“A species (or any other natural kind) is not defined by its essential traits but rather by the morphogenetic process that gave rise to it. Rather than representing timeless categories, species are historically constituted entities, the resemblance of their members explained by having undergone common processes.”
“The cube would not remain invariant under rotations by, say, 45 degrees, but a sphere would. Indeed, a sphere remains visually unchanged under rotations by any amount of degrees. Mathematically this is expressed by saying that the sphere has more symmetry than the cube relative to the rotation transformation. That is, degree of symmetry is measured by the number of transformations in a group that leave a property invariant, and relations between figures may be established if the group of one is included in (or is a subgroup of the group of the other. Classifying geometrical objects by their degrees of symmetry represents a sharp departure from the traditional classification of geometrical figures by their essences. While in the latter approach we look for a set of properties common to all cubes, or to all spheres, groups do not classify these figures on the basis of their static properties but in terms of how these figures are affected (or not affected) by active transformations, that is, figures are classified by their response to events that occur to them. Another way of putting this is that even though in this new approach we are still classifying entities by a property (their degree of symmetry, this property is never an intrinsic property of the entity being classified but always a property relative to a specific transformation.”
“The complexity of the distribution of singularities makes a great difference in our interpretation of the modal structure of state space. A state space with a single attractor, and a single basin encompassing the entire space, has a unique end state for the evolution of the system. Concentrating on this atypical case, therefore, can mislead us into thinking that determinism implies a single necessary outcome. On the other hand, space with multiple attractors breaks the link between necessity and determinism, giving a system a "choice" between different destinies, and making the particular end state a system occupies a combination of determinism and chance.”
“The possible and the virtual are distinguished by the fact that one refers to the form of identity in the concept, whereas the other designates a pure multiplicity which radically excludes the identical as a prior condition... To the extent that the possible is open to "realization" it is understood as an image of the real, while the real is supposed to resemble the possible. That is why it is difficult to understand what existence adds to the concept when all it does is double... Actualization breaks with resemblance as a process no less than it does with identity as a principle. In this sense, actualization or differenciation is always a genuine creation. Actual terms never resemble the singularities they incarnate.. For a potential or virtual object to be actualized is to create divergent lines which correspond to-without resembling—a virtual multiplicity."
“A relation of greater or lesser resemblance, multiplicities imply divergent realizations which bear no similarity to them. These formal differences, I said, are insufficient to characterize the distinction between essences and multiplicities as immaterial entities whose job is to account for the genesis of form: replacing eternal archetypes involves supplying an alternative explanation of morphogenesis in the world. Unlike essences which assume that matter is a passive receptacle for external forms, multiplicities are immanent to material processes, defining their spontaneous capacity to generate pattern without external intervention. I used certain features of mathematical models (state spaces) to define the nature of multiplicities: a multiplicity is defined by distributions of singularities, defining tendencies in a process; and by a series of critical transitions which can take several such distributions embedded within one another and unfold them. Finally, I said that a population of such concrete universals forms a real dimension of the world…The discontinuous and divisible space of our everyday world was specified entirely by analogy with a purely mathematical construction, the hierarchy of geometries first dreamt by Felix Klein. Eliminating the metaphorical content will involve not only a thorough ontological analysis of state space so that its topological invariants can be separated from its variable mathematical content, but in addition, a detailed discussion of how these topological invariants may be woven together.”
“Michael Ghiselin who has been arguing for decades that a species, formed through the double process of natural selection and reproductive isolation, does not represent a higher ontological category than the individual organisms that compose it. Unlike the relation between a natural kind and its members, which is one of exemplification or instantiation, the relation of individual species to individual organisms is one of whole and parts, much as the relation between an organism and the individual cells that compose it. Moreover, unlike the relation between a particular instance and a general type, the relation of parts to whole is causal: the whole emerges from the causal interactions between the component parts.“
“A heterogeneous space made out of a population of multiplicities, each of which is a topological space on its own. The virtual continuum would be, as it were, a space of spaces, with each of its component spaces having the capacity of progressive differentiation. Beside this multiplication of spaces, we need a way of meshing these together into a heterogeneous whole. Deleuze, in fact, refers to the virtual continuum as a plane of consistency.”
“Relation is not a rate of change of one quantity relative to another, but the rate at which two quantities change relative to each other. As Deleuze puts it, virtual relations must involve a purely reciprocal determination between their elements, a reciprocal synthesis between pure changes or differences which should not presuppose any prior individuation.”
“In communication theory, the actual occurrence of an event is said to provide information in proportion to the probabilities of the event's occurrence: a rare event is said to provide more information on being actualized than a common one. These events, each with its own probability of occur-rence, may be arranged in a series. When two separate series of events are Placed in communication, in such a way that a change in probabilities in one series affects the probability distribution of the other, we have an information channel.”
“As Prigogine and Nicolis put it, a process "in the regime of uniform steady state ignores time. But once in the periodic regime, it suddenly 'discovers' time in the phase of the periodic motion...We refer to this as the breaking of temporal symmetry.”
“Whatever is future or past in relation to a certain present (a certain extension or duration) belongs to a more vast present which has a greater extension or duration. There is always a more vast present which absorbs the past and the future. Thus, the relativity of past and future with respect to the present entails a relativity of the presents.”
“The surface of a lake affords a walking medium to a small insect but not to a large mammal. A similar point applies to time scales. Each level of temporal scale defines what oscillators at that level "perceive" as relevant change: certain cycles are simply too slow for them to appear as changing or moving relative to a faster level, and vice versa, certain oscillations are much too fast for them to even count as existing for oscillators operating at longer time scales.“
“As Stuart Kauffman puts it:
…In a genomic system, each gene responds to the various products of those genes whose products regulate its activity. All the different genes in the network may respond at the same time to the output of those genes which regulate them. In other words, the genes act in parallel. The network, in so far as it is like a computer program at all, is like a parallel-processing network. In such networks, it is necessary to consider the simultaneous activity of all the genes at each moment.”
“Results would constitute the spatial aspect of the virtual. To this, a temporal dimension, which Deleuze calls "Aion", should now be added. As he writes, the specification of the virtual implies, on the one hand, a space of nomad distribution in which singularities are distributed (Topos); on the other hand, it implies a time of decomposition whereby this space is subdivided into sub-spaces. Each one of these sub-spaces is successively defined by the adjunction of new points ensuring the progressive and complete determination of the domain under consideration (Aion). There is always a space which condenses and precipitates singularities, just as there is always a time which progressively completes the event through fragments of future and past events.”
“The temporality of the virtual should not be compared to that of the processes governed by the laws of relativity, but to the temporality of the laws themselves. Unlike experimental laws (like Boyle's law of ideal gases) which simply record laboratory regularities, fundamental laws (such as Newton's or Einstein's) are not mere mathematical re-descriptions of experience. Although Physicists do not usually speculate about the ontological status of fundamental laws, to philosophers these laws are supposed to be eternal, and to be valid simultaneously throughout the universe. In other words, in Philosophical discussions fundamental laws enjoy the same form of timelessness as immutable essences. And it is this form of time that the virtual is supposed to replace. Nevertheless the question remains, what form of temporality would allow the absolute coexistence of virtual events?“
“The events involved in the construction of virtual space, the progressive unfolding of virtual multiplicities as well as the stretching of their singularities into series of ordinary points, need to be thought as pure becomings in this sense. In this construction, as Deleuze says, "Time itself unfolds... instead of things unfolding within it ... [Time] ceases to be cardinal and becomes ordinal, a pure order of time." Unlike actual time, which is made exclusively out of presents (what is past and future relative to one time scale is still the living present of a cycle of greater duration), a pure becoming would imply a temporality which always sidesteps the present, since to exist in the present is to be, no longer to become. This temporality must be conceived as an ordinal continuum unfolding into past and future, a time where nothing ever occurs but where everything is endlessly becoming in both unlimited directions at once, always "already happened" (in the past direction) and always "about to happen" (in the future direction). And unlike actual time which is asymmetric relative to the direction of relative pasts and futures, a pure becoming would imply a temporality which is perfectly symmetric in this respect, the direction of the arrow of time emerging as a broken symmetry only as the virtual is actualized.”
“To put this in linguistic terms, if we posed the problem "Why was this rabbit eaten?", one answer may be framed at the population level (because of the large number of foxes) and another at the organism level (because it passed through the capture space of a specific fox at a specific time). In other words, one problem is "Why was this rabbit eaten (as opposed to not eaten)?" while the other is "Why was this rabbit eaten (by this particular fox as opposed by this or that other fox)?". The second contrast space includes much that is irrelevant to the question since, given a high enough density of foxes, if this rabbit had not been eaten by this fox it would have been eaten by another. In other words, there is a certain degree of redundant causality operating at the micro-level, so that framing the question at that level is bound to yield the wrong distribution of the important and the unimportant.”
“Here the problem for the population of molecules is to find (or compute its way to) a minimal point of energy, a problem solved differently by the molecules in soap films (which collectively solve a minimization problem stated in surtace-tension terms) and by the molecules in crystalline structures (which collectively solve a bonding energy problem. It is as if an ontological problem, whose conditions are defined by a unique singularity, "explicated" itself as it gave rise to a variety of geometric solutions (spherical bubbles, cubic crystals). This intimate relation between epistemology and ontology, between problems posed by humans and self-posed virtual problems, is characteristic of Deleuze.“
“Many times the individuation of a phenomenon not only precedes the development of a theory that will explain it, but it remains in this problematic state, crying out for an explanation, for many decades.”
“The mathematical difference between linear and nonlinear equations is explained in terms of the superposition principle, which states that given two different solutions of a linear equation, their sum is also a valid solution. In other words, once we have discovered a few solutions to an equation many more can be obtained for free via the superposition principle. In an era characterized by the general scarcity of exact solutions, such a principle must have seemed like a gift from the optimizing rationality of God. Conversely, failure to obey this principle promoted the neglect of nonlinear equations. In the terms I have been using in this chapter we may say that superposition, that is, a property of the behaviour of solutions, biased the process of accumulation that created the population of models making up the theoretical component of classical mechanics. The requirement of exact solvability promoted the accumulation of linear models at the expense of nonlinear ones, and even the few nonlinear models allowed to become part of the population were used only in a linearized form.”
“In a Deleuzian ontology there exist two histories, one actual and one virtual, having complex interactions with one another. On one hand there is a historical series ot actual events genetically involved in the production of other events, and on the other, an equally historical series of ideal events detining an objective realm of virtual problems of which each actualized individual is but a specific solution.“