Fascism. Drunken Risibility

You must create your life, as you’d create a work of art. It’s necessary that the life of an intellectual be artwork with him as the subject. True superiority is all here. At all costs, you must preserve liberty, to the point of intoxication. — Gabriele d’Annunzio

The complex relationship between fascism and modernity cannot be resolved all at once, and with a simple yes or no. It has to be developed in the unfolding story of fascism’s acquisition and exercise of power. The most satisfactory work on this matter shows how antimodernizing resentments were channeled and neutralized, step by step, in specific legislation, by more powerful pragmatic and intellectual forces working in the service of an alternate modernity.

The word fascism has its root in the Italian fascio, literally a bundle or sheaf. More remotely, the word recalled the Latin fasces, an axe encased in a bundle of rods that was carried before the magistrates in Roman public processions to signify the authority and unity of the state. Before 1914, the symbolism of the Roman fasces was usually appropriated by the Left. Marianne, symbol of the French Republic, was often portrayed in the nineteenth century carrying the fasces to represent the force of Republican solidarity against her aristocratic and clerical enemies. Italian revolutionaries used the term fascio in the late nineteenth century to evoke the solidarity of committed militants. The peasants who rose against their landlords in Sicily in 1893–94 called themselves the Fasci Siciliani. When in late 1914 a group of left-wing nationalists, soon joined by the socialist outcast Benito Mussolini, sought to bring Italy into World War I on the Allied side, they chose a name designed to communicate both the fervor and the solidarity of their campaign: the Fascio Rivoluzionario d’Azione Interventista (Revolutionary League for Interventionist Action). At the end of World War I, Mussolini coined the term fascismo to describe the mood of the little band of nationalist ex-soldiers and pro-war syndicalist revolutionaries that he was gathering around himself. Even then, he had no monopoly on the word fascio, which remained in general use for activist groups of various political hues. Officially, Fascism was born in Milan on Sunday, March 23, 1919. That morning, somewhat more than a hundred persons, including war veterans, syndicalists who had supported the war, and Futurist intellectuals, plus some reporters and the merely curious, gathered in the meeting room of the Milan Industrial and Commercial Alliance, overlooking the Piazza San Sepolcro, to “declare war against socialism . . . because it has opposed nationalism.” Now Mussolini called his movement the Fasci di Combattimento, which means, very approximately, “fraternities of combat.”

Definitions are inherently limiting. They frame a static picture of something that is better perceived in movement, and they portray as “frozen ‘statuary’” something that is better understood as a process. They succumb all too often to the intellectual’s temptation to take programmatic statements as constitutive, and to identify fascism more with what it said than with what it did. The quest for the perfect definition, by reducing fascism to one ever more finely honed phrase, seems to shut off questions about the origins and course of fascist development rather than open them up. Fascism, by contrast, was a new invention created afresh for the era of mass politics. It sought to appeal mainly to the emotions by the use of ritual, carefully stage-managed ceremonies, and intensely charged rhetoric. The role programs and doctrine play in it is, on closer inspection, fundamentally unlike the role they play in conservatism, liberalism, and socialism. Fascism does not rest explicitly upon an elaborated philosophical system, but rather upon popular feelings about master races, their unjust lot, and their rightful predominance over inferior peoples. It has not been given intellectual underpinnings by any system builder, like Marx, or by any major critical intelligence, like Mill, Burke, or Tocqueville. In a way utterly unlike the classical “isms,” the rightness of fascism does not depend on the truth of any of the propositions advanced in its name. Fascism is “true” insofar as it helps fulfill the destiny of a chosen race or people or blood, locked with other peoples in a Darwinian struggle, and not in the light of some abstract and universal reason.

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Capital as a Symbolic Representation of Power. Nitzan’s and Bichler’s Capital as Power: A Study of Order and Creorder.

The secret to understanding accumulation, lies not in the narrow confines of production and consumption, but in the broader processes and institutions of power. Capital, is neither a material object nor a social relationship embedded in material entities. It is not ‘augmented’ by power. It is, in itself, a symbolic representation of power….

Unlike the elusive liberals, Marxists try to deal with power head on – yet they too end up with a fractured picture. Unable to fit power into Marx’s value analysis, they have split their inquiry into three distinct branches: a neo-Marxian economics that substitutes monopoly for labour values; a cultural analysis whose extreme versions reject the existence of ‘economics’ altogether (and eventually also the existence of any ‘objective’ order); and a state theory that oscillates between two opposite positions – one that prioritizes state power by demoting the ‘laws’ of the economy, and another that endorses the ‘laws’ of the economy by annulling the autonomy of the state. Gradually, each of these branches has developed its own orthodoxies, academic bureaucracies and barriers. And as the fractures have deepened, the capitalist totality that Marx was so keen on uncovering has dissipated….

The commodified structure of capitalism, Marx argues, is anchored in the labour process: the accumulation of capital is denominated in prices; prices reflect labour values; and labour values are determined by the productive labour time necessary to make the commodities. This sequence is intuitively appealing and politically motivating, but it runs into logical and empirical impossibilities at every step of the way. First, it is impossible to differentiate productive from unproductive labour. Second, even if we knew what productive labour was, there would still be no way of knowing how much productive labour goes into a given commodity, and therefore no way of knowing the labour value of that commodity and the amount of surplus value it embodies. And finally, even if labour values were known, there would be no consistent way to convert them into prices and surplus value into profit. So, in the end, Marxism cannot explain the prices of commodities – not in detail and not even approximately. And without a theory of prices, there can be no theory of profit and accumulation and therefore no theory of capitalism….

Modern capitalists are removed from production: they are absentee owners. Their ownership, says Veblen, doesn’t contribute to industry; it merely controls it for profitable ends. And since the owners are absent from industry, the only way for them to exact their profit is by ‘sabotaging’ industry. From this viewpoint, the accumulation of capital is the manifestation not of productive contribution but of organized power.

To be sure, the process by which capitalists ‘translate’ qualitatively different power processes into quantitatively unified measures of earnings and capitalization isn’t very ‘objective’. Filtered through the conventional assessments of accountants and the future speculations of investors, the conversion is deeply inter-subjective. But it is also very real, extremely imposing and, as we shall see, surprisingly well-defined.

These insights can be extended into a broader metaphor of a ‘social hologram’: a framework that integrates the resonating productive interactions of industry with the dissonant power limitations of business. These hologramic spectacles allow us to theorize the power underpinnings of accumulation, explore their historical evolution and understand the ways in which various forms of power are imprinted on and instituted in the corporation…..

Business enterprise diverts and limits industry instead of boosting it; that ‘business as usual’ needs and implies strategic limitation; that most firms are not passive price takers but active price makers, and that their autonomy makes ‘pure’ economics indeterminate; that the ‘normal rate of return’, just like the ancient rate of interest, is a manifestation not of productive yield but of organized power; that the corporation emerged not to enhance productivity but to contain it; that equity and debt have little to do with material wealth and everything to do with systemic power; and, finally, that there is little point talking about the deviations and distortions of ‘financial capital’ simply because there is no ‘productive capital’ to deviate from and distort.

Jonathan Nitzan, Shimshon Bichler- Capital as Power:_ A Study of Order and Creorder 

 

Sobolev Spaces

For any integer n ≥ 0, the Sobolev space Hⁿ(R) is defined to be the set of functions f which are square-integrable together with all their derivatives of order up to n:

f ∈ Hⁿ(R) ⇐⇒ ∫_-∞^∞ [f² + ∑_k=1ⁿ (d^kf/dx^k)² dx ≤ ∞

This is a linear space, and in fact a Hilbert space with norm given by:

∥f∥_Hⁿ = ∫_-∞^∞ [f² + ∑_k=1ⁿ (d^kf/dx^k)²) dx]^1/2

It is a standard fact that this norm of f can be expressed in terms of the Fourier transform fˆ (appropriately normalized) of f by:

∥f∥²_Hⁿ = ∫_-∞^∞ [(1 + y²)ⁿ |fˆ(y)|² dy

The advantage of that new definition is that it can be extended to non-integral and non-positive values. For any real number s, not necessarily an integer nor positive, we define the Sobolev space H^s(R) to be the Hilbert space of functions associated with the following norm:

∥f∥²_H^s = ∫_-∞^∞ [(1 + y²)^s |fˆ(y)|² dy —– (1)

Clearly, H⁰(R) = L²(R) and H^s(R) ⊂ H^s′(R) for s ≥ s′ and in particular H^s(R) ⊂ L²(R) ⊂ H^−s(R), for s ≥ 0. H^s(R) is, for general s ∈ R, a space of (tempered) distributions. For example δ(k), the k-th derivative of a delta Dirac distribution, is in H^{−k−1/2</sup−ε}(R) for ε > 0.

In the case when s > 1/2, there are two classical results.

Continuity of Multiplicity:

If s > 1/2, if f and g belong to H^s(R), then fg belongs to H^s(R), and the map (f,g) → fg from H^s × H^s to H^s is continuous.

Denote by C_bⁿ(R) the space of n times continuously differentiable real-valued functions which are bounded together with all their n first derivatives. Let Cⁿ_b0(R) be the closed subspace of C_bⁿ(R) of functions which converges to 0 at ±∞ together with all their n first derivatives. These are Banach spaces for the norm:

∥f∥C_bⁿ = max_0≤k≤n sup_x |f^(k)(x)| = max_0≤k≤n ∥f(k)∥ C⁰_b

Sobolev embedding:

If s > n + 1/2 and if f ∈ H^s(R), then there is a function g in Cⁿ_b0(R) which is equal to f almost everywhere. In addition, there is a constant c_s, depending only on s, such that:

∥g∥_Cbⁿ ≤ c_s ∥f∥H^s

From now on we shall always take the continuous representative of any function in H^s(R). As a consequence of the Sobolev embedding theorem, if s > 1/2, then any function f in H^s(R) is continuous and bounded on the real line and converges to zero at ±∞, so that its value is defined everywhere.

We define, for s ∈ R, a continuous bilinear form on H^−s(R) × H^s(R) by:

〈f, g〉= ∫_-∞^∞ (fˆ(y))’ gˆ(y)dy —– (2)

where z’ is the complex conjugate of z. Schwarz inequality and (1) give that

|< f , g >| ≤ ∥f∥_H^−s∥g∥_H^s —– (3)

which indeed shows that the bilinear form in (2) is continuous. We note that formally the bilinear form (2) can be written as

〈f, g〉= ∫_-∞^∞ f(x) g(x) dx

where, if s ≥ 0, f is in a space of distributions H^−s(R) and g is in a space of “test functions” H^s(R).

Any continuous linear form g → u(g) on H^s(R) is, due to (1), of the form u(g) = 〈f, g〉 for some f ∈ H^−s(R), with ∥f∥_H^−s = ∥u∥_(H^s)′, so that henceforth we can identify the dual (H^s(R))′ of H^s(R) with H^−s(R). In particular, if s > 1/2 then H^s(R) ⊂ C⁰_b0 (R), so H^−s(R) contains all bounded Radon measures.

Whitehead’s Anti-Substantivilism, or Process & Reality as a Cosmology to-be. Thought of the Day 39.0

Treating “stuff” as some kind of metaphysical primitive is mere substantivilism – and fundamentally question-begging. One has replaced an extra-theoretic referent of the wave-function (unless one defers to some quasi-literalist reading of the nature of the stochastic amplitude function ζ[X(t)] as somehow characterizing something akin to being a “density of stuff”, and moreover the logic and probability (Born Rules) must ultimately be obtained from experimentally obtained scattering amplitudes) with something at least as equally mystifying, as the argument against decoherence goes on to show:

In other words, you have a state vector which gives rise to an outcome of a measurement and you cannot understand why this is so according to your theory.

As a response to Platonism, one can likewise read Process and Reality as essentially anti-substantivilist.

Consider, for instance:

Those elements of our experience which stand out clearly and distinctly [giving rise to our substantial intuitions] in our consciousness are not its basic facts, [but] they are . . . late derivatives in the concrescence of an experiencing subject. . . .Neglect of this law [implies that] . . . [e]xperience has been explained in a thoroughly topsy-turvy fashion, the wrong end first (161).

To function as an object is to be a determinant of the definiteness of an actual occurrence [occasion] (243).

The phenomenological ontology offered in Process and Reality is richly nuanced (including metaphysical primitives such as prehensions, occasions, and their respectively derivative notions such as causal efficacy, presentational immediacy, nexus, etc.). None of these suggest metaphysical notions of substance (i.e., independently existing subjects) as a primitive. The case can perhaps be made concerning the discussion of eternal objects, but such notions as discussed vis-à-vis the process of concrescence are obviously not metaphysically primitive notions. Certainly these metaphysical primitives conform in a more nuanced and articulated manner to aspects of process ontology. “Embedding” – as the notion of emergence is a crucial constituent in the information-theoretic, quantum-topological, and geometric accounts. Moreover, concerning the issue of relativistic covariance, it is to be regarded that Process and Reality is really a sketch of a cosmology-to-be . . . [in the spirit of ] Kant [who] built on the obsolete ideas of space, time, and matter of Euclid and Newton. Whitehead set out to suggest what a philosophical cosmology might be that builds on Newton.

US Stock Market Interaction Network as Learned by the Boltzmann Machine

Price formation on a financial market is a complex problem: It reflects opinion of investors about true value of the asset in question, policies of the producers, external regulation and many other factors. Given the big number of factors influencing price, many of which unknown to us, describing price formation essentially requires probabilistic approaches. In the last decades, synergy of methods from various scientific areas has opened new horizons in understanding the mechanisms that underlie related problems. One of the popular approaches is to consider a financial market as a complex system, where not only a great number of constituents plays crucial role but also non-trivial interaction properties between them. For example, related interdisciplinary studies of complex financial systems have revealed their enhanced sensitivity to fluctuations and external factors near critical events with overall change of internal structure. This can be complemented by the research devoted to equilibrium and non-equilibrium phase transitions.

In general, statistical modeling of the state space of a complex system requires writing down the probability distribution over this space using real data. In a simple version of modeling, the probability of an observable configuration (state of a system) described by a vector of variables s can be given in the exponential form

p(s) = Z⁻¹ exp {−βH(s)} —– (1)

where H is the Hamiltonian of a system, β is inverse temperature (further β ≡ 1 is assumed) and Z is a statistical sum. Physical meaning of the model’s components depends on the context and, for instance, in the case of financial systems, s can represent a vector of stock returns and H can be interpreted as the inverse utility function. Generally, H has parameters defined by its series expansion in s. Basing on the maximum entropy principle, expansion up to the quadratic terms is usually used, leading to the pairwise interaction models. In the equilibrium case, the Hamiltonian has form

H(s) = −h^T_s − s^TJs —– (2)

where h is a vector of size N of external fields and J is a symmetric N × N matrix of couplings (T denotes transpose). The energy-based models represented by (1) play essential role not only in statistical physics but also in neuroscience (models of neural networks) and machine learning (generative models, also known as Boltzmann machines). Given topological similarities between neural and financial networks, these systems can be considered as examples of complex adaptive systems, which are characterized by the adaptation ability to changing environment, trying to stay in equilibrium with it. From this point of view, market structural properties, e.g. clustering and networks, play important role for modeling of the distribution of stock prices. Adaptation (or learning) in these systems implies change of the parameters of H as financial and economic systems evolve. Using statistical inference for the model’s parameters, the main goal is to have a model capable of reproducing the same statistical observables given time series for a particular historical period. In the pairwise case, the objective is to have

⟨s_i⟩_data = ⟨s_i⟩_model —– (3a)

⟨s_is_j⟩_data = ⟨s_is_j⟩_model —– (3b)

where angular brackets denote statistical averaging over time. Having specified general mathematical model, one can also discuss similarities between financial and infinite- range magnetic systems in terms of phenomena related, e.g. extensivity, order parameters and phase transitions, etc. These features can be captured even in the simplified case, when s_i is a binary variable taking only two discrete values. Effect of the mapping to a binarized system, when the values s_i = +1 and s_i = −1 correspond to profit and loss respectively. In this case, diagonal elements of the coupling matrix, J_ii, are zero because s²_i = 1 terms do not contribute to the Hamiltonian….

US stock market interaction network as learned by the Boltzmann Machine