Deleuze's "ontological difference" between virtual multiplicity and intensive individuation processes can help us think the ontological status of "model" in its relation to the events it models. The "doubling" of difference in the post title means that the multiplicity (the model) is differential (a-centered) and that its actualizations are all different events. Translating into other terms, the second claim is that the Deleuzean scheme accounts for the "multiple realizability" of models (but please note that Deleuze would not use this term because for him the virtual is real, so individuation is actualization rather than realization).
In Difference and Repetition, a multiplicity is defined as a set of differential elements, differential relations, and singularities. So we here see difference sense 1 ("differentiation"): such a multiplicity is "differentiated" (it has no central controlling point) and has the ontological status of "virtuality" (Deleuze likes to cite Proust here: the virtual is "real without being actual, ideal without being abstract"). Linked intensive processes will individuate or actualize this multiplicity, with a series of cascading differentiations occuring when those processes hit singularities or thresholds in their relative values; passing these thresholds triggers qualitative changes in the system (cell differentiation in ontogeny is a clear biological model here).
Difference sense 2 ("differenciation"): the multiplicity is a model and the different individuated events are separate actualizations of that model; in even simpler langauge, the multiplicity is a pattern and the events are processes conforming to the pattern -- echoing the book's title, although different events, they repeat the model. (It's vital to note that this is not a Platonistic model; the multiplicities or patterns are not fixed Ideas, but change, via "counter-effectuation," in relation to the individuation processes that actualize them. In the case of a repetition of the Gulf Oil Disaster (GOD), food webs may have been weakened to the point that a much smaller event could have much greater damage; in model terms, the singularity or threshold for food web destruction would have become much lower.)
We see how this scheme presents an ontology for the construction of a model for other spills drawn from a complex event like the GOD of 2010-present (not just "2010," because its effects are far from exhausted) when looking at this article in Bioscience, "A Tale of Two Spills: Novel Science and Policy Implications of an Emerging New Oil Spill Model." (Thanks to Scott Eustis at healthygulf.org for the pointer.)
Note the doubled difference here: 1) the way in which the model of such spills is a multiplicity linking many interactive processes (differentiation qua a-centered set); 2) for it to be a model, it must be applicable to other spills, not just the GOD (differenciation qua multiple realizability).
The following passage from the Bioscience article is pitched in terms of what we don't understand, but should understand, in order to have a good model, but that shouldn't stop us:
Several serious gaps in scientific understanding exist that inhibited the capacity of the NRDA process to determine the ecosystem impacts of the DWH well blowout and that may have prevented the collection of the information necessary to detail all the important damages to the deepwater pelagic and benthic resources and their ecosystem functions.
- First, detailed understanding of the physicochemical behavior of oil, gas, and dispersants when they are released under the environmental conditions that prevailed at the wellhead is incomplete.
- Second, knowledge of the transport and fate of oil and gas depends on the challenging task of coupling dynamic changes in buoyancy with accurate, real-time, three-dimensional physical circulation models of the ocean.
- Third, quantitative measures of the dispersion of oil into fine droplets and the creation of subsurface oil–gas–water–gas-hydrate emulsions that, to some degree, resulted in seafloor deposition (Joye et al. 2011, Reddy et al. 2012) are needed in order to depict the fate of the released hydrocarbons and the extent of biological exposures. Such dispersion and subsurface retention of hydrocarbons probably accelerates microbial degradation (Kujawinski et al. 2011) yet simultaneously enhances exposure and magnifies injury to animals of the deep-sea water column and seafloor.
- Fourth, consequences for at-risk functional groups, such as particle feeders, are unclear, particularly at mesopelagic and bathypelagic depths, where baseline community characterization and functional biology are poorly documented. The taxon-specific toxicity (Lenihan et al. 2003) of hydrocarbons and dispersants must also be integrated into the understanding of biological oceanographic processes. The potentially important indirect and delayed consequences (Peterson et al. 2003) of impacts may include reductions in particle filtration capacity and prey availability to higher order consumers (Hawkins and Southward 1992).
- Finally, the large subsidy of fixed carbon to the ocean ecosystem and the stimulation of heterotrophic microbial production present a conceptual challenge to biological oceanography. Microbially mediated biogeochemical cycling and the production of microbial biomass in the deep sea have yet to be fully integrated into our understanding of carbon flows into food webs that support the larger marine animals that are most valued by people.
With some translation / simplification we see that a deep-sea oil spill event can be modeled on the basis of a differential multiplicity, that is, the interaction of the following processes:
- How the oil, gas, and dispersant mixture is formed under the conditions of water pressure, water current turbulence, etc., at the point of the spill
- How the bouyancy of oil and gas is affected by water circulation patterns
- How droplets of oil are
- formed by the disperant's action to create "subsurface oil–gas–water–gas-hydrate emulsions"
- as these processes relate to the linkage of
- the acceleration of "microbial degradation"
- to the exposure and damage to organisms (such damage itself being the result of multiple processes)
- The ripple effects of organism damage throughout food webs.
- The effects of the microbially processed oil on food webs reaching to seafood people eat.
Each of the links of processes has thresholds at which the system changes its behavior pattern. What makes this a model for future spills is abstracting the relations of the variables from the values of those variables in the GOD.
Now do working scientists "need" to know the Deleuzean scheme to understand the ontology of models? Of course not; the folks who produced this oil spill model did perfectly well without distinguishing the virtual status of a model from the intensive processes that actualize that model in different events. But that doesn't mean we philosophers shouldn't consider Deleuze's framework as providing an explicit ontology for doubled difference: the a-centered or differential set of processes in the model and the distinction of differentiated model and differenciated events.