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 #12: Jean-Baptiste Dumas (1844)

Vous voyez qu’à la considérer ainsi, la machine animale devient bien plus facile à comprendre ; c’est l’intermédiaire entre le règne végétal et l’air […] (Essai de statique chimique)

[Translation (from Art and Ecology in Nineteenth-Century France by Greg M. Thomas): “the animal machine is [simply] the intermediary between the plant kingdom and the air […]”

On Waves and Cycles

In political science – and the social sciences in general – there is a perennial debate about the character of change – whether change comes in waves or if instead it is cyclical. This is most prominent in discussions clarifying and giving shape to the nature of revolution, a focal concern in the West since first Mercantilism and then Enlightenment triggered modalities of regicide, revolt, and rebellion across formerly feudal Europe, thus paving the way for republicanism, parliamentarianism, representational democracy, and other liberal and self-governing forms of government in tandem with rational (and irrational) arguments against divinized hierarchies and monarchical power [NOTE: our newest augmentations to participatory governance were shaped to accommodate the Industrial Revolution and, even more recently, the Digital Information age; exactly what these tweaks were (beyond a widening definition of citizen) and their larger significance remain contentious and on-going]. A historical generality can be drawn: anything which hampered (or seemed to hamper) the cultural flow of the age (be it the flow of goods, ideas, capital, binary code, etc. ) was seen as a form of tyranny, a word that still today harkens back to the authoritarian rule of unchecked kings, and sentenced (sometimes swiftly, sometimes haphazardly) to be lopped-off. The debate between waves and cycles has to do with explaining the continuity of tyrannical hampering (i.e. Why does authoritarian injustice keep bubbling up after both rhetorical advancements and cultural practices – even laws! – become bedrocks of developed civilizations?) – and the always-recurrent response or corrective to privileged impingements, now ambiguously referred to simply as “change”. Is change seasonal, or is change generative?

This well-known dualism is strangely united in its use of ecologically-centered metaphors. Waves are as well known a natural phenomena as any; when one thinks of how metaphorically they apply to political analysis of revolutions, it is hard not to think of Katsushika Hokusai’s “The Great Wave off Kanagawa”. The idea is clear: the phenomenon is a one-off swelling tied to the contingency of the moment (the political philosophy of Alain Badiou and his notion of the “Event” seems closely related). On the other hand, the cyclical or seasonal metaphor is equally rooted in ecological consciousness. There is in fact no true cycle outside of the natural world, merely analogies, or else a mechanical rotation, which is a synthetic (robotic) imitation/doubling of a cyclical process. Claude Monet’s “Haystack” series is illustrative of the idea as it relates to our understanding of historical revolutions: different but not different; each historical event offering up a variant refraction of another (or all others); slight shifts sometimes apprehended imperceptibly, other times seen as unheimlich. The issue that these ecology-minded metaphors pose is that ecological change is essential to explain socio-cultural change, yet at the same time, it is ecological change which is now the tyrannical thing. This the case whether one is a tree-hugging environmentalist or a hoax-mongering conspiracy theorist: ecology – including the ecological forms of waves and cycles – hampers cultural flow. Social and political change in an ecologically terrifying world has, therefore, paradoxically lost – or is in the process of losing – its metaphors.

The problem is classic chicken-and-egg algebra, and not unlike etymological questions that surround ancient myths. Take the word odyssey as a structural example: Homers’ Odyssey is the story of Odysseus’s great odyssey. When we use the word odyssey now, are we using a word that is itself being poeticized by the Greeks, or is it only after the story of Odysseus that we then use the word that first referred to Odysseus’s-quest to now mean epic-journey? (This is an especially improbable head-scratcher when you think about how many hundreds of years the story was orally circulated before it was finally transcribed) Is The Odyssey a story of a prescribed word or a word born of a story? In political and social terms, global warming has returned us to a place of similarly uncertain origins, a “nonlocality” where historical causalities seem to have arrived in a state of suspended animation.

Seneca unwittingly points to such a suspension or gap in On the Shortness of Life:

Men are tight-fisted in keeping control of their fortunes, but when it comes to the matter of wasting-time, they are positively extravagant in the one area where there is honor in being miserly.

This quote pops with irony in our age of click-bait, fake news, and touch screens, but his simple point (Why waste your life?) is undermined by something more deeply disturbing: Is life nothing more than wasting-time? David Foster Wallace’s repetitive use of “wastoid” in The Pale King makes this point well: something at first mocking becomes descriptive and in the end a poignant rephrasing of “human”. Importantly, both Seneca and Wallace still rely on an ecological metaphor to shape their rhetorical/poetical expressions, as the abstraction of time is not mechanized without the observable change of the natural world, in this sense wasting, decomposition, decay. The day before last, Stephen Hawking said we wastoids have roughly one more millennia to whizz toward another rock because this one won’t fit the bill. It is hard to imagine a future where technical marvels advance while the foundations of our understanding of the world – the world itself – becomes violently uninhabitable.

Word #10: “glottochronology” (n.)

n. [Linguistics]

  1. The application of statistics to vocabulary to determine the degree of relationship between two or more languages and the chronology of their splitting off from a common ancestor.

Or, as its conceiver Morris Swadesh hypothesized, “[i]f we can show by means of comparative linguistics that various people spoke similar languages sometime in the past, we can infer the identities of those predecessor languages, and thus even more intimate connections between all human cultures … arriving eventually at an original tongue” (quoted in About a Mountain, 126)


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 #7: John D’Agata/Vic Baker (2010)

Vic was in a safari hat and sandals an white athletics socks, and as we spoke in his office one late fall morning he looked over my shoulder into lamp without a shade.

“People have this really weird conception of science,” he said. “They think that it’s the one reliable source for information that we have. They think that even if their public leaders and not to be trusted, and their newspapers are inaccurate, and cultural and religious morals are treacherously shifting, that science, at the very least, will provide a stable compass. But the problem is that science can’t do that. Science is alive, it evolves. It occasionally establishes a fact, but, if given enough time, it’ll probably refute that fact. Remember when the Earth was flat? Remember when the sun and all the other planets spun around the Earth? Remember when humans became sick because the gods were angry with us? Science just uses a kind of rhetoric that sounds authoritative. Just like any other form of communication, however, science is susceptible to abuse, inaccuracy, and just bad interpretation. And that’s what’s wrong with Yucca. The public wants o have some assurance that all this waste that we’re producing is going to be safe in that mountain. So the Department of Energy creates all these computer models to try to prove that that’s the case. They measure and measure and measure and measure till they get the results that they want. And then whammy: Surprise! Their computers predict that everything will turn out fine at Yucca Mountain. Phew!”

He pulled the left sock on his left foot up.

“Well, I’m sorry,” said Vic. I’ve got news for everybody. Our descendants are going to live in a reality in the future; they’re not going to live in a computer simulation.”

And then the other sock.

“The problem with wanting unwaveringly definitive results from science is that whenever we say we have an ‘answer,’ we also tend to believe that we’ve revealed some sort of ‘truth.’ But real scientists don’t settle so firmly into answers. They always leave a little wiggle room for new evidence to change their minds. The very fact that we still even have something that’s called ‘geology’ is an indication that we admit that we don’t have all the answers. That we’re still investigating.”

From D’Agata’s About a Mountain (W.W. Norton, 110-111).