mathematics | Susan Eyre

‘And here is one of the map’s most important characteristics: the viewer is positioned simultaneously inside and outside it. In the act of locating themselves on it, the viewer is at the same moment imaginatively rising above (and outside) it in a transcendent moment of contemplation, beyond time and space, seeing everywhere from nowhere.’ Jerry Brotton in A History of the World in 12 maps

Locked down editing video work. Setting off at dawn and wearing a headcam I walked the most direct route to each of the four points due North, East, South and West of my home. I chose a three mile radius as this approximates the distance to my horizon at sea level.

I am interested in how space is perceived as a plotted dimension, as abstract space calculated mathematically but perhaps not something we can visualise and as imagined space.

I aim to relate these different perspectives on space to broader knowledge. In my film there are three speculative viewpoints; ‘the seeker’ who wishes to discover what is beyond the horizon, ‘the seer’ who imagines what might be beyond and ‘the scientist’ who offers abstract theories.

In the film I explore connections and hierarchies of physical dimensions and perception, the use of contour lines on maps, foliation and patterns in soap film membranes or marbling.

Foliation is the decomposition of shape into lines and circles. It occurs in geology as repetitive layering in metamorphic rocks and in mathematics as the analysis of curves and surfaces. The math’s language is way beyond what I can understand but it does have connections with holonomy and manifolds and Poincaré which I am interested in though I am yet to get to grips with any firm understanding. The notion of leaves (slices) allows for an intuitive way of thinking about a foliation. In mathematics, topology compares shapes to see if they have the same number of holes and handles and can therefore be moulded from one shape into the other by stretching, twisting, crumpling and bending, but not tearing or gluing.

I took many films of soap film membranes and have been exporting the final single frame at the moment the bubble bursts. I have used these frames to create sequences of collated membrane bursts. We may live in a multiverse of bubbles each with wildly different laws of physics. String theory allows for many universes with different physical laws. It may be possible our universe could suddenly transform into a universe with different properties. If it did happen it would be so fast we wouldn’t even register it.

I made a silver cape for some green screen filming in character as the seer. Learning lots about Adobe After Effects so if the editing requires I drop this section then the hours put in won’t be entirely wasted and the cape will come in for when next door can have their parties again.

Thinking about making new work that interacts in real time with cosmic rays as they hit the Earth’s atmosphere and shower down upon us.

Cosmic rays, some travelling from other galaxies, pass through us and our world continuously, creating an almost tangible contact with outer space. Witnessing this incredible activity helps us look beyond what our immediate senses tell us exists and consider the interconnectedness of our universe.

We are made of carbon. Most of the carbon in the world is carbon-12 which contains six neutrons and six protons. Protons and atomic nuclei created by events such as exploding stars speed across space and collide violently with the Earth’s atmosphere creating a chain reaction of cascading particles. Some of these particles created are neutrons which can smash into atoms of nitrogen to create carbon-14 which has six protons and eight neutrons.

Cosmic ray activity gives us carbon dating techniques. Carbon-14 is unstable and therefore radioactive. It has a half-life of 5,730 years. This means if a sample of a tree contains 64 g of radioactive carbon, then after 5,730 years it will contain 32 g, after another 5,730 years that will have halved again to 16 g. Radioactive decay is random but in a sample there are enough atoms to work out an average time it will take for the nucleus to lose the extra neutrons.

Carbon-14 atoms in the atmosphere combine with oxygen to create radioactive carbon-dioxide. This radioactive carbon-dioxide is absorbed by plants which are eaten by animals. When an organism dies no more carbon-14 will be absorbed. The existing carbon-14 will start to decay. By measuring the radioactivity, the current carbon-14 content can be determined and the time of death established.

A planet with twice the mass of Jupiter has been discovered orbiting HD70642 in an almost circular orbit. This means it is possible that Earth-type planets may be orbiting further in. In all other planetary systems discovered with massive planets they usually have disruptive closer elliptical orbits which would destroy any smaller planets on a circular orbit. Hope to return to my studio soon to continue work on ’90 light years home’ which will use a raster pattern on folded paper looking at mapping out a space ship as a star map using 137 points. As physicist Laurence Eaves states – ‘The number 137 would be the one you’d signal to aliens to indicate that we have some measure of mastery over our planet and understand quantum mechanics.’

137 comes from the fine-structure constant, also known as Sommerfeld’s constant and is represented by the alpha symbol α. Using several fundamental constants found in nature to give a fundamental physical constant. This number represents the strength of electromagnetic interaction between elementary charged particles which is the probability that an electron will absorb a photon.

I watched the Hito Steyerl lecture as part of the Dramaturgies of Resistance online event series. ‘At this unprecedented time, when it seems as if “everything is canceled,” Steyerl’s most recent work explores the complex relation between spread (of conspiracy theories no less than viral contagion) and simulation (from the automization of performance to our capacities for virtual interaction with statistical probability of human risk).’

I was excited to find the lecture covered topics very relevant to my research into abstract space at the moment such as objects in topology. The Alexander horned sphere is a pathological object in topology. It is formed by starting with a standard torus, removing a radial slice of the torus and connecting a standard punctured torus to each side of the cut, interlinked with the torus on the other side. A pathological object is one which possesses deviant, irregular or a counterintuitive property, in such a way that distinguishes it from what is conceived as a typical object in the same category.

The opposite of pathological is well-behaved.

Mathematician Shing-Tung Yau set out to discover if there could be a spacetime which contains no matter but in which there is still gravity caused by the topology of the space. In 1977 he solved the Calabi Conjecture posed by Eugenio Calibi in 1954 who was interested in whether a certain type of topology guarantees a certain type of geometry. Topology looks at the overall form of an object and recognizes shapes that have an equivalent topology but different geometry such as a doughnut and a coffee cup as they can be morphed from one to the other. Topologists generally study manifolds. Manifolds are shapes that could be flat when looked at close up such as the earth’s surface or a ball if you were an ant. Each point on the surface can be mapped using two coordinates onto a 2 D plane and the shape is finite. Taking the average of all the curvatures at every point on the surface gives what’s called the Ricci curvature. A doughnut which is a 2D manifold mapped in this way has a Ricci curvature of zero which shows that a manifold can have a zero Ricci curvature at every point without being flat. There are also shapes which look 3D when seen up close and need 3 coordinates to map them. In mathematics it is possible to think of Euclidean (flat) space in any number of dimensions by increasing the number of coordinates you use giving manifolds in many dimensions. Transferring this equation to physics Ricci curvature describes the curvature of spacetime that’s induced by matter being present if this curvature is zero then it describes a spacetime with no matter. Yau proved that this type of manifold could exist in all dimensions. This type of manifold is known as the Calabi-Yau manifold. Particularly in superstring theory, the extra dimensions of spacetime are sometimes conjectured to take the form of a 6-dimensional Calabi–Yau manifold, which led to the idea of mirror symmetry.