this is a radical idea even today, let alone in 1844.

His clearest articulation of his “organic structure” of language is the conclusion to the introduction:

Words, therefore, are more than signs and forms; and their mysterious and beneficent influence is there most powerfully manifested, where the language has sprung spontaneously from the minds of the people, and on its own native soil.

Precarity and its Sponsors

When you drive as much as I have this year, sometimes you forget exactly what germinates a line of thought, even an obsessional line of thought. All you know is that you were driving at the time. The image I’m reminded of appears off the main road – it might actually be Main Street – to and from Catskills High School off the NY Thruway: there are beautiful views of the mountains cut in zigzags by rust-belt industrialization, a towering railroad bridge, decrepit estates hugging eroded cliffs, businesses racked by plywood, exhausted human beings. My thought, barreling through beauty and blight, is that while it’s cliché to note how cities are alienated from the natural world, there’s barely a city on earth whose locus isn’t a river, a bay, a lake, a shore—and isn’t that a contradiction? March’s issue of Harper’s features a piece by Elizabeth Royte called “The Hidden Rivers of Brooklyn” about urban spelunking and the search for ancient waterways trickling up in New Yorker’s basements. Only a few months after this recollected I time, I moved to a coastal city, which is, topographically speaking, where you’ll find half of humanity on a given day. Long story short, I don’t know why I am fixated on this absurdity of Modernity where, although we predominantly inhabit the world in indifference to or defiance of our natural surroundings, we predominantly  do so at exactly those geographical spots where nature is its most animate and fertile and chaotic and wondrous.

I’m continually fascinated (and a bit perturbed) by how between the disciplines there are many different names to talk about the same thing; this can be instructive, like a kind of academic Rashomon, but also a kind of decadence where a discipline is simply air-guitaring with newfangled jargon (think Silicon Valley). In my reflections above, I am leaning on the words “contradiction” and “absurdity” – which in other disciplines can be referred to as conflicts, paradoxes, tensions, antagonisms, negations, on and on. In France during the Occupy Wall Street heyday, protestors began using the term “precarity” to name what it was they were protesting (OWS in Zuccotti Park were heavily criticized by sympathetic know-betters who said they needed to adopt a platform so they could achieve a tangible result from their work). Precarity in many ways speaks to being stuck driving-while-thinking, and thus unable to write down one’s thoughts (a sociological study of Cuomo’s 91 texting zones or so-called “Text Stops” would be fascinating to read; commissioning the NSA to produce a Humanities study with their illegally mined data and not military-industrial reports would be an interesting act of bureaucratic atonement). Precarity also is exactly the name that fits Deborah Brandt’s definition of literacy in her deeply insightful paper, Sponsors of Literacy. Brandt writes,

“literacy as a resource becomes available to ordinary people largely through the mediations of more powerful sponsors. These sponsors are engaged in ceaseless processes of positioning and repositioning, seizing and relinquishing control over meanings and materials of literacy as part of their participation in economic and political competition. In the give and take of these struggles, forms of literacy and literacy learning take shape.”

Throughout 2016, the question of just what is “literacy” has proven vexing, but Brandt seems to see fluctuating inconsistency as a key feature of literacy, which has all kinds of repercussions for the initial frame of inquiry.

By focusing on the “sponsors” of literacy, Brandt is smartly consolidating a lot of politically-charged language into a term new in this theoretical form: patrician philanthropy, corporate advertising, community organizing, social customs, wealth concentration, resource distribution, political representation, family structures, on and on. Importantly, Brandt’s personified literacy sponsors are not necessarily intentional actors, nor are literacy practitioners self-consciously intentional in a given literacy’s formation, practice, or outcome. I think because of this point of sponsorship, literacy is sufficiently distinct from Dewey’s “education is life” algebra (i.e., education happens, thus literacy is enabled). The following quote is an extended list of this unintended enabling and its outcomes (which now becomes hard to distinguish from what we call “the world” or “history”):

This analysis of sponsorship forces us to consider not merely how one social group’s literacy practices may differ from another’s, but how everybody’s literacy practices are operating in differential economies, which supply different access routes, different degrees of sponsoring power, and different scales of monetary worth to the practices in use. In fact, the interviews I conducted are filled with examples of how economic and political forces, some of them originating in quite distant corporate and government policies, affect people’s day-to-day ability to seek out and practice literacy. As a telephone company employee, Janelle Hampton enjoyed a brief period in the early 1980s as a fraud investigator, pursuing inquiries and writing up reports of her efforts. But when the breakup of the telephone utility reorganized its workforce, the fraud division was moved two states away and she was returned to less interesting work as a data processor. When, as a seven-year-old in the mid-1970s, Yi Vong made his way with his family from Laos to rural Wisconsin as part of the first resettlement group of Hmong refugees after the Vietnam War, his school district which had no ESL programming-placed him in a school for the blind and deaf, where he learned English on audio and visual language machines. When a meager retirement pension forced Peter Hardaway and his wife out of their house and into a trailer, the couple stopped receiving newspapers and magazines in order to avoid cluttering up the small space they had to share. An analysis of sponsorship systems of literacy would help educators everywhere to think through the effects that economic and political changes in their regions are having on various people’s ability to write and read, their chances to sustain that ability, and their capacities to pass it along to others. Recession, relocation, immigration, technological change, government retreat all can-and do-condition the course by which literate potential develops.

In this way, we are always the authors of our natural disasters since, after all, nature cannot destroy nature but merely makes itself look different. Education seems to become another of these “tensions” if not an outright contradiction: it aims to make people not just aware but knowledgeable of the literacies that they are already practicing, while also making them aware of the literacies of others because by doing this they will become more knowledgeable about not just their own literacies but the nature of their sponsorships, whether governing or precarious.

On Memory

When one speaks of memory, they more often than not mean one of two things. Memory refers mainly to 1) the ability of recalling to mind past experiences, knowledge, and even vague, seemly unformed ideas, like half-dreams, or illusory sense details; or else 2) the conscious, here-and-now presence of those exact thoughts upon the person. With this second meaning, memory is experienced as the opposite of an ability (like trying to remember the digits of π, or the trivial order of U.S. Presidents, etc.) and connotes instead a kind of involuntary mental flash, an unprovoked assault of emotions, remembrances that well up as though cast by a spell (or, as Proust attests, an olfactory spirit), thus triggering an unintentionally potent emotional consciousness, itself unpredictably recalled. Memory is a human enterprise as much as it is an alienating shock to the system. The question then arises as to whether this is a case of one word meaning two separate experiences – two unique phenomena – or whether these oppositional characteristics are both, paradoxically, essential features of this profound thing we call memory.

Evoking the concept of memory, Francis Bacon in The Advancement of Learning describes two categories of student assessment practiced in medieval universities (by way of being critical of their supposed distinction): verbatim and ex tempore. Verbatim (still in our colloquial) denotes the quoting in complete passages of existing discourse in order for students to buttress the persuasiveness of an argument or stake directional paths through logical conundrums. This oral feature of ancient societies is today often distained as rote, insulating a kind of automaton-like inhumanity, even though what has replaced the by-gone culture of oral memorializing is one that leaves all data collection and storage to an entirely externalized machine (more often than not, one branded Google). Humanity in effect is perhaps now nothing but the retrievers of answers; we are the dogs of microchips.

On the other hand, ex tempore (modified in the adjective/adverb form extemporaneous/ly) responds to prompts and academic quagmires through more personalized, off-the-cuff remarks designed to highlight either a learned mind or an ignorant one, a sharp philosopher or a stumped lollygag. Ex tempore refers to the impromptu – what Bacon calls “present” (anticipating Bergson’s vitality) – spontaneity essential to human culture that should not be overlooked by grand systems of organization, least not education.

In a surprisingly modern twist, Bacon goes onto the argue that poetry (“poesy”) is evidence that even the presence of blocked intellect (i.e. one who fails at both verbatim and ex tempore) does not prove the quality of mind:

Poesy is a part of learning in measure of words for the most part restrained, but in all other points extremely licensed, and doth truly refer to the Imagination; which, being not tied to the laws of matter, may at pleasure join that which nature hath severed, and sever that which nature hath joined, and so make unlawful matches and divorces of things.

In other words, the existence of poetry is proof that this complimentary duality of verbatim and ex tempore is in no way comprehensive of the human mind (or the so-called “domiciles” of Early Modern understanding: Memory, Rationality and Imagination). Herein, memory’s disputed territory is further obscured by its conceptual collision with Imagination, or invention: “unlawful matches” “not tied to the laws of matter”. This creative hybridity is something usually not associated with a memory, until of we realize that, in an age where reference to Rashomon is commonplace, this dynamic understanding of memory as not mere recall is hardly controversial. The concept of a “mnemonic device” is another classic example of how correlative data requires an element of fantasy in order to work with any consistency. The advent of clockworks and increasingly complex navigational tools during this period further lead to Bacon’s pre-Romantic notion that Nature was a machine – a kind of God-clock – of which human endeavors work to uncover little-by-little proof of its ingenious intricacies. No wonder then that Romantics (after Alexander von Humbodt) insist poetry (and the Arts in general) is essential for any scientific understanding.

Applied to the phenomena of memory, memories are analyzed not because they exist but because they are experienced. As much as the research sciences delve into the human mysteries of memory (through neuroscience, the psychological study of PTS and trauma, AI and cognitive robotics, etc.) there will still exist the profound need to creatively express our memories in words, in language, in songs, and in poems. The conundrum then of the contradictory definitions of memory is not located internally in their descriptions per se, but in their non-poetic state, in their failure to account for the creative imperative of memory.