Graviton Fields Under Helicity Rotations. Thought of the Day 156.0

Einstein described gravity as equivalent to curves in space and time, but physicists have long searched for a theory of gravitons, its putative quantum-scale source. Though gravitons are individually too weak to detect, most physicists believe the particles roam the quantum realm in droves, and that their behavior somehow collectively gives rise to the macroscopic force of gravity, just as light is a macroscopic effect of particles called photons. But every proposed theory of how gravity particles might behave faces the same problem: upon close inspection, it doesn’t make mathematical sense. Calculations of graviton interactions might seem to work at first, but when physicists attempt to make them more exact, they yield gibberish – an answer of “infinity.” This is the disease of quantized gravity. With regard to the exchange particles concept in the quantum electrodynamics theory and the existence of graviton, let’s consider a photon that is falling in the gravitational field, and revert back to the behavior of a photon in the gravitational field. But when we define the graviton relative to the photon, it is necessary to explain the properties and behavior of photon in the gravitational field. The fields around a “ray of light” are electromagnetic waves, not static fields. The electromagnetic field generated by a photon is much stronger than the associated gravitational field. When a photon is falling in the gravitational field, it goes from a low layer to a higher layer density of gravitons. We should assume that the graviton is not a solid sphere without any considerable effect. Graviton carries gravity force, so it is absorbable by other gravitons; in general; gravitons absorb each other and combine. This new view on graviton shows, identities of graviton changes, in fact it has mass with changeable spin.

When we derive various supermultiplets of states, at the noninteracting level, these states can easily be described in terms of local fields. But, at the interacting level, there are certain ambiguities that withdraw as a result of different field representations describing the same massless free states. So the proper choice of the field representation may be subtle. The supermultiplets can then be converted into supersymmetric actions, quadratic in the fields. For selfdual tensor fields, the action must be augmented by a duality constraint on the corresponding field strength. For the graviton field,

The linearized Einstein equation for g_μν = η_μν + κh_μν implies that (for D ≥ 3)

R_μν ∝ ∂²h_μν + ∂_μ∂_νh – ∂_μ∂^ρh_νρ – ∂_ν∂^ρh_ρμ = 0 —– (1)

where h ≡ h_μμ and R_μν is the Ricci tensor. To analyze the number of states implied by this equation, one may count the number of plane-wave solutions with given momentum q^μ. It then turns out that there are D arbitrary solutions, corresponding to the linearized gauge invariance h_μν → h_μν + ∂_μξ_ν + ∂_νξ_μ, which can be discarded. Many other components vanish and the only nonvanishing ones require the momentum to be lightlike. Thee reside in the fields h_ij, where the components i, j are in the transverse (D-2) dimensional subspace. In addition, the trace of h_ij must be zero. Hence, the relevant plane-wave solutions are massless and have polarizations (helicities) characterized by a symmetric traceless 2-rank tensor. This tensor comprises 1/2D(D-3), which transform irreducibly under the SO(D-2) helicity group of transverse rotations. For the special case of D = 6 spacetime dimensions, the helicity group is SO(4), which factorizes into two SU(2) groups. The symmetric traceless representation then transforms as a doublet under each of the SU(2) factors and it is thus denoted by (2,2). As for D = 3, there are obviously no dynamic degrees of freedom associated with the gravitational field. When D = 2 there are again no dynamic degrees of freedom, but here (1) should be replaced by R_μν = 1/2g_μνR.

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Ricci-Flat Metric & Diffeomorphism – Does there Exist a Possibility of a Complete Construction of a Metric if the Surface isn’t a Smooth Manifold? Note Quote.

Using twistors, the Gibbons-Hawking ansatz is generalized to investigate 4n-dimensional hyperkähler metrics admitting an action of the n-torus Tⁿ. The hyperkähler case could further admit a tri-holomorphic free action of the n-torus Tⁿ. It turns out that the metric may be written in coordinates adapted to the torus action, in a form similar to the Gibbons-Hawking ansatz in dimension 4, and such that the non-linear Einstein equations reduce to a set of linear equations (essentially saying that certain functions on Euclidean 3-space are harmonic). In the case of 8-manifolds (n = 2), the solutions can be described geometrically, in terms of arrangements of 3-dimensional linear subspaces in Euclidean 6-space.

There are in fact many explicit examples known of metrics on non-compact manifolds with SU(n) or Sp(2n) holonomy. The other holonomy groups automatically yielding Ricci-flat metrics are the special holonomy groups G₂ in dimension 7 and Spin(7) in dimension 8. Until fairly recently only three explicit examples of complete metrics (in dimension 7) with G₂-holonomy and one explicit example (in dimension 8) with Spin(7)-holonomy were known. The G₂-holonomy examples are asymptotically conical and live on the bundle of self-dual two-forms over S⁴, the bundle of self-dual two-forms over CP², and the spin bundle of S³ (topologically R⁴ × S³), respectively. The metrics are of cohomogeneity one with respect to the Lie groups SO(5), SU(3) and SU(2) × SU(2) × SU(2) respectively. A cohomogeneity-one metric has a Lie group acting via isometries, with general (principal) orbits of real codimension one. In particular, if the metric is complete, then X is the holomorphic cotangent bundle of projective n-space T^∗CPⁿ, and the metric is the Calabi hyperkähler metric.

The G₂-holonomy examples are all examples in which a Lie group G acts with low codimension orbits. This is a general feature of explicit examples of Einstein metrics. The simplest case of such a situation would be when there is a single orbit of a group action, in which case the metric manifold is homogeneous. For metrics on homogeneous manifolds, the Einstein condition may be expressed purely algebraically. Moreover, all homogeneous Ricci-flat manifolds are flat, and so no interesting metrics occur. Then what about cohomogeneity one with respect to G, i.e., the orbits of G are codimension one in general? Here, the Einstein condition reduces to a system of non-linear ordinary differential equations in one variable, namely the parameter on the orbit space. In the Ricci-flat case, Cheeger-Gromoll theorem implies that the manifold has at most one end. In the non-compact case, the orbit space is R₊ and there is just one singular orbit. Geometrically, if the principal orbit is of the form G/K, the singular orbit (the bolt) is G/H for some subgroup H ⊃ K; if G is compact, a necessary and sufficient condition for the space to be a smooth manifold is that H/K is diffeomorphic to a sphere. In many cases, this is impossible because of the form of the group G, and so any metric constructed will not be complete.

Fascism’s Incognito – Conjuncted

“Being asked to define fascism is probably the scariest moment for any expert of fascism,” Montague said.

Brecht’s circular circuitry is here.

Allow me to make cross-sectional (both historically and geographically) references. I start with Mussolini, who talked of what use fascism could be put to by stating that capitalism throws itself into the protection of the state when it is in crisis, and he illustrated this point by referring to the Great Depression as a failure of laissez-faire capitalism and thus creating an opportunity for fascist state to provide an alternative to this failure. This in a way points to the fact that fascism springs to life economically in the event of capitalism’s deterioration. To highlight this point of fascism springing to life as a reaction to capitalism’s failure, let me take recourse to Samir Amin, who calls the fascist choice for managing a capitalist society in crisis as a categorial rejection of democracy, despite having reached that stage democratically. The masses are subjected to values of submission to a unity of socio-economic, political and/or religious ideological discourses. This is one reason why I call fascism not as a derivative category of capitalism in the sense of former being the historic phase of the latter, but rather as a coterminous tendency waiting in dormancy for capitalism to deteriorate, so that fascism could then detonate. But, are fascism and capitalism related in a multiple of ways is as good as how socialism is related with fascism, albeit only differently categorically.

It is imperative for me to add by way of what I perceive as financial capitalism and bureaucracy and where exactly art gets sandwiched in between the two, for more than anything else, I would firmly believe in Brecht as continuing the artistic practices of Marxian sociology and political-economy.

The financial capitalism combined with the impersonal bureaucracy has inverted the traditional schematic forcing us to live in a totalitarian system of financial governance divorced from democratic polity. It’s not even fascism in the older sense of the term, by being a collusion of state and corporate power, since the political is bankrupt and has become a mediatainment system of control and buffer against the fact of Plutocracies. The state will remain only as long as the police systems are needed to fend off people claiming rights to their rights. Politicians are dramaturgists and media personalities rather than workers in law.  If one were to just study the literature and paintings of the last 3-4 decades, it is fathomable where it is all going. Arts still continue to speak what we do not want to hear. Most of our academics are idiots clinging on to the ideological culture of the left that has put on its blinkers and has only one enemy, which is the right (whatever the hell that is). Instead of moving outside their straightjackets and embracing the world of the present, they still seem to be ensconced in 19th century utopianism with the only addition to their arsenal being the dramatic affects of mass media. Remember Thomas Pynchon of Gravity’s Rainbow fame (I prefer calling him the illegitimate cousin of James Joyce for his craftiness and smoothly sailing contrite plots: there goes off my first of paroxysms!!), who likened the system of techno-politics as an extension of our inhuman core, at best autonomous, intelligent and ever willing to exist outside the control of politics altogether. This befits the operational closure and echoing time and time again that technology isn’t an alien thing, but rather a manifestation of our inhuman core, a mutation of our shared fragments sieved together in ungodly ways. This is alien technologies in gratitude.

We have never been natural, and purportedly so by building defence systems against the natural both intrinsically and extrinsically. Take for example, Civilisation, the most artificial construct of all humans had busied themselves building and now busying themselves upholding. what is it? A Human Security System staving off entropy of existence through the self-perpetuation of a cultural complex of temporal immortalisation, if nothing less and vulnerable to editions by scores of pundits claiming to a larger schemata often overlooked by parochiality. Haven’t we become accustomed to hibernating in an artificial time now exposed by inhabiting the infosphere, creating dividualities by reckoning to data we intake, partake and outtake. Isn’t analysing the part/whole dividuality really scoring our worthiness? I know the answer is yes, but merely refusing to jump off the tongue. Democracies have made us indolent with extremities ever so flirting with electronic knowledge waiting to be turned to digital ash when confronted with the existential threat to our locus standi.

But, we always think of a secret cabal conspiring to dehumanise us. But we also forget the impersonality of the dataverse, the infosphere, the carnival we simply cannot avoid being a part of. Our mistaken beliefs lie in reductionism, and this is a serious detriment to causes created ex nihilo, for a fight is inevitably diluted if we pay insignificance to the global meshwork of complex systems of economics and control, for these far outstrip our ability to pin down to a critical apparatus. This apparatus needs to be different from ones based on criticism, for the latter is prone to sciolist tendencies. Maybe, one needs to admit allegiance to perils of our position and go along in a Socratic irony before turning in against the admittance at opportune times. Right deserves tackling through the Socratic irony, lest taking offences become platitudinous. Let us not forget that the modern state is nothing but a PR firm to keep the children asleep and unthinking and believing in the dramaturgy of the political as real. And this is where Brecht comes right back in, for he considered creation of bureaucracies as affronting not just fascist states, but even communist ones. The above aside, or digression is just a reality check on how much complex capitalism has become and with it, its derivatives of fascism as these are too intertwined within bureaucratic spaces. Even when Brecht was writing in his heydays, he took a deviation from his culinary-as-ever epic theatre to found a new form of what he called theatre as learning to play that resembled his political seminars modeled on the rejection of the concept of bureaucratic elitism in partisan politics where the theorists and functionaries issued directives and controlled activities on behalf of the masses to the point of submission of the latter to the former. This point is highlighted not just for fascist states, but equally well for socialist/communist regimes reiterating the fact that fascism is potent enough to develop in societies other than capitalistic ones.

Moving on to the point when mentions of democracy as bourgeois democracy is done in the same breath as regards equality only for those who are holders of capital are turning platitudinous. Well, structurally yes, this is what it seems like, but reality goes a bit deeper and thereafter fissures itself into looking at if capital indeed is what it is perceived as in general, or is there more to it than meets the eye. I quip this to confront two theorists of equality with one another: Piketty and Sally Goerner. Piketty misses a great opportunity to tie the “r > g” idea (after tax returns on capital r > growth rate of economy g) to the “limits to growth”. With a careful look at history, there are several quite important choice points along the path from the initial hope it won’t work out that way… to the inevitable distressing end he describes, and sees, and regrets. It’s what seduces us into so foolishly believing we can maintain “g > r”, despite the very clear and hard evidence of that faiIing all the time… that sometimes it doesn’t. The real “central contradiction of capitalism” then, is that it promises “g > r”, and then we inevitably find it is only temporary. Growth is actually nature’s universal start-up process, used to initially build every life, including the lives of every business, and the lives of every society. Nature begins building things with growth. She’s then also happy to destroy them with more of the same, those lives that began with healthy growth that make the fateful choice of continuing to devote their resources to driving their internal and external strains to the breaking point, trying to make g > r perpetual. It can’t be. So the secret to the puzzle seems to be: Once you’ve taken growth from “g > r” to spoiling its promise in its “r > g” you’ve missed the real opportunity it presented. Sally Goerner writes about how systems need to find new ways to grow through a process of rising intricacy that literally reorganizes the system into a higher level of complexity. Systems that fail to do that collapse. So smart growth is possible (a cell divides into multiple cells that then form an organ of higher complexity and greater intricacy through working cooperatively). Such smart growth is regenerative in that it manifests new potential. How different that feels than conventional scaling up of a business, often at the expense of intricacy (in order to achieve so called economies of scale). Leaps of complexity do satisfy growing demands for productivity, but only temporarily, as continually rising demands of productivity inevitably require ever bigger leaps of complexity. Reorganizing the system by adopting ever higher levels of intricacy eventually makes things ever more unmanageable, naturally becoming organizationally unstable, to collapse for that reason. So seeking the rise in productivity in exchange for a rising risk of disorderly collapse is like jumping out of the fry pan right into the fire! As a path to system longevity, then, it is tempting but risky, indeed appearing to be regenerative temporarily, until the same impossible challenge of keeping up with ever increasing demands for new productivity drives to abandon the next level of complexity too! The more intricacy (tight, small-scale weave) grows horizontally, the more unmanageable it becomes. That’s why all sorts of systems develop what we would call hierarchical structures. Here, however, hierarchal structures serve primarily as connective tissue that helps coordinate, facilitate and communicate across scales. One of the reasons human societies are falling apart is because many of our hierarchical structures no longer serve this connective tissue role, but rather fuel processes of draining and self-destruction by creating sinks where refuse could be regenerated. Capitalism, in its present financial form is precisely this sink, whereas capitalism wedded to fascism as an historical alliance doesn’t fit the purpose and thus proving once more that the collateral damage would be lent out to fascist states if that were to be the case, which would indeed materialize that way.

That democracy is bourgeois democracy is an idea associated with Swedish political theorist Goran Therborn, who as recent as the 2016 US elections proved his point by questioning the whole edifice of inclusive-exclusive aspects of democracy, when he said,

Even if capitalist markets do have an inclusive aspect, open to exchange with anyone…as long as it is profitable, capitalism as a whole is predominantly and inherently a system of social exclusion, dividing people by property and excluding the non-profitable. a system of this kind is, of course, incapable of allowing the capabilities of all humankind to be realized. and currently the the system looks well fortified, even though new critical currents are hitting against it.

Democracy did take on a positive meaning, and ironically enough, it was through rise of nation-states, consolidation of popular sovereignty championed by the west that it met its two most vociferous challenges in the form of communism and fascism, of which the latter was a reactionary response to the discontents of capitalist modernity. Its radically lay in racism and populism. A degree of deference toward the privileged and propertied, rather than radical opposition as in populism, went along with elite concessions affecting the welfare, social security, and improvement of the working masses. This was countered by, even in the programs of moderate and conservative parties by using state power to curtail the most malign effects of unfettered market dynamics. It was only in the works of Hayek that such interventions were beginning to represent the road to serfdom thus paving way to modern-day right-wing economies, of which state had absolutely no role to play as regards markets fundamentals and dynamics. The counter to bourgeois democracy was rooted in social democratic movements and is still is, one that is based on negotiation, compromise, give and take a a grudgingly given respect for the others (whether ideologically or individually). The point again is just to reiterate that fascism, in my opinion is not to be seen as a nakedest form of capitalism, but is generally seen to be floundering on the shoals of an economic slowdown or crisis of stagflation.

On ideal categories, I am not a Weberian at heart. I am a bit ambiguous or even ambivalent to the role of social science as a discipline that could draft a resolution to ideal types and interactions between those generating efficacies of real life. Though, it does form one aspect of it. My ontologies would lie in classificatory and constructive forms from more logical grounds that leave ample room for deviations and order-disorder dichotomies. Complexity is basically an offspring of entropy.

And here is where my student-days of philosophical pessimism surface, or were they ever dead, as the real way out is a dark path through the world we too long pretended did not exist.

Complicated Singularities – Why Should the Discriminant Locus Change Under Dualizing?

Consider the surface S ⊆ (C^∗)² defined by the equation z₁ + z₂ + 1 = 0. Define the map log : (C^∗)² → R² by log(z₁, z₂) = (log|z₁|, log|z₂|). Then log(S) can be seen as follows. Consider the image of S under the absolute value map.

The line segment r₁ + r₂ = 1 with r₁, r₂ ≥ 0 is the image of {(−a, a−1)|0 < a < 1} ⊆ S; the ray r₂ = r₁ + 1 with r₁ ≥ 0 is the image of {(−a, a−1)|a < 0} ⊆ S; and the ray r₁ = r₂ + 1 is the image of {(−a, a−1)|a > 1} ⊆ S. The map S → |S| is one-to-one on the boundary of |S| and two-to-one in the interior, with (z₁, z₂) and (z̄₁, z̄₂) mapping to the same point in |S|. Taking the logarithm of this picture, we obtain the amoeba of S, log(S) as depicted below.

Now consider S = S × {0} ⊆ Y = (C^∗)² × R = T² × R³. We can now obtain a six-dimensional space X, with a map π : X → Y, an S¹-bundle over Y\S degenerating over S, so that π⁻¹(S) →^≅ S. We then have a T³-fibration on X, f : X → R³, by composing π with the map (log, id) : (C^∗)² × R → R³ = B. Clearly the discriminant locus of f is log(S) × {0}. If b is in the interior of log(S) × {0}, then f⁻¹(b) is obtained topologically by contracting two circles {p₁} × S¹ and {p₂} × S¹ on T³ = T² × S¹ to points. These are the familiar conical singularities seen in the special Lagrangian situation.

If b ∈ ∂(log(S) × {0}), then f⁻¹(b) has a slightly more complicated singularity, but only one. Let us examine how the “generic” singular fiber fits in here. In particular, for b in the interior of log(S) × {0}, locally this discriminant locus splits B into two regions, and these regions represent two different possible smoothings of f⁻¹(b).

Assume now that f : X → B is a special Lagrangian fibration with topology and discriminant locus ∆ being an amoeba. Let b ∈ Int(∆), and set M = f⁻¹(b). Set M^o = M\{x₁, x₂}, where x₁, x₂ are the two conical singularities of M. Suppose that the tangent cones to these two conical singularities, C₁ and C₂, are both cones of the form M⁰. Then the links of these cones, Σ₁ and Σ₂, are T²’s, and one expects that topologically these can be described as follows. Note that M^o ≅ (T²\{y₁, y₂}) × S¹ where y₁, y₂ are two points in T². We assume that the link Σ_i takes the form γ_i × S¹, where γ_i is a simple loop around y_i. If these assumptions hold, then to see how M can be smoothed, we consider the restriction maps in cohomology

H¹(M^o, R) → H¹(Σ₁, R) ⊕ H¹(Σ₂, R)

The image of this map is two-dimensional. Indeed, if we write a basis eⁱ₁, eⁱ₂ of H¹(Σ_i, R) where eⁱ₁ is Poincaré dual to [γ_i] × pt and eⁱ₂ is Poincaré dual to pt × S¹, it is not difficult to see the image of the restriction map is spanned by {(e¹₁, e²₁)} and {(e¹₂, −e²₂)}. Now this model of a topological fibration is not special Lagrangian, so in particular we don’t know exactly how the tangent cones to M at x₁ and x₂ are sitting inside C³, and thus can’t be compared directly with an asymptotically conical smoothing. So to make a plausibility argument, choose new bases fⁱ₁, fⁱ₂ of H¹(Σ_i, R) so that if M(a,0,0), M(0,a,0) and M(0,0,a) are the three possible smoothings of the two singular tangent cones at the singular points x₁, x₂ of M. Then Y(M_i^(a,0,0)) = πafⁱ₁, Y(M_i^(0,a,0)) = πafⁱ₂, and Y(M_i(0,0,a)) = −πa(fⁱ₁ + fⁱ₂).

Suppose that in this new basis, the image of the restriction map is spanned by the pairs (f¹₁, rf²₂) and (rf¹₂, f²₁) for r > 0, r ≠ 1. Then, there are two possible ways of smoothing M, either by gluing in M₁^(a,0,0) and M₂^(0,ra,0) at the singular points x₁ and x₂ respectively, or by gluing in M₁^(0,ra,0) and M₂^(a,0,0) at x₁ and x₂ respectively. This could correspond to deforming M to a fiber over a point on one side of the discriminant locus of f or the other side. This at least gives a plausibility argument for the existence of a special Lagrangian fibration of the topological type given by f. To date, no such fibrations have been constructed, however.

On giving a special Lagrangian fibration with codimension one discriminant and singular fibers with cone over T² singularities, one is just forced to confront a codimension one discriminant locus in special Lagrangian fibrations. This leads inevitably to the conclusion that a “strong form” of the Strominger-Yau-Zaslow conjecture cannot hold. In particular, one is forced to conclude that if f : X → B and f’ : X’ → B are dual special Lagrangian fibrations, then their discriminant loci cannot coincide. Thus one cannot hope for a fiberwise definition of the dualizing process, and one needs to refine the concept of dualizing fibrations. Let us see why the discriminant locus must change under dualizing. The key lies in the behaviour of the positive and negative vertices, where in the positive case the critical locus of the local model of the fibration is a union of three holomorphic curves, while in the negative case the critical locus is a pair of pants. In a “generic” special Lagrangian fibration, we expect the critical locus to remain roughly the same, but its image in the base B will be fattened out. In the negative case, this image will be an amoeba. In the case of the positive vertex, the critical locus, at least locally, consists of a union of three holomorphic curves, so that we expect the discriminant locus to be the union of three different amoebas. The figure below shows the new discriminant locus for these two cases.

Now, under dualizing, positive and negative vertices are interchanged. Thus the discriminant locus must change. This is all quite speculative, of course, and underlying this is the assumption that the discriminant loci are just fattenings of the graphs. However, it is clear that a new notion of dualizing is necessary to cover this eventuality.

Fascism’s Incognito – Brechtian Circular Circuitry. Note Quote.

Carefully looking at the Brechtian article and unstitching it, herein lies the pence (this is reproduced via an email exchange and hence is too very basic in arguments!!):

1. When Brecht talks of acceding to the capitulation of Capitalism, in that, being a historic phase and new and old at the same time, this nakedest manifestation of Capitalism is attributed to relationality, which are driven by functionalist propositions and are non-linear, reversible schemas existing independently of the specific contents that are inserted as variables. This may sound a bit philosophical, but is the driving force behind Brecht’s understanding of Capitalism and is perfectly corroborated in his famous dictum, “Reality as such has slipped into the domain of the functional.” This dictum underlines what is new and what is old at the same time.

2. Sometime in the 30s, Brecht’s writings corroborated the linkages between Capitalism and Fascism, when the victories of European fascism prompted consideration of the relationship between collective violence and regressive social configurations. At its heart, his corpus during the times was a defining moment of finance capital, an elaborate systemic treatment of economic transactions within the literary narrative with fascistic overtones. It is here the capitalist is consummate par excellence motivated by the rational calculus (Ayn Rand rings the bells!!!). Eschewing the narrative desire of the traditional dramatic novel, Brecht compels the readers without any recourse to emotional intensity and catharsis, and capturing the attention via phlegmatic and sublimated pleasures of logical analysis, riddle solving, remainder less, and bookkeeping. This coming together of the financial capital with the rise in European Fascism, despite leading to barbaric times in due course, brought forth the progeny of corporation merging with the state incorporating social functions into integrated networks of production and consumption. What Brecht reflects as barbaric is incidentally penned in these tumultuous ear, where capital evolves from Fordist norms into Corporations and in the process atrophy human dimensions. This fact is extrapolated in contemporary times when capital has been financialized to the extent of artificial intelligences, HFTs and algorithmic decision making, just to sound a parallel to Nature 2.0.

But, before digressing a bit too far, where is Brecht lost in the history of class consciousness here? With capital evolving exponentially, even if there is no or little class consciousness in the proletariat, there will come a realization that exploitation is widespread. This is the fecund ground when nationalist and fascist rhetoric seeds into a full-grown tree, inciting xenophobias infused with radicalization (this happened historically in Italy and in Germany, and is getting replicated on micro-to-macro scales contemporarily). But, what Brecht has failed to come to terms with is the whole logic of fascists against the capitalist. Fascists struggle with the capitalist question within their own circles (a far-fetched parallel drawn here as regards India is the right ideologue’s opposition to FDI, for instance). Historically speaking and during times when Bertotl was actively writing, there were more working class members of the Italian fascists than anyone else with anti-capitalist numbers. In Nazi Germany, there were close to 30 per cent within stormtroopers as minimal identifies and sympathizers with communism. The rest looked up to fascism as a stronger alternative to socialism/communism in its militancy. The intellectual and for moral (might be a strikethrough term here, but in any case…) tonic was provided for by the bourgeois liberals who opposed fascism for their capitalist bent. All in all, Brecht could have been prescient to say the most, but was too ensconced, to say the least, in Marxist paradigms to analyze this suturing of ideological interests. That fascism ejected itself of a complete domineering to Capitalism, at least historically, is evident from the trajectory of a revolutionary syndicalist, Edmondo Rossoni, who was extremely critical of internationalism, and spearheaded Italian fascist unions far outnumbering Italian fascist membership. Failure to recognize this fractious relationship between Fascism and Capitalism jettisons the credibility of Brechtian piece linked.

3. Althusser once remarked that Brecht’s work displays two distinct forms of temporality that fail to achieve any mutual integration, which have no relation with one another, despite coexisting and interconnecting, never meet one another. The above linked essay is a prime example of Althusser’s remark. What Brecht achieves is demonstrating incongruities in temporalities of capital and the human (of Capitalism and Barbarianism/Fascism respectively), but is inadequate to take such incongruities to fit into the jigsaw puzzle of the size of Capitalism, not just in his active days, but even to very question of his being prescient for contemporary times, as was mentioned in point 2 in this response. Brecht’s reconstructing of the genealogy of Capitalism in tandem with Fascism parses out the link in commoditized linear history (A fallacy even with Marxian notion of history as history of class consciousness, in my opinion), ending up trapped in tautological circles, since the human mind is short of comprehending the paradoxical fact of Capitalism always seemingly good at presupposing itself.

It is for these reasons, why I opine that Brecht has a circular circuitry.