What is a singularity? It is a simple question, but any answer is not so simple and I am not so sure. There are the scientific answers. Whatever. They are too simple, because they assume too much.
In The Logic of Sense Deleuze isolates the ‘fourth person singular’ as a dimension of language found in the infinitive verb — to walk, to battle, to die. Each singularity correlates to a singular event — a walk, a battle, a death. Think about an infant learning to walk. The infant does not internalise in a conscious manner the biomechanics of the act of ‘controlled falling’. There is no fully thought concept of ‘walking’ present in the infant’s mind before walking. How do I know that? Think of stroke or spinal injury patients who are taught to walk again.
The act of walking is perfectly singular — everyone/every situation has a walk — and immanent to the act itself. Each act of walking does not actualise ‘to walk’ (the third person infinitive) of every possible act of walking. There is always an otherwise to walking that remains dormant as pure potential captured by the infinitive ‘to walk’. Each act of walking belongs to the series of walking. ‘A walk’ is the pure event of this series.
The next problem relates not to the complexity of events — the above example of walking is already highly complex — but to the complicatedness of situations. A ‘situation’, as I am using it here, is a manifold of events, which, for example, may contain millions of events and therefore millions of singularities. How does one talk about the singular dimension of a situation? In A Thousand Plateaus Deleuze and Guattari introduce the concept of Haecceity:
There is a mode of individuation very different from that of a person, subject, thing, or substance. We reserve the name haecceity for it. A season, a winter, a summer, an hour, a date have a perfect individuality lacking nothing, even though this individuality is different from that of a thing or a subject. They are haecceities in the sense that they consist entirely of relations of movement and rest between molecules or particles, capacities to affect and be affected. […] Tales must contain haecceities that are not simply emplacements, but concrete individuations that have a status of their own and direct the metamorphosis of things and subjects. Among types of civilizations, the Orient has many more individuations by haecceity than by subjectivity or substantiality: the haiku, for example, must include indicators as so many floating lines constituting a complex individual. In Charlotte Bronte, everything is in terms of wind, things, people, faces, loves, words. […] A degree of heat, an intensity of white, are perfect individualities; and a degree of heat can combine in latitude with another degree to form a new individual, as in a body that is cold here and hot there depending on its longitude. […] A degree of heat can combine with an intensity of white, as in certain white skies of a hot summer. This is in no way an individuality of the instant, as opposed to the individuality of permanences or durations. A tear-off calendar has just as much time as a perpetual calendar, although the time in question is not the same. There are animals that live no longer than a day or an hour; conversely, a group of years can be as long as the most durable subject or object. We can conceive of an abstract time that is equal for haecceities and for subjects or things. (261)
A haecceity correlates to the ‘thisness’ of a singular actualisation. Although they do not argue it, I want to suggest that their concept of haecceity allows Deleuze and Guattari to deal with the problem of the complicatedness of situations. ‘Individuality’ as used in the above extract from A Thousand Plateaus relates to the singular nature of a “season, a winter, a summer, an hour, a date”. These individuated ‘things’ do not correlate to a singularity but a whole constellation of singularities.
This is not a problem of rhizomatics or the mechanics of complexity, rather it is a problem of language. The most obvious example of a singularity is found in the infinitive verb. Yet, like any mode of representation, any infinitive verb is a reduction. ‘To walk’ surely contains the singularity of ‘a walk’ when actualised or in potential, but ‘a walk’ is constituted by many singularities. Think of all the movements of the body demanded when walking. ‘To move’ is another infinitive correlating to ‘a move(ment)’. There is a fluidity of the body whereby one might suggest that the whole body moves in a singular movement when walking. Why separate the arms from the legs from the hips? Indeed, think of all the movements required of the body when living! Why separate out one particular movement — a walk — from the fluidity of living? Or, for that matter, from the fluidity of the chaosmos? Because we can, because of language, because of sense.
Deleuze’s solution to this problem is partially answered in The Logic of Sense in his concept of death and of the crack-up. Death is a pure event. The ‘crack-up’ is a crack that forms on the surface of all things. It is a little bit of death in everything. I shall write a follow up post to this expanding on this point asÂ my current bed-time reading is “Pure Immanence… a Life”. I have a feeling he will expound the other side of the event.