Archive for the ‘Ilya Prigogine’ Category

Manuel DeLanda “Intensive Science and Virtual Philosophy”

DeLanda, Manuel 2011. Intensive Science and Virtual Philosophy. London; New York: Bloomsbury Academic.

2. The Actualization of the Virtual in Space
Much as a thermodynamic intensive process is characterized by the productive role which differences play in the driving of fluxes, so in the enlarged sense a process is intensive if it relates difference to difference. Moreover, as the example of assembly processes based on adaptive components showed, the flexible links which these components afford one another allow not only the meshing of differences, but also endow the process with the capacity of divergent evolution, that is, the capacity to further differentiate differences. (67)

[…] in the case of singularities the existence of the virtual is manifested in those situations where intensive differences are not cancelled. (68)

As Prigogine and Nicolis put it, „without the maintenance of an appropriate distance from from equilibrium, nonlinearity cannot by itself give rise to multiple solutions. At equilibrium detailed balance introduces a further condition that restricts and even uniquely fixes” the solution. In other words, to exhibit their full complexity nonlinear systems need to be driven away from equilibrium, or what amounts to the same thing, appropriately large differences in intensity need to be maintained by external constraints and not allowed to get cancelled or be made to small. In this sense, as these authors say, „nonequilibrium reveals the potentialities hidden in the nonlinearities, potentialities that remain dormant at or near equilibrium.” (69)

A nonlinear system with multiple attractors […] continues to display its virtuality even once the system has settled into one of its alternative stable states, because the other alternatives are there all the time, coexisting with the one that happens to be actualized. (69-70)

In other words, unlike the linear and equilibrium approach to science which concentrates on the final product, or at best on the process of actualization but always in the direction of the final product, philosophy should move in the opposite direction: from qualities and extensities, to the intensive processes which produce them, and from there to the virtual. (70-71)

Deleuze, in fact, refers to the virtual continuum as a plane of consistency, using the term „consistency” in a unique sense, and in particular, in a sense having nothing to do with logical consistency, that is, with the absence of contradiction. Rather, consistency is defined sa the synthesis of heterogeneities as such. (72)

[…] none of these concepts can presuppose individuation. They need to be transformed to become fully pre-individual notions so that they can form the logical and physical basis for the genesis of individuals. (73-74)

Much as virtual differential relations must be distinguished from individuating functions, virtual singularities should be distinguished from individuated states. (74)

Deleuze: „What is an ideal event? It is a singularity – or rather a set of singularities or of singular points characterizing a mathematical curve, a physical state of affairs, a psychological and moral person. Singularities are turning points and pints of inflection; bottlenecks, knots, foyers, and centers; points of fusion, condensation and boiling; points of tears and joy, sickness and health, hope and anxiety, „sensitive points” […] [Yet, a singularity] is essentially pre-individual, non-personal, and a-conceptual. It is quite indifferent to the individual and the collective, the personal and the impersonal, the particular and the general – and to their oppositions. Singularity is neutral.” (75 – Logic of Sense, p. 52)

[…] infinite ordinal series. Unlike and infinite series of cardinal numbers (one, two, three …) an ordinal series (first, second, third …) does not presuppose the existence of fully individuated numerical quantitities. To be defined an ordinal series demands only certain asymmetrical relations between abstract elements, relations like that of being in between two other elements. In other words, it is only the order in a sequence that matters, and not the nature (numerical or otherwise) of the elements so ordered. (76)

Two metric entities, two lengths, for example, can be divided in a simple way into basic numerical units. This allows them to be exaclty compared since we can establish unambisguously the numerical identity of the two lengths. Ordinal series, on the other hand, behave more like topological spaces, where we can rigorously establish that a point is nearby another, but not by exactly how much (given that their separation may be stretched or compressed). (76)

As a relation, an ordinal distance cannot be divided, and its lack of dividibility into identical units implies that two ordinal distances can never be exactly compared although we can rigorously establish that one is greater or less than another. The difference between two distances, in other words, cannot be cancelled through numerical identity, so the results of these comparisons are always anexact yet rigorous. In short, ordinal distances are a nonmetric or non-quantitative concept. Deleuze adopts these ideas from Russell but breaks with him at a crucial point: he does not conceive of the priority which the ordinal has over the cardinal as being purely logical or conceptual, but as being ontological. In other words, Deleuze establishes a genetic relationship between serial order and its defining nonmetric distances, on one hand, and numerical quantities, on the other. An ordinal series which is dense (that is, where between any two elements there is always another one) would form a one-dimensional continuum out of which cardinal numbers would emerge through a symmetry-breaking discontinuity. (76-77)

Multiplicities should not be conceived as possessing the capacity to actively interact with one another through these series. […] Deleuze views multiplicities as incorporeal effects of corporeal causes, that is, as historical results of actual causes possessing no causal powers of their own. (77-78)

[…] the ideal events forming a virtual series must not be conceived as having numerical probabilities of occurrence associated with them; they must be arranged in series using only ordinal distances, and be distinguished from one another exclusively by the difference between the singular and the ordinary, the rare and the common, without further specification. In other words, the coupled changes in distributions which constitute an information transfer should not be conceived as changes in conditional probabilities, but simply changes in the distribution of the singular and the ordinary within a series. (79)

Unlike the a priori grasp of essences in human thought postulated by those who believe in such entitities, there would be an empiricism of the virtual. The concepts of virtual multiplicity, quasi-causal operator and the plane of consistency would be, in this sense, concrete empirico-ideal notions, not abstract categories. (80)

In the vicinity of the bifurcation the capacity to transmit information is maximized. (81)

3. The Actualization of the Virtual in Time
The term „reversibility of time” has nothing to do with the idea of time flowing backwards, that is, with a flow of time going from the future towards the past. Rather it refers to the fact that if we took a certain process, seen as a series of events, and reversed their sequential order, the relevant properties of the process would not change. (98)

The Deleuzian ontology I have described in these pages is […] one characterizing a universe of becoming without being. Or more exactly, a universe where individual beings do exist but only as the outcome of becomings, that is, of irreversible processes of individuation. (99)

The term „extensive” may be applied to a flow of time already divided into instants of a given extension or duration, instants which may be counted using any device capable of performing regular sequences of oscillations. (99)

Thinking about the temporality involved in individuation processes as embodying the parallel operation of many different sequential processes throws new light on the question of the emergence of novelty. If embryological processes followed a strictly sequential order, that is, if a unique linear sequence of events defined the production of an organism, then any novel structures would be constrained to be added at the end of the sequence (in a process called „terminal addition”). On the contrary, if embryonic development occurs in parallel, if bundles of relatively independent processes occur simultaneously, then new designs may arise from disengaging bundles, or more precisely, from altering the duration of one process relative to another, or the relative timing of the start or end of a process. This evolutionary design strategy is known as heterochrony, of which the most extensively studied case is the process called „neoteny”. (111-112)

Neoteny illustrates that novelty need not be the effect of terminal addition of new features, but on the contrary, that it can be the result of a loss of certain old features. (112)

To Deleuze this aspect of individuation processes (an aspect which must be added to population thinking to complete the Darwinian revolution) is highly significant because it eliminates the idea that evolutionary processes possess an inherent drive towards an increase in complexity, an idea which reintroduces teleology into Darwinism. (112)

[…] whereas embryogenesis is a procss through which a yet unformed individual becomes what it is, acquiring a well-defined inside (the intrinsic properties defining its being), symbiosis represents a process through which a fully formed being may cease to be what it is to become something else, in association with something heterogeneous on the outside. (116)

[…] the successive determination of sub-spaces to which Deleuze refers is simply the progressive unfolding of multiplicities through a series of symmetry-breaking events. The form of temporality involved in this unfolding, however, should be conceived in a very different way from that in which actual bifurcation events occur. The latter involve a temporal sequence of events and stable states, the sequence of phase transitions which yields the series of stable flow patterns conduction-convection-turbulence, for example. Moreover, as each bifurcation occurs, only one of the several alternatives available to the system is actualized. […] In a virtual unfolding, on the other hand, the symmetry-breaking events not only fully coexist with one another (as opposed to follow each other), but in addition, each broken symmetry produces all the alternatives simultaneously, regardless of whether they are physically stable or not. (119-120)

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. (120)

[…] 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. (121-122)

In epistemological terms to extract an ideal event from an actually occurring one is, basically, to define what is problematic about it, to grasp what about the event objectively stands in need of explanation. This involves discerning in the actual event what is relevant and irrelevant for its explanation, what is important and what is not. That is, it onvolves correctly grasping the objective distribution of the singular and the ordinary defining a well-posed problem. To give consistency to these well-posed problems, in turn, means to endow them with a certain autonomy from their particular solutions, to show that problems do not disappear behind actualized individuals. (129-130)

4. Virtuality and the Laws of Physics
Part of what made possible the replacement of causes by laws was a view of causality as an inherently linear relation, such that, given a particular cause, the same effect was bound to be reproduced. (149)

In a typical nonlinear state space, subdivided by multiple attractors and their basins of attraction, the structure of the space of possibilities depends not on some extrinsically defined relation (specifying what is an inessential change) but on the distribution of singularities itself. (160)

In a linear causal chain, effects do not react back on their causes, that is, in these chains causal influence is not reciprocal. […] small causes always produce small effects. In other words, without feedback the intensity of the effect will tend to be proportional to that of the cause, while in the presence of reciprocal interaction causal influence may be reduced or increased. (168)


Ilya Prigogine & Isabelle Stengers “Dynamics from Leibniz to Lucretius”

January 10, 2013 Leave a comment

Prigogine, Ilya; Isabelle Stengers 1982. Postface: Dynamics from Leibniz to Lucretius. – Serres, Michel. Hermes: Literature, Science, Philosophy. Baltimore; London: The Johns Hopkins University Press, 135-158

Newtonian  physics  posits  a  body  assumed  to  be  isolated, endowed with a rectilinear and uniform inertial movement, and calculates the modifications of this movement as determined by the action of forces. For Leibniz,  the forces  are  not “given”  and  are  in no way  the real  causes of the  modification  of a  movement  but rather are  local properties within a  dynamic  system:  at  every  point,  they  characterize  a  momentary  state belonging to a series regulated  by a law. (141)

The  optimal point of view on  a system,  the  best  choice  of variables,  is therefore the one that cancels out the potential energy redefined in terms of  these  variables.  And  dynamic  theory  tells  us  that  every  integrable system  can  be  represented  in  this  way -can  be  redefined  as  a  set  of “units”  evolving in  a  pseudo-inertial  movement,  without any interaction among the “units.” Each “monadic unit” is no longer determined in each of its movements by interactions with the aggregate ; each deploys its own law for  itself,  alone  in  a system  which  it reflects intrinsically, because  its very definition supposes and translates this system in every detail. There is full passage between the local  and  the  global. (144)

Quantum mechanics thus presents a reversal of perspective relative to classical  style.  It  is  no  longer  a  question  of looking  for  simplicity  at  the level  of  elementary  behavior.  Dynamic  simplicity,  as  reflected  by  the possibility  of  a  completely  monadic  represen tation,  belongs,  in  fact,  to the macroscopic world, to  the world on our scale. Our  physics is a science created by macroscopic  beings,  created  with conceptual  tools and instruments  that  belong  to  the  macroscopic  world.  It  is  from  that  position, when  we  question  the  world  of  quanta,  that  we  must  choose  what  will allow  us  to  express  matters  in  terms  of  measurable,  reproducible,  and communicable properties. We can no  longer allow ourselves, as far as the physical  world  is  concerned ,  the  privileged  point  of  view  which,  when pushed  to  its limit, we once could  have iden tified as that of God. (147)

We  can  see  how unfortunate  was the widespread assumption that quantum mechanics “discovered”  that the process of measurement disturbs the system nwasured. Uncontrollably modifying; the values of certain parameters in order to ascertain the value of others. Such an assumption in fact implies that only an arbitrary positivistic prohibition pn’vt’nts us from speaking; of “hidden variables,” that is to say, pr(‘vents us from affirming; that the system  in question is, at every moment, defilwd by tht, St’t of physical parameters, even if all of them cannot be known simultaneously. The actual situation is entirely different. The real discovery of quantum mechanics, as it is expressed by the inseparable character of reversible (‘volution and irreversible reduction, is not that tht, process of measurement disturbs, but rather that it participates in the definition of, the measured parameter, so that this parameter cannot be attributed to the quantum system “in itself” and one cannot speak of “hidden variables.” As Niels Bohr repeatedly said, quantum  mechanics  discovered  the  necessity of choic(‘, choosing; what question to ask,  in other  words, choosing; both  the  instrumental  framework  of the  question  and one of the complementary descriptions articulated among; themselves by formalism but irreducible to a single description. (147 – footnote)

“The world as it is is not the product of my  representation ;  my  knowledge,  on  the  contrary,  is a  product  of the world  in  the  process  of becoming.  Things  themselves  choose,  exclude, meet, and give rise to one  another.” (151 – Serres „Hermes IV“, 157-158)

An  unstable  system,  on  the  other  hand,  is  a  system  in  which  the initial  conditions  determining  various  qualitatively  distinct  behaviors are not  clearly  separated  but are,  on  the  contrary,  as close  as one  might wish. We are all familiar with this sort of intimate mixture -it is described by  number  theory: every  rational  number  is  surrounded  by  irrationals, and every irrational by rationals. Similarly, whatever the neighborhood defined for an  initial  state, one always finds at least one other state giving rise  to  a  qualitatively different behavior,  just as  oscillation  and rotation are qualitatively different. (151)

Under  these  conditions,  in  order  to  predict  deterministically  the  type of behavior  the  system  will  adopt,  one  would  need  infinite precision.  It is of no use  to  increase  the  level  of precision  or even to make  it tend toward infinity;  uncertainty  always  remains  complete -it  does  not  diminish  as precision  increases.  That  means  that  divine  knowledge  is  no  longer implied in human knowledge as its limit,  as that toward which one might tend with increasing precision ; it is something other, separated by a gap. (152)

It is not  a  question  of recognizing  that we  are  incapable  of calculating  such  traj ectories;  rather,  it is  a  question of  realizing  that  the  trajectory  is  not  an  adequate  physical  concept  for these  systems.  Henceforth  the  field  of  dynamics  will  appear  larger systems  described  in  terms  of  trajectories  with  their  determinist  and reversible properties are only a particular class within that field. (152)

Creative  chaos is illegality itself, for its description dissolves the distinction between the macroscopic state  and  the microscopic fluctuation ; correlations can appear among distant events; local deviations echo throughout the  system -the matrix-state  in  which  fluctuations are  amplified and from  which things  are born. (153-154)

And  thus  Serres  is  correct:  the question  is  reversed.  It  is  no  longer necessary to ask where the clinamen comes from or how one might justify the  disturbing  of  laws.  All  laminar  flows  can  become  unstable  past  a certain  threshold of velocity,  and  that  was  known  just as  the  productive nature  of  organized  forms,  of  bifurcating  evolution,  of  what  we  call dissipative  structures,  was  known.  One  must  ask  how  an  abstraction  of this  knowledge  could  have  been  made  to  describe  the  world  in  order, subject to a universal law. We already know one answer given by Serres. Classical science is a science of engineers who knew, of course, that their flows were never perfectly laminar, but who made  the theory of laminar flow perfectly controllable and directable, the only flow for which knowing is controlling. (154)