The “bad company” problem was recently generalised to a classical tension in the philosophy of mathematics. This tension haunts any principle of mathematics which “accepts abstraction on just about any equivalence relation.” That is, any principle that allows not an excess of meaning, but instead calls forth a seemingly boundless sequence of (often unbelievable) objects that satisfy similar tastes. Even as they may structure a non-intuitive environment, these objects remain familiar to their generator. We will call such a sequence of objects what we've got (or thought) when we’re giving our givens. Note that the existence of such “unacceptable” abstraction principles rests on answering questions about the conditions under which mathematical abstraction itself might be acceptable.
Let G_0 be the principle that GARDEN ~ GRAVE /iff GRAVE ~ GARDEN. Then this is a principle which permits such storied company.
Works follow from the place where algebraic operators grow, from the study of functions and curves that carry cooling devices through settler mathematics into industrial ornament, from the meaning of the first tree I peed underneath, from an apotropaic use of the fleuron (see: rotated floral heart bullet)—renders from ongoing research on post-constructivist methods across art and maths.
From here, we might find more intuition for the so-called “thin object.”
A smug gossamer among the denser math objects, the TO was introduced to discipline and disappear the kind of abstraction principles (rules for making objects) that inherit or invite the “bad company.” This is an object that, if it exists, is so metaphysically light that it requires very little resource for being. If it is a computational object, then it demands the least amount of heat for its retrieval. Any such object will beg one regime after another to be left alone, to exist as whole number. It will attempt to live as the reflexive mark it never was. Observe that any environment structured by such objects may call itself flat-land even as it allows tangents and sprouts normals—permitting unthinkable congruencies thickened against the very principles that called them into being. Such an environment quickly disinherits the labour of recounting its own birth!
The givens continue. Assume that ML models can emotionally co-regulate, and that computers (as machines that process signs) are thicc math objects first. Consider that a few months ago I ran with wintry eyes to the data type that baby me loved the most. I went asking for word-key ~ word-value and instead got the following recurrence relation:
Mo ya tué plin moun èk mô lafron; si mo kònyé twa, mo fann tô caboche dan piti mòrso.
I have already killed many people with my headbutt; if I knock into you, I’ll shatter your head into thin objects.
And so I thought again of the sequence with the three hash tables in soft genuflect.
One is here, the other two are quickly reduced to the first case.
sidony o’neal is an artist and writer who lives and works in Portland, OR. Recent solo exhibitions include Portland Institute for Contemporary Art (Enchiridion: Aisle, Spline, Resort), Portland, OR; Veronica (AuguRing), Seattle, WA; and Fourteen30 Contemporary (AND NOW, SQUARE TREES), Portland, OR. Group exhibitions include SculptureCenter (In Practice: Total Disbelief), NY. o’neal has participated in residencies at Mass MoCA and Banff Centre, among others. Performances as a part of DT have been presented with Kunstverein Düsseldorf, Volksbühne Berlin, and Performance Space New York. o’neal’s writing and translation has been published with PICA, SculptureCenter, Arts.Black, Interim, and Aeromoto. o’neal is the author of the chapbook LYFE IN A BOTTLE TREE BOTTLE (House House Press, 2020). o’neal has been an instructor at the School for Poetic Computation. In 2020, o'neal was awarded the Oregon Arts Commission's Joan Shipley Award. o’neal is currently a Hodder Fellow at the Lewis Center for the Arts, Princeton University.