Over the years I’ve written on this question obsessively, coming back to it again and again.  I draw the term, of course, from Deleuze.  It is a key one within his ontology; every bit as important as concepts such as multiplicity and virtuality.  In onticology, singularities are part of what constitute the virtual proper being of things, their unique being, their haecceity or thisness.  Yet the concept of singularity is extremely elusive.  The singularities that populate a thing are something that can be alluded to without it being possible to represent them.  Deleuze is careful to distinguish singularities from individuals.  As he repeatedly states throughout Difference and Repetition, “individuation is not the individual”.  Individuation refers to those processes by which an individual is produced.  Singularities are central actors in that process of individuation.  They are not something outside of things– they are strictly immanent in things –but neither are they the qualities (such as color, texture, taste, etc) or shape of things.  Rather, they are that within a thing that will generate qualities and shape when a thing enters into a particular field of forces.  Other fields of forces would lead to the genesis of other qualities and shapes.

In The Logic of Sense, Deleuze gives us some provocative examples of singularities.  He writes that, “[s]ingularities are turning points and points of inflection; bottlenecks, knots, foyers, and centers; points of fusion and condensation, and boiling; points of tears and joy, sickness and health, hope and anxiety, ‘sensitive’ points” (63).  From these examples, we get the sense that singularities are points of tension and potentiality within matter or a thing that are absolutely unique to that thing.  As in the case of the wood to the right above, examples of singularities would be the knot, the grain of the wood, its wetness and density, etc.

read on!

But already this example and photograph risk betraying everything that is important about the concept of singularity.  One will say “ah, the singularity is the knot!  the singularity is the grain of the wood!  singularities are qualities after all!”  But that’s not at all it.  Really we can only understand the concept of singularity if we think in terms of a play of forces or encounters between things.  The singularities are themselves never present in a quality.  Rather, they can only be inferred in and through engagement with materials.  You can’t discern singularities simply by looking at things.  No, you have to interact with things to get a sense of what singularities are.  In A Thousand Plateaus Deleuze and Guattari give an illuminating example:

On the one hand, to the formed or formable matter we must add an entire energetic materiality in movement, carrying singularities or haecceities that are already like implicit forms that are topological, rather than geometrical, and that combine with processes of deformation:  for example, the variable undulations and torsions of the fibers guiding the operation of splitting wood.  On the other hand, to the essential properties of matter deriving from the formal essence we must add variable intensive affects, now resulting from the operation, now on the contrary making possible:  for example, wood that is more or less porous, more or less elastic and resistant.  At any rate, it is a question of surrendering to the wood, then following where it leads by connecting operations to a materiality, instead of imposing a form upon a matter.  (408)

A moment later Deleuze and Guattari remark that “…matter-flow can only be followed” (409).  This is what it means to say that nonhumans are actants, that they are actors in their own right.  In the passage above, Deleuze and Guattari are critiquing, following Simondon, the hylomorphic conception of things whereby a thing is a unity of form and matter where form is something applied to a formless and homogeneous matter from without.  Under the hylomorphic model, form– which is treated as the masculine, intelligible principle –is always thought of as coming from without from a model, whether in the mind of God or humans –imposed on passive and homogeneous matter.  Deleuze and Guattari’s point is that matter, things, are already populated by singularities, this “energetic” dimension of matter that contributes to what the thing will be in a play of forces.  As the wood chopper brings his axe down upon the wood, it is not simply the will of the woman that gives form to the firewood.  Rather, the singularities that populate the wood contribute just as much to the shape of the firewood as the axe and the action of the woman.  What we have here is a play of forces between the woman, the axe, and the wood that precipitate the firewood.  We don’t have a smooth imposition of form on a passive and formless matter of wood.  The singularities that populate the wood contribute something as well, but we only can discern what they contributed after the fact.  And, of course, the woman and the axe assemblage have their own singularities as well.  It’s likely that were literary critics to turn their attention to firewood they would discover that there is a style of firewood that differs from body-axe assemblage to body-axe assemblage as a result of the singularities pregnant in the person doing the chopping.

This is why singularities are topological rather than geometrical.  In geometry a equilateral triangle is an equilateral triangle and a right triangle is a right triangle and a square is a square and a rectangle a rectangle.  In topology a series of singularities can undergo a variety of transformations that allow the triangle to become a square and so on.  Topological figures don’t have a fixed form, but are formable.  Now imagine a variety of different people carving the piece of wood depicted at the beginning of this post.  Each person will have to follow the singularities of the wood, but those singularities will be actualized in very different ways.  One person will perhaps carve a face, another a different face, yet another an eagle or the head of a gazelle, yet another undulating waves or a forest.  The singularities are capable of generating a variety of actualized forms, but have none of these forms a priori.  Here the art is as much a result of the matter as it is of the tools used and the artist.

Yet these examples already imply that there’s something special about the human/thing relation.  But that’s not the point at all.  What’s important to understand is that this is how it is with all relations between things.  All things are populated by singularities and all singularities actualize themselves differently (what I call “local manifestations”) depending on the field of forces they enter into (what I call regimes of attraction).  Indeed, the grain of the wood in the picture at the beginning of this post, as well as its knots, did not fall from the sky.  No, that tree became what it was by navigating a field of forces that involved trees that crowded out its source of light as it grew (hence the wavy grain that resulted as it bent and grew in particular directions to reach light), that arose as a result of the direction from which wind predominantly blew, as a result of the amount of rainfall, as a result of insects and animals in its vicinity and living on it, etc.  It is said that the superior qualities of the famous Stradivarius violins was not so much the result of superior craftsmanship as peculiar grains of wood formed during the little ice age in a particular forest.  Those forces caused trees to grow in particular ways that generated optimal sound quality, and the singularities of these instruments have not ceased to be explored by various musicians.

Nor should we assume that the singularities of a thing are fixed.  Singularities can change as in the case of land that is over-farmed by one crop, becoming barren for that crop or taking on capacities to support other crops.  Singularities mutate and change as a result of the events that take place with respect to them.  Previous singularities appear, others disappear, and often the entity is destroyed altogether as a result of operations that were too much for it.  This is the basic idea behind the concepts of local manifestation, virtual proper being, and regimes of attraction.  Virtual proper being is the domain of singularities populating a thing.  Local manifestation is the actualized properties of a thing such as the particular properties of a tree.  Regimes of attraction are the field of forces within which a thing actualizes itself giving it unique and specific qualities.

In this regard, the category of “thing” is less a figure of mastery or identity, than the figure of gift and surprise as Derrida theorized the gift in his later work.  Spinoza tells us that we never know what a body can do.  In onticology we can translate this as “we never know what a thing can and will do.  Things will always surprise us– hence their nature as “pure gift”, gift without economy or exchange –because things always harbor topological singularities who’s effects, when entering into this field of forces, cannot be calculated.  And herein lies a certain ethic of caution and humility with respect to things.  We never know fully what they do when they enter into this particular constellation of forces.