Transcendental EntitIES
The origin of mathematics remains a mystery, but it is apparent that mathematics advanced with civilization, and civilization was able to advance because of mathematics. It has had a tremendous impact on society, arguably reshaping who we are as a species - from the invention of counting in ancient Sumeria in 8,000 BC to today’s ubiquitous use of artificial intelligence.
Over time mathematics has become more abstract and further removed from our everyday experiences. In 2016 neuroscience researchers showed through brain imaging that the parts of the brain that mathematicians use for high-level mathematical reasoning do not overlap with those parts of the brain involved in language processing. Mathematical reasoning is not founded on language competence. Yet, for mathematicians to communicate their work with each other, these ideas have to be converted to language - and new mathematical concepts need new language to be developed. With recent advances in mathematics, and hyper-specialization in every field from finance to medicine, the expert’s conception and articulation of the theoretical and applied sciences has diverged far afield from that of the lay person’s.
In this project I explore mathematical objects discovered in the last 50 years. I select these abstract objects from academic journals, where they have already been transformed from free mathematical concepts to bounded formal language. Like in Giorgio de Chirico’s metaphysical paintings in his mannequin cycle, I free these objects from the limits of logic, rationality and common sense. The final images are single exposures, often over 20 minutes long, reflecting this escape from the mathematical language. The image titles are the names of the mathematical objects, and the caption is a simplified definition of that object.
QUANDLE: a quandle is a set with a binary operation that is idempotent, invertible and self-distributive
PERIOD: a period is a countable sub-algebra of the complex numbers that contains all algebraic numbers and many transcendental numbers
GERBE: a gerbe is a geometrical object whose equivalence classes are elements in the next sheaf cohomology group
GROPE: a grope is a 2-dimensional complex with one boundary circle, which is the union of compact, connected and oriented 2-manifolds, each of which also have a single boundary circle
POLYPUS DECOMPOSITION: a polypus decomposition is a structure for open, connected, saturated sets with a compact nucleus that is a connected manifold with boundary and corners; if r=8 a more precise term is octopus decomposition
STACK: a stack is a category fibered in groupoids which has a smooth covering by an affine variety
MONSTER: the Monster is the largest known sporadic simple group and the automorphism group of the Griess algebra, with approximately as many elements as the number of elementary particles in the planet Jupiter
SYZYGY: a syzygy is an element of a finitely generated module over a commutative ring where its product with the generators is zero
TRAIN TRACK: a train track is a smooth 1-complex whose vertices are called switches, and whose edges are called branches, such that at each switch there is a unique tangent line and the switch has an open neighborhood in the train track which is a union of smoothly embedded open arcs
PERVERSE SHEAF: a perverse sheaf is a bounded constructible complex where the dimension over the complex space of the closure of the set of points at which the stalk is non-zero is less than the point
TOPOS: a topos is a category equivalent to the category of sheaves of sets on a site which admits finite projective limits, where quotients by equivalence relations exist, and the sum of the family of objects is disjoint and commutes with base change