Rhizomatic Extreme-Right.


In the context of the extreme right-wing politics in the contemporary age, groupuscules can be defined as numerically negligible political, frequently meta-political, but never party-political entities formed to pursue palingenetic ideological, organizational or activistic ends with an ultimate goal of overcoming the decadence of the liberal-democratic system. Though, they are fully formed and autonomous, they have small active memberships and minimal, if any public visibility or support, which is now inflating. Yet they acquire enhanced influence and significance through the ease with which they can be associated, even if only in the minds of political extremists, with other group lets which are sufficiently aligned ideologically and tactically to complement each other’s activities in their bid to institute a new type of society. As a result the groupuscule has Janus-headed characteristic of combining organizational autonomy with the ability to create informal linkages with, or reinforce the influence of other such formations. This enables groupuscules, when considered in terms of their aggregate impact on politics and society, to be seen as forming a non-hierarchical, leaderless and centreless, or rather polycentric movement with fluid boundaries and constantly changing components. This groupuscular right has the characteristics of a political and ideological subculture rather than a conventional political party movement, and is perfectly adapted to the task of perpetuating revolutionary extremism in an age of relative political stability.

The outstanding contrast between the groupuscular and party-political organization of the extreme right is that instead of being formed into a tree-like hierarchical organisms it is now rhizomatic. The use of the term was pioneered in the spirit of post-structuralist radicalism by Deleuze and Guattari to help conceptualize the social phenomena to which, metaphorically at least, the attributes of supra-personal organic life-forms can be ascribed, but which are not structured in a coherently hierarchical or systematically interconnected way which would make tree-based or dendroid metaphors appropriate. When applied to groupuscular right the concept of rhizome throws itself into relief its dynamic nature as a polycentric, leaderless movement by stressing that it does not operate like a single organism such as a tree with a tap-root, branch and canopy, and a well-defined beginning and an end. Instead, it behaves like the root-system of some species of grass or tuber, displaying multiple starts and beginnings which intertwine and connect with each other, constantly producing new shoots as others die off in an unpredictable, asymmetrical pattern of growth and decay. If a political network has a rhizomes political structure it means that it forms a cellular, capillary network with ill-defined boundaries and no formal hierarchy or internal organizational structure to give it a unified intelligence. Thanks to its rhizomic structure the groupuscular right no longer emulates a singular living organism, as the slime-mould is so mysteriously capable of doing. Nor is it to be seen as made up of countless tiny, disconnected micro-organisms. Instead, following an internal dynamic which only the most advanced life sciences can model with any clarity, the minute bursts of spontaneous creativity which produce and maintain individual groupuscules constitute nodal points in a force-field or web of radical political energy which fuels the vitality and viability of the organism as a whole. These qualities duplicate the very features of the Internet for making it impossible to shut down or wipe out the information it contains simply by knocking out any one part of it, since there is no mission control to destroy. The groupuscularity of the contemporary extreme right makes it eminently able to survive and grow even if some of the individual organizations which constitute it are banned and their websites closed down.

From Slime Mould to Rhizome



Fortune of the Individuals Restricted to Integers: Random Economic Exchange Between Populations of Traders.


Consider a population of traders, each of which possesses a certain amount of capital which is assumed to be quantized in units of minimal capital. Taking this latter quantity as the basic unit, the fortune of an individual is restricted to the integers. The wealth of the population evolves by the repeated interaction of random pairs of traders. In each interaction, one unit of capital is transferred between the trading partners. To complete the description, we specify that if a poorest individual (with one unit of capital) loses all remaining capital by virtue of a “loss”, the bankrupt individual is considered to be economically dead and no longer participates in economic activity.

In the following, we consider a specific realization of additive capital exchange, the “random” exchange, where the direction of the capital exchange is independent of the relative capital of the traders. While this rule has little economic basis, the model is completely soluble and thus provides a helpful pedagogical point.

In a random exchange, one unit of capital is exchanged between trading partners as represented by the reaction scheme (j, k) → (j ± 1, k ∓ 1). Let ck(t) be the density of individuals with capital k. within a mean-field description, ck(t) evolves according to

dck(t)/dt = N(t) [ck+1(t) + ck-1(t) – 2ck(t)] —– (1)

with N(t) ≡ M0(t) = ∑k=1 ck(t), the population density. The first two terms account for gain in ck(t) due to the interactions (j, k + 1) → (j + 1, k) and (j, k − 1) → (j−1, k), respectively, while the last term accounts for the loss in ck(t) due to the interactions (j, k) → (j±1, k∓1).

By defining a modified time variable,

T = ∫0dt’N(t’) —– (2)

equation (1) is reduced to the discrete diffusion equation

dck(T)/dT = ck+1(T) + ck-1(T) – 2ck(T) —– (3)

The rate equation for the poorest density has the slightly different form, dc1/dT = c2 − 2c1, but may be written in the same form as equation (3) if we impose the boundary condition c0(T) = 0.

For illustrative purposes, let us assume that initially all individuals have one unit of capital, ck(0) = δk1. The solution to equation (3) subject to these initial and boundary conditions is

ck(T) = e−2T [Ik−1(2T) − Ik+1(2T)] —– (4)

where In denotes the modified Bessel function of order n. consequently, the total density N(t) is

N(T) = e−2T [I0(2T) + I1(2T)] —– (5)

To re-express this exact solution in terms of the physical time t, we first invert equation (2) to obtain t(T) = ∫0T dT′/N(T′), and then eliminate T in favor of t in the solution for ck(T). For simplicity and concreteness, let us consider the long-time limit. From equation (4),

ck(T) ≅ k/√(4πT3) exp (-k2/4T) —– (6)

and from equation (5),

N(T) ≅ (πT)−1/2 —– (7)

Equation (7) also implies t ≅ 2/3 √(πT3) which gives

N(T) ≅ (2/3πt)1/3 —– (8)


ck(t) ≅ k/3t exp [-(π/144)1/3 k2/t2/3] —– (9)

Note that this latter expression may be written in the scaling form ck(t) ∝ N2xe−x2, with the scaling variable x ∝ kN. One can also confirm that the scaling solution represents the basin of attraction for almost all exact solutions. Indeed, for any initial condition with ck(0) decaying faster than k−2, the system reaches the scaling limit ck(t) ∝ N2xe−x2. On the other hand, if ck(0) ∼ k−1−α, with 0 < α < 1, such an initial state converges to an alternative scaling limit which depends on α. These solutions exhibit a slower decay of the total density, N ∼ t−α/(1+α), while the scaling form of the wealth distribution is

ck(t) ∼ N2/αCα(x), x ∝ kN1/α —– (10)

with the scaling function

Cα(x) = e−x20 du e−u2 sinh(2ux)/u1+α —– (11)

Evaluating the integral by the Laplace method gives an asymptotic distribution which exhibits the same x−1−α as the initial distribution. This anomalous scaling in the solution to the diffusion equation is a direct consequence of the extended initial condition. This latter case is not physically relevant, however, since the extended initial distribution leads to a divergent initial wealth density.

Production of the Schizoid, End of Capitalism and Laruelle’s Radical Immanence. Note Quote Didactics.


These are eclectics of the production, eclectics of the repetition, eclectics of the difference, where the fecundity of the novelty would either spring forth, or be weeded out. There is ‘schizoproduction’ prevalent in the world. This axiomatic schizoproduction is not a speech act, but discursive, in the sense that it constrains how meaning is distilled from relations, without the need for signifying, linguistic acts. Schizoproduction performs the relation. The bare minimum of schizoproduction is the gesture of transcending thought: namely, what François Laruelle calls a ‘decision’. Decision is differential, but it does not have to signify. It is the capacity to produce distinction and separation, in the most minimal, axiomatic form. Schizoproduction is capitalism turned into immanent capitalism, through a gesture of thought – sufficient thought. It is where capitalism has become a philosophy of life, in that it has a firm belief within a sufficient thought, whatever it comes in contact with. It is an expression of the real, the radical immanence as a transcending arrangement. It is a collective articulation bound up with intricate relations and management of carnal, affective, and discursive matter. The present form of capitalism is based on relationships, collaborations, and processuality, and in this is altogether different from the industrial period of modernism in the sense of subjectivity, production, governance, biopolitics and so on. In both cases, the life of a subject is valuable, since it is a substratum of potentiality and capacity, creativity and innovation; and in both cases, a subject is produced with physical, mental, cognitive and affective capacities compatible with each arrangement. Artistic practice is aligned with a shift from modern liberalism to the neoliberal dynamic position of the free agent.

Such attributes have thus become so obvious that the concepts of ‘competence’, ‘trust’ or ‘interest’ are taken as given facts, instead of perceiving them as functions within an arrangement. It is not that neoliberal management has leveraged the world from its joints, but that it is rather capitalism as philosophy, which has produced this world, where neoliberalism is just a part of the philosophy. Therefore, the thought of the end of capitalism will always be speculative, since we may regard the world without capitalism in the same way as we may regard the world-not-for-humans, which may be a speculative one, also. From its inception, capitalism paved a one-way path to annihilation, predicated as it was on unmitigated growth, the extraction of finite resources, the exaltation of individualism over communal ties, and the maximization of profit at the expense of the environment and society. The capitalist world was, as Thurston Clarke described so bleakly, ”dominated by the concerns of trade and Realpolitik rather than by human rights and spreading democracy”; it was a ”civilization influenced by the impersonal, bottom-line values of the corporations.” Capitalist industrial civilization was built on burning the organic remains of ancient organisms, but at the cost of destroying the stable climatic conditions which supported its very construction. The thirst for fossil fuels by our globalized, high-energy economy spurred increased technological development to extract the more difficult-to-reach reserves, but this frantic grasp for what was left only served to hasten the malignant transformation of Earth into an alien world. The ruling class tried to hold things together for as long as they could by printing money, propping up markets, militarizing domestic law enforcement, and orchestrating thinly veiled resource wars in the name of fighting terrorism, but the crisis of capitalism was intertwined with the ecological crisis and could never be solved by those whose jobs and social standing depended on protecting the status quo. All the corporate PR, greenwashing, political promises, cultural myths, and anthropocentrism could not hide the harsh Malthusian reality of ecological overshoot. As crime sky-rocketed and social unrest boiled over into rioting and looting, the elite retreated behind walled fortresses secured by armed guards, but the great unwinding of industrial civilization was already well underway. This evil genie was never going back in the bottle. And thats speculative too, or not really is a nuance to be fought hard on.

The immanence of capitalism is a transcending immanence: a system, which produces a world as an arrangement, through a capitalist form of thought—the philosophy of capitalism—which is a philosophy of sufficient reason in which economy is the determination in the last instance, and not the real. We need to specifically regard that this world is not real. The world is a process, a “geopolitical fiction”. Aside from this reason, there is an unthinkable world that is not for humans. It is not the world in itself, noumena, nor is it nature, bios, but rather it is the world indifferent to and foreclosed from human thought, a foreclosed and radical immanence – the real – which is not open nor will ever be opening itself for human thought. It will forever remain void and unilaterally indifferent. The radical immanence of the real is not an exception – analogous to the miracle in theology – but rather, it is an advent of the unprecedented unknown, where the lonely hour of last instance never comes. This radical immanence does not confer with ‘the new’ or with ‘the same’ and does not transcend through thought. It is matter in absolute movement, into which philosophy or oikonomia incorporates conditions, concepts, and operations. Now, a shift in thought is possible where the determination in the last instance would no longer be economy but rather a radical immanence of the real, as philosopher François Laruelle has argued. What is given, what is radically immanent in and as philosophy, is the mode of transcendental knowledge in which it operates. To know this mode of knowledge, to know it without entering into its circle, is to practice a science of the transcendental, the “transcendental science” of non-philosophy. This science is of the transcendental, but according to Laruelle, it must also itself be transcendental – it must be a global theory of the given-ness of the real. A non- philosophical transcendental is required if philosophy as a whole, including its transcendental structure, is to be received and known as it is. François Laruelle radicalises the Marxist term of determined-in-the-last-instance reworked by Louis Althusser, for whom the last instance as a dominating force was the economy. For Laruelle, the determination-in-the-last-instance is the Real and that “everything philosophy claims to master is in-the-last-instance thinkable from the One-Real”. For Althusser, referring to Engels, the economy is the ‘determination in the last instance’ in the long run, but only concerning the other determinations by the superstructures such as traditions. Following this, the “lonely hour of the ‘last instance’ never comes”.



In many areas of mathematics there is a need to have methods taking local information and properties to global ones. This is mostly done by gluing techniques using open sets in a topology and associated presheaves. The presheaves form sheaves when local pieces fit together to global ones. This has been generalized to categorical settings based on Grothendieck topologies and sites.

The general problem of going from local to global situations is important also outside of mathematics. Consider collections of objects where we may have information or properties of objects or subcollections, and we want to extract global information.

This is where hyperstructures are very useful. If we are given a collection of objects that we want to investigate, we put a suitable hyperstructure on it. Then we may assign “local” properties at each level and by the generalized Grothendieck topology for hyperstructures we can now glue both within levels and across the levels in order to get global properties. Such an assignment of global properties or states we call a globalizer. 

To illustrate our intuition let us think of a society organized into a hyperstructure. Through levelwise democratic elections leaders are elected and the democratic process will eventually give a “global” leader. In this sense democracy may be thought of as a sociological (or political) globalizer. This applies to decision making as well.

In “frustrated” spin systems in physics one may possibly think of the “frustation” being resolved by creating new levels and a suitable globalizer assigning a global state to the system corresponding to various exotic physical conditions like, for example, a kind of hyperstructured spin glass or magnet. Acting on both classical and quantum fields in physics may be facilitated by putting a hyperstructure on them.

There are also situations where we are given an object or a collection of objects with assignments of properties or states. To achieve a certain goal we need to change, let us say, the state. This may be very difficult and require a lot of resources. The idea is then to put a hyperstructure on the object or collection. By this we create levels of locality that we can glue together by a generalized Grothendieck topology.

It may often be much easier and require less resources to change the state at the lowest level and then use a globalizer to achieve the desired global change. Often it may be important to find a minimal hyperstructure needed to change a global state with minimal resources.

Again, to support our intuition let us think of the democratic society example. To change the global leader directly may be hard, but starting a “political” process at the lower individual levels may not require heavy resources and may propagate through the democratic hyperstructure leading to a change of leader.

Hence, hyperstructures facilitates local to global processes, but also global to local processes. Often these are called bottom up and top down processes. In the global to local or top down process we put a hyperstructure on an object or system in such a way that it is represented by a top level bond in the hyperstructure. This means that to an object or system X we assign a hyperstructure

H = {B0,B1,…,Bn} in such a way that X = bn for some bn ∈ B binding a family {bi1n−1} of Bn−1 bonds, each bi1n−1 binding a family {bi2n−2} of Bn−2 bonds, etc. down to B0 bonds in H. Similarly for a local to global process. To a system, set or collection of objects X, we assign a hyperstructure H such that X = B0. A hyperstructure on a set (space) will create “global” objects, properties and states like what we see in organized societies, organizations, organisms, etc. The hyperstructure is the “glue” or the “law” of the objects. In a way, the globalizer creates a kind of higher order “condensate”. Hyperstructures represent a conceptual tool for translating organizational ideas like for example democracy, political parties, etc. into a mathematical framework where new types of arguments may be carried through.