This article in the NYT (previously noticed by mammoth and jargon etc) reports on studies of large-scale fluid-dynamics at Monterey Bay in California. Scientists using a land-based network of high-frequency radar sensors have made detailed maps of flows and currents, revealing a ‘hidden skeleton’ of hydronamic structures that determine their movements. Across the mouth of the bay, for example, is a line of turbulence, ‘like the filaments created by stirring milk into cold coffee’. This line forms a barrier: a floating object on one side will drift out to sea, while on the other it will not escape the bay. The structure is not fixed in place, but although it drifts, it doesn’t disperse.

“The structures are invisible because they often exist only as dividing lines between parts of a flow that are moving at different speeds and in different directions… ‘They aren’t something you can walk up to and touch… but they are not purely mathematical constructions, either’… The line is not a fence or a road, but it still marks a physical barrier.”

The article refers to these as Lagrangian coherent structures, and points out that they exist in water currents, turbulent airflow, and blood circulation. A more general term for these regularities in dynamic systems is singularity. Singularities can be static (the rest state of a system for example), or periodic (an oscillating equilibrium like a pendulum or orbital path). The collection of singularities that determine the behaviour of a system forms an invariant manifold. Manuel Delanda describes them this way:

“Singularities may influence behaviour by acting as attractors for the trajectories. What this means is that a large number of different trajectories, starting their evolution at very different places in the manifold, may end up in exactly the same final state (the attractor), as long as all of them begin somewhere within the ‘sphere of influence’ of the attractor (the basin of attraction)…  singularities are said to represent the inherent or intrinsic long-term tendencies of a system.”

It is fascinating to consider the possibilites of specifying matter not through its static positions, or as a series of temporal frames, but in terms of the singularities which form it: an invisible topography. The currently ubiquitous arch-school procedure of analysing a dynamic condition and then using it to generate static form barely scratches the surface of this way of specifying matter and its behaviour.

Three Curious Singularities

The behaviour of two masses orbiting each other can be accurately modelled using the equations of classical mechanics; but as soon as a third is added to the scenario it becomes irreducibly complex. This is the famous three-body problem. However, in the complex phase-space of a three-body system, there are five stable points – called Lagrange points – in this system, at which one object will remain stationary relative to the others. From a spaceship at a Lagrange point, the sun and earth would appear fixed.

Above the Catatumbo River in Venezuela, there is a lightning storm that has been there at least since the sixteenth century. On each of about 150 nights per year there are over 200 lightning strikes. The storm, which was first described by Francis Drake in 1595 complaining that the lightning gave away the position of his soldiers waiting to capture the city of Maracaibo, is fed by anomalies of atmospheric composition, and is a major source of the world’s ozone.

Solitons are stable waves which form in turbulent conditions. Rogue waves, spontaneously generated mountains of water, are believed to be phenomena of this kind, as is the Morning Glory Cloud, which forms over the Gulf of Carpenteria in North Australia. In studies of traffic flows, the term ‘jamiton‘ has been proposed (I’m not sure if that’s serious or not).

We never begin anything on a blank slate – there are always already things in progress, things that may have gone around hundreds of times before. We are continually stepping in and out of loops. They enfold us, entangle us – it is a wonder we do not see our own backs. Water molecules are so mobile that a glass of water from your tap today almost certainly contains at least one molecule of the water Jesus was baptised in. Your blood circulates, circadian rhythms governed by daylight control your digestive systems, your brain chemistry, and your body temperature. Your sleep phases are cyclical. Even in the linear expedition of walking from A to B, we employ the biomechanical cycle of walking: the same step repeated many times. Runners analyse their gait in great detail, looking for the most efficient biomechanical loop. Oscillations of rubidium atoms and vibrations of quartz crystals permit us to measure time. Weather patterns like El Niño and glacial periods recur more-or-less regularly. The Arctic Tern migrates from the Arctic to the Antarctic and back again every year. The pro-surfing circuit follows summer around the globe. Our planet turns, the moon passes through its phases, our star, throbbing with cyclical sunspots circles the black hole at the centre of our galaxy.

A loop begins and ends in the same place. A loop can be a path: the Link bus route, a holiday roadtrip, fitness trails, heritage walks, the planned new rail link under the city from Britomart to Mt Eden. Routines and habits are often cyclical: most days we go to the same places, eat according to the same ritualised practices, perhaps live from paycheck to paycheck, or work at a job that requires us to do the same thing repeatedly. Most hospital visits are return visits. How many times have you been to the same movie theatre? Rituals can be mind-numbing or Sisyphean, but equally comforting or enriching. Many of our mechanisms are based on loops, cycles, oscillations, vibrations: scuba rebreathers, amplifiers and synthesisers, software AI routines. Recycling, rehabilitating, and reusing are processes which attempt to close loops to reduce wastage, or to produce waste which can be fed into other cycles and processes.

We habitually address exceptional spaces; spaces for special events; the out-of-the-ordinary; the linear; the historical. But what about the cyclical, the repeated, the looped?