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A stone-thrower’s spacetime
A 64-year-old man in sunglasses and a powder-blue overshirt throws a stone at a barbed wire fence. Beyond that is a blue and white watchtower, in which there are soldiers – or not. A photograph of this, taken on 3 July 2000 near Fatima Gate: a border post, south Lebanon.
This will serve as our datum, with all time and space coordinates measured against this moment. A stone-thrower’s spacetime, anchored to a non-event.
In New York City, sixteen days and > 9,000 km away from where the photograph was taken. American and Israeli journalists accuse the thrower of participating in a stoning. The photo becomes evidence of his participation in a daily ritual of violence – against a fence, a watchtower, a border post, an occupying army. Proof of barbarism. In rebuttal, the stone-thrower declares the incident “basically trivial”. Trivia: information with little or no value. Mathematically, a solution readily obtainable from the context, a claim with no need for proof. The stone-thrower suggests that “one stone tossed into an empty place scarcely warrants a second thought”.
According to various dubious sources, 3,020 years before this photo and 180 km south of what will eventually become Fatima Gate, a young shepherd slings a stone at the forehead of a giant. David, the canonical stone-thrower. After his stone comes the giant’s own sword. A Goliath beheaded. The shepherd becomes a giant-slayer, the giant-slayer becomes a symbol for the weak. The trouble of smallness: a stone gathered from the ground is a tiny thing, a shepherd smaller still in the face of a giant. All this in walking distance from another border, the 1949 Armistice Agreement line – green. Beyond that, Hebron, the West Bank. The Oxford Learner’s Dictionary describes a giant-slayer: a small or weak person or organisation [which] tries to defeat another much larger or stronger opponent.[1] An allegory for justice.
Around 370 years before our stone-thrower – a painting by Artemisia Gentileschi of the shepherd, conventionally depicted without stone in hand, sitting on the severed head of the giant.[2] The painting itself recovered from the injustice of memory. The giant’s sword, prominent in the frame as a symbol of strength. The stone, a symbol of the weak, missing, unseen.
Another painting, again stoneless, with sword proud – and another, and another. The most famous depiction comes 496 years before our thrower. A stone-thrower carved in stone, big-headed in cut marble, sling in one hand, the other hand oversized with fingers curled into a stone-holder’s gesture, but still without stone. A secret weapon, or the ongoing suspicion of one.[3] Perhaps our stone-thrower’s defence holds: “one stone tossed into an empty place scarcely warrants a second thought”.
Second thoughts, a kind of post-sight. An anonymous letter written in December 1976, 25 years before our stone-thrower. A rock-throwing account, published in 2015 by the Guardian, reads:
“Hundreds upon hundreds of students lined Klipfontein Road. The cops had used force to disperse them which infuriated onlookers. Then the rock-throwing began… The cops baton charged them again. They dispersed. Whistles could be heard all over and regrouped again. By now the kids were really angry. They started up a chant. ‘We are not afraid to die. We shall sacrifice.’”
New York, March 2001, eight months after the stone is thrown. Another defence by the stone-thrower proceeds, meekly: “It was a pebble”. Inoffensive. A “symbolic gesture of joy”.[4] Eight months before that, New York still. 19 July 2000. A declaration against the stone-pebble-thrower: “there is no such thing as ‘symbolic’ rock-throwing just as there is no such thing as a ‘symbolic’ stabbing or shooting”.[5]
A rock-stone-pebble is a physical object, a contiguous collection of matter constrained by a defined boundary. A mode, a way of describing a collection of masses. A rock-stone-pebble-thrower is a system in which multiple objects interact. A way of describing a potential transfer of energy. This is not an abstract metaphor but one description amongst many.
There is no reliable formula to reproduce co-incidental pairings. Two or more incidents intersect, combine, correlate. A small pebble flies through the air in accordance with Newton’s laws of motion. Acted upon by a force equal to its acceleration multiplied by its mass. The arc of the pebble is described by the interaction of planetary gravity with the mass of the stone, the thrust of the throwing arm (145 kph maximum) and the drag resistance of the surrounding atmosphere. Each factor described by other forces – the ambiguities of time, the indeterminacy of speed and position. Rules of thumb. Intra-actions. In classical mechanics, everything governed by the laws of physics occurs within a structure of time reversal symmetry (T-symmetry). The calculations that describe physical events work both forward and backward through time.
44 years before the rock-stone-pebble is thrown. A story told by my mother. Her own grandmother – on 9 August 1959 with 20,000 other South African women – stands silent for 30 minutes outside the Prime Minister’s office. Then, fists raised (a stone-holder’s gesture), they sing a freedom song newly composed for this occasion:
Wathint` abafazi, Strijdom!
Wathint` imbokodo uzo kufa!Now you have touched the women, Strijdom!
You have struck a rock(You have dislodged a boulder!)
You will be crushed!
Amidst the ongoing search for an appropriate term – rock, stone, pebble, boulder – frustrated by the problem of translation. Seventeen years after the rock-stone-pebble, 2017. Raafat Majzoub, artist, architect, writer, builds a garden of forgiveness out of stones in Beirut, Lebanon. Raafat’s subtitle: How to own a land that can not be stolen.[6] A conversation in Paris, undated: une pierre n’égale pas un rocher.[7] The problem of giving name to a geo-ethical proposition, projectile, propulsion. A piece of the ground, a massive thing, tiny enough to fit in a single hand. Land, the verb. A nomenclature for insurrection. No specific name, only a naming, the ongoingness of a stone becoming. And the uncertainty of it.
To throw is human. Amongst primates, the mechanics of our bodies reveal selection for this action. According to Lieberman et al., this is because we have “a slender flexible waist, [which] allows us to twist the torso in relation to our hips and legs, and a twist in the shape of the humerus, the bone that connects the shoulder to the elbow.”[8] What came first, the ability or the need? The upper limit of human throwing speeds is about 40 metres per second. A million kilometres away from Earth, 99942 Apophis – a stony-type asteroid named after Apep, Ancient Egyptian serpent god of uncertainty, chaos and unbecoming – moves toward the Earth at 30.73 kilometres per second.
99942 Apophis, approaching.
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Precovery
Astronomers continually search old images of the night sky, seeking to make ‘precovery’ – or pre-discovery recovery – observations of SSSBs. Small solar system bodies: the recent technical term for celestial bodies including asteroids, comets, minor planets, and other irregularly shaped objects. Precovery is a practice of digging through residual data, the backgrounds of images and other superfluous material produced in the process of doing other, unrelated, astronomical work. Looking for as-yet-unperceived objects in existing observations. Reprocessing noise to locate signals which were always already there, in what Moten calls, our “supersensible and nonsensical surround”.[9] Surrounded. In a perception space overdetermined by the fact of observation – the regulation of apparition – precovery suggests the necessity of an alter-perceptive programme. A haunting. A backwards propagation of perception as a necessity for a forward projection of the perceived object.
For astronomers, the aim is to determine an orbital solution for a given object. To know where this object will be in the future. And, for certain objects on particular trajectories, to know whether we – this planet – will be there at that time too, or not. The task is prediction. Within the framework of orbital mechanics, path prediction is rendered as a mathematical problem dependent on observational data over time for its solution. Within the framework of observation, data is an archival problem dependent on interest and intention. The data always contains more than it appears to. Looking, as a matter of course, is never innocent. Within a signal-seeking practice, the problem is always noise and the elimination thereof. For precovery, noise is the ground of possibility. The less constrained the archive, the wider the field of view, and the higher the potential for recovery.
Recovery suggests the repossession of something we once had. A lost thing. This, in the history and present of SSSB determination, is a key practice. For example, the recovery of the dwarf planet Ceres eleven months after its initial observation by Giuseppe Piazzi, the recovery of Neptune 234 years after its initial observation by Galileo, or the recovery of the Jovian moon Ganymede 1,975 years after its observation by Gan De. This kind of recovery is still the case for lost NEOs (near-Earth objects) observed once, but subsequently lost.
Pre-discovery recovery also refers to the practice of actively searching for observed objects in records not traditionally considered archival – i.e., non-Western celestial records, cultural archives, etc. In all cases, the precovery reconfigures the sequence of perception and observation. To see is not necessarily to know. Any observation contains in it more than the observer might recognise. There are ways of looking that do not see. And perhaps most critically, what has been seen can be seen again, differently, with different eyes. A helical structure of perception. An asteroid approaches. It always has been approaching.
On 27 December 2004, four years after our rock-stone-pebble is thrown – a precovery observation of images made nine months earlier, on 15 March 2004, provided new data on NEO 2004MN4. Combining this precovery observation with so-called discovery observations made on 19 June 2004, astronomers were able to derive an improved orbit solution for 2004MN4 – otherwise known as 99942 Apophis.
The non-sequential structure of the perception of NEO 2004MN4 is standard in identifying SSSBs. The period between the earliest and latest observation (called the observation arc) determines the accuracy of an orbital solution (the astronomical computation of the path of an object travelling through space). 2004MN4’s first orbital solution described a perturbed orbit which put the asteroid on a collision course with the Earth. With impact scheduled for 2029, this immediately made 2004MN4 the most potentially hazardous object ever detected.
Precovery and ongoing observation of 2004MN4 produced a reliable orbit solution, triggering a ‘numbering’ – the attribution of a permanent number based on sufficiently securing its orbital path – and a ‘naming’. For 2004MN4, this permanent designation is 99942 Apophis. This name tells us that it is the 99,942nd designated minor object since 1 Ceres’ discovery by Piazzi in 1802. Or, more accurately, since the introduction of a naming-numbering system based on sequence of discovery for small, star-like bodies in 1892.[10] These observations of 99942 Apophis indicated a very high chance of colliding with the Earth on Friday the 13th (spooky) of April 2029, and again in 2039 and 2068. This is a sequence of probabilities, not multiple impacts. 99942 Apophis can only impact the Earth once, catastrophically, but the orbital equations don’t know this. In December 2004, 99942 Apophis was placed at level 4 on the Torino Impact Hazard Scale. By 2005, observations of 99942 Apophis ruled out a 2029 impact by a probability of 98%. 2039 and 2068, however, were still potential impact dates. Observations by the Goldstone Deep Space Communications Complex in 2013 ruled out the possibility of a 2039 impact. However, simulations in 2013 suggested that non-gravitational effects could lead to a 2068 impact. By 2021, Jet Propulsion Lab observations had reduced the uncertainty of 99942 Apophis’s orbital path and eliminated any chance of it impacting Earth in the next 100 years. This knot of solutions, revisions and re-solutions, like the orbital paths they describe, twist and turn as they encounter new (or old) observations. On its 2029 close approach, 99942 Apophis will pass within the ring of geostationary satellite orbits, closer than a weather satellite, but not close enough to hit the planet, yet. Its ‘perturbed orbit’ will keep it on the Minor Planet Center’s list of Potentially Hazardous Asteroids for thousands of years.
On 21 February 2021, at 8:22am UTC, 99942 Apophis was removed from NASA’s Sentry Earth impact monitoring list. An asteroid approaches, misses. For now.
- The worldlessness of rocks
12 October 2021. 21 years after our rock-stone-pebble thrower. Panashe Chigumadzi writes:
“‘Ilizwe lifile!’ The world is dead! Our ancestors cried as the 1779-1879 Wars of Dispossession expanded the reach of 1652’s settler colonial conquest deep into the South African interior. Our ancestors cried that it was not only Black people who suffered a social death, but the land, indeed, the world, suffered death too.”[11]
A space-rock is any gravitationally-bound, chemically-bonded solid body. My definition. We exclude gaseous bodies but retain dust (what is dust but a gathering of tiny rocks?). A man in a powder-blue overshirt picks up a space-rock (which is what all rocks are). A series of photographs capture the complex series of “movements starting from the legs, progressing up through the pelvis and trunk, and culminating in a ballistic motion in the arm”.[12] A space-rock follows a ballistic trajectory through empty space. Without achieving escape velocity, the rock is bound to the Earth’s gravitational field and destined to trace a parabolic path until it is acted upon by another force (usually, and ultimately, the ground itself). Physics regards celestial objects as phenomena occurring beyond the Earth. Unworldly objects related to extraterrestrial affairs. The Earth itself is also a celestial object, but only when viewed from the outside. A space-rock. Worldlessness is the alter-physics of the dispossessed. A lived-experience of those excluded from the world. An ancestral cry: we too are beyond the Earth. Stone in hand, a space-rock-stone-pebble thrower is a celestial phenomenon. Ballistics has its roots in the Greek word βάλλειν, meaning ‘to throw’. Most commonly associated with long-range explosive weapons, ballistics is the subfield of mechanics concerned with the behaviour and impact effects of projectiles. Although their trajectory through space is described by the same mathematical equations, a rock-stone-pebble is not a bullet-rocket-missile.
The Vredefort impact structure is the largest impact structure visible on Earth. A two-hour drive outside of Johannesburg. Approximately 2,023 million years before our rock-stone-pebble thrower was photographed in his powder-blue overshirt and sunglasses, the path of another space-rock intersected with the orbital path of the Earth. This asteroid, approximately 25 km in diameter, had a vertical velocity of 25 km per second. Its impact produced a 300 km-wide crater and distorted the geology of a continent. 114 years before the rock-stone-pebble was thrown, an Australian prospector discovered the gold on the reef uplifted by the impact of that crater millions of years before – inaugurating the South African gold rush. An intensification of the settler onslaught on native land and life followed. The invention of Apartheid. Nineteen years after the rock-stone-pebble was “tossed” toward a border fence, Masande Ntshanga describes this Southern African space-rock impact in his science fiction novel Triangulum:
“Think a billion years. Think billion and then add another billion. That’s how long ago it was when an asteroid hit our planet forming the Vredefort Crater in the Free State. Here’s what that means. The impact crater created a fork in the path for us… the impact revealed secrets to our ancestors about our origins, through fossils, but it also warped the basin in the north, allowing colonists to discover gold in 1886… That began the purchasing of machines and petroleum en masse. That part’s not a secret. The consolidation of the Union of South Africa as a manufacturing state, a slave camp, and whatever we have now. This is what we call The Left Hand. The Path of the Machine.” [13]
The Chicxulub crater, the second-largest impact structure on Earth, was formed 66 million years before our rock-stone-pebble was thrown. Buried underneath the Yucatán Peninsula in Mexico and named after the Chicxulub Pueblo, this was the meteorite strike responsible for the Cretaceous extinction event. The meteorite that killed the dinosaurs. The meteorite that sparked the mammalian explosion. A world-ender/world-starter. What the poet Keorapetse Kgositsile calls “the pulse of the beginning the end and the beginning”.[14] The Chicxulub impact is estimated to have released the equivalent of 72 trillion tons of TNT. The estimate for the Vredefort impact is 100 trillion tons.
Trinitrotoluene (2-methyl-1,3,5-trinitrobenzene) is a synthetic chemical compound mostly used as an explosive material. TNT. Its ubiquity has made its explosive yield the standard comparative convention for the kinetic energy released by bombs and meteorite impacts. Although their effects are described using the same units of explosive force, a space-rock on a potential impact course with the Earth is not a MK84 general-purpose bomb.
- The problem of smallness
An orbital solution is the mathematical and observational determination of a celestial object’s path over time. The outcome of a set of equations which model the problem of position (relative location) and motion (change over time) as mathematical and graphical expressions. This solution, like a space-rock, is always in motion. An observation determines the position of a celestial object relative to a space-time coordinate system. The relationship between position and motion is fundamentally uncertain. Position: a photograph taken at Fatima Gate, 3 July 2000, shows a space-rock-stone-pebble in a thrower’s outstretched hand. A potential orbital problem. As an object moves, its position changes, giving information about its velocity and acceleration. Additional observations transform a position in space into a line through space over time. A single image is insufficient. A solution is not a fixed determination but a model based on the accuracy of measurement and the appropriateness of the predictive framework. A solution changes continuously as more observations produce more data, as more appropriate models are employed. One space-rock-stone-pebble tossed into an empty place always warrants a second thought.
Everything interacts. In orbital dynamics, stability and predictability are tied to mass. The larger a body, the greater its mass and gravitational force, and the less it is affected by the relative motion of other bodies. The smaller a body, the more – and more often – it is affected by the gravitational effects of other bodies ∴ the more unpredictable its path. Smaller objects are more affected by supposedly negligible forces. Light pressure. The mechanical force of sunlight pushing against the surface of an object. Starlight. Orbital decay. The effect of fluid friction – atmospheric particles in the path of an orbiting object. Space wind. Tiny forces, otherwise too faint and subtle to calculate, grow meaningful in the path of small objects. The smaller an object, the more observations needed to determine its path. The smaller an object, the harder it is to observe.
An orbital solution is abstracted from multiple forces and interactions to form a prediction model. This requires generalising certain conditions (so-called ‘rules of thumb’), ignoring others (assuming the non-interference of outside bodies), and reducing the system to a two-body approximation of forces (a Kepler problem). This abstraction produces an idealised elliptical orbit. Approaches that do not follow this reduction-abstraction model tend toward chaotic solutions. A two-body orbital problem has an exact solution ∴ and scientists prefer to describe all orbital solutions in two-body terms. Where there are more than two bodies? Remove those bodies from the solution. It is easier to ignore small objects and weak forces than to solve for them. Ignore but try not to lose them, for small objects pose the greatest threat. Many-body problems (involving three or more bodies) are much more complex, producing only approximate solutions which lead to non-linear and chaotic dynamics over time. The future state of the system is not predictable from its present state. For small objects, the cost of reduction-abstraction undermines the model’s predictive potential. For a given period of observations (the orbital arc), the orbital solution of a small object can only be calculated to a certain degree over a given time period. As more observations are made, the orbital solution is recalculated and resolved. These solutions are mathematically and observationally demanding. They are also fleeting. Small objects produce orbital problems that insist on helical relations. Revise the problem, revisit the observations, reconstruct the solution. SSSB orbits are not only computationally chaotic (i.e., difficult to model), they are also evolutionary. Events external to a model’s parameters and the object’s observational arc can change its orbital solution. In small object indexes, this is called the uncertainty parameter – the extent to which we can determine the exact path of an object for the next ten years.
Uncertainty is key to determining the potential hazardousness of a space object. Anything ≥ 140 metres ⌀ and < 19.5 lunar distances (7.6 million km) from the Earth is formally known as a Potentially Hazardous Object (PHO). At this distance from the Earth, the uncertainty of small object orbital paths means we can not be too sure if or when these objects might intersect with our elliptical orbit. SSSBs, like any space-rocks, resolve ambivalently. We cannot tell, beyond a certain horizon in time, where they might be, and ∴ whether they might make contact with the Earth. Let’s call this a first-order resolution. A potentially hazardous object moves – will it hit? This is a risk assessment weighing the chance of impact against the size of the object, a classic formula: Risk = Likelihood × Loss. A 64-year-old man in sunglasses and a powder-blue overshirt throws a space-rock-stone-pebble at a barbed wire fence ∴ tracing a path against a hierarchy of values. One stone tossed into an empty place and a stoning. A stone becoming. Wathint` abafazi, Wathint` imbokodo.[15] Fists raised in a stone-thrower’s gesture ∴ across space and time. One name amongst many and a naming. 29 years after the space-rock-stone-pebble is thrown, an asteroid named Apophis 99942, Ancient Egyptian God of unbecoming and chaos, approaches the Earth. 13 April 2029. An ongoing orbital solution determines a near miss. Allegories for justice. Ramon Amaro reminds us that “the reconciliation of an algorithmic solution is a settlement of debt, or an assumption of ownership over a set of values that designate truth-based conclusions.”[16] An alter-physics for after-the-end-of-the-world on a colonial planet – “the pulse of the beginning the end and the beginning”.[17] Let’s call this a second-order resolution. A potentially hazardous object moves – what do you have to lose?
