Espartaco

“Is that to say we are against Free Trade? No, we are for Free Trade, because by Free Trade all economical laws, with their most astounding contradictions, will act upon a larger scale, upon the territory of the whole earth; and because from the uniting of all these contradictions in a single group, where they will stand face to face, will result the struggle which will itself eventuate in the emancipation of the proletariat.”

Karl Heinrich Marx · Marx-Engels Collected Works, Vol. VI, p. 290

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Category: Dialectical Materialism

  • THE SINKING OF ANTI-MARX

    THE SINKING OF ANTI-MARX

    Polemic · Political economy · 2022–2025

    The Sinking of Anti-Marx

    Kliman and Astarita against Rallo: the full sequence of a debate on the transformation problem —and a reply on why Walras cannot be “sequential.”

    Between 2022 and 2025 a debate unfolded that is almost never read in full. In late 2022 Juan Ramón Rallo published the two volumes of Anti-Marx. Crítica a la economía política marxista, advertised by its publisher as “the most ambitious critique of Marxism written to date.” Andrew Kliman answered in September 2024. Rallo replied in April 2025. Kliman closed in May 2025. In parallel, a year earlier, Rolando Astarita had answered the critique that Anti-Marx directs against Fred Moseley, and Rallo answered him the following day.

    What follows is that entire sequence, arranged by argument rather than by date: first what Rallo concedes, then each of his criticisms in its conceptual core, and then the answer it received. Where there is a counter-reply, the counter-reply comes next, and each front closes with the last word of whoever answered. At the end, my own replies.

    · · ·

    IWhat Rallo concedes

    It is worth fixing first what Rallo grants, and not out of courtesy: a good part of Kliman’s argument is built on those concessions, and without them the rest of the discussion is unintelligible. Kliman highlights them, moreover, because they are unusual in anti-Marx literature: Rallo neither hides them nor buries them in a footnote.

    Kliman fixes the value of these admissions with a conditional: they are irrelevant only if the demolition that follows works. If it does not, they are “not meaningless concessions about a merely mathematical solution, but significant concessions about a genuine economic solution.” The whole of the rest of the debate is, at bottom, the question of whether the demolition works.

    · · ·

    IIFirst front: values and prices of production

    Round 1 · Rallo (2022) · The critique

    Conceptual core. Temporal single-system valuation produces, period after period, changing relative prices between constant and variable capital. If capitalists maximize profits and the elasticity of substitution between means of production and labour-power is non-zero, that change in relative prices forces them to recombine inputs: to use less of what has become dearer and more of what has become cheaper. But then the relations of production of the following period are not those of the previous one, the output produced in t does not match the demand of t+1, and simple reproduction breaks down.

    Hence the verdict:

    The [temporal single-system interpretation] is not an economic solution to the transformation problem, but a merely mathematical solution with the appearance of an economic solution (since it is a mathematical solution incoherent with the economic conditions that would permit the simple reproduction of capital), whereas the simultaneist solutions to the transformation problem are solutions that respect macroeconomic equilibrium but at the cost of sacrificing either the labour theory of value or the theory of exploitation.

    Rallo, Anti-Marx, vol. 2, § 5.4.1

    The demand is set out as four conditions that, according to Rallo, any solution must satisfy at once: aggregate equality of value and price of production; aggregate equality of surplus value and profit; static equilibrium (supply = demand sector by sector); and dynamic equilibrium, defined as “the absence of incentives, within the structure of prices of production itself, to modify the relations of production that engendered that structure of prices of production.”

    Round 2 · Kliman (September 2024) · The answer

    1. The argument is a boomerang

    Kliman concedes at the outset what has to be conceded: some production processes require fixed proportions and others allow substitution, and Rallo is right that the latter exist. He concedes profit-maximizing behaviour as well. And he then shows that, once those two premises are accepted, the argument does not strike temporalism alone: it strikes Bortkiewicz first.

    The reason is a misidentification. Rallo conflates changes in prices with temporally determined prices. He believes that in the simultaneist “solutions” prices do not change, because input prices are forced to equal output prices. But the transformation, as Bortkiewicz, Sweezy and Rallo himself conceive it, is the move from a system in which commodities exchange at their values to one in which they exchange at their prices of production. That move is, by definition, a change in relative prices. With maximization and substitution, it triggers exactly the recombination of inputs that Rallo demands, and therefore breaks simple reproduction.

    Kliman does this with Bortkiewicz’s own numbers. In the “value system” Department III uses Technique A (50 units of Good 1 and 150 units of living labour to produce 200 units of output); in the “price system” Good 1 becomes dearer relative to the wage rate, Technique B (10 units of Good 1 and 225 units of labour) becomes the cost-minimizing method, and firms switch —as Rallo recommends. The result: Department III’s rate of profit rises to 27.7 % against 25 % in the other two, demand for Good 1 falls below supply, excess demand for the wage good appears, and the “price system” is no longer in equilibrium in any sense. Its prices are no longer prices of production, because profit rates are not equalized.

    If one rejects any “solution” incompatible with simple reproduction, one must reject not only Marx’s account, but also Bortkiewicz’s “correction” and every existing and potential simultaneist solution.

    And with this falls, in passing, Sweezy’s classic formulation —“the passage from value calculation to price calculation has no connection with the question of whether the economic system as a whole is stationary or expanding”—: given the restrictions Rallo himself adds, moving from one calculation to the other has everything to do with that question.

    2. What a price of production really is in Marx

    The second move is exegetical and decides the rest. Marx treats separately the formation of a general rate of profit (ch. 9 of volume III) and its equalization (ch. 10). Likewise, the formation of prices of production is one thing and exchanges at prices of production are another. Prices of production always exist: as a concept in the heads of capitalists and economists, as a benchmark of success, as a minimum target for viability and —above all— as the average over time of the market prices that fluctuate around them.

    Rallo had written that “the concept of a long-run equilibrium price is meaningless within an economy that is not in equilibrium.” Kliman answers with the analogy that circulated most widely of anything in the exchange:

    This is like saying that the concept of average family size is meaningless whenever there is no family of average size.

    Average U.S. family size in 2022 was 3.13 people. No family had 3.13 members.

    3. Two concepts of equilibrium

    Hence the distinction that orders the whole front: there is equilibrium as a state of balance (supply equal to demand) and equilibrium as a state of rest (the future repeating the past: stationary prices, simple reproduction, unchanging input–output relations). Marx’s prices of production are balance prices; they need not be, and generally are not, rest prices. Requiring rest is not a requirement of the theory: it is an additional restriction, and often an obstacle, because it may be incompatible with the equalization of profit rates.

    4. The generality of the procedure

    The close is the one Kliman will repeat in 2025. The data with which Marx calculates are the capital investments, the components of cost price, and the surplus values. Not among the data are the physical input–output relations, the physical quantities, the assumption that input prices equal output prices, or simple reproduction. They are not there because they are irrelevant to the calculation.

    In short, Marx’s procedure is completely general. It does not rest on any restrictive assumptions.

    Kliman, 2024

    In passing, Kliman dismantles Rallo’s attempt (§ 5.3.5 of volume 2) to prove that the law of value does not determine the general rate of profit: what Rallo proves, by altering a few of Bortkiewicz’s figures, is that the law of value does not determine the rate of Bortkiewicz’s “price system” —something Bortkiewicz himself proclaimed. It is a petitio principii: one starts from a model that presupposes Marx was wrong, and uses it to prove that Marx was wrong. Worse: those rates of profit are false, because they presuppose that every department sells everything it produces, and that does not happen once input substitution breaks simple reproduction.

    Round 3 · Rallo (13 April 2025) · The counter-reply

    1. “Kliman concedes my point without conceding it”

    Rallo takes a sentence from Kliman’s close —“it would be fatuous to require that we solve a problem that has no solution”— and reads it as a capitulation: if the problem has no solution, then the transformation problem has no solution, temporalism included. QED.

    2. The three “excuses”

    He enumerates the cases in which, according to Kliman, temporalism would be compatible with simple reproduction, and dismisses each. That capitalists do not maximize or that substitution is impossible amounts, he says, to admitting there is no general solution —and it suffices that some processes admit substitution for the problem to return. That exchanges take place at prices differing from prices of production is inadmissible if, as Kliman himself defines them, prices of production are the long-run average of market prices. And that inputs and outputs both exchange at prices of production is precisely Bortkiewicz’s case, in which —Rallo holds— the twofold aggregate equality does not hold.

    3. The direction of Bortkiewicz’s procedure

    The most ambitious move. Kliman is wrong, says Rallo, to read Bortkiewicz’s scheme as a temporal transition from the value system to the price system. The simultaneist solution is atemporal:

    Table I is not a temporal antecedent of Table II or Table III; it is a logical antecedent […] there exists a single productive structure derived from the system of prices of production, which can be expressed / represented / computed in terms of values (of hours of social labour).

    Rallo, 2025

    If this were so, Kliman’s objection would dissolve: there would be no passage from one productive structure to another, and therefore no input substitution and no breakdown of simple reproduction in Bortkiewicz’s scheme. It would occur only under temporal determination.

    Round 4 · Kliman (15 May 2025) · The close

    1. The decontextualized quotation

    Kliman takes up Ángel Barroso’s observation: the quoted passage “presents Kliman as if he were admitting that the Marxist transformation problem has no solution, when in fact he is saying something very different.” What has no solution is the problem as Rallo formulates it, because Rallo demands mutually incompatible conditions. Saying that a problem is insoluble is not the same as saying that a formulation is contradictory.

    2. The five-line demonstration

    Kliman decides not to argue method and to prove the result directly. In any period, for any sector j:

    (1)   Wj = Cj + Vj + Sj      (2)   Pj = Cj + Vj + πj

    (3)   ∑Pj = ∑Wj    by the demonstration in ch. 5 of volume I: exchange redistributes value, it does not create it

    (4)   ∑Cj + ∑Vj + ∑πj = ∑Cj + ∑Vj + ∑Sj  ⇒  (5)   ∑πj = ∑Sj

    And since the denominator is the same invested capital, the rate of profit “in price” equals the rate “in value.”

    The key lies in the definition of C and V: they are the actual cost of the means of production consumed and of hiring the workers. There is no constant capital equal to the value of the means of production and another equal to what was paid for them. Single system means one system. No special-case restriction enters the derivation; therefore no special case can invalidate it. To refute the equalities one would have to refute the demonstration in chapter 5 of volume I —which neither Bortkiewicz nor Rallo attempted.

    3. The equalities hold even in Rallo’s own case

    Kliman takes Rallo’s “dynamic equilibrium” —which he renames static equilibrium, since there is nothing dynamic about it: “the motionless equilibrium of a dead body, eternally at rest”— and the exact figures from page 204 of Bortkiewicz. Read as a single system, with C and V taken as the money costs actually laid out, they give:

    Single system, on Bortkiewicz’s own figures
    Dept.CVSWπPS/(C+V)π/(C+V)
    I28896604449648015.6 %25.0 %
    II128128803366432031.3 %25.0 %
    III6496602204020037.5 %25.0 %
    Total4803202001000200100025.0 %25.0 %

    Total price 1000 = total value 1000; total profit 200 = total surplus value 200; the rate “in price” 25 % = the rate “in value” 25 %. The three equalities hold inside the very case Rallo constructed so that they would fail. And they hold again in a case with the same physical data but different prices, non-stationary and without simple reproduction; and in period 14 of Table 1 of Kliman and McGlone (1988), which Rallo cites in his own book.

    The diagnosed error is uncomfortably precise: Rallo does not compare the price and profit of the single system against the value and surplus value of the single system. He compares the price figures of Bortkiewicz’s “price system” against the value figures of a separate “value system” that the temporal single-system interpretation rejects outright. He is assessing a single-system interpretation with dual-system instruments.

    4. The three “highly exceptional” cases exhaust the universe

    Rallo called “highly exceptional assumptions” the three cases Kliman had enumerated. Kliman crosses them in a two-by-two table —exchange at prices of production yes/no, against maximization with substitution yes/no— and shows that the three, taken together, cover every possible combination. The rhetoric of exceptionality was concealing an exhaustive enumeration.

    5. The textual evidence on Bortkiewicz

    Against Rallo’s claim about the direction of Bortkiewicz’s procedure, Kliman asks for the evidence and answers: there is none. No quotations, no paraphrase, no page references. Rallo’s justification is that the alternative strikes him as “unthinkable.” Kliman sets against this six textual supports from pages 199–205: Bortkiewicz says he will proceed without reversing Marx’s way of presenting the problem; he states as his third limiting assumption “we shall assume simple reproduction,” with no restriction on its scope; he declares that his equations (1)–(3) satisfy “the conditions of simple reproduction”; he writes that “the problem is now to convert these value expressions into price expressions” and announces his “correct transition from value magnitudes to price magnitudes”; and he obtains his price expressions by multiplying the value expressions by each department’s price/value ratio —that is, by leaving the physical quantities of the value system untouched and revaluing them.

    Rallo’s whole story about how Bortkiewicz proceeds is a fabrication.

    6. And the direction makes no difference

    The final move closes every exit. Suppose, says Kliman, that Rallo were right and the transition ran from prices to values. One gets the same thing: a change in relative prices that induces input substitution, imbalance between supplies and demands, and the breakdown of simple reproduction. The “value system” economy turns out to be physically distinct from the “price system” economy, and comparing their aggregates is comparing Poland’s total price with Russia’s total value. If instead Table I is read as a thought experiment —a merely logical antecedent— the thought experiment violates Rallo’s own substitution restriction: with substitutable inputs, the imaginary change of prices induces imaginary substitution and an imaginary breakdown of simple reproduction. Real apples against imaginary oranges. And if maximization is dropped to avoid this, the capitalists of the imaginary system will optimize something else, or nothing, and will likewise have no incentive whatever to sustain the other system’s physical structure.

    The root of the problem is that Rallo imposed the input-substitution restriction on top of the simple-reproduction one. In a transition from one set of relative prices to another, these two restrictions are simply incompatible.

    Kliman, 2025

    Rallo’s complete set of restrictions can be satisfied in one case only: when relative prices are stationary. Temporal single-system valuation can satisfy it, because it is compatible with stationary prices —as the table above shows. Simultaneist solutions cannot, because on their conception of the transformation, the transformation itself is a change in relative prices.

    · · ·

    IIISecond front: the Okishio “theorem”

    Round 1 · Rallo (2022) · The critique

    Conceptual core. Rallo reproduces Kliman’s numerical example and does indeed obtain a falling general rate of profit with rising organic composition and a constant real wage. But he holds that this refutes nothing, because what temporalism “really does […] is estimate a general rate of profit different from the one the Okishio Theorem itself estimates.” And he adds the decisive premise: “Recall that the Okishio Theorem defined the general rate of profit as that value which made it possible to equalize intratemporally (in each period t) the equilibrium prices of inputs and outputs.” If that is the definition, then computing another rate does not refute the theorem: it changes the subject.

    Round 2 · Kliman (September 2024) · The answer

    1. A formula is not a definition

    The claim is false as a matter of fact: the writings of Okishio and Roemer contain no such definition. They contain formulas in which input and output prices are equal, which is not the same thing. “The definition of a mathematical object is given by […] listing the properties the object is required to have”; formulas are not lists of required properties. The static-equilibrium character of the Okishian rate is a conclusion of the theorem, not a premise —something Okishio and Roemer claimed to have deduced, not something they stipulated. Kliman had already explained this on page 118 of Reclaiming Marx’s “Capital”; Rallo does not answer that explanation.

    2. The burden of proof

    Here is the heart of it. The “theorem” is a claim about Marx’s rate of profit: Okishio wrote that “our conclusions are negative to the Marxian Gesetz des tendenziellen Falls der Profitrate.” The burden of proof therefore falls on whoever claims that this rate cannot fall. And correspondingly, whoever refutes the theorem need only show that the rate as Marx defines it can fall under the conditions in which the theorem says it cannot. He need not show that his rate satisfies Okishio’s preferred definition, or Rallo’s. Defining the rate of profit as a static-equilibrium rate illicitly shifts the burden of proof. And it is obvious that Marx never defined the general rate of profit as the value that intratemporally equalizes the equilibrium prices of inputs and outputs.

    3. The OT1 / OT2 equivocation

    Kliman revives his analysis of Robin Hahnel’s manoeuvre, which Rallo repeats. Two distinct theorems are invoked alternately under one name. OT1 is a theorem about real capitalism, which would assert that labour-saving technical change does not by itself reduce the rate of profit; it is false. OT2 is a purely mathematical theorem, free of logical flaw, whose “rate of profit” is a mathematical object and not the rate of real capitalism; it is true but harmless. Using the same term in two senses within one argument is an equivocation, and an equivocation invalidates the argument.

    As a libertarian, Rallo wants to be free to choose. I have no interest in restricting that freedom. So, Dr. Rallo: which will it be, OT1 or OT2? It is your choice. I only insist that you cannot have it both ways.

    Kliman, 2024

    Kliman notes further that Rallo’s long analysis of the convergence of the temporal rate toward the Okishian rate if productivity growth stopped forever is not about the matter at issue: it is about conditions contrary to those the theorem is about. And he records the asymmetry of standards: a writer scrupulous about the realism of technological assumptions when it comes to input substitution is wholly unconcerned with that realism when it comes to rising productivity.

    There is no counter-reply on this front. In April 2025 Rallo announced that he would examine the arguments against the Okishio theorem in a later text; his reply of that month is confined to the transformation problem and likewise does not directly address the demolition of his attempt to refute the law of value.

    · · ·

    IVAstarita against Rallo: Moseley and economic time

    A year before the exchange with Kliman, Rolando Astarita had answered the critique that Anti-Marx directs against Fred Moseley. Moseley’s thesis is that no transformation of input values is required, because capitalists always acquire them at their prices of production —or at market prices oscillating around them— and because the variables are determined sequentially rather than simultaneously. If that is right, Böhm-Bawerk’s objection, the pillar of nearly all anti-Marx discourse, collapses.

    Round 1 · Rallo (2022) · The critique of Moseley

    Conceptual core. Rallo grants that in Moseley’s scheme, with inputs and outputs already in prices of production, there is interdepartmental equilibrium: IIc = Iv + Ib = 190. But he holds that the equilibrium is fragile. If the rate of profit varies —say, if wages rise by 20 % and the rate falls from 33 % to 25 %— the prices of constant and variable capital vary, and the equilibrium breaks: IIc = 190 while Iv + Ib = 177.5, a gap of 12.5. Conclusion: Moseley’s sequential method must be replaced by the simultaneous resolution of a system of equations, in Bortkiewicz’s manner.

    Round 2 · Astarita (19 March 2023) · The answer

    1. Economic time is not abolished by decree

    In reality, capitalists acquire constant capital and labour-power at prices of production, so that what they do approximates the sequential method. There is no simultaneous resolution of input and output prices: to assume one is to annul economic time. The use of simultaneous equations may be granted in determinate circumstances, with the framing conditions made explicit; but when the change in variables is as large as a 20 % wage increase, there is no way to pass over the disequilibria and the adjustment dynamics that follow. Moseley, in personal communication, puts it plainly: once the change occurs, “there will be a process of adjustment toward the new equilibrium which will take some time.”

    To think of an economy in which new equilibrium prices are established instantaneously is to abstract from the real movements inherent in an economic system in which the law of value imposes itself through permanent oscillations and contradictions.

    Astarita, 2023

    2. The Austrian contradiction

    The second move is ad hominem in the legitimate sense of the term: it points to an incoherence between the position held and the framework from which it is held. To suppress disequilibria by resorting to a system of equations is to return to the disappearance of economic time that Walras carried out in Lesson 20 of the Elements of Pure Economics, where not only are production plans and service prices decided simultaneously, but production occurs instantaneously. And Walras says so himself:

    Production requires a certain lapse of time. We shall resolve this second difficulty purely and simply by abstracting from that lapse.

    Walras, Elements of Pure Economics, Lesson 20

    Astarita underscores the paradox: it is an Austrian who recommends the Walrasian approach, when the Austrian school itself has been its most persistent critic. He cites Huerta de Soto against “the negative effects that mathematical formalism and the pernicious obsession with analyses based on full information and equilibrium have had on the development of our science,” and his call to replace it with “a theory of prices that explains how they are formed dynamically as the result of a sequential and evolutionary process […] and not by the intersection of mysterious curves or functions devoid of all real entity.” Hence the question: “Or is it that when it comes to criticizing Marxists, anything goes?”

    3. The disequilibrium closes by itself

    The third move is arithmetical. Astarita takes the disequilibrium Rallo exhibits as proof of failure and lets it run through the sequential method: each round’s prices of production enter as the next round’s input prices. The gap between IIc and Iv + Ib behaves as follows:

    Sequential closing of the interdepartmental disequilibrium
    Round3456789
    Gap12.508.065.043.181.941.320.85
    Rate of profit25.00 %25.41 %25.86 %25.90 %26.04 %26.08 %

    Tendentially, prices of production approach the equilibrium prices between sectors. But this is not an instantaneous solution. There is a process; time counts.

    Astarita, 2023

    Round 3 · Rallo (20 March 2023) · The answer

    1. Walras as a point, not an instant

    That I am an Austrian does not mean I accept every argument the Austrian School advances. […] Walrasian equilibrium is relevant not because it must necessarily show us an instantaneous adjustment of all economic variables, but because it shows us the equilibrium point toward which we shall tend to move sequentially through the market. Therefore, if there are perturbations in the market, the only thing that changes is the equilibrium point to which the system will have to adjust. This is not equivalent to holding that the system adjusts instantaneously (however much Walras did indeed neglect to set out that crucial adjustment process).

    Rallo, 2023

    2. The concession turned into a weapon

    If inputs are bought and sold at their prices of production and not at their values, then perturbations in the general rate of profit alter the price of those inputs and hence interdepartmental equilibrium. Which —Rallo notes— Astarita concedes when he sets out how the market sequentially reaches a new equilibrium.

    3. The aggregate that does not come back

    The real blow. The sequential solution shows that a transformation problem does exist, because the new aggregate of prices of production —927.97 in Astarita’s Table 9— neither coincides nor converges with the initial aggregate of 960. And if, as Marx says, the sum of the prices of production of the total social product must equal the sum of its values, and there has been no change in social labour time in that economy —only the rate of surplus value changed— then the aggregate should not have changed either. It changed. Therefore Moseley’s solution is no solution.

    Editorial note: the exchange continued. Astarita published a “Reply to Rallo’s reply” and Rallo added up to a fourth counter-reply. I cut the exposition at this round because it is the one that closes the argument I want to intervene in; the subsequent thread does not alter the conceptual structure of the disagreement.

    · · ·

    VMy replies

    Reply I. Walras is not sequential: the ontological commitment of a formalism

    The defence Rallo puts up against Astarita is admirably economical: Walrasian equilibrium —he says— does not claim to show an instantaneous adjustment of all variables, but the point toward which the system tends sequentially; if there are perturbations, the only thing that changes is the destination. In two sentences, simultaneism is converted into a theory of process. I hold that this conversion is not a clarification: it is a conceptual error, and one of the kind that matters.

    1. What a theory declares about itself and what its formalism commits it to

    I begin with the point of method, because everything else depends on it. Whether instantaneous adjustment is or is not “the relevant thing” for the author’s own subjective consideration is immaterial to the assessment of the theory. A theory is not what its expositor declares about it; it is what its apparatus does. In scientific-theoretical practice, and most especially on formal terrain, the ontological commitment of a formulation is not negotiated by way of gloss: if the system of equations values inputs and outputs with a single price vector, then the system asserts that identity, whatever interpretation the author may prefer to place on it afterwards. There is a difference between self-interpretation and operative commitment, and Rallo’s whole manoeuvre consists in asserting the first against the second.

    2. What simultaneism precisely is

    In this discussion, “simultaneous equations” does not mean “system of equations” generically. It means simultaneous valuation: inputs and outputs of the same period determined by a single price vector. On that sense —which is the one the term bears in the literature, not a stipulation of mine— the implication is analytic: whoever values in this way is a simultaneist, in the way a bachelor is unmarried. There is no disputable inference to be rescued. I make the criterion explicit because a reader coming from outside this terminological universe may suppose that exhibiting any system of equations suffices to undo the charge, and that door is worth closing in advance:

    A system is simultaneist if and only if it values the inputs and the outputs of one and the same production period with one and the same price vector; that is, if its apparatus lacks a temporal index distinguishing pt from pt+1.

    It is temporalist if and only if that index exists and operates: the prices at which inputs are bought at the start of the period are not obliged to coincide with the prices of the outputs emerging at the end.

    The difference is not notational, and it is seen most clearly where it touches the accounts. Forcing the input price to equal the output price amounts to revaluing the capital advanced at the current prices of the end of the period: constant capital enters the calculation at what it would cost to replace it today. Temporal determination does the opposite: constant capital enters at what was actually laid out when it was bought. Hence Kliman’s insistence, at every step of his demonstration, that C and V are the actual costs. And hence, too, that the Okishian rate of profit is by construction the rate that would obtain if the prices of the outputs emerging from production equalled the prices those same articles had on entering: it is a rate computed at replacement cost, not at actual cost.

    On this criterion the Walrasian system is simultaneist in the strict sense, and not by a hostile reading: because in it the determination of all prices and all quantities is a single act of solution, with no temporal index separating input valuation from output valuation. What Rallo calls “the point toward which we shall tend to move sequentially” is, in the apparatus, the solution of the system; and the solution of the system is the object the apparatus determines, not a destination the apparatus describes it as approaching.

    3. Walras’s own confession

    The commitment does not even need reconstructing: it is declared. In Lesson 20 of the Elements, Walras states the problem and resolves it by elimination: “Production requires a certain lapse of time. We shall resolve this second difficulty purely and simply by abstracting from that lapse.” From which it follows that “productive services can be transformed instantaneously into products.” This is not a consequence imputed to him by his adversaries: it is the methodological decision the author takes, states and justifies. To call “sequential” a system whose builder declared that he had suppressed the period of production is not a generous interpretation; it is a false description.

    It will be said that tâtonnement supplies the missing sequentiality. It does not. Walrasian groping is a pre-trading recontracting procedure in which, by construction, no exchange is executed at disequilibrium prices and no production process elapses: it is a computational metaphor for the act of solving the system, not a process in economic time. Groping describes how the solution is found, not how an economy moves. Conflating the two is precisely the slip I am denouncing.

    4. The instrument is not neutral

    Here one must stop, because something larger than this debate is at stake. There circulates a tacit premise according to which a formalism is a container: a neutral tool applicable to any content and committing one to nothing. It is false, and it is the source of the costliest epistemological errors in the discipline. To choose a formalism is to choose an ontology: to decide what entities there are, what relations order them and what may be predicated of them. An apparatus that suppresses the period of production is not describing in less detail an object that endures; it is describing another object.

    From this follows what matters. A historian who characterizes his object as a long-dated process, constituted by an irreversible succession of forms, cannot formalize it with equations that abolish duration without falling into incoherence. It is not a matter of taste, nor of fidelity to the author’s spirit: instruments must be congruent with the theory, because the instrument is a thesis about the object. The inference from “Marx’s object is constituted by irreversible duration” to “the adequate instrument cannot be one that abolishes duration” is not a psychological motive nor a school preference: it is a methodological requirement, and it follows from the non-neutrality of the formalism just stated.

    To attribute to an author a formalism incongruent with the ontology he himself declares is not to interpret him: it is to impute an incoherence to him. And whoever imputes, proves.

    The corollary reverses the burden of proof, and it is the exact structure Kliman deploys against Okishio on the other front: the burden belongs to whoever asserts. Marx’s simultaneist interpreters never took it up. They assumed the apparatus was neutral and that applying it said nothing about the object. It said everything.

    5. The symmetry, and why it is in fact worse

    With that in hand, the operation inverse to Rallo’s is precisely describable: packaging Marx as a simultaneist and putting him in the same bag as Walras and Sraffa. Marx was a historical materialist; time is not in his analysis a dispensable, trivial or secondary dimension, but the very form in which the object exists. The circuit M–C…P…C’–M’ is irreversibly ordered; capital advanced precedes value produced; the procedure of chapter 9 of volume III computes prices of production from given cost prices and surplus values, at no point forcing equality between input and output prices; and chapter 6 of that same volume is devoted entirely to what happens when the price of raw material varies after it has been bought —with its tying-up and release of capital—, an analysis wholly without object if inputs and outputs are valued with the same price vector.

    It is worth saying what work that textual evidence does, because it is not the work it appears to do. It is not what establishes the point: the point was established in the preceding movement, by methodological route. It does something else, and it is what closes the last available exit: it blocks the escape of conceding the congruence requirement and then holding that Marx was in fact incoherent with himself, or that he lacked the tools and tacitly presupposed stationarity. He did not presuppose it. What he did, chapter after chapter, was analyse precisely the cases in which it does not hold.

    And the symmetry breaks against Rallo. In Marx’s case there is a real interpretive gap: Marx wrote no system of equations, so the simultaneist formalism is imposed on him by the interpreter, and there can therefore be argument about whether the imposition is faithful. In Walras’s case there is no gap at all: Walras wrote his equations. The two operations are therefore not equivalent in gravity.

    To reinterpret Marx as a simultaneist is a disputable reading. To reinterpret Walras as sequential is a rewriting.

    6. The dilemma: either reference or determination

    There is, besides, a problem of internal coherence that Rallo’s formulation cannot absorb. Recall what he demanded of Moseley: not that he acknowledge a reference point, but that he replace the sequential method with simultaneous resolution in Bortkiewicz’s manner. That is, that he adopt the simultaneous system as the method of determination of prices of production. Then:

    • If Walrasian equilibrium is only a reference point toward which the system tends, it cannot be the method of determination that was to replace Moseley’s —because an attractor does not determine the trajectory, and Moseley’s question is precisely how the prices at which inputs are actually bought get determined.
    • If it is the method of determination, then it does assert the simultaneity Rallo says it does not assert, and Astarita’s objection stands without a further line.

    Rallo needs both at once. It is the same structure Kliman points out on the other front: one cannot have it both ways.

    7. The moving target: his own restrictions destroy the fixity of the point

    This is, to my mind, the decisive point, and it is wholly internal to his position. The “fixed point plus sequential approach” defence works only if the equilibrium point can be determined independently of the trajectory. But Rallo is, throughout the debate with Kliman, the one who most insists on two assumptions: capitalists maximize and inputs are substitutable. Combined, those two assumptions imply that every change in relative prices induces a change of technique; every change of technique alters the input–output structure; and an altered input–output structure defines a different equilibrium point. The destination shifts while the system approaches it.

    Put otherwise: under Rallo’s restrictions, equilibrium is path-dependent. And a path-dependent equilibrium is not a Walrasian equilibrium; it is precisely what a temporal determination describes. Kliman formulates the same result from his side: when supply and demand curves shift in response to the price changes they themselves provoke, “there ceases to be a unique equilibrium price,” and every price that realizes the average rate of profit with supply equal to demand is a correct price of production. Input substitution, invoked to sink temporalism, sinks the fixity of the Walrasian point first.

    8. Arithmetical corollary: the aggregate of 927.97

    Rallo’s final blow against Astarita remains to be met: that the aggregate of prices of production falls from 960 to 927.97 without social labour time having changed, and that the Marxist equality is therefore violated. This argument presupposes that the magnitude of total value is fixed by labour time independently of the money costs actually advanced. That is, exactly, a dual-system premise —the very one Kliman diagnoses in 2025— and the arithmetic suffices to show it.

    On a single-system reading, the total price of the product is the constant capital actually laid out plus the new value created by living labour. With the figures of Astarita’s own tables:

    Round 3 :   C = 480.00  +  N = 480.00  →  P = 960.00

    Round 4 :   C = 467.50  +  N = 480.00  →  P = 947.50

    Round 9 :   C = 447.97  +  N = 480.00  →  P = 927.97

    N = V + S stays at 480 in every round, exactly as Astarita states: aggregate value added does not change. The only thing that falls is C, and the aggregate falls by precisely that magnitude.

    The aggregate equality is violated in no round: it holds identically in all of them, because total value is C + N with C measured in money actually advanced. What changes is the aggregate, and it changes for the right reason: the money cost of the means of production fell without the labour time embodied in them falling. To demand that the aggregate remain at 960 is to demand that constant capital be accounted at embodied value rather than at actual cost —that is, to demand two systems where there is one. The 2023 blow against Astarita and the error Kliman diagnoses in 2025 are the same error, two years apart.

    A due precision: Kliman classifies Moseley’s reading among the simultaneous single-system ones rather than the temporal ones, whereas Astarita emphasizes its sequential determination. The discrepancy is real and I do not disguise it. But the corollary just set out does not depend on that difference: it depends only on the single-system premise, which Moseley, Astarita and Kliman share and which Rallo, on both fronts, fails to apply.

    · · ·

    Reply II. On the aggregate equalities

    Here I have little to add, and saying so is part of the argument. Rallo’s objection —that in the case of twofold equilibrium the twofold aggregate equality does not hold— has already been answered in the only way such a thing is answered: by deriving it from the premises with no special-case restriction, and then verifying it inside the very case Rallo built for it to fail in. The five-line demonstration and the single-system table on Bortkiewicz’s figures are reproduced above. The rest —the exhaustiveness of the three “highly exceptional” cases, the total absence of textual evidence about the direction of Bortkiewicz’s procedure, the structural incompatibility between input substitution and simple reproduction— is in the text of May 2025, and I refer to it without attempting to improve on it.

    Reply III. On the Okishio “theorem”

    The same. The matter is settled in two moves that admit no reply: first, that a formula is not a definition, so that the static-equilibrium character of the Okishian rate is a conclusion and not a premise; second, that the burden of proof belongs to whoever asserts that Marx’s rate cannot fall, and that refuting the theorem therefore requires only showing that this rate can fall under the conditions in which the theorem denies it —which Rallo’s own computations confirm. The OT1/OT2 disjunction closes the exit: either the theorem is about real capitalism, and then it is false, or it is about a mathematical object, and then it is harmless. There is no third option, and ambiguity between the two is not a position but a fallacy of equivocation.

    · · ·

    VIAssessment

    The residue of the debate is more precise than is usually admitted. Rallo conceded that temporal single-system valuation is the exegetically most faithful interpretation of Marx, that it preserves the basic equalities of the system and that values continue to regulate production and exchange. He then set out to demolish that interpretation by stacking two restrictions —profit maximization and input substitutability— which, applied consistently, demolish first the simultaneist correction he defends. And the Okishio front never even opened: it closed on the burden of proof.

    But what interests me is not the scoreboard. It is the methodological core the two fronts share, and which the exchange with Astarita exhibits in pure form: the question of whether time is a dimension of the object or a nuisance to be abstracted from. Walras answered that question explicitly and chose abstraction. Marx chose the opposite, which is why his central category is capital advanced, a term that means nothing unless there is a before and an after. Between those two options there is no synthesis available by way of gloss. One chooses.

    · · ·

    Sources

    1. Juan Ramón Rallo, Anti-Marx. Crítica a la economía política marxista, Deusto, 2 vols., 2022.
    2. Andrew Kliman, “Rallo’s Anti-Marx Critique of Marx and the TSSI: A Response,” With Sober Senses, 4 September 2024.
    3. Juan Ramón Rallo, “Réplica a Andrew Kliman: la TSSI no soluciona el problema de la transformación,” Utilidad marginal, 13 April 2025.
    4. Andrew Kliman, “The Negative Marginal Utility of Rallo’s Reply to Andrew Kliman,” With Sober Senses, 15 May 2025.
    5. Rolando Astarita, “Respuesta a la crítica de Rallo a Moseley,” 19 March 2023.
    6. Juan Ramón Rallo, “Réplica a Rolando Astarita sobre la (mala) solución que ofrece Fred Moseley al problema de la transformación de Marx,” Utilidad marginal, 20 March 2023.
    7. Fred Moseley, Money and Totality, Brill, 2016. — Ladislaus von Bortkiewicz, “Value and Price in the Marxian System,” 1907. — Nobuo Okishio, “Technical Changes and the Rate of Profit,” Kobe University Economic Review 7, 1961.

    Rallo’s and Astarita’s texts are in Spanish; translations of the passages quoted here are mine, checked against the published English versions of Kliman’s two articles. Quotations from Anti-Marx are taken from those articles and from the sections indicated.

  • Marxist Philosophy of Science: The Newspaper — 2026-08-29

    Economy · Politics · Technology
    Marxist Philosophy of Science:

    The Newspaper

    Today’s headlines reveal a world grappling with geopolitical tensions in the Middle East, with the father of a Palestinian-American teen killed by Israeli troops speaking out, Iran conditioning any agreement with the US on ending the Gaza war and Israeli withdrawal from Lebanon, while India strengthens its Eurasian influence through the SCO, and technological developments continue to reshape industries as OpenAI ends its partnership with Cursor after SpaceX’s acquisition and multiplayer functionality is developed for Claude, all amid public backlash to Samsung’s leaked Galaxy S27 Ultra.

    · · ·
    Economy & Politics

    Father of Palestinian-American teen killed by Israeli troops speaks to RT

    Mohammed Rabee, father of 14-year-old Amer Rabee killed by Israeli troops in 2025, accuses Washington of abandoning his family despite his son’s US citizenship. The US State Department offered condolences but little action has been taken.

    “He was always thinking he’s American, so he’s protected. He’s free.”

    Solidarity is the path

    A statement emphasizes that being a colony or under US domination is the worst fate for a nation, highlighting the importance of solidarity in national sovereignty.

    “Ser una colonia o estar bajo el yugo del yanqui es lo peor que le pueda ocurrir a una nación”

    Iran conditions any agreement with US on end of Gaza war and Israeli withdrawal from Lebanon

    Iran’s Secretary of Supreme National Security Council Mohsen Rezaei demands permanent cessation of wars in Western Asia, prioritizing Lebanon and Gaza, as condition for understanding with Washington.

    “Defenderemos al Líbano con todas nuestras fuerzas y le proporcionaremos apoyo”

    India’s commitment to the SCO highlights its Eurasian influence strategy

    India’s participation in the Shanghai Cooperation Organization’s 25th anniversary summit reflects its strategy to maintain influence in Eurasia despite connectivity challenges, evolving from observer to full member.

    Samsung leaks Galaxy S27 Ultra and social media reacts negatively

    Samsung inadvertently leaked details about the Galaxy S27 Ultra, prompting negative reactions on social media. The leak appears to have occurred through official channels.

    Technology

    OpenAI to End Partnership With Cursor After SpaceX Acquisition

    OpenAI announced it will terminate its partnership with AI-coding agent Cursor following Cursor’s acquisition by SpaceX. The decision reflects concerns over potential conflicts of interest between the companies.

    “OpenAI said it will end its partnership with Cursor after the AI-coding agent’s acquisition by SpaceX, according to a post on X.”

    Multiplayer functionality developed for Claude

    A developer created an MCP server enabling direct session connections between separate Claude accounts using single-use codes. The implementation uses end-to-end encryption with no central server.

    “You run create_invite, get a short single-use code, and send it to your friend over whatever channel you already use.”

    Daily readings

    USD/BRL 2026-08-28 5.1641
    USD/CNY 2026-08-28 6.7209
    USD/EUR 2026-08-28 0.8589
    USD/JPY 2026-08-28 159.68
    USD/MXN 2026-08-28 16.9481
    2026-08-29

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  • Marxist Philosophy of Science: The Newspaper — 2026-08-28

    Economy · Politics · Technology
    Marxist Philosophy of Science:

    The Newspaper

    Today’s edition explores the intersection of geopolitical tensions and technological competition, as Russia receives innovation proposals while developing systems to interfere with Starlink, the US leverages nuclear agreements for diplomatic gains, and Meta advances AI consumer tools amid growing concerns about privacy and reliability in artificial intelligence.

    · · ·
    Economy & Politics

    Russia Receives Innovation Cooperation Proposals from 30 Countries – Putin

    President Vladimir Putin announced that Russia has received innovation cooperation proposals from approximately 30 countries across Europe, North America, and the Middle East. These proposals will be submitted to the Russian government for further consideration, potentially opening new opportunities for Russian industries and expanding international cooperation.

    “We’ve received proposals not only from all constituent entities of Russia but also from some 30 foreign countries, including from Europe, North America, the Middle East, and other regions of the world”

    Trump Uses Saudi Nuclear Agreement as Leverage for Saudi-Israel Normalization

    The nuclear agreement signed with Saudi Arabia in July has been transformed by President Trump into a tool to pressure for normalization between Riyadh and Tel Aviv. The treaty originally permitted peaceful energy cooperation but has now become a diplomatic lever.

    Russia Begins Mass Production of System to Interfere with Starlink

    Russia has started mass production of the Volná Kupol Garant electronic warfare system designed to counteract the Starlink satellite system. The system effectively blinds satellite antennas without affecting ground terminals and has proven effective in countering US/Ukrainian kamikaze drones controlled via Starlink during attacks on Crimea.

    “The Volná Kupol Garant system has proven effective and we have begun producing it in series. Now quantity has become quality, and in essence, we have closed the sky to Starlink actions where we need it. It is unbearably painful for the enemy”

    ArcelorMittal Soars 130% on Ibex, Continues Upward Trajectory

    ArcelorMittal has experienced a remarkable 130% increase on the Ibex index, continuing its upward trajectory. The steel company’s exceptional performance has positioned it as one of the standout performers in the Spanish stock market.

    CIA Director’s Moscow Visit Sparks Speculation Among Russian Media

    CIA Director John Ratcliffe made a secretive visit to Moscow, confirmed by Russian SVR head Sergey Naryshkin. The visit has sparked various theories in Russian media about its purpose, including discussions on Ukraine, nuclear concerns, and intelligence cooperation. The secretive nature of the visit highlights ongoing tensions and potential backchannel communications between the US and Russia.

    “”The Americans can see that Moscow’s and Kiev’s positions are 100% incompatible. As master negotiators, they are asking whether there is some kind of middle ground.” – Sergey Markelov, political analyst”

    Tropical Storm Dolly Forms in Atlantic Ocean

    Tropical Storm Dolly has formed in the Atlantic Ocean, currently located approximately 2,505 kilometers east of the Lesser Antilles. The storm is moving westward at 39 kilometers per hour. Meteorologists are monitoring its trajectory as it continues its path across the ocean.

    US Pursues Access to Venezuelan Oil Resources

    The United States has restored diplomatic relations with Venezuela and is collaborating with the interim government of Delcy Rodríguez following the ousting of President Nicolás Maduro. Despite Venezuela’s diminished oil production, the country still possesses some of the world’s largest oil reserves, making it strategically important to the US.

    Technology

    Meta Developing AI Agent Hatch for Consumer Purchases and Reservations

    Meta is developing an AI agent called Hatch that can make purchases and reservations on behalf of users. The system will integrate with services like DoorDash, Etsy, Reddit, Yelp, and Outlook, featuring a customizable panel for organizing tools. Premium access is expected to cost $199.99 per month, with a new AI model called Watermelon reportedly planned for October.

    AI-Generated Images Found in Google Earth Raise Reliability Concerns

    AI-generated images have been circulating within Google Earth, a platform used for viewing real-world locations. This mixing of artificial and real content risks spreading misinformation through a source typically considered reliable. The article calls on Google to detect and remove such material to maintain user trust.

    “El problema no está solo en que una imagen sea artificial, sino en que pueda confundirse con una captura real.”

    Reddit Post Questions Privacy Trade-Offs for AI Convenience

    A Reddit post explores whether users are trading privacy for AI convenience by allowing systems access to personal data like emails, locations, and potentially financial information. The author questions if consolidating this data with one AI creates greater risks than spreading it across different services. The post highlights how we may already be sacrificing privacy for convenience without fully considering it.

    “Would you rather give one ai access to almost everything if it made it significantly more useful or spread different pieces across different ai companies so no single one has the full picture?”

    Developer Creates Tool to Bypass Claude Enterprise Restrictions

    A developer created “Jean-Claude,” a Node.js MITM proxy that intercepts Claude Code’s calls to enterprise settings and serves custom configurations instead. The tool allows users to bypass restrictions like disabled auto mode or denied commands set by administrators. The developer notes this enables them to restore auto mode without their manager’s knowledge.

    “Claude Code asks what it’s allowed to do; Jean-Claude whispers “whatever you want, king.””

    Daily readings

    USD/BRL 2026-08-28 5.1641
    USD/CNY 2026-08-28 6.7209
    USD/EUR 2026-08-28 0.8589
    USD/JPY 2026-08-28 159.68
    USD/MXN 2026-08-28 16.9481
    2026-08-28

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  • OFF-THE-CUFF REFLECTIONS: TOPOLOGY AND GEOMETRICAL CHANGE (2021)

    OFF-THE-CUFF REFLECTIONS: TOPOLOGY AND GEOMETRICAL CHANGE (2021)

    Philosophy of Mathematics · Topology · Dialectics

    What Remains When Everything Changes Shape?

    A guided reading of Toward a Dialectical-Materialist Interpretation of Topology, by José Mauricio Gómez Julián
    · · ·

    Imagine a coffee mug made of rubber. We can stretch it, compress it, twist it, and gradually deform it into something resembling a doughnut. To ordinary geometry, the mug and the doughnut are very different objects: they have different curvatures, lengths, and proportions. Topology, however, asks a deeper question: did their essential structure really change, or did we merely alter their metric appearance?

    That question — what may vary without an object ceasing to belong to the same structural class — lies at the conceptual heart of topology. But José Mauricio Gómez Julián’s essay seeks to go one step further. Rather than merely presenting mathematical definitions, it reconstructs the history of the discipline in order to ask what philosophical meaning lies in studying precisely those properties that remain through certain transformations.

    The journey moves through Leibniz, Euler, Cantor, Dedekind, Poincaré, Peano, Brouwer, and Hausdorff; through the bridges of Königsberg, the paradoxes of dimension, set theory, continuity, and homeomorphisms. Eventually, these threads are brought together in a proposal: to read topological structure from a dialectical-materialist perspective, as a mathematical way of thinking about the relationship among transformation, invariance, structure, and qualitative change.

    01 · The Fundamental Problem From Measuring Objects to Studying Relations

    For centuries, thinking geometrically meant above all thinking in terms of magnitudes: lengths, areas, angles, distances, and proportions. Topology introduces a change in perspective. What matters is no longer exclusively how much something measures, but also how its parts are related.

    The essay finds a decisive antecedent in Gottfried Wilhelm Leibniz. In the seventeenth century, Leibniz imagined a geometria situs, a “geometry of position”: a discipline in which the relative arrangement of elements would take priority over their magnitude. The intuition was remarkably modern. Two configurations might differ in their metric dimensions and yet share something deeper in their organization.

    Topology asks less about how much an object measures than about which relations survive when its shape changes.

    This is also the first useful key for readers coming from economics or the social sciences. An economic network may change enormously in the volume of its transactions without necessarily changing its basic pattern of connections; an institution may grow or shrink while preserving certain internal relations; a political structure may undergo quantitative modifications without yet experiencing a qualitative transformation in its organization.

    This does not automatically turn such questions into problems of mathematical topology. It does, however, help us grasp the intuition that interests the essay: distinguishing between changes of magnitude or appearance and changes of structure.

    02 · Königsberg, 1736 Euler and the Birth of a New Way of Seeing

    One of the foundational episodes in this history takes place in the Prussian city of Königsberg. The city was divided by the Pregel River and connected by seven bridges. The problem was easy to state: was it possible to take a continuous walk crossing every bridge exactly once?

    Leonhard Euler realized that the distances, the sizes of the islands, and the lengths of the bridges were irrelevant. Each landmass could be replaced by a point, and each bridge by a connection between points. The physical problem was thus transformed into an abstract structure.

    The Mathematical Idea

    What we would now call a graph preserves only the information relevant to the problem: which vertices are connected by which edges. The Königsberg problem is a problem of an Eulerian traversal: it asks whether every edge can be traversed exactly once.

    Euler showed that this was impossible. All the relevant vertices had odd degree, whereas a traversal using each edge exactly once can have only zero or two vertices of odd degree.

    Yet for the historical argument of the essay, the decisive point is not merely the solution. It is the method of abstraction. Euler deliberately removed information about magnitude in order to preserve a structure of relations. A real city, with water, bridges, and distances, became a mathematical object whose organization could be studied independently of scale.

    03 · A Productive Crisis Cantor and the Strange Problem of Dimension

    The next major leap appears in the nineteenth century with Georg Cantor and set theory. Cantor discovered that the points of a line segment and the points of a square can be placed in one-to-one correspondence: both sets have the same cardinality.

    This result was profoundly counterintuitive. A segment appears one-dimensional and a square two-dimensional. How could they contain, in a precise sense, the “same number” of points?

    An Essential Distinction

    Having the same cardinality does not mean having the same topological dimension. That was precisely the problem: counting points is not enough to capture what intuitively distinguishes a line from a surface.

    In philosophical terms, the contradiction between geometric intuition and set-theoretic result forced mathematics to reformulate the question. If dimension could not simply be reduced to the number of coordinates or to the cardinality of points, a deeper structural property had to be discovered.

    The essay places particular emphasis on episodes of this kind: contradictions do not appear merely as unpleasant accidents in science, but as engines of conceptual development. A notion that once seemed self-evident — “dimension” — becomes problematic, and by becoming problematic it forces the construction of a deeper theory.

    1676 · Leibniz

    Imagines a geometry based on position rather than magnitude.

    1736 · Euler

    Reduces the Königsberg problem to a structure of vertices and connections.

    1877 · Cantor

    Correspondence between sets of different apparent dimensions destabilizes the old geometric intuition.

    Late 19th Century

    Dedekind, Peano, and others force mathematics to distinguish among cardinality, continuity, and dimension.

    Early 20th Century

    Poincaré, Brouwer, and Hausdorff consolidate the problems that will shape modern topology.

    04 · When a Definition Also Asks About the World Poincaré: Continuity, Cuts, and Meaning

    Henri Poincaré occupies a special place in the story because his questions about dimension did not arise solely from technical difficulties. He was also interested in understanding why we experience space as three-dimensional, what relationship exists between mathematical geometries and physical space, and where our geometric intuitions come from.

    His idea was to think about dimension through cuts. In intuitive terms, the dimension of a continuum could be investigated by asking what kind of object must be removed in order to divide it. A line can be disconnected by removing a point; separating a surface generally requires something of higher dimension.

    The essay grants this idea particular philosophical significance. A dimension no longer appears merely as a coordinate drawn along an axis, but begins to be related to the way in which the parts of a space are connected.

    A structure is defined not only by its components, but by the system of relations that makes those components into a whole.

    Poincaré did not thereby provide the final mathematical word on dimension. His proposal encountered difficulties and would eventually be replaced by more robust formulations. Yet for the historical reading developed in the article, that is precisely the point: a formulation may be mathematically superseded while still preserving a fertile philosophical intuition.

    05 · The Consolidation of the Discipline Brouwer, Hausdorff, and Modern Topology

    L. E. J. Brouwer brought the problem of dimension to a new level of rigor. Among his fundamental contributions was the invariance of dimension: Euclidean spaces of different dimensions cannot be equivalent through a homeomorphism. A line and a plane do not become structurally identical no matter how ingenious the correspondence between their points may be.

    The result is important because it separates two ideas that Cantor had forced mathematicians to confront: two sets may have the same cardinality and yet possess different topological structures.

    Felix Hausdorff, in turn, contributed to transforming topology and set theory into increasingly abstract and systematic disciplines. By the beginning of the twentieth century, mathematical “space” no longer had to be imagined as a physical room filled with geometric points. Its elements could be functions, sequences, or other abstract objects.

    This generalization is decisive. Topology ceases to be merely a strange geometry of deformable surfaces. It becomes a language for speaking about continuity, neighborhoods, convergence, connectedness, and structure across enormously broad classes of mathematical objects.

    06 · The Mathematical Core What Is a Topology, Really?

    We can now state the idea precisely. Let X be a set. A topology on X is a collection τ of subsets of X — called open sets — satisfying certain rules.

    ∅, X ∈ τ
    arbitrary unions of members of τ belong to τ
    finite intersections of members of τ belong to τ

    The pair (X, τ) is called a topological space. What matters is that τ determines what it means to be “near,” what continuity means, and how the space is organized without requiring any numerical notion of distance.

    A metric may tell us that two points are 3.7 units apart. A topology can study relations of proximity and continuity even when no distance function exists at all.

    Concept Intuition
    Metric Allows distances between points to be quantified.
    Topology Describes a structure of neighborhoods, continuity, and more general spatial relations.
    Homeomorphism A continuous bijection with continuous inverse between two topological spaces.
    Topological invariant A property that remains unchanged under homeomorphisms.

    The Famous “Rubber-Sheet Geometry”

    From here comes the classical metaphor. We may stretch, compress, or twist an object as long as we do not cut it or glue together parts that were previously separate. A circle can be deformed into an ellipse without leaving its topological class.

    A sphere can be deformed into an ellipsoid. Creating a hole in the sphere in order to transform it into a torus, however, requires a topologically radical modification: we are no longer merely changing distances and curvatures, but the structure of the object itself.

    The Central Point

    In topology, “preserving structure” does not mean preserving visual appearance or distances. It means preserving those relations encoded by the topological structure. Mathematically, the relevant notion of equivalence is the homeomorphism.

    07 · From Formalism to Meaning The Dialectical-Materialist Reading

    Up to this point, we have topology. The specifically philosophical move of the essay begins when it asks what this kind of mathematics tells us about the relationship among structure, transformation, and permanence.

    The author’s proposal begins by distinguishing between changes that affect certain properties of a system without destroying its fundamental structure and changes that do alter that structure. The distinction immediately recalls a central category of dialectics: not every quantitative modification yet constitutes a qualitative change.

    A topological object may be stretched, twisted, or deformed within certain limits while retaining its invariants. But when it is torn, when a new connection is created, or when an essential connection is eliminated, a different class of structure appears.

    The essay interprets this difference through the dialectical relation between form and essence. Form may vary considerably while certain internal relations remain stable; when transformations reach the very organization constitutive of the system, change ceases to be merely formal and becomes qualitative.

    Invariance does not mean immobility: something may change profoundly in appearance while preserving, through those transformations, a determinate structure.

    This is perhaps the most interesting conceptual bridge proposed by the text. “Remaining” and “changing” cease to be mutually exclusive absolutes. A system can change precisely because it possesses a structure within which certain changes are possible. That same structure also determines which transformations would cease to count as internal modifications and instead become a rupture.

    Homeomorphism and Structure

    The homeomorphism therefore acquires special philosophical importance for the author. Technically, two spaces are homeomorphic when there exists between them a continuous bijection whose inverse is also continuous. Philosophically, the article interprets this as a formalization of the idea that externally different configurations may share the same structural organization.

    This is not because a mug and a torus are “the same thing” in every possible sense, but because a particular level of abstraction permits them to be treated as equivalent with respect to the properties studied at that level.

    This connects with another important epistemological thesis of the essay: every science abstracts. Physics, chemistry, biology, economics, and mathematics isolate particular relations in order to investigate them. To abstract does not necessarily mean to deny the rest of reality; it means provisionally selecting which relations will be treated as essential for a particular problem.

    08 · An Excursion Beyond Mathematics From Abstract Space to DNA

    To show that topological language is not confined to geometric exercises, the essay turns to a particularly suggestive example: the structure of DNA.

    DNA molecules can form coiled, knotted, and interlinked structures. During real biological processes, enzymes known as topoisomerases can temporarily cut a strand, allow changes in the molecule’s entanglement, and then reconnect it. Knot theory and other topological tools are useful precisely for describing aspects of these configurations.

    Here, the old metaphor of “cutting and gluing” ceases to be merely a pedagogical image. The connectivity of a molecular structure can undergo physically real modifications.

    Why the Example Matters

    The article uses DNA as an epistemological illustration: changing a quantity — length, twist, distance — is not the same thing as changing the constitutive relations of a structure. When a connection is broken and recomposed, the kind of transformation is qualitatively different.

    From the dialectical perspective developed by the author, this case illustrates a more general idea: systems possess relatively stable properties, but that stability exists within processes of transformation. Some transformations may accumulate or reach a point at which a qualitatively different organization emerges.

    09 · The Thesis in Perspective What the Essay Proposes — and What It Does Not

    It is useful to distinguish carefully between two levels. The first is strictly mathematical: topological spaces, continuity, homeomorphisms, invariants, and dimension have formal definitions and results that do not depend on accepting a Marxist philosophy.

    The second level is interpretive. The article argues that the history and conceptual structure of topology can be understood particularly fruitfully through dialectical-materialist categories: structure, relation, transformation, invariance, essence, form, and qualitative change.

    In other words, the argument is not that a theorem of topology can be derived from Marx. Nor does it claim that a homeomorphism and a dialectical contradiction are literally the same concept. The project is to seek a structural correspondence: to show that certain relations formally discovered by mathematics may acquire epistemological meaning when placed within a more general conception of change and structure.

    Seen in this way, the historical reconstruction is not decorative. Cantor challenges an inherited intuition about dimension; Peano shows that continuity can produce phenomena that intuition did not anticipate; Poincaré attempts to redefine the problem; Brouwer introduces new proofs and new abstractions; Hausdorff helps systematize the language. The modern concept emerges through conflicts, reformulations, and successive theoretical developments.

    That historical movement is precisely what makes the article’s dialectical reading attractive: a scientific theory does not appear finished from the outset. Its categories develop through concrete contradictions that force earlier concepts to be revised, some of their elements preserved, and others abandoned.

    The Question That Remains

    Perhaps the most powerful intuition a non-specialist reader can take away is this: knowing something does not consist solely in measuring its visible properties. We may also ask which relations make that thing the structure it is, which modifications it can undergo without ceasing to preserve that structure, and what kind of transformation would have to occur for a different structure to emerge.

    Topology provides an extraordinarily precise mathematical language for one version of that question. Gómez Julián’s essay proposes that dialectical materialism, in turn, provides a way of interrogating its philosophical meaning.

    · · ·

    The journey that begins with bridges, points, and lines thus ends with a much broader question. What does it mean to say that something remains “the same” while changing? Which transformations are accidental with respect to a structure, and which alter what constitutes it? How can continuity be distinguished from rupture?

    These are mathematical questions when we speak of topological spaces. But they are also questions that reappear, in different forms, when we study physical, biological, economic, or social systems. The philosophical wager of the article is precisely that this recurrence should not be treated as a merely verbal coincidence: it deserves to be investigated as a correspondence among forms of structure, transformation, and invariance.

  • ON THE POLITICAL ECONOMY OF THE SYRIAN CONFLICT (2017 ESSAY)

    ON THE POLITICAL ECONOMY OF THE SYRIAN CONFLICT (2017 ESSAY)

    Essay · Political Economy · Geopolitics

    ON THE POLITICAL ECONOMY OF THE SYRIAN CONFLICT
    (2017)

    I · SectionIntroduction

    The key to understanding the present is understanding the past, just as the key to looking toward the future is understanding the present: “Men make their own history, but they do not make it as they please, under circumstances chosen by themselves, but under circumstances directly encountered, given and transmitted from the past.” (Marx, The Eighteenth Brumaire of Louis Bonaparte, 1975).

    The Syrian political conflict is a conflict among the interests of nation-states and, consequently, it cannot be understood without first understanding what a State is, because otherwise it will also be impossible to understand which sectors of society carry their interests from the national sphere into the international sphere through the State itself.

    In general terms, this concept appears implicitly as far back as the philosophers of ancient Greece, although it is in Machiavelli’s work that the word “State” appears for the first time, where he says: “All states, all dominions that have held and hold power over men have been and are either republics or principalities.” (Machiavelli, 2006, p. 13). Subsequently, throughout history, different political theorists would define it in different ways. Here, two orthodox definitions will be introduced and then contrasted with a heterodox definition. The two orthodox definitions belong to the last classical treatise writer (Hegel) and the last modern treatise writer (Weber).

    Hegel writes on the matter: “The State, precisely, as universal and objective freedom, in the free autonomy of the individual will; the State, which as a real and organic spirit, a) of a people, b) through the relations of the specific national spirits, c) realizes and manifests itself in Universal History as the universal spirit of the world. The Law of the State is supreme.” (Hegel, 1968, p. 33).

    Weber, for his part, writes: “For sociology the reality ‘state’ is not necessarily composed of its juridical elements; or, more precisely, it does not derive from them. In any case there is no collective personality in action. When one speaks of the ‘state,’ the ‘nation’ (…) one refers only to the development, in a certain form, of the social action of a number of individuals, whether real or constructed as possible (…)” (Weber, 2002, p. 12). Having clarified this, he states: “The State, like the political associations that preceded it, is a relation of domination of men over men based on the means of legitimate coercion (that is, regarded as legitimate). Thus, for it to subsist it is necessary that the dominated submit to the authority of those who dominate in each case. When and why they do so can be understood only when the internal motives of justification and the external means on which domination rests are known.” (Weber, 2002, p. 1057).

    Machiavelli’s definition explicitly says little or nothing about the political motives underlying the formation of the State; implicitly, however, it suggests the State’s repressive role or, in his words, “the dominions that have held and hold power over men.” In Hegel’s case, a romantic vision of the State is presented, which is hardly surprising, since for this author the State was the will of God. Historical evidence, of course, shows that the State has little or nothing to do with the free autonomy of individual freedom and therefore cannot be universal and objective freedom either, since individual freedom is the sine qua non condition of universal or general freedom. It is precisely from this definition that the naïve view arises that the State is all of us. If this were so, there would be no way in which the State could be the organic spirit of a people, although it does possess a real existence as a social fact[1] through the relations among specific national spirits. Ultimately, if the State were all of us, there would be no need to create institutions that protect the rights of individuals against the State itself.

    Weber’s definition sheds light on the necessary condition for the State to subsist (the submission of the dominated to the dominant) and the sufficient condition (possessing means of coercion regarded as legitimate). The necessary condition of subsistence is, in turn, the circumstance that makes its existence possible, while the sufficient condition is the most important circumstance guaranteeing its perpetuation. Yet the most important question in terms of political philosophy is precisely the one Weber refuses to answer: why does one sector of society accept submission to another sector? How does a State concentrate the monopoly of physical violence?

    The preceding questions could be answered from Rousseau’s point of view. He wrote: “I suppose men to have reached the point at which the obstacles to their preservation in the state of nature exceed the forces that each individual can employ to maintain himself in that state. Then this primitive condition can no longer subsist, and the human race would perish unless it changed its manner of being. Now, since men cannot generate new forces, but only unite and direct those that already exist, they have no other means of preserving themselves than to form by aggregation a sum of forces capable of overcoming resistance, to bring them into play toward a single end, and to make them act together and in conformity. This sum of forces can arise only from the cooperation of many; but since the strength and freedom of each man are the principal instruments of his preservation, how can he commit them without harming himself and neglecting the obligations he owes to himself? This difficulty, reduced to my subject, may be stated in the following terms: ‘To find a form of association which will defend and protect with the common force the person and goods of each associate, and by which each, uniting with all, nevertheless obeys only himself and remains as free as before.’ Such is the fundamental problem to which the Social Contract provides the solution. The clauses of this contract are so determined by the nature of the act that the slightest modification would render them useless and without effect; so that, although they may never have been formally stated, they are everywhere the same and have everywhere been tacitly recognized and admitted, until, when the social pact is violated, each person recovers his original rights and regains his natural freedom, losing the conventional freedom for which he had renounced the former.” (Rousseau, 2007, pp. 45–46).

    Rousseau’s view, although broadly correct, contains a certain romanticism and leaves questions unanswered. It is romantic to think that a social institution as complex and historically rooted as the State would disappear at the slightest violation of the contract established among the sectors of society involved in that contract. Nor does Rousseau explain the historical pattern that determines how the clauses of such a contract are formulated at each historical moment in the transition from one form of State to another. All sciences seek, in their object of study (for the social sciences, that object is society), to establish general patterns of behavior that allow them to predict future changes in that object, because the ultimate purpose of the social sciences is not merely to explain a social fact, but to predict the behavior of the fact analyzed over time[2]; in that sense, explaining it is only an inevitably necessary step toward achieving that end.

    Once the above is established, the following question arises inexorably: is there a general pattern across the different societies that have existed in human history which explains why the clauses of the different social contracts that emerged in the transition from one social formation to another were established in a particular way? The answer is yes. Rousseau already leaves implicit a fundamental point: necessity as the foundation of the birth of the social contract or, what amounts to the same thing, a clear position on the fundamental problem of philosophy—that material causes determine and subordinate the realm of ideas.

    Rousseau is not alone in taking this position. As can be seen, Weber also attributes the subsistence of the State (what has here been called the “sufficient condition”) to possession of the means of legitimate coercion, that is, the monopoly of physical violence. Weber’s first cause or necessary condition is the submission of the dominated to the dominant, which is itself explained by internal motives of justification (which will evidently have an explanation rooted in the historical conditions of the moment) and the external means (which are objective) on which domination rests.

    Durkheim also proceeds along these lines when he states: “Thus, we must consider social phenomena in themselves, independently of the subjects who form a representation of them; they must be studied from the outside, as external things, for it is as such that they present themselves to us (…) A thing is recognized principally by the fact that it cannot be modified by a simple decree of the will. This does not mean that it resists every modification, but rather that to produce a change it is not enough merely to desire it; an effort, more or less arduous, is also required because of the resistance it opposes to our action and which, moreover, cannot always be overcome. We have already seen that social facts possess this property. Far from being a product of our will, they determine it from outside; they are like molds into which we are compelled to cast our actions.” (Durkheim, 2009, pp. 83–84). Machiavelli states that “Principalities are either hereditary (…) or new.” (Machiavelli, 2006, p. 13), and throughout his work he explains that new principalities are generally acquired by arms and virtue or by the arms and fortune of others. Comte, for his part, writes: “But this provisional instinct, without which science would then have lacked suitable nourishment, must ultimately become habitually subordinated to a just systematic appreciation, as soon as the full maturity of the positive state has made it possible always to apprehend sufficiently the true essential relations of each part with the whole, so as constantly to offer a broad horizon to the most eminent investigations while nevertheless avoiding all puerile speculation.” (Comte, 2017, p. 23). Finally, Marx, an author who will be examined in greater depth below, likewise takes a position along the same lines.

    As can be seen, one of the two great theorists of Political Law[3], one of the greatest political theorists in human history, and the four founding fathers of Sociology are clear, despite their theoretical differences, on the point under discussion[4].

    Having established the above, we can proceed to the next stage of the analysis. Humanity has witnessed four different social formations: a) primitive community, b) slavery, c) feudalism, and d) capitalism.

    If the Social Sciences are indeed sciences and, moreover, the emergence of the different social contracts corresponding to each of the social formations set out above obeys objective factors, the first task is to determine which objective factor is the most important of all. This poses no great intellectual challenge, because before anything else the human species seeks, and has always sought, to obtain the means of subsistence necessary for survival. In this sense, the production of those means of subsistence stands as humanity’s most important material or objective factor, although, contrary to what economicism assumes, it is not the only one.

    “In the production of their life, men enter into definite relations that are necessary and independent of their will, relations of production which correspond to a definite stage of development of the material productive forces. The totality of these relations of production constitutes the economic structure of society, the real basis on which a legal and political superstructure rises and to which definite forms of social consciousness correspond.” (Marx, A Contribution to the Critique of Political Economy, 1989, pp. 7–8).

    It is therefore the relations of production—those relations which members of a society establish in response to necessity at a particular historical level of technological development—that condition social life and around which a particular culture arises, reinforcing them and allowing them to remain stable over time. This in turn means that a particular social contract is constructed around the relations that members of society establish in order to secure the production of their means of subsistence. These social relations of production will also express the degree of development of the productive forces of the period, which in turn will shape the way in which the clauses of the social contract are designed. Now, do members of society establish these relations on equal terms? The answer is emphatically no. Once human beings became sedentary, the enslavement of members of one gens by another and the emergence of the social division of labor gave rise to the slave mode of production. Equality was thereafter erased from the fate of human society, and the social relations of production established in every historical-social formation became a clear expression of the relation between dominant and dominated: slaveholders and slaves, feudal lords and serfs, capitalists and proletarians. The common denominator of these power relations among social classes, expressed in the legal relations of each period (which are no more than the expression of relations of production on the juridical plane), is that one social class possesses the material means for producing wealth—the means of production—while another social class possesses only its labor power with which to secure its subsistence.

    This distribution of the means of production does not, of course, obey the whims of history or random events whose explanations are isolated in character. Rather, in general terms[5], it results from one sector of society finding itself, through historical evolution, in a privileged position that it uses to accentuate its differences from the rest of society, accumulating wealth from that position and achieving a monopoly over the means of exercising physical violence. In Europe, for example, the capitalist class has its origins in the Middle Ages among small merchants, a status accessible only to free men rather than serfs. By buying in the countryside at a lower price than they sold in the city, they began the accumulation of wealth that in its contemporary form we know as capital. Yet the primitive accumulation of capital was not limited to this: independent producers were also expropriated from their lands by force of gunpowder and blood, and decrees were even issued by different kings permitting the opening of the tombs of saints and other religious figures of Catholicism in order to extract any piece of gold—including dental prostheses—which could then be minted into coin.

    Once the foregoing has been established, the State can therefore be defined as the political organization of the economically dominant class whose ultimate purpose is to maintain the existing order and crush the resistance of the other classes through possession of the monopoly of physical violence. It is therefore unsurprising that the process of State formation consisted in setting apart a special public power with its army, police, prisons, and coercive institutions of various kinds.

    In this sense, speaking of democracy, defined as a “Form of political regime based on the proclamation of the principles of the power of the people, the freedom and equality of citizens. Democracy presupposes recognition of the principle of the subordination of the minority to the majority, the electability of the principal organs of State power, and the existence of political rights and freedoms.” (Oníkov & Shishlin, 1980, p. 140), lacks real meaning.

    Contemporary evidence of the foregoing is provided by the 2001 Nobel laureate in Economics, Joseph Stiglitz, who writes: “Finance is not the only area in which foreign investment has been an ambiguous blessing. In some cases, new investors persuaded governments (often with bribes) to grant them special privileges, such as tariff protection. In many cases the U.S., French, or other advanced industrial-country governments exerted pressure, reinforcing the notion in developing countries that it was perfectly appropriate for authorities to intervene in the private sector and presumably collect from it. In some cases, the role of the State seemed relatively innocuous (although not necessarily incorruptible). When U.S. Secretary of Commerce Ron Brown traveled abroad, he was accompanied by American businessmen seeking contacts with those emerging markets and entry into them. Presumably, the chances of obtaining a seat on the plane increased if one made significant campaign contributions.” (Stiglitz, 2003, p. 100).

    · · ·

    II · SectionHistorical Background of Syria

    Syria is a country whose population is concentrated in the northwest of its territory, which is due to the fact that only 0.06% of its surface area has water. According to (Datosmacro, 2017), Syria has a population of 18,502,413 inhabitants and a total area of 185,180 km.2, which is equivalent to a population density of approximately 100 inhabitants per square kilometer.

    According to (OPEC, 2017), Syria has 2.5 billion barrels of oil in reserve, ranking 31st in the world; however, these are only proven oil reserves[6]. According to (CIA, 2017), Syria also ranks 43rd worldwide in terms of proven natural-gas reserves, with 240,700,000,000 m.3

    This significant quantity of natural resources, while not representing proportions of global reserves as important as those of other countries—for example Iran (the country with the 5th-largest proven oil reserves and the 2nd-largest proven natural-gas reserves) or Iraq (the country with the 4th-largest proven oil reserves and the 11th-largest proven natural-gas reserves)—is sufficient reason for different nations to have a geopolitical interest in Syria. There is, however, an even more important reason: Syria borders Iraq, and Iraq in turn borders Iran, as can be seen below:

    Figure 1
    Map of the Iran–Iraq–Syria gas pipeline.
    Source: (RT, Economía, 2017)

    As can be seen, the gas pipeline runs from the Iranian coast across the Iran–Iraq and Iraq–Syria borders until it reaches the Syrian coast. Its final purpose is to supply European consumers, as well as consumers in the countries through which the pipeline passes. Syria is therefore geopolitically fundamental: whoever controls that country controls the pipeline’s final outlet and, with it, the supply of natural gas to Europeans; if, in addition, Iraq and Iran are controlled, one has in hand one of the most profitable businesses a company could imagine.

    The matter does not end there. To move the oil extracted from any of these countries, one must also go around the entire Arabian Peninsula or around the entire African continent.

    Figure 2
    Map of oil and natural-gas infrastructure in Saudi Arabia and the surrounding region.
    Source: (EIA, 2017)

    Since Euclid, it has been known that the shortest distance between two points is a straight line. Construction of the Trans-Arabian Pipeline began in 1947 and was administered primarily by the U.S. company Bechtel[7]. The pipeline was originally intended to terminate in Haifa, which at the time lay within the British Mandate for Palestine; because of the establishment of the State of Israel, however, an alternative route through Syria was established, and Lebanon was selected for one of the export terminals at Sidon. As (Little, 2003, pp. 12–13) notes, the Syrian government initially opposed the plan but ratified construction of the pipeline in 1949 after a military coup overthrew the democratic government there, and oil transport through the pipeline finally began in 1950. This coup against the government of the day—which had been chosen through free elections—was promoted by the CIA, and authoritative voices such as (Massad, 2017)[8], (Little, 2003)[9], and even declassified CIA records confirm it. Although that pipeline is no longer strategically important today, it serves as a historical reference point for understanding who has continued to destabilize Syria and why, a matter that will be examined in greater depth below.

    Although the Trans-Arabian Pipeline is no longer strategically important in geopolitical terms, Syria certainly remains so, because going around the Arabian Peninsula and crossing the Suez Canal significantly increases transport costs and also the time required to realize oil as a commodity.

    Figure 3
    Map of oil infrastructure and routes associated with regional transport.
    Source: (Puzzle de la Historia, 2017)

    As can be seen, going around the Arabian Peninsula in order to reach the Suez Canal (where fees are paid) involves traveling 11,600 kilometers, while avoiding the Suez Canal requires going around Africa, a distance of 19,800 kilometers. To give the reader a sense of scale, traveling through the Suez Canal would amount to 22.3 times the distance between Paso Canoas and Peñas Blancas, while avoiding it would mean traveling 38.05 times that same distance[10].

    Would it not be simpler to trade the oil if it could be taken out in a straight line through Syria? The answer is yes. Doing so, however, would require political control of Syria. This makes the country a fundamental geopolitical point, because whoever controls Syria will control not only those reserves of natural resources—oil and natural gas—but also the most efficient commercial route for placing them in Western markets.

    This highly strategic commercial position—in terms of any commodity, not only oil and natural gas—has made Syria desirable to various empires throughout world history, from the Persians and Greeks, through the Romans, and ultimately the Turks.

    Let us reconstruct some of that history in order to see the political evolution of the territory now known as Syria and thereby understand both the reasons for its relatively recent emergence as a nation-state and the climate of instability that has arisen within it and in its surroundings.

    The Roman Empire underwent an administrative division initiated with the tetrarchy[11] of Emperor Diocletian (284–305) and consolidated by Emperor Theodosius I (379–395), who divided it between his two sons: Arcadius became emperor of the East and Honorius emperor of the West. What remained of the Roman Empire after Odoacer (King of the Heruli) deposed the last Western Roman emperor (Romulus Augustulus) in 476 was conquered by Islam, becoming the Ottoman Empire[12] on May 29, 1453. The Ottoman Empire would then endure until the First World War (WWI).

    After WWI, small countries appeared on the map for the first time, among them Syria on September 1, 1918. Like every historical event, this occurrence was not arbitrary. As with the emergence of Iraq, Jordan, and others, it resulted from the fact that the French and British could not defeat the Ottoman Empire alone, making it necessary not only to ally with one another but also to secure the support of civilians residing within the empire. To win their favor, they promised them “Greater Palestine,” that is, a single nation for all Arabs.

    In secret, however, France and the United Kingdom concluded the Sykes–Picot Agreement[13], which consisted of distributing the geopolitical control they would exercise over the territory occupied by the Ottoman Empire in the event that they won the war. Napoleon is said somewhere to have remarked that, if one wished to succeed in politics, the key was to promise everything and fulfill nothing; that is precisely what the Europeans did, and the promise of a single nation for all Arabs was never fulfilled. Instead, as part of a distribution of Ottoman territory among the European powers of the time, they created many relatively small nation-states.

    Figure 4
    Map of the Sykes–Picot Agreement of May 1916.
    Source: (Encyclopædia Britannica, 2017)

    It was in this context, after the victory of the European nations, that Syria appeared and came under French control, a state of affairs that lasted until the end of the Second World War (WWII).

    As reported in (U.S. Department of the Army, 2017), shortly after the end of WWII, during 1944 the Syrian government assumed the functions of fourteen administrative departments that had been under direct French control since 1920. These included departments responsible for matters such as customs, social affairs, excise taxes, supervision of concessionary companies, and oversight of tribes. France retained control of social, cultural, and educational services, as well as the Levant Special Forces[14], which were used for security purposes. Despite French opposition, the Soviet Union in July and the United States in September 1944 granted Syria and Lebanon unconditional recognition as sovereign states; British recognition followed a year later. These Allied nations pressured France to evacuate Syria.

    The new Syrian government demanded the immediate and unconditional transfer of the Levant special troops to Syrian control or their dissolution, and threatened to form a national army unless that step was taken. France, however, made the withdrawal of the troops conditional on Syria signing a treaty that would assign France a privileged position in the country.

    In January 1945, the Syrian government announced the formation of a national army, and in February it declared war on the Axis powers (principally Germany, Italy, and Japan). In March, the country became a founding member of the United Nations (UN), an indication of its sovereign status, and in April it affirmed its commitment to the idea of Arab unity by signing the Arab League pact.

    Before introducing Israel’s role in Syria’s historical and current situation, it is necessary to discuss the ideological-religious conflicts in the region.

    Shortly after the end of WWII, the Arab Socialist Ba’ath Party was founded, hereafter referred to as BA’ATH in reference to the ideology of this pan-Arab party, which combined the old aspirations for a single Palestinian nation with a secular ideology and socialist foundations. It came to power in 1963 in Syria and Iraq; the Syrian and Iraqi factions of the BA’ATH clashed in 1966 and thereafter acted independently. This produced an ideological fragmentation in the region, dividing it essentially into two blocs: Syria’s allies and Iraq’s allies.

    Shortly before the BA’ATH came to power, Syria united with Egypt (with which it did not even share a border) to form the United Arab Republic between 1958 and 1961. The alliance did not last long, but it endured long enough for Egypt to persuade Syria to nationalize its natural resources. The failure of this union was not due to random or arbitrary factors either. In 1961 there was a coup d’état in Syria sponsored by the radical Syrian army, after which the country and its population endured a tyrannical government for two years; another coup followed in 1963, the one in which the BA’ATH took power in both Syria and Iraq in that same year.

    In this 1963 coup, Háfez al-Assad appeared for the first time as a political figure and became head of the BA’ATH State; the same occurred in Iraq with Saddam Hussein, also a member of the BA’ATH Party. With the Cold War, which began in 1947, Syria aligned itself with the Soviet Union, while a recently created nation-state aligned itself with NATO. Israel must now be introduced into the international setting.

    Between 1936 and 1939, a revolt took place in the Palestinian territories controlled by the United Kingdom—those formed after the defeat of the Ottoman Empire—whose cause was protest against Jewish immigration, since Arabs and Jews possessed ideological-religious differences that were irreconcilable within the framework of Middle Eastern culture. The revolt arose because of the United Kingdom’s consent to Jewish immigration into Palestinian territories[15] and its refusal to hold democratic elections to decide the future of the Jews. Since Palestinians had historically occupied those territories for centuries, they possessed an overwhelming demographic majority that would have resolved the elections in their favor.

    Thus, after the French and British withdrew from what had formerly been Ottoman territory, and amid the ideological-religious conflicts between Palestinians and Jews in the area, the United Nations General Assembly met on November 29, 1947, following the report of the Peel Commission (which evaluated the causes of the conflict), and approved a plan dividing Palestine into two States. Curiously, the plan awarded 53.6% of the territory to the Jews and 48.7% to the Arabs, while determining that Jerusalem—which represented an area equivalent to 2.7%—would be a corpus separatum administered by the United Nations. The fact that, for political reasons (Israel would be a Western ally in the Middle East), the Jews were given lands that had been occupied by Palestinians for centuries, and that despite Palestinians making up 67% of the population compared with 33% represented by Jews, the latter were awarded a larger share of the territory, led the countries representing Palestine to intervene militarily in the territory assigned to the Jews two weeks after the UN resolution was adopted. Jerusalem subsequently ceased to be a corpus separatum and became the capital of the State of Israel, with the complicity and silence of its Western allies. According to Israeli professor David Grossman, this would later mean that “since 1967, those who set the agenda and benefit from the budgets (in Israel) are the right and the settlers, a small devout group that has kidnapped an entire nation and confiscated our future.” (Grossman, 2010).

    The foregoing caused Israel’s neighbors not to recognize it as a legitimate nation-state and, once the Europeans had departed, to attack Israel instead.

    Since then, through force and the complicity of the West, and since the artificial creation of the State of Israel, geographic changes have taken place in the proportion of territory occupied by Palestinians, as shown below.

    Figure 5
    Cartographic sequence showing territorial changes in Palestine from before 1948 through 2014.
    Source: (Miller, 2017)

    This problem extends beyond geography; it concerns the distribution of resources per capita and, with it, quality of life. We will now briefly examine the variation in population density from before 1948 to 2014.

    Given the geographic change undergone by Palestinian territory, and using the total-population figures from (Datosmacro, 2017) beginning in 1970, we can calculate changes in Palestine’s population density. According to (Simpson, 2017), before 1948 Palestinian territory covered 26,626 km.2 and had an estimated population of 1,061,270 inhabitants, equivalent to 39.86 inhabitants per square kilometer. If Palestinian territory became 48% of the original in 1947 with the UN resolution, then the territory would have amounted to 12,780.48 km.2; assuming that the population did not vary significantly during that period (and even if it did, there are insufficient data to perform the calculation), the resulting population density would have been 83.03. In 1967 Palestinian territory was only 22% of the original, equivalent to 5,857.72 km.2; given that by 1970 the Palestinian population had risen to 1,124,293, this would imply a population density of 191.93 inhabitants per square kilometer. Finally, in 2014 Palestinian territory was only 12% of the original, equivalent to 3,195.12 km.2, and with a population of 4,422,143 reported by the source cited above, the resulting density would be 1,384.03 inhabitants per square kilometer. This would imply an approximate increase in population density of 3,372.23%. It is not difficult to imagine the economic difficulties that this increase in demographic pressure has implied for the Palestinian people in terms of implementing social policies, income-distribution policies, and other related government actions, even without counting the destruction of wealth caused by the wars with Israel. Conversely, it is also not difficult to imagine the economic advantages this has afforded Israel, whose population, as seen above, was the minority occupying those territories, without yet considering the substantial financing provided by the United States to Israel in various political and social areas, including the war against the Palestinian people and against countries that do not align themselves with its interests, as detailed by (Sparrow, 2017). The United States also used economic leverage in the international arena: it was the country that contributed the most to UNESCO (22%) and withdrew that support from the institution after Palestine was admitted, as reported by (El Mundo, 2017).

    What have the industrialized powers done in the face of such a violation of the civil rights of the Palestinian population? Absolutely nothing. They have simply made requests that have no coercive force, leaving Israel free to comply with them or not; naturally, those requests have not been obeyed, while the blood of hundreds of victims has been shed. According to (TeleSUR, 2017), between April and May 1948—the first year of the State of Israel—the Israelis took several Arab cities under the UN partition plan, but on April 10 the first massacre by Jewish militiamen against 100 Palestinian peasants in the village of Deir Yassin was recorded, forcing thousands of Arab civilians to flee the region. In 1967, during the Six-Day War, which began on June 5, Israel militarily occupied the West Bank and Gaza Strip, Syria’s Golan Heights, and the Sinai Peninsula. During the military offensive, Mirage 3 aircraft of the Israeli army destroyed more than 400 Arab aircraft. Those battles reportedly left 776 Israelis dead, 2,563 wounded, and 15 prisoners. On the Arab side, there were at least 24,000 dead, 45,000 wounded, and 6,000 prisoners. Between 1975 and 1981, the number of deaths officially recorded by Palestinian and UN organizations was 170, although reports from human-rights organizations speak of more than 3,000 additional deaths not officially recorded.

    In 1982, the death toll rose sharply, with 11,275 deaths recorded in the Lebanon War, where the Zionist army under then Minister of Defense Ariel Sharon launched “Operation Peace for Galilee” on June 6, with the objective of destroying the Palestine Liberation Organization (PLO), which was concentrated in Beirut after being expelled from Jordan in 1970. In the Sabra and Shatila massacre, 675 Israeli soldiers, around 9,800 Syrian soldiers, and Palestinian militiamen died. Between 2000 and 2010, an estimated 7,342 Palestinians, mostly civilians, died as a result of bombings and land and sea attacks by the Israeli army. Finally, during Israel’s prolonged occupation of Palestine, more than 1,500 civilians died and 1,215 Palestinians were displaced because of the demolition of homes by Israeli authorities. In the Gaza Strip conflict, 86% of the dead were Palestinians.

    Ultimately, “Does the so-called international community exist? Is it anything more than a club of merchants, bankers, and warriors? Is it anything more than the stage name the United States adopts when it puts on theater?” (Galeano, 2017).

    Háfez al-Assad’s arrival in power did not alter the conflicts already present in the region, specifically between Syria and Israel. Later, with the Cold War placing the two countries in different ideological blocs, tensions intensified and Syria entered into an open war against Lebanon.

    Syria’s complications were not yet over, and the ideological frictions within the region were exploited by its allies. Before proceeding to describe that social fact, however, the genesis of the political-ideological factions among the Palestinian people will be introduced.

    Contrary to what is commonly assumed, Arabs are not necessarily Muslims, although most of them are. The following table presents this segmentation.

    Table 1
    Table showing the division between Shiite Islam and Sunni Islam and the political or armed factions mentioned in the article.
    Source: Author’s own elaboration.

    The proportion between Sunnis and Shiites is shown below.

    Figure 6
    Map of the Islamic world showing the proportions of Sunni and Shiite populations.
    Source: (RT, Sunitas y chiitas: ¿Qué es lo que los separa?, 2017)

    It is estimated that Sunnis account for roughly 80–90% and Shiites for 10–20%. In Syria, because Háfez al-Assad’s government belonged to the Shiite minority while governing a Sunni majority, strong opposition movements began to emerge and were suppressed by gunpowder and blood. This internal conflict in Syria was exploited by Sunni Islamists, who took up arms against Háfez al-Assad; once again, the revolt was put down at the cost of many lives. Háfez al-Assad died in 2000 and was succeeded by Bashar al-Assad.

    As (Rafizadeh, 2017) notes, once Bashar al-Assad came to power he proposed neoliberal-style economic openings with the goal of joining the World Trade Organization (WTO). These policies even led the United States to lift its opposition to Syria entering the organization, and with 153 members in favor, the WTO granted Syria observer status[16]. However, as the cited author observes, this economic reformism was not accompanied by income-redistribution policies (as is characteristic of the neoliberal model) and generated social unrest in the country. This forced the Syrian president to return to his father’s economic policies.

    Several years later, the “Arab Spring”[17] reached Syria. There, “dozens of people demonstrated in Dar’a in the south of the country demanding freedom, political reforms and action against corruption, peaceful acts controlled by the Syrian police without violent incidents. The march against the government was launched on Internet social networks and supported by thousands of people who backed a Syrian revolution against President Bashar al-Assad until freedom and justice were achieved, but mobilization in the streets was limited. In response, Al-Assad announced economic reforms, amnesty for prisoners, and greater Internet access. The situation of instability continued throughout 2011, attracting international attention and raising the possibility that the UN Security Council might impose sanctions similar to those applied to Libya.” (EcuRed, 2017).

    Some argue that the “Arab Spring” was a social movement sponsored by the United States to destabilize governments in the region that were not aligned with its interests, as investigative journalist Lee Stranahan put it: “When Barack Obama took office as president in 2008 with Hillary Clinton as Secretary of State, one of his first foreign-policy steps was his speech in Cairo, Egypt, where he stated, in the presence of members of the Muslim Brotherhood, that ‘a new era had begun in the U.S. attitude toward Islam’ (…) What followed was the wave of Arab Spring uprisings throughout the region, which, despite initially being regarded as ‘bold movements of people desperate for freedom,’ were in fact ‘a way for Islamists to dethrone the more secular military dictators of the region (…) The U.S. openly called for the overthrow of Al Assad despite the fact that it was clear that the outcome of this overthrow would be the seizure of control by Islamist groups (…) Syria proved resistant’ to Obama and Clinton’s regime-change efforts, even though the U.S. supplied weapons to the so-called ‘rebels’ that ultimately ended up in the hands of Islamist groups.” (Stranahan, 2017).

    Likewise, according to U.S. attorney John F. Kennedy Jr.: “Our war against Bashar al Assad did not begin with the peaceful civil protests of the Arab Spring in 2011, but in 2000, when Qatar offered to build a $10 billion gas pipeline through Saudi Arabia, Jordan, Syria, and Turkey.” (Kennedy, 2017).

    Julian Assange, founder of WikiLeaks, takes a similar line, stating: “The Syrian chapter goes back to 2006, when in a very important cable Ambassador Roebuck, based in Damascus, responds to a discussion about a plan to overthrow the Assad Government in Syria (…) When the United States needs to do something, it brings together the different arms of U.S. power, which include the military, Intelligence, finance, commerce, and its information power.” (Assange, 2015). Assange also states that “Within those military strategies, the journalist highlights the role of apparently civilian institutions, such as the National Endowment for Democracy (NED) and the United States Agency for International Development (USAID) (…) Assange also mentions the alignment of the International Monetary Fund (IMF) with Washington’s foreign policy when it comes to weakening or destabilizing countries through their finances.” (HISPANTV, 2017).

    One fact does not, of course, exclude the other. From the standpoint of Western conceptions of political philosophy, many countries in the region have unfinished business regarding the political freedoms they grant their citizens. After the democratic opening, however, Bashar revived his neoliberal policies by promoting privatizations in order to smooth relations with the United States and its allies, while making no concession to the opposition movement in Syria. Thus, despite his economic-liberalization policies, as (RPP Noticias, 2017) reports, the United States and the other aligned countries called for the Syrian president’s resignation, and Obama announced economic sanctions against Syria, including a prohibition on trade with the Arab country. In the words of the U.S. Department of State: “The United States government has repeatedly called on President Bashar al-Assad to step down and has led the efforts of the international community to work toward a negotiated political solution to the conflict.” (U.S. Department of State, 2017).

    In its attempts to overthrow Bashar al-Assad, the United States financed the creation of the Islamic State, according to Julian Assange: “Thus, for example, the disastrous intervention—absolutely disastrous—in Libya, the destruction of Gaddafi’s Government, which led to the occupation by Islamic State of large segments of that country, the flows of weapons going to Syria, guided by Hillary Clinton toward jihadists inside Syria, including Islamic State, are there in those emails. There are more than 1,700 emails from the Hillary Clinton collection that we have released on Libya alone.” (RT, 2017).

    In addition, the Obama administration allowed Islamic State to grow in the expectation that this would help force the overthrow of the Syrian president, as John Kerry stated at the time: “We knew that it (Daesh) was growing, we were watching, we saw Daesh strengthening and we thought that threatened Al-Assad (…) We thought that we could probably get Al-Assad to come and negotiate, but instead of negotiations we found that Al-Assad got Putin to support him (…) The Russians have intervened because they do not want to see a Daesh government […] Unfortunately, the Russians have changed the situation. They have changed the equation.” (RT, 2017).

    Figure 7
    Demographic map of Syria.
    Source: (Heritage for Peace, 2017)

    Ultimately, the reader should remember that 241 years ago the United States, France, and England were the United States, France, and England and governed themselves; 100 years ago, by contrast, Syria did not exist on the map, and 72 years ago it did not govern itself. Moreover, unlike the Western countries just mentioned, Syria never decided its own borders: they were decided for it on the basis of geopolitical convenience rather than criteria grounded in its economic, demographic, cultural, and social needs. The country therefore contains profound design errors—errors in its geographical architecture. It is difficult to imagine implementing social projects in a country such as Syria, where water exists only in a small part of the territory and where a desert of 200,000 square miles lies between the population and its sources of natural resources (as can be seen in Figure 7), according to (Encyclopædia Britannica, 2017). It is also a country that has continually been destabilized and even controlled by the principal powers of the West, and where a profound ideological-religious contradiction, combined with foreign interventionism, makes it extraordinarily difficult to achieve the minimum social and political cohesion required to move forward as a nation-state. It is therefore not surprising that the BA’ATH repeatedly uses repression to remain in power, or that this produces social eruptions that reach the level of civil war, as has occurred in various Western countries during the past century when they faced socioeconomic problems of far smaller magnitude than Syria’s.

    · · ·

    III · SectionWars as a Mechanism for Offsetting the Fall in the Average Rate of Profit

    “War, then, is not a relation of man to man, but of State to State, in which individuals are enemies only accidentally, not as men nor even as citizens, but as soldiers: not as members of their country, but as its defenders. Finally, a State can have as its enemy only another State, and not men, since between things of different natures no true relation can be established.” (Rousseau, 2007, p. 42).

    As Rousseau argues, wars set States against one another. In the first section of this research, however, it was shown that States respond to the interests of the dominant class at each specific stage of historical-social development. When two nation-states confront one another, what lies behind the conflict is a confrontation between the interests of the dominant classes within each of them. The constant interventionism of the United States in Syria is not the product of chance or coincidence; rather, it obeys inexorable economic laws belonging to the capitalist mode of production, specifically the law of the tendency of the average rate of profit to fall.

    “(…) as the historical-natural process we call human society unfolds, Capitalism develops the productive forces to an unprecedented level and thereby generates an increase in the proportion of accumulated surplus value allocated to the acquisition of constant capital at the expense of the proportion allocated to variable capital (because technological innovation reduces necessary labor time and increases surplus labor time). Proportionally, however, the reduction in necessary labor time will be smaller than the increase in total capital or, what amounts to the same thing, increases in the rate of surplus value will be smaller than increases in total capital, and thus a downward tendency in the average rate of profit will emerge, which Marx called the law of the tendency of the rate of profit to fall.” (Gómez, 2017, pp. 51–52)

    In weighted-average terms, the foregoing means simply that the technological innovations undertaken by capitalist firms will not proportionally offset the increase in total investment and, consequently, the average rate of profit will tend downward. There are, however, counteracting causes that turn the law into a law of tendency. In Marx’s words: “(…) we see that instead of the difficulty with which economists have hitherto struggled, namely explaining the fall in the rate of profit, the inverse difficulty arises: explaining why this fall is not greater or more rapid. This is undoubtedly due to the play of influences that counteract and neutralize the effects of this general law, giving it merely the character of a tendency, which is why we present the fall in the general rate of profit here simply as a tendency to fall.” (Marx, Capital, Volume III, 2010, p. 232).

    Marx enumerated the most general causes that make the fall in profit a tendential law: an increase in the degree of exploitation of labor (the intensity and/or duration of the working day), a reduction of wages below their value (below the value of labor power), the cheapening of the elements that make up constant capital (fixed capital and intermediate consumption), relative overpopulation (the role played by the mass of unemployed workers in wage determination), foreign trade, and the increase in share capital (which generates dividends).

    Despite these counteracting causes, however, the fall in the rate of profit asserts itself tendentially, as shown below.

    Figure 8
    Chart showing the downward tendency of the average rate of profit.
    Source: Author’s own elaboration based on (Marquetti & Foley, 2017).

    Although capitalism has been the first socioeconomic formation (SEF) to exhibit cyclical crises and to make use of elements foreign to the essence of its economic philosophy, it has also shown an enormous capacity to reinvent itself and recover. In this sense, it has increasingly and more clearly employed mechanisms that were previously less prominent—for example, wars.

    Figure 9
    Chart of Kondratiev long waves and cycles of prosperity.
    Source: (Allianz Global Investors, 2017)

    Figure 9 shows a Kondratiev long wave, named after the economist Nikolai Kondratiev, who argued that the capitalist economic cycle as a whole follows periodic fluctuations in economic activity that can be represented as waves. Each wave has different stages. The starting point represents the beginning of economic activity, which expands until it reaches a peak; after that, markets become saturated as a result of overproduction (production greater than what the market, given a particular level of purchasing power, can absorb), causing capitalist economies to slow until they reach what we now know as financial crises.

    In Kondratiev’s words: “It is generally recognized today that the dynamics of economic life under the capitalist social order are not simple and linear in character, but rather complex and cyclical. Nevertheless, science has clarified very little about the nature and types of cyclical movements, which resemble oscillations. When we speak of cycles in economics, we generally refer to cycles of activity lasting seven to eleven years. But it is evident that these movements are not the final type of economic cycle. In reality, the dynamics of economic life are more complicated. In addition to the cycles already mentioned, which we shall agree to call ‘intermediate,’ it has recently been shown that the existence of still shorter oscillations, lasting approximately three and a half years, is probable. But this is not all. There are real grounds for supposing the existence of large oscillations of approximately fifty years in the capitalist economy, a fact that makes the problem of economic dynamics even more complex.” (Kondrátiev, 2017)

    Kondratiev is referring here to the three principal cycles of economic activity: Kitchin cycles (short duration), Juglar cycles (intermediate duration), and Kondratiev cycles (long duration). This section will focus on the latter, the long cycles.

    It is true that Kondratiev’s analysis is rough and relatively mechanical because it lacks a prior theoretical formulation. This leaves him unable to establish precise duration intervals for the long waves or explain the causes of those intervals; nor does it allow him to examine deeply either the reasons that give rise to crises or those that permit capitalist economies to recover, much less the causes of the point-to-point transition within the wave. Nevertheless, it does provide a general idea of the behavior of economic activity and makes it possible to identify certain patterns of behavior that can be connected with what has been developed throughout this research.

    As can be seen in Figure 9, each Kondratiev cycle has corresponded to some technological revolution. The expansionary phase begins once the innovation is introduced and, as a snowball effect develops—that is, as the innovation spreads beyond the innovating firm to imitating firms—economic activity flourishes. Once all sectors of the economy, or at least the most important ones, have adopted the innovation and produced what their production-possibility frontier permits, the economy stagnates. After some time, stagnation gives way to slowdown and finally to economic recession. It can also be seen how a new technological revolution begins the recovery and opens the curtain on a new phase, or wave, of the economic cycle. Statistically speaking, these long waves have been found to last between forty and sixty years, tending more toward the upper than the lower limit.

    What Kondratiev proves unable to explain, however, is why economic crises become deeper as the economic cycle advances. Nor does he explain why it becomes more difficult to emerge from them, or the consequences this has for the average rate of profit, capital accumulation, and competition. In general terms, this can be explained by the fact that as capitalist economies develop—and with them technological development—it becomes increasingly difficult to carry out revolutions in production techniques. Among other factors, competition forces firms constantly to introduce small innovations; as society reaches a given degree of development of its productive forces, these become increasingly costly (as explained above) and their impact on the average rate of profit becomes progressively smaller. At the same time, every SEF has shown insurmountable limits to its capacity for technological innovation. For primitive communities, for example, it would have been impossible to construct the carriages and armor produced by the Roman Empire under the slave mode of production, just as it would have been impossible for the Romans to conceive the construction of mills powered by water or wind, and for those societies in turn to discover nuclear energy. What does this mean? Simply that as historical-social development advances, each mode of production gradually exhausts its capacity for technological innovation, which also means that technological revolutions become increasingly less close at hand.

    The foregoing has two fundamental consequences. The first is an intensification of the downward tendency of the average rate of profit; the second is the centralization of capital, that is, the deepening of inefficient and weakly competitive market structures such as monopolies, monopsonies, oligopolies, oligopsonies, and others. This in turn has important effects on capital accumulation. The most important is that market structures lacking efficiency and competitiveness move away from the average rate of profit because their profit margins rise as a result of their market power[18], while firms with an average level of technology simultaneously see their rate of profit fall and firms with below-average technology are penalized by competition through bankruptcy and are absorbed by other firms, generally those with greater market power. This economic phenomenon occurs because technological innovations, for the reasons already discussed, become increasingly costly.

    The matter does not end there, because market structures to which the average rate of profit does not apply and which possess significant market power—for example, monopolies—are free to slow technological innovation because they do not face competition[19]. In this way they move still farther from the downward tendency of the average rate of profit, since their profit margins are above the average. It is not uncommon to observe, for example, that monopoly profit rates tend to rise during financial crises while the average rate of profit plummets.

    It might seem that these kinds of market structures, which promote inefficiency and lack of competitiveness, are an economic alchemy for capitalist firms. Since Adam Smith, however, economic science has understood the inverse relationship between wages and profits. Consequently, the measures by which firms distance themselves from the fall in the average rate of profit can only be possible at the cost of implementing the factors mentioned earlier by Marx. There is various evidence of this. One recent example occurred in France, an industrialized economy whose large companies were nevertheless forced to introduce greater flexibility into the labor market. Actions of this type by those operating within such market structures generate social discontent and, on many occasions, large generalized protests, as reported by (Yárnoz, 2017), one of which ended with 60 French people detained and 40 injured in a single day.

    There is, of course, a palliative measure for this problem which, while not representing a definitive solution, contributes to slowing the natural course of economic laws: wars.

    Figure 10
    Chart of a Kondratiev wave with wars and economic cycles.
    Source: (Kondratieff Winter, 2017)

    As can be seen, wars have played a major role in the recovery of capitalist economies when they have gone through crises of overproduction. This is clearly not a new phenomenon: it can be observed at least as far back as 1812, when capitalism had existed for only 23 years if its political establishment in France is dated to the storming of the Bastille in 1789. What explains this? The answer is quite simple. Part of the unemployed labor force leaves the economy, which raises wages (given the resulting shifts in the labor-supply curve, holding labor demand constant); purchasing power therefore rises and production is stimulated again. In addition, many unemployed workers die in war (so firms do not have to pay severance compensation, for example), while the Government assumes responsibility for subsidizing their families (with taxes paid by those same families). The “benefits” of war for the economy do not end there. In many countries war destroys land and industry, reducing the stock of available fixed capital. Holding other factors constant, if demand for fixed capital remains unchanged while its supply declines, its market price rises. Machinery that had been undergoing depreciation as a result of use and new technologies therefore experiences a slowing of that process, which in turn slows the need for innovation. Finally, war itself promotes economic activity by activating industries closely linked to weapons manufacturing and even industries that benefit significantly from arms production. These factors lead to higher stock-market valuations for companies wholly or partly connected to this industry, because greater economic activity increases their profitability.

    Industries most closely linked to arms production are those that belong directly to the weapons industry. “These are the first 10 companies on the 2011 ranking (figures in parentheses correspond to the 2010 ranking):

    1 (1). Lockheed Martin (United States). Missile systems, electronics, and aerospace. Sales of $36.270 billion in 2011. Net profits: $2.655 billion. 123,000 employees (132,000).

    2 (3). Boeing (United States). Aircraft, electronics, missiles, aerospace. Sales of $31.830 billion. Net profits of $4.018 billion. 171,700 employees (160,500).

    3 (2). BAE Systems (United Kingdom). Aircraft, artillery, missiles, military vehicles, ships. Sales of $29.150 billion. Net profits of $2.349 billion. 93,500 employees (98,200).

    4 (5). General Dynamics (United States). Artillery, electronics. Sales of $23.760 billion. Net profits of $2.526 billion; 95,100 employees (90,000).

    5 (6). Raytheon (United States). Missiles, electronics. Sales of $22.470 billion. Net profits of $1.896 billion. 71,000 employees (72,400).

    6 (4). Northrop Grumman (United States). Aircraft, electronics, missiles, warships. Sales of $21.390 billion. Net profits of $2.118 billion. 72,500 employees (117,100).

    7 (7). EADS (EU). Aircraft, electronics, missiles. Sales of $16.390 billion. Net profits of $1.442 billion. 133,120 employees (121,690).

    8 (8). Finmeccanica (Italy). Aircraft, artillery vehicles, missiles. Sales of $14.560 billion. Net profits of $902 million. 70,470 employees (75,200).

    9 (9). L-3 Communications (United States). Electronics. Sales of $12.520 billion. Net profits of $956 million. 61,000 employees (63,000). 10 (10). United Technologies (United States). Aircraft, electronics, engines. Sales of $11.640 billion. Net profits of $5.347 billion. 199,900 employees (208,220).”

    Source: (Moreno, 2017)

    As can be seen, of the nine companies mentioned, six are American and the other three belong to countries allied with the United States. Even public officials can benefit from war, as has been the case with Donald Trump. According to (Boggioni, 2017), Trump owns shares in Raytheon, the company that manufactures Tomahawk missiles, and therefore benefited from having initiated the attack on Syria, because Raytheon’s shares appreciated, as can be seen below.

    Figure 11
    Screenshot of the Raytheon (RTN) stock quotation included in the article.
    Source: (Raytheon, 2017)

    Nor is the impact of wars on industries only partially connected with warfare negligible, such as steel producers, pharmaceutical companies, oil producers, among others.

    In modern times, oil is fundamental to all productive processes, while natural gas also plays an important role in combustion, to the point that many regard it as the fuel of the future. If to the foregoing we add the savings in transport and commercialization costs represented by the possibility of moving these resources out in a straight line (through Syria), the significant quantity of resources the country possesses, its geopolitically strategic position on the map, and the law of the tendency of the average rate of profit to fall, it becomes entirely natural to understand the reasons why the United States conducts its current foreign policies toward Syria.

    · · ·

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    Yárnoz, C. (April 15, 2017). Decenas de miles de personas desfilan en la mayor protesta contra la reforma laboral en París. Retrieved from El País: http://internacional.elpais.com/internacional/2016/06/14/actualidad/1465886786_716533.html

    Article notes

    [1] This refers to Durkheim’s definition of a social fact, which consists of “Every way of acting, whether fixed or not, capable of exercising an external constraint upon the individual; or again, every way of acting which is general throughout a given society while at the same time existing in its own right, independently of its individual manifestations.” (Durkheim, 2009, p. 68).

    [2] In general, all sciences have as their ultimate aim the prediction of changes over time in their object of study.

    [3] Rousseau is referred to here; the other is Thomas Hobbes.

    [4] Of course, this is not a reference to a mechanistic approach in which the objective world determines the world of ideas. There is no doubt that the world of ideas has influence over and a capacity to transform the objective world, as Durkheim expressed. What is argued here is that, in the last instance, the material conditions of existence determine the world of ideas.

    [5] For further discussion, one may consult Engels’s The Origin of the Family, Private Property and the State, as well as Chapter XXIV of Volume I of Marx’s Capital, entitled “The So-Called Primitive Accumulation,” for the case of Europe, or Rafael Menjívar Larín’s Acumulación Originaria y Desarrollo del Capitalismo en El Salvador for the general case of Latin America.

    [6] Proven oil reserves are those that can be extracted profitably with current technology, taking into account the price of oil in the year being analyzed. These estimates are based on geological and engineering analyses, so the quantities established enjoy a high degree of confidence.

    [7] The largest construction and civil-engineering company in the United States.

    [8] Arab intellectual who serves as Professor of Modern Politics and History at Columbia University.

    [9] Professor of History at Clark University.

    [10] According to Google Maps, the distance between the two borders is 520.4 kilometers.

    [11] A form of government in which power is shared by four persons who call themselves tetrarchs.

    [12] Turks who conquered what is now known as Syria and its surroundings, founding that empire.

    [13] Its name derives from the fact that it was secretly negotiated by François Georges-Picot (a French diplomat and lawyer) and Mark Sykes (a lawyer by profession and member of the English nobility).

    [14] Military units formed during the period of the French Mandate in Syria, in addition to the Army of the Levant. These were French armed forces that occupied part of Western Asia between WWI and WWII and were composed of locally recruited personnel, who ultimately became the basis of the national armies of Syria and Lebanon.

    [15] Due in some measure to the persecution they suffered from the so-called “Axis of Evil,” composed principally of Germany, Italy, and Japan.

    [16] Countries that are in the process of negotiating their accession to the WTO.

    [17] “The name by which the media identified the series of popular and political demonstrations that took place in the Arab region mainly from the beginning of 2011 and led to the fall of the dictatorships of Ben Ali in Tunisia and Hosni Mubarak in Egypt, the intensification of violence in Yemen, and the civil war in Libya. Some international analysts have found points of similarity between the Arab Spring and anti-crisis demonstrations in Europe, Asia, and the United States.” (EcuRed, 2017).

    [18] When speaking of the existence of an average rate of profit, reference is made to a weighted average of sectoral rates of profit. The weighting factor is simply each firm’s share of the total capital existing in an economy—that is, the proportion that its investment represents of the total investment available to a society at a given moment in time. The existence of this average rate does not presuppose a static economy; on the contrary, it arises from the very economic dynamic by which capitalist firms rapidly migrate from one productive branch to another over time in search of the highest profit margins for their investments. It is precisely this process that produces an approximate equalization of sectoral profit rates and thereby makes the existence of the average rate of profit possible.

    [19] In the case of market structures such as oligopolies, the issue can vary. Although most of the time they collude and behave as a monopoly, on some occasions they compete, and their analysis then becomes more similar to that of competitive market structures than to that of noncompetitive ones.

    End · 2017
  • ON THE NEGATIVE BINOMIAL 2 DISTRIBUTION

    ON THE NEGATIVE BINOMIAL 2 DISTRIBUTION

    Probability · Count Data · Hierarchical Models

    When Counts Refuse to Behave: Understanding the Negative Binomial II as a Measurement Instrument

    A guided reading of José Mauricio Gómez Julián’s 2020 essay Some Reflections on the Negative Binomial Distribution II as a Measurement Instrument—tracing the argument from geometric series and probability mixtures to overdispersion, latent heterogeneity, and simulation in R.

    Mauricio Gómez Julián · Theoretical & Applied Probability · Approx. 15-minute read
    Reading note. This essay explains the paper on its own terms while keeping the mathematics technically precise. Where a qualification is needed—especially in the passage from an exponential mixing distribution to the general Negative Binomial II—it is marked explicitly rather than silently altering the paper’s argument.

    The question behind the paper

    Count data appear everywhere. An economist counts firm failures, strikes, defaults, patents, accidents, or entries into a market. A political scientist counts protests, cabinet changes, violent events, legislative vetoes, or international disputes. A biologist counts surviving organisms, mutations, infections, or offspring. The elementary model for many such problems is the Poisson distribution. But real counts often fluctuate more than a Poisson model allows. Their variance is larger than their mean: the data are overdispersed.

    The Negative Binomial II—usually abbreviated NB2—is one of the central statistical instruments for precisely that situation. Yet Gómez Julián’s paper is not content to present the NB2 probability mass function, list its moments, and move on. Its organizing question is broader: what kind of object is a probability distribution, where does it come from, what other distributions does it contain or presuppose, and what is gained when we understand its construction rather than merely its final formula?

    The paper therefore has two explicit axes. The first, and more important one, studies NB2 as the outcome of a wider theoretical structure involving hierarchical models and probability mixtures. The second studies NB2 as an individual distribution—its form, interpretation, moments, and practical use, including hand calculations and R. The intended unity between these axes is philosophical as well as mathematical: probability distributions are treated as instruments for measuring natural and social phenomena under uncertainty, and the paper argues that their history, formal structure, scientific interpretation, and application should not be torn apart.

    The distribution is easier to understand when we see not only the finished formula, but also the process that produces it.
    · · ·

    Why begin with the geometric series?

    The paper begins surprisingly far away from count-data regression: with the geometric series, its historical roots, and its relation to the binomial theorem. This is deliberate. Gómez Julián wants the reader to see the Negative Binomial II as part of a mathematical genealogy rather than as a formula that appeared fully formed.

    The route is roughly this: the geometric series provides a simple infinite expansion; differentiation exposes a recurring combinatorial pattern; that pattern is used to motivate the binomial expansion; and replacing the ordinary exponent with a negative one leads to the negative binomial series. The point is not merely algebraic. The paper repeatedly emphasizes the movement from simpler structures to more general ones and from one family of mathematical objects to another.

    1 + x + x2 + x3 + ··· = 1 / (1 − x),   |x| < 1 binomial expansion negative binomial series The paper’s algebraic genealogy in compressed form

    For a nontechnical reader, the important idea is simple: a probability distribution can be understood through the transformations and relationships that generate it. The paper later reinforces this visually with a large network diagram of probability distributions, reproduced from ProbOnto, in which distributions are connected by transformations, limiting relations, and special cases. NB2 is therefore presented as one node in a densely connected mathematical ecology, not as an isolated technique.

    Probability as a measurement problem

    Before building the NB2, the paper stops to ask what “probability” means. This is not a decorative philosophical detour. Gómez Julián’s position is that formal probability calculus and philosophical interpretation cannot be completely divorced, because statistical conclusions depend on what we think probabilities are measuring and on how the scientific problem is conceptualized.

    The paper adopts an explicitly objective and dialectical-materialist orientation. Randomness is treated primarily as an epistemological condition: events appear random because their causes are unknown, too numerous, or too complicated to represent completely. At the same time, the Kolmogorov axioms provide the formal mathematical framework that makes probability calculations coherent. The paper also draws on objective Bayesianism to argue that degrees of belief should be constrained by evidence, scientific theory, and the probability calculus rather than reduced to arbitrary personal opinion.

    Why this matters statistically

    A model is not chosen only because its formula is convenient. The scientific description of the process determines which random variables, conditional relationships, latent quantities, and parameterizations are meaningful. That principle becomes concrete once the paper turns to hierarchical models.

    A family, not an isolated formula

    The paper next introduces the distributions needed for its construction: Bernoulli, Binomial, Poisson, and Exponential. Each plays a distinct role.

    Distribution Plain-language role Role in the paper
    Bernoulli One trial with two possible outcomes. The elementary unit from which repeated success/failure experiments are built.
    Binomial Counts successes in a fixed number of Bernoulli trials. The first level of the hierarchical construction.
    Poisson Counts occurrences when events arrive with a given mean rate. Makes the number of opportunities or events itself random.
    Exponential Models waiting time or positive continuous variation associated with a Poisson process. Introduces variation in the Poisson rate across observational units.

    This sequence already contains the paper’s methodological intuition. A complex phenomenon can be decomposed into simpler probabilistic stages, each corresponding to a different part of the scientific story. Instead of forcing all uncertainty into a single flat formula, a hierarchical model lets uncertainty enter at more than one level.

    Hierarchies, mixtures, and latent variables

    A hierarchical model specifies variables and parameters in stages. A mixture model appears when a parameter in one probability distribution is itself treated as a random quantity governed by another distribution. The parameter that seemed fixed at the lower level becomes variable at the higher level.

    That is the key conceptual move in the paper. It is also why Gómez Julián brings in the language of latent variables: some of the forces producing observed variation may not be directly observed, but their consequences can still be represented probabilistically. In applied work, this is familiar. Two factories, municipalities, firms, hospitals, or individuals may face different underlying event rates even if we initially write one common Poisson equation for all of them.

    The paper links this mathematical construction to the Hegelian distinction between Being-in-itself and Being-for-itself. Stripped of the philosophical vocabulary, its statistical meaning is fairly intuitive. Studying NB2 “in itself” means studying the wider process and network of relationships from which it emerges. Studying NB2 “for itself” means taking the marginalized distribution as a distinct object and examining its own formula, parameters, moments, and applications.

    The first mixture: Binomial inside Poisson

    The first major construction uses a biological example. Imagine an insect that lays many eggs. Conditional on a mother having laid Y eggs, each egg survives independently with probability p. The number of surviving eggs, X, is therefore Binomial. But instead of fixing the number of eggs Y, the paper lets it vary according to a Poisson distribution with mean λ.

    X | Y ~ Binomial(Y, p)
    Y ~ Poisson(λ) First hierarchical model

    Marginalizing means asking for the distribution of X after summing out the intermediate variable Y. Algebraically, we combine all the possible values of Y, weighted by how probable each one is. The result is elegant:

    X ~ Poisson(λp) After marginalizing over Y

    In modern probability language, this is a version of Poisson thinning. If the total number of opportunities is Poisson and each opportunity independently survives with probability p, then the surviving count is also Poisson, with its mean reduced from λ to λp. The paper also derives the same conclusion through iterated expectations:

    E[X] = E{E[X | Y]} = E[pY] = pλ

    For the paper, this is more than a computational trick. It shows how a hierarchical process that appears to contain two random layers can be “compressed” into a simpler marginal law without erasing the scientific interpretation that motivated the hierarchy.

    When the Poisson rate itself varies

    The next step introduces another level of heterogeneity. Suppose there are many insect mothers, and the Poisson mean is not the same for every mother. The paper now treats the rate itself as random:

    X | Y ~ Binomial(Y, p)
    Y | Λ ~ Poisson(Λ)
    Λ ~ Exponential(β) Three-stage hierarchy in the paper

    The statistical intuition is important. Variation does not occur only in the observed count; it can also occur in the underlying rate that generates the count. Once the rate differs across observational units, the final distribution becomes more dispersed than a single-rate Poisson model. This is precisely the kind of latent heterogeneity that makes the negative binomial family useful in economics, epidemiology, demography, political science, and many other count-data settings.

    The paper shows that the mean of the full hierarchy can be obtained by repeatedly conditioning and averaging, arriving at E[X] = pβ under its parameterization. It then integrates out the random Poisson rate and identifies the resulting expression with the negative binomial form.

    Technical qualification added for accuracy

    There is an important distinction here. An Exponential distribution is a Gamma distribution with shape parameter equal to 1. Therefore, a Poisson–Exponential mixture produces the geometric distribution, which is a special case of the negative binomial with r = 1. The general NB2 with arbitrary dispersion parameter r arises from a Poisson–Gamma mixture. Thus, the paper’s core intuition—random heterogeneity in the Poisson rate generates negative-binomial-type overdispersion—is correct, but the fully general NB2 requires the Gamma mixing family rather than the Exponential distribution alone.

    This qualification actually sharpens the paper’s broader message. The geometric distribution, the exponential distribution, the gamma family, Poisson processes, and the negative binomial are not unrelated objects. They sit inside a network of special cases and mixture relationships. The more general Gamma mixing distribution preserves the same hierarchical logic while extending the model beyond the r = 1 case.

    · · ·

    The NB2 “for itself”: what the finished distribution tells us

    Once the hierarchy has been “compressed,” the paper turns to the Negative Binomial II as an object in its own right. One common parameterization writes the probability of observing x failures before the r-th success as:

    P(X = x) = Γ(x + r) / [Γ(r) Γ(x + 1)] · pr · (1 − p)x,   x = 0, 1, 2, …

    Here, p is the success probability and r is the target number of successes. The distribution answers a reversed version of the familiar Binomial question. The Binomial asks: how many successes occur in a fixed number of trials? The negative binomial asks: how many failures occur before a fixed number of successes is reached?

    The paper’s most important statistical property appears in its first two moments. With q = 1 − p:

    μ = E[X] = rq / p
    Var(X) = rq / p2 = μ + μ2/r

    That final equality is the bridge to modern count-data econometrics. The Poisson distribution imposes Var(X) = μ. NB2 allows:

    Var(X) = μ + αμ2,   where α = 1/r

    In other words, variance can grow faster than the mean. The smaller r is—or, equivalently, the larger the heterogeneity parameter α is—the more dispersion the model permits. As heterogeneity vanishes, NB2 approaches the Poisson benchmark. This is why the paper presents NB2 as a more flexible instrument for count data when the Poisson equality between mean and variance is too restrictive.

    Feature Poisson Negative Binomial II
    Mean μ μ
    Variance μ μ + αμ²
    Extra heterogeneity Not separately modeled Captured through α (or r)
    Typical use Equidispersed counts Overdispersed counts

    For an econometrician, this variance function is often the fastest route to understanding NB2. For a broader reader, an intuitive translation is enough: NB2 expects the world to be more uneven than a simple Poisson process. Some units have persistently higher event rates than others; unobserved conditions vary; clusters form; the same mean can coexist with much wider dispersion.

    The maintenance example: counting failures before the fourth alarm

    The paper gives a concrete industrial interpretation. Imagine fixed capital—a machine—producing parts. A part is either satisfactory or defective. A monitoring system treats a defective part as the event of interest because it signals the need for maintenance. Assume independent Bernoulli trials and a constant defect probability.

    Gómez Julián sets r = 4, p = 0.005, and asks for the probability of observing exactly x = 100 failures before the fourth success, using the negative binomial mass function. Substitution gives:

    P(X = 100 | r = 4, p = 0.005) ≈ 0.000067

    The number is tiny—about 6.7 chances in 100,000. The statistical interpretation is not that “100 failures happen and then four successes happen” as two separate blocks. Rather, among an ongoing sequence of independent trials, exactly 100 non-events occur before the fourth event of interest is reached.

    The paper checks the result manually, with a Texas Instruments calculator, and with R. It then plots the corresponding distribution, illustrating how a small success probability pushes substantial probability mass toward relatively large counts before the required number of successes is accumulated.

    What the R simulation is trying to show

    The final applied part of the main text shifts from evaluating a probability to generating pseudo-random data. The paper constructs a custom card-drawing experiment: repeatedly sample from a 52-card deck until a specified rank appears, record how many draws were required, and repeat the experiment many times. It then compares the histogram produced by that “from first principles” counting procedure with a histogram generated by R’s built-in rnbinom function.

    The figures for 50, 100, 150, and 200 repetitions show the same qualitative pattern: a strongly right-skewed count distribution with many small values and a long tail. The pedagogical purpose is clear. Software is not magic. A built-in random generator is implementing a probabilistic structure that can also be approximated through an explicit sequence of elementary trials.

    A convention to watch in R

    R’s rnbinom convention counts the number of failures before a specified number of successes. A hand-built routine that counts the total number of draws including the successful draw differs by one when size = 1. For an exact one-to-one comparison, the manual routine and the software call should use the same counting convention. This does not erase the pedagogical point of the simulation, but it matters for exact numerical equivalence.

    The broader lesson is useful far beyond R. Simulation can reveal what a distribution means operationally: not merely how its formula looks, but what repeated mechanism would generate data with that shape.

    NB1, Bayes, and the annexes: why the paper keeps widening the frame

    The annexes extend the same relational approach. The paper distinguishes NB2 from NB1, emphasizing that different negative-binomial parameterizations answer slightly different counting questions. In the NB1 presentation used there, the random variable is the total number of Bernoulli trials needed to reach r events of the chosen type; in the NB2 presentation, the random variable is restricted to the number of failures before those r successes.

    The paper also returns to conditional probability, total probability, inverse probability, and objective Bayesianism. This may seem far removed from overdispersed count data, but it serves the same philosophical thesis: statistical formulas must be understood through the relationships they encode. Conditional probability is not merely a ratio; it represents a structured dependence between events. Bayesian updating is not merely algebra; it connects prior knowledge, evidence, and posterior assessment.

    Finally, the paper gives a more general NB2 expression in terms of the Gamma function and reports estimators based on the first two sample moments. This again links the abstract distribution to empirical work: the population parameters acquire meaning only because sample information provides a route to estimation.

    What should we take away?

    Gómez Julián’s paper is best read as an extended argument against treating the Negative Binomial II as a black-box formula. Its distinctive contribution is not a new NB2 estimator or a new regression algorithm. It is an attempt to reconstruct the distribution through several layers at once: historical, algebraic, probabilistic, computational, applied, and philosophical.

    For the nontechnical reader, the central statistical lesson can be stated in one sentence: when counts vary more than a single-rate Poisson model permits, the extra variability can often be understood as heterogeneity in the underlying event rate, and the negative binomial family provides a natural way to represent it.

    For the econometrician, the key signature is the NB2 variance function, Var(Y) = μ + αμ². For the mathematician, the paper is an invitation to follow the transformations linking geometric series, binomial expansions, gamma functions, conditional distributions, and marginalization. For the philosopher of science, its central claim is methodological: the formal instrument, the scientific object, the history of the instrument, and the interpretation of uncertainty should be studied in relation rather than isolation.

    And for the applied researcher, perhaps the most useful question is the simplest one: what process would have to be operating for this distribution to be a sensible measurement instrument? Once that question is asked, NB2 stops being just a convenient correction for overdispersion. It becomes a hypothesis about how heterogeneity enters the data-generating process.

    A distribution is most informative when its probability law and its generating story tell the same scientific story.
    In one compact map

    Bernoulli gives the elementary success/failure trial; Binomial aggregates such trials at a fixed size; Poisson makes the number or rate of occurrences stochastic; Gamma heterogeneity lets that Poisson rate vary across units; marginalizing the latent rate yields the Negative Binomial II, whose variance can exceed its mean.

    This explainer follows the architecture and substantive aims of Gómez Julián’s paper while separating the paper’s own philosophical framing from the technical qualifications added here for mathematical precision.

    Read the Original Paper ↗
    Editorial-academic layout · Playfair Display · Lora · DM Mono
  • RATE OF PROFIT, UNIT ROOTS, AND NON-STATIONARITY OF TIME SERIES

    Political Economy · Econometrics · Time Series

    When Economies Do Not Return

    Unit Roots, Profitability, and Marx’s Falling Rate of Profit

    A guided reading of José Mauricio Gómez Julián’s 2020 essay on non-stationarity, permanent economic shocks, investment, and the long-run dynamics of capitalist profitability.

    GÓMEZ JULIÁN · 2020 · EXPLAINER · ≈ 15 MIN READ

    1. The question beneath the statistics

    A recession ends. Factories reopen, employment begins to rise and gross domestic product starts growing again. But has the economy actually returned to the path it was following before the crisis? Or has the crisis changed the path itself?

    That deceptively simple question sits at the heart of Gómez Julián’s essay On the Law of the Tendential Fall in the Average Rate of Profit: Unit Roots and Non-Stationarity of Time Series. The paper brings together a technical problem in time-series econometrics and a much older problem in political economy: Karl Marx’s claim that the average rate of profit is subject to a long-run tendency to fall.

    The connection may initially seem strange. A unit root belongs to the vocabulary of stochastic processes, forecasting and econometrics. Marx’s falling rate of profit belongs to theories of accumulation, technological change, crisis and class relations. Gómez Julián’s argument is that they meet at one fundamental idea: economic history may leave permanent traces.

    If shocks alter the future path of an economy rather than merely disturbing it temporarily, history is not noise around the model. History becomes part of the model.

    The paper therefore treats non-stationarity as more than an annoying statistical property that must be removed before running a regression. It interprets it as evidence against a picture of capitalism in which every disturbance is followed by an automatic return to an unchanged long-run equilibrium.

    The route from that proposition to Marx, however, has several stages. Understanding them separately is the easiest way to see both what is powerful about the argument and where econometric caution is required.

    · · ·

    2. Stationarity: does the economy forget?

    In everyday language, something stationary remains roughly where it is. In time-series analysis the meaning is more precise. A weakly stationary process has a constant mean and variance through time, and the covariance between two observations depends on how far apart they are—not on the historical date at which they occur.

    The intuitive issue is memory. Imagine an economic variable fluctuating around a stable center. A recession pushes it downward, but forces inside the system progressively pull it back. Given enough time, the effect of the original shock fades. The process “forgets.”

    Now imagine another process. A negative shock pushes the variable downward and the next period begins from that lower level. Later shocks are added to everything that happened before. The effects accumulate. There is no built-in statistical mechanism guaranteeing a return to the old path. This second world is the natural habitat of the unit root.

    Process What happens after a shock? Long-run intuition
    Stationary The shock gradually dies out. The series tends to return toward a stable distribution.
    Trend-stationary The shock dies out around a deterministic trend. The long-run path moves predictably with time.
    Difference-stationary The shock changes the level of the series permanently. The level follows a stochastic trend; differences may be stationary.

    This distinction matters enormously for economics. If output is trend-stationary, a recession is essentially a temporary displacement from a pre-existing trajectory. If output contains a unit root, the recession can change the trajectory from which the future proceeds. Growth may resume without the lost output ever being recovered.

    A useful distinction

    Recovery of the growth rate is not the same thing as recovery of the level. An economy can start growing at 3 percent again while remaining permanently poorer than it would have been had the crisis never occurred.

    3. What a unit root actually means

    The paper introduces the idea through the simplest autoregressive model. Let the current value of a variable depend on its previous value plus a new disturbance:

    Yt = ρYt−1 + ut ρ is the autoregressive coefficient; ut is the new shock.

    When the absolute value of ρ is below one, the influence of an old shock becomes progressively smaller. The process is mean-reverting under the usual conditions. But when ρ = 1, we obtain:

    Yt − Yt−1 = ut or, equivalently, ΔYt = ut

    This is the canonical random walk. Today’s level contains yesterday’s level in full. Every shock is therefore incorporated into the future path. The variance of the level grows with the horizon, and conventional statistical inference applied mechanically to such levels can become misleading.

    This is why unit roots are associated with the famous problem of spurious regression. Two unrelated trending series can produce an impressive coefficient, a high R-squared and apparently significant test statistics simply because both contain persistent stochastic trends.

    The econometric response is not to declare all relationships between non-stationary variables meaningless. Rather, researchers ask whether the variables are cointegrated—whether some stable long-run combination of them exists—or otherwise transform and model the series in a way consistent with their integration properties.

    Technical translation

    A unit root does not mean that a variable literally moves at random in every economically relevant sense. It means that, within the statistical representation, shocks to the level are not forced to disappear. The economic interpretation of those shocks still requires theory.

    · · ·

    4. The Mankiw–Krugman dispute: will lost output come back?

    Gómez Julián devotes a substantial part of the paper to a remarkably public argument that unfolded after the 2008 financial crisis. The Obama administration’s Council of Economic Advisers expected a strong rebound. The underlying intuition was familiar: unusually weak growth during a recession should eventually be followed by unusually strong growth as the economy returns toward normal.

    Gregory Mankiw objected. Drawing on earlier work with John Campbell, he argued that aggregate output behaves much more persistently than the conventional picture of temporary deviations from a stable trend would suggest. If a fall in output can have a permanent component, then one cannot simply assume that everything lost during a recession will be recovered through subsequent above-normal growth.

    Conditional recovery versus unconditional forecasting

    Mankiw’s point was subtler than “recoveries never happen.” If one knew with certainty that a recession had ended, then strong post-recession growth might indeed be likely. But a forecast made in real time does not possess that information. There remains some probability that the recession will continue, that another contraction will follow, or that part of the loss reflects a permanent change rather than temporary under-utilization.

    Arnold Kling supplied an especially intuitive version of the contrast. Suppose output is low because frightened households temporarily postpone purchases. Once fear disappears, spending can rebound: that resembles a trend-stationary story. But suppose resources have been committed to the wrong houses, technologies or forms of human capital. Those resources cannot simply be unspent. The economy may grow again, but some of the loss remains in history.

    Krugman and DeLong: look at unemployment

    Paul Krugman and Brad DeLong approached the problem from another angle. High unemployment and low capacity utilization indicate unused resources. If unemployment is far above normal, they argued, one should expect it to fall; combined with Okun’s law, that creates a case for unusually rapid output growth during recovery.

    DeLong supported the argument with a relationship between unemployment and subsequent GDP growth. Mankiw’s response was econometric rather than rhetorical: he suspected that the apparent relationship was being driven disproportionately by observations surrounding the exceptionally strong recovery after the 1981–82 recession.

    The subsequent calculations discussed in Gómez Julián’s paper were revealing. For the full sample, the regression produced an adjusted R-squared of about 11 percent and a t-statistic of 3.5. Removing eight quarters associated with the Reagan-era rebound reduced the adjusted R-squared to about 5 percent and the t-statistic to 2.1. The relation did not literally vanish, but its apparent strength became substantially more dependent on a particular historical episode.

    A later study by David Cushman, also reviewed in the paper, went further. Cushman asked what a conventional econometric forecaster working in 2009 might have concluded. His results supported Mankiw’s skepticism about the stronger rebound projections and judged DeLong’s dynamic Okun-law specification to perform poorly relative to alternative forecasts.

    Why this episode matters for the paper

    Gómez Julián treats this debate as empirical evidence against automatically assuming mean reversion in macroeconomic aggregates. The central issue is not whether recessions are followed by recoveries. They usually are. The issue is whether a recovery necessarily restores the counterfactual path that existed before the recession.

    5. From persistent shocks to profitability

    At this point the paper changes scale. The argument is no longer merely about forecasting GDP after a recession. Gómez Julián asks what kind of economic mechanism could make history matter so persistently.

    Olivier Blanchard provides an important bridge. Writing about financial crises, Blanchard observed that, across countries, output often does not return to its old trend path after a crisis. Instead, the economy can remain permanently below it. That is a profound distinction: the rate of growth can normalize while the level of productive activity remains permanently reduced.

    Gómez Julián then connects this phenomenon to Marxian political economy. Marx’s law of the tendential fall in the rate of profit is not a claim that profitability must decline mechanically every year. It is a claim about a long-run force generated by capitalist accumulation, operating through a system that also contains counteracting influences and recurrent cyclical recoveries.

    In broad Marxian terms, profit must be evaluated relative to the capital advanced to obtain it. Technical development raises productivity, but capitalist competition also encourages firms to substitute machinery, infrastructure and other forms of accumulated capital for living labor. The paper emphasizes the resulting relationship between the organic composition of capital, profitability and the development of productive forces.

    The crucial insight is that a cyclical rebound and a secular tendency are perfectly compatible. A profit rate can fall, recover sharply, experience another boom and still exhibit a lower long-run trajectory across successive historical cycles.

    Figures 4–7 in the paper Gómez Julián reproduces estimates assembled by Michael Roberts showing a declining long-run rate of profit for major G20 economies, a rising organic composition of capital alongside falling profitability, and a longer historical series in which repeated recoveries occur inside a broader downward movement. The figures are used as corroborating evidence for the Marxian tendency, not as new estimates produced by Gómez Julián himself.

    This is the point at which non-stationarity acquires its political- economic meaning in the paper. If crises leave lasting scars, and if the variable organizing accumulation itself evolves historically, then “returning to normal” cannot simply mean returning to an eternal statistical center. What counts as normal after one historical cycle may already differ from what counted as normal before it.

    6. Do profits lead investment?

    The argument still requires another link. Even if profitability follows an important long-run trajectory, why should it organize the broader movement of output and employment? Gómez Julián’s answer is investment.

    Investment expands productive capacity, creates demand for machinery and construction, reorganizes labor and shapes future production. If changes in profitability systematically precede changes in investment, then profitability becomes a plausible transmission mechanism between Marx’s theory of accumulation and the macroeconomic path observed in time-series data.

    Kothari, Lewellen and Warner Using U.S. corporate data, they find that profits and stock returns predict changes in investment up to roughly a year and a half ahead and absorb much of the predictive content attributed to variables such as interest rates, volatility, credit spreads and Tobin’s q.
    Michael Roberts The paper uses Roberts’s international estimates of profitability to argue that the long-run decline is visible not merely in a single recession but across a much broader historical sequence of booms, crises and partial recoveries.
    José A. Tapia Granados Using 251 quarters of U.S. data, Tapia compares competing endogenous theories of the business cycle and reports evidence more consistent with profits leading investment than with investment independently determining subsequent profits.

    Tapia’s result is particularly important for Gómez Julián because it reverses a familiar Keynesian or Minskyan narrative in which autonomous investment “calls the tune.” In the interpretation favored by the paper, expected profitability is what gives capitalists the incentive to accumulate. Investment therefore reacts to profit conditions, and movements in profitability propagate into the wider economy.

    Figures 8–11 The tables reproduced from Tapia show the behavior of profits, investment and wages around U.S. expansions and recessions; regressions in which lagged profits help explain investment; and Granger-causality tests in which profits contain substantial predictive information for subsequent private fixed investment.

    The paper’s final causal picture can therefore be reconstructed as a sequence:

    The proposed chain

    profitability → investment → production and employment → crisis/recovery path

    If profitability is historically conditioned, and investment depends strongly on profitability, then successive periods of accumulation do not begin from a clean slate. Each begins with a capital stock, a profit environment and a productive structure inherited from the preceding period.

    · · ·

    7. What the evidence can—and cannot—establish

    This is also where precision becomes especially important. The paper brings together several empirical facts that can be mutually reinforcing, but they are not logically interchangeable. A careful reading should keep four distinctions in view.

    Four econometric guardrails

    • A unit root does not imply a downward trend. It implies persistence: shocks to the level need not disappear. A unit-root process can wander upward, downward or in both directions. The sign of a long-run profitability tendency must come from additional theory and evidence.
    • A falling series need not contain a unit root. A variable may decline around a deterministic trend while its deviations from that trend remain stationary. “Falling” and “non-stationary” answer different statistical questions.
    • Economic plausibility does not by itself eliminate spurious regression. Temporal precedence and a strong substantive mechanism are important for causal interpretation, but regressions among persistent series still require appropriate treatment of unit roots, cointegration and dynamic specification.
    • Granger causality is predictive, not automatically structural. If profits Granger-cause investment, past profits improve forecasts of investment conditional on the model. That is meaningful evidence about temporal ordering, but additional assumptions are required to establish the full causal mechanism.

    These qualifications do not destroy Gómez Julián’s central argument. They make its strongest defensible form clearer.

    Non-stationarity contributes evidence for persistence and historical dependence. Blanchard contributes evidence that major crises can leave output permanently below its old trajectory. The profitability literature cited by Gómez Julián contributes a separate claim: the average rate of profit displays a long-run declining tendency. Kothari, Lewellen and Warner and Tapia contribute another link: profitability contains important information about subsequent investment.

    The Marxian conclusion emerges from the combination of these propositions, not from the unit root alone.

    Non-stationarity supplies the memory. Profitability supplies the direction proposed by the theory. Investment supplies the transmission mechanism.

    This distinction is essential because it transforms a potentially overextended statistical claim into a much richer research program. Instead of asking whether one test can “prove Marx,” the relevant questions become: How persistent are shocks to output and profitability? Are breaks temporary or permanent? How should the profit rate itself be measured? Does profitability lead accumulation across countries and historical regimes? And does the long-run trajectory survive alternative specifications?

    Those are empirical questions—and therefore questions on which Marxian, Keynesian and mainstream econometric approaches can genuinely confront one another using evidence.

    8. Why this matters beyond econometrics

    It would be easy to treat the unit-root controversy as a specialist dispute about the properties of an autoregressive coefficient. Gómez Julián’s paper insists that much more is at stake.

    Consider the expression the economy will return to normal. It sounds descriptive, almost innocent. Statistically, however, it embeds a hypothesis. It assumes that there exists some stable reference path toward which the economy tends to return after a disturbance.

    If the process is strongly path-dependent, that assumption may fail. A banking crisis can destroy firms, interrupt careers, cancel investment projects and alter the capital stock. A prolonged recession can change the composition of production. Investment not undertaken today means productive capacity that does not exist tomorrow. The future therefore reflects not only current conditions but also the sequence by which those conditions were reached.

    For political scientists, this has an immediate implication. Economic crises cannot always be understood as temporary deviations after which politics resumes on an unchanged material foundation. If output, employment, investment and profitability carry historical scars, then crises can alter the terrain on which subsequent distributional conflicts and policy decisions occur.

    For economists, the message is equally important. Choosing between a stationary and non-stationary representation is never merely a cosmetic preprocessing decision. It changes what the model says an economic shock is. In one representation, the shock is a temporary displacement. In another, it becomes part of the state from which all subsequent development proceeds.

    And for readers of Marx, the paper offers an unusual bridge between nineteenth-century political economy and modern time-series reasoning. Marx’s theory is historical in structure: accumulation changes the conditions under which the next round of accumulation occurs. Gómez Julián’s use of non-stationarity gives that historical intuition a statistical analogue. The economy need not circle eternally around an unchanged center because the process itself can transform the point from which the next movement begins.

    9. The argument in one view

    Stripped of its polemical edges, the paper can be summarized as a five-part argument.

    Macroeconomic time series can be highly persistent. Treating every recession as a temporary deviation from an invariant trend is therefore an empirical assumption, not a statistical law.
    Some major shocks leave permanent output losses. The post-crisis economy may grow again without recovering the level it would otherwise have reached.
    Profitability is central to capitalist investment. The evidence reviewed in the paper indicates that profits possess substantial predictive power for subsequent investment.
    The average rate of profit exhibits a historical tendency. The Marxian studies cited by Gómez Julián interpret long-run profitability data as showing a secular downward movement interrupted by cyclical recoveries and counter-movements.
    The economy therefore has memory. If profitability conditions accumulation and crises alter the subsequent path, capitalist development should be modeled as a historical process in which past states help create future ones.

    That final proposition is the most intellectually interesting part of Gómez Julián’s essay. The significance of non-stationarity is not that a statistical test can settle a two-century debate in political economy. It is that the statistical language of permanent shocks, stochastic trends and path dependence is difficult to reconcile with a simplistic image of economic history as temporary noise around an eternally self-restoring equilibrium.

    Marx’s falling rate of profit and the unit-root literature are not the same theory, and one does not mechanically prove the other. But they meet around a common challenge: what if the economic system carries its own history forward?

    Once that possibility is admitted, a crisis is not merely something that happens to an otherwise unchanged economy. It becomes one of the events through which the economy itself is historically made.

    · · ·

    Conclusion: taking history seriously

    The paper begins with an econometric distinction but ends with a claim about the nature of political economy. Stationarity describes a world capable, under appropriate conditions, of forgetting. Unit-root behavior describes a world in which disturbances can survive inside the future.

    Gómez Julián argues that the second image is more compatible with the historical character of capitalist development and with Marx’s analysis of accumulation. The evidence on permanent output losses challenges easy assumptions of automatic restoration; the evidence on profits and investment gives profitability a mechanism through which it can shape the real economy; and the cited long-run profit-rate estimates provide the directional component required for the Marxian argument.

    The technically careful conclusion is therefore stronger when stated modestly. Unit roots do not demonstrate the falling rate of profit. What they undermine is the presumption that economic disturbances must disappear without changing the long-run path. Once persistence is combined with evidence about the historical movement of profitability and its relationship to accumulation, the paper’s central thesis comes into view.

    The deepest question is not whether an economy eventually grows again. It is whether, after history has happened, the old path still exists to be returned to.
    Principal works discussed in the paper

    Campbell, J. Y. & Mankiw, N. G. (1987). Are Output Fluctuations Transitory?

    Blanchard, O. (2009). Sustaining a Global Recovery.

    Cushman, D. O. (2013). Paul Krugman Denies Having Concurred With an Administration Forecast: A Note.

    Kothari, S., Lewellen, J. & Warner, J. (2017). The Behavior of Aggregate Corporate Investment.

    Roberts, M. (2020). A World Rate of Profit: A New Approach and More on a World Rate of Profit.

    Tapia Granados, J. A. (2013). Does Investment Call the Tune? Empirical Evidence and Endogenous Theories of the Business Cycle.

    Read the Original Paper (In Spanish)
    EXPLANATORY ESSAY BASED ON JOSÉ MAURICIO GÓMEZ JULIÁN (2020) · UNIT ROOTS · NON-STATIONARITY · POLITICAL ECONOMY
  • The Shape of a Crisis: A General Theory of Capitalist Cycles

    The Shape of a Crisis: A General Theory of Capitalist Cycles

    Thesis Release · Political Economy

    The Shape of a Crisis

    A general theory of the cycles of the dynamics of the capitalist system in the long run — now available in English

    Every few years the same story is told twice. First, that the economy has entered a new era in which the old rules no longer apply. Then, some months later, that what happened was an accident: a shock, a bubble, a virus, a war. Both tellings share a premise so quiet that it is rarely examined — that the rise and the fall are separate events, and that a good theory of the good years need not be a theory of the bad ones.

    The thesis released today argues the opposite, and then goes to some length to measure it. The boom and the crisis are not two phenomena but two moments of one: the crisis of overproduction is the mechanism by which capitalism restores the conditions of an accumulation that its own success had eroded. Devaluation clears the field; new methods of production are introduced under duress; profitability recovers on the ruins. The recovery is not the negation of the crisis. It is its product.

    That claim is old. What is new here is the attempt to make it decidable — to state it in a form that quarterly data on the United States economy between 1992 and 2024 could have contradicted, and then to check whether they do.

    Three questions, and why the order matters

    The investigation is organised around one general objective — to analyse the long-run cyclical behaviour of U.S. capitalism in the light of the dominant economic theories — and three specific ones, asked strictly in this order:

    • Which theory explains and predicts best? Not which is most elegant, or most widely taught, but which survives being pointed at the data.
    • Which factors generate the cycle? Economic and extra-economic alike — the thesis refuses in advance to treat wars and monetary policy as noise sitting outside a clean economic mechanism.
    • By which rules do those factors interact? A list of causes is not a theory. The theory is in the grammar that binds them.

    The order is not decorative. A great deal of applied economics answers the third question with machinery borrowed from a theory it never subjected to the first. Here the selection of the framework is itself a result, defended before it is used.

    Five families of an old argument

    Before measuring anything, the thesis maps the terrain. Economic thought on the cycle is sorted into five groups: the pre-Kondratieff non-heterodox schools; the Kondratieff school; the post-Kondratieff marginalist and neoclassical schools; the heterodox schools; and the historiographic vision of long waves, which reads the cycle through the archives rather than through the equations.

    With that map in hand, three long-running disputes are adjudicated rather than summarised. Does the crisis originate in overproduction or in underconsumption? Is a sustained expansion of credit a symptom of recovery, or of the exhaustion of the conditions that made recovery possible? Is there really an inverse relation between inflation and unemployment, or is the appearance of one an artefact of the precariousness of the labour market? Each is answered, and each answer carries consequences later, when the model is specified.

    A framework that states its own conditions of failure

    A substantial part of the theoretical apparatus is devoted to a materialist characterization of the dialectical method: its fundamental categories, a Marxist ontology built from a metalogical gnoseology, and an explicit treatment of verification, falsification and decidability. The purpose is unglamorous and indispensable — to fix, in advance, which propositions of the theory are empirically decidable and which are interpretive. Without that boundary, no amount of subsequent statistics can tell you what has been tested.

    Ten dials, seven of them internal

    The empirical core is a Bayesian generalized linear model of the growth of U.S. real output, estimated with Hamiltonian Monte Carlo and cross-validated against machine-learning and deep-learning competitors. It retains thirteen coefficients across ten factors. Seven are economic:

    FactorWhat it registers
    Net Average Rate of Profit (ARoP)The central variable of the accumulation process, and the one whose long-run tendency the theory predicts.
    Elasticity of the gross rate of surplus value to the average organic composition of capitalHow the exploitation of labour power responds when the technical structure of capital changes.
    Non-residential fixed investmentThe pace of accumulation in the productive sector; the hinge between boom and crisis.
    Inventory-to-sales ratioThe gap between producing value and realising it on the market.
    S&P 500Financialization, entering through a natural cubic spline with three degrees of freedom.
    Non-financial private sector creditThe credit system as the accelerator and the brake, splined with two degrees of freedom.
    Capitalist R&D spendingThe innovative impulse; the second largest coefficient in the model.

    And three are extra-economic: military spending (splined with three degrees of freedom), the federal surplus or deficit, and the effective federal funds rate. Their presence is not a concession to realism. It follows from the argument that an imperial economy counteracts the tendency of its own profit rate to fall by means that are not internal to its national accounts.

    The Average Rate of Profit carries the fourth largest coefficient of the thirteen — behind only the intercept, R&D spending, and one basis function of the splined S&P 500. The conclusion the author draws from its behaviour is worth quoting in substance: what is favourable to the global process of capital accumulation is not thereby favourable to the dynamics of aggregate growth. The two are not the same quantity, and treating them as one is precisely the confusion the cycle punishes.

    Note, too, what the splines are doing. Three of the ten factors would not sit still in a straight line. That is not a technical footnote: it is the first quantitative sign that the interaction of these factors involves thresholds and turning points rather than a stable proportionality.

    Not random. Chaotic.

    “Unpredictable” and “random” are not synonyms, and the difference decides what kind of science economics can be. A random system has no internal structure to find. A chaotic one is rigidly determined and still unpredictable at long horizons, because arbitrarily small differences in initial conditions grow exponentially apart.

    Three measurements place the U.S. economy in the second category. The Lyapunov exponent is positive (approximately $0.0515$): small perturbations amplify rather than dissipate. The correlation dimension is not an integer ($3.32798$): the attractor reconstructed by Takens’ theorem has a fractal structure, patterns repeating across scales of time and magnitude — which is what “cyclical, but not periodic” means when it is stated precisely. And recurrence quantification finds high determinism alongside variability in laminarity and in the maximum diagonal line length: underlying deterministic structures that themselves evolve.

    $\lambda > 0 \quad\text{with}\quad D_2 = 3.32798 \notin \mathbb{Z}$

    Read together, these say something a forecaster should find sobering and a theorist should find encouraging. The long-horizon forecast is not merely hard; it is structurally bounded. But the structure that bounds it is real, stable and measurable — which is exactly what a theory of the cycle needs to have something to explain.

    The shape of time

    The most unusual instrument in the thesis is topological. The idea is to stop asking how big the numbers are and start asking which observations can see which. Convert the series into a directed visibility graph — a link from one quarter to another when the second is visible from the first over the intervening data — and study the order structure that results.

    Two topologies are built on it, and they disagree in an informative way.

    • The coarser Alexandrov topology, built on temporal reachability, turns out to be connected. At the level of its order structure the economy is globally a single piece: every observation is bound to every other by chains of temporal visibility. There is no quarter that stands apart.
    • The finer Nada topology is locally fragmented — six components under the natural visibility graph, thirty-six under the horizontal one. Zoom in, and the fabric shows seams: structural discontinuities at the level of closed neighbourhoods.

    Global unity and local rupture at once. That duality is not a contradiction to be resolved; it is the object being described. And a third measurement gives the whole thing a direction: the bitopological analysis yields $D = +4$, meaning that expansions generate more temporal visibility than contractions. The cycle is not symmetric in time. Growth accumulates gradually and in view; collapse happens abruptly and blind. Run the film backwards and it is recognisably the wrong film.

    ⚠️ Why you must not “clean” the crises

    There is a habit in applied work of treating extreme values as contamination and smoothing them away by discontinuous imputation. Here that habit is shown to be a category error with a measurable price. The extreme fluctuations of the 2020 crisis belong to a connected block even under the finer topology; severing them is a topological rupture, not a cleaning operation. The thesis reports the consequence directly: models fitted after such imputation performed worse, because one was using predictors suited to one phenomenon — real output growth — to predict a qualitatively different one: real output growth after the crisis had been removed from it. The crises are not noise around the cycle. They are the cycle.

    The grammar of the cycle

    The third question receives a seven-part answer. The factors interact through feedback (the rate of profit shapes investment, investment shapes the organic composition of capital, which feeds back into the rate of profit); time lags (R&D and fixed investment pay out on a delay, and the delay is itself cycle-generating); non-linearity (thresholds and regime changes, which is why three factors needed splines); deterministic chaos; sectoral interdependence between the department producing means of production and the one producing means of consumption; topological structure, global connectedness with local fragmentation; and the influence of the global context, which is how military spending and the S&P 500 enter a nominally domestic account.

    The unifying claim is that each phase of the cycle contains the seed of its own negation. New methods of production introduced during the crisis lay the foundations of the next boom; the overaccumulation of the boom prepares the ground for the next crisis. Innovation initially arrests the fall of the profit rate and ultimately deepens it — through the way the degree of exploitation of labour power responds, over time, to the very methods introduced to raise it.

    What a cycle is for

    The thesis closes on a question most treatments never pose. If the cycle is a mechanism, what does it accomplish? Two answers, at different depths. Its intermediate practical end is to restart the process of capital accumulation once instability has reached a critical level — this the mechanism achieves, repeatedly, at a cost borne unevenly. Its definitive practical end is to lay the material and spiritual conditions for a reorganization of the fundamental productive structure of society, one capable of a stability beyond what the capitalist mode of production can reach within its own limits.

    What this establishes, and what it does not

    The evidence supports the claim that classical Marxist economic theory possesses the greatest explanatory and predictive capacity for long-run cycles among the theories examined here, on this economy, over this period. It is a comparative result on the United States between 1992 and 2024, quarterly — not a universal proof, and not a forecast. The thesis is explicit about the cost of its own data: the Average Rate of Profit and the average rate of surplus value were available only annually through 2020, and completing the series to 2024 required temporal disaggregation and prediction, which puts a wider band of uncertainty around the most recent quarters. The philosophical, historical, conceptual and statistical scope of each result is distinguished in the text, and results unfavourable to the hypotheses are reported alongside the favourable ones.

    About this edition

    This is the English edition of a thesis originally written in Spanish and submitted to the Universidad Latina de Costa Rica for the degree of Licentiate in Economics. It is interdisciplinary by construction, drawing on Marxist political economy, dialectical and historical materialism, the history and historiography of economic thought, the philosophy and methodology of science, econometrics, Bayesian statistics, the theory of complex systems and topology.

    The edition carries a Note on the Translation that fixes the rendering of the terms whose Spanish usage is technical and not interchangeable with their nearest English cognates — gnoseology, sublation, long wave, solvent demand, technique — and records the editions from which quotations are taken, including the two distinct English and Spanish editions of the Soviet philosophical dictionary, which are cited under different transliterations because they are different books with different pagination.

  • CAPITAL ACCUMULATION THROUGH DISPOSSESSION OF INDIGENOUS PEOPLE IN COSTA RICA

    CAPITAL ACCUMULATION THROUGH DISPOSSESSION OF INDIGENOUS PEOPLE IN COSTA RICA

    Costa Rica’s Democratic Myth: How Indigenous Dispossession Built the Country’s Agrarian Wealth
    Reading Notes · Political Economy · Latin American History

    Costa Rica’s Democratic Myth:
    How Indigenous Dispossession
    Built the Country’s Agrarian Wealth

    A plain-language reading of a groundbreaking study that dismantles the “White Legend” — and asks why a “democratic” state systematically violates the very rights it claims to protect.

    Based on: Gómez Julián, J. M. (2026). Revista de Historia, N.º 93, pp. 1–45.

    Costa Rica likes to think of itself as the exception. A small, peaceful republic nestled between two oceans, crowned with universal healthcare, no army since 1948, and a democratic tradition so stable that political scientists have called it the “Switzerland of Central America.” This flattering self-image — what scholars have long called the “White Legend” (Leyenda Blanca) — is one of the most durable stories in Latin American politics. It is also, according to a meticulous new study by Costa Rican economist José Mauricio Gómez Julián, profoundly misleading.

    Published in the Revista de Historia (University of Costa Rica, No. 93, 2026), the article sets out to do something ambitious: not merely to describe the well-documented inequality in Costa Rican land ownership — earlier scholars had already done that — but to explain why a formally democratic state produces, protects, and reproduces extreme agrarian concentration, generation after generation, and why the systematic violation of indigenous territorial rights is not an unfortunate glitch in the system but one of its operating mechanisms.

    The answer, the author argues, lies in understanding land dispossession not as a historical accident but as a structural feature of capital accumulation — a process that began with Spanish colonialism, was formalized by the liberal republic, was turbocharged by coffee and banana exports, and continues today under the twin guises of “conservation” and legal impunity.

    0.7258
    Gini coefficient for land concentration in Costa Rica’s southern region (Coto Brus). For context: 0 means perfect equality, 1 means one person owns everything. Sweden’s is around 0.53.

    The Numbers Behind the Myth

    Before we get to history, let’s sit with some uncomfortable statistics — the kind that rarely appear in Costa Rica’s tourism brochures.

    The Gini coefficient — the standard measure of inequality, where 0 is perfect equality and 1 is total concentration — tells a stark story. In Costa Rica’s southern region, land concentration reaches 0.7258. In Guanacaste’s cattle ranches, it climbs as high as 0.9. Nationally, the figure hovers around 0.796. For perspective: the top 1% of farms holds more than 37% of all agricultural land, while the bottom 39% of farms collectively own just 0.2%.

    And the people who work the land? Between two-thirds and three-quarters of Costa Rica’s agricultural workforce is landless — a proportion higher than anywhere else in Central America. In some regions like Coto Brus, more than 90% of farms lack legal titles.

    These figures are not from a radical pamphlet. They come from rigorous academic work by scholars like Mitchell Seligson, Marc Edelman, Charles Brockett, Jeffery Paige, and James Dunkerley — researchers who compared census data with actual property records and found that the state’s own statistics systematically underestimate the degree of concentration. Gómez Julián builds on their empirical foundation but adds a layer they largely did not: a categorical political-economic explanation of why this pattern persists within a formally democratic state.

    “Nearly three-quarters of the Costa Rican peasantry today are landless” — a fact that contradicts the national story of a country of small, equal farmers.

    A Timeline of Dispossession: From Encomienda to Enclave

    The article reconstructs the history of indigenous land loss in Costa Rica across five major phases. Each one reveals a different mechanism, but all serve the same structural function: clearing land and resources for capital accumulation.

    1. Colonial Foundations (pre-1821)

    Spanish conquest introduced three key instruments of dispossession: encomiendas (assigning indigenous labor to settlers), reducciones (forced resettlement into concentrated villages), and composiciones fraudulentas (legal maneuvers to convert indigenous land into colonial property). Roman law justified the entire operation by declaring indigenous lands to be property of the Spanish Crown. Though later laws like the Leyes Nuevas of 1542 formally attempted to protect indigenous peoples, the legislation on “vacant lands” (baldíos) declared as empty the very territories where indigenous communities lived, making them available for non-indigenous appropriation. By the end of the colonial period, a fragile but real legal recognition of “indigenous property” still existed through reducciones and “indigenous neighborhoods.” This legal floor is precisely what the post-colonial liberal state would systematically dismantle.

    2. The Liberal Republic Strikes (1821–1880)

    Independence did not bring recognition — it accelerated dispossession. In 1841, under the dictatorship of Braulio Carrillo, the Código General formally abolished the communal indigenous land regime as a protected legal category. Then, in 1882, Presidential Decree No. XIV declared vast stretches of northern territory — including the homeland of the Maleku people (historically called “Guatuso”) — to be baldíos: vacant state land open to appropriation by non-indigenous settlers and ranchers. The Maleku suffered what the article describes as one of the most intense proportional territorial and demographic reductions in Costa Rican indigenous history.

    1841
    Year the Código General, under dictator Braulio Carrillo, formally abolished communal indigenous land tenure — legalizing de facto what colonial expansion had already done.

    3. Coffee, the Beneficio, and Silent Proletarianization (1830–1930)

    The coffee boom created Costa Rica’s agrarian structure — and its contradictions. Unlike Guatemala or El Salvador, Costa Rica did not develop enormous haciendas. The largest farm was 604 hectares; the average was 41. By 1963, 58.5% of cultivated land was in units smaller than 35 hectares. This is the image the “White Legend” celebrates: a nation of smallholders.

    But the fine print tells a different story. Over 70% of the rural population was landless — a higher proportion than anywhere else in Central America. Power concentrated not through land-grabbing alone but through the beneficio (coffee-processing mill): in 1850, just sixteen beneficios controlled 85% of coffee exports, and access to the beneficio determined a small producer’s ability to finance and sell their crop. Credit systems tied small producers to merchant-landowners in relationships of dependency. Land prices inflated roughly twenty-fold in thirty years, incentivizing small producers to sell their parcels and then sell their labor.

    Critically, the Huetar people of Orosí resisted the coffee frontier around 1860 — an episode largely absent from standard histories of the coffee cycle. The “virtual absence of indigenous population” in the Central Valley during the great coffee expansion, which Dunkerley cited as one factor explaining Costa Rica’s distinct political development, was not a pre-existing geographic condition. It was, the article argues, the result of colonial epidemics (severe die-offs between 1576 and 1581), the legal dissolution of communal landholding in the 19th century, and physical displacement in the face of the advancing coffee frontier.

    4. Bananas, the Atlantic Enclave, and the Displacement of the Bribri and Cabécar (1870–1940)

    On Costa Rica’s Caribbean side, a parallel story unfolded — this one driven by foreign capital. The Soto-Keith Contract of 1883 granted Minor Keith 800,000 acres of state land, a 99-year railway lease, and sweeping tax exemptions. By 1890, his operation was the largest banana producer on Earth. The standard narrative presents this as development on “vacant land.”

    It was not. The Bribri and Cabécar peoples who inhabited the Talamanca valley were forced to move inland, deeper into their ancestral territory, because the banana concession included a significant portion of indigenous lands along the Sixaola river basin. The article calls this one of the key regional mediations of the dispossession process: the banana enclave was not merely a deal between a state and a transnational — it was a concrete mechanism of indigenous dispossession, legally articulated through the fiction of the baldío and materially executed through corporate control of Caribbean space.

    The United Fruit Company (UFCO) would later reduce its Atlantic plantations, face a major strike in 1934, and eventually shift production to the Pacific after the sigatoka disease devastated crops in 1938. But the damage was done: the “absence of indigenous population” in banana-region analyses reproduces, with different words, the same ideological device that operates in the coffee narrative — it naturalizes absence by hiding the dispossession that produced it.

    5. Limited Reform, Titulación, and the Persistence of Inequality (1957–1990)

    Costa Rica did attempt reform. International Convention 107 of the ILO (approved domestically in 1959) recognized indigenous and tribal peoples’ rights. Law 2825 of 1961 repealed the baldíos framework and declared such lands “state property” grounded in the social function of ownership. The Indigenous Law of 1977 (Law 6172) reserved portions of territory for indigenous peoples and granted full legal capacity to their communities through Asociaciones de Desarrollo Integral (ADIs).

    Yet the contradictions were glaring. The 1961 law allowed expropriation of idle land but required cash payment at market value — a provision that severely limited implementation. By 1970, only 1,272 families had been settled on roughly 35,400 hectares. The titling program backed by USAID reached a partial result of about 20,462 titles (some 339,761 hectares) by September 1979, at a rate of 425 titles per month against a theoretical capacity of 900–1,000.

    The results were telling. After receiving a title, the proportion of beneficiaries with access to credit rose from 18% to 31.7% — but the Gini coefficient for titled land was about 0.708, and when all land possessed by beneficiaries (titled plus other holdings) was included, it rose to nearly 0.781, almost identical to the national figure. Titling did not correct structural inequality — it potentially consolidated it. As the article puts it: these programs reached only a fraction of landless families while maintaining the fundamental structures of concentration.

    “Titling does not correct structural inequality and may consolidate it.”

    Conservation as Dispossession: The Modern Face of an Old Story

    One of the most striking arguments in the article is that the Costa Rican state itself — not just private ranchers or transnational corporations — has become a primary agent of indigenous dispossession, and it has done so wearing the respectable clothes of environmentalism.

    In 1982, Costa Rica created the Parque Internacional La Amistad (PILA), which was recognized as a UNESCO Biosphere Reserve that same year and as a World Heritage Site in 1983. What the celebratory narrative omits is that the park appropriated, as state-managed protected area, significant extensions of ancestral territory claimed by the Bribri and Cabécar peoples — without prior, free, and informed consultation. Its buffer zone includes the indigenous territories of Ujarrás, Salitre, and Cabagra. Inside the Biosphere Reserve, sixteen indigenous territories of five different peoples are situated. The state thus re-emerged, in this phase, as the principal agent of dispossession, this time through the legal figure of conservation.

    A similar dynamic operates through the Pago por Servicios Ambientales (PSA) — Costa Rica’s flagship Payment for Environmental Services program, administered by FONAFIFO. As documented by researcher Vargas Mena, the PSA has operated inside officially recognized indigenous territories. The forest, the water, and even the air (in the form of the carbon market) are commodified as “environmental services” whose monetary yield flows out of indigenous territory or is captured through institutional mechanisms that subordinate community decisions to the timelines and requirements of external agencies. This is not, the article argues, a correction of agrarian capitalism — it is a new phase of it.

    Add to this the contemporary presence of pineapple and palm oil multinationals in the southern zone, whose expansion encroaches on Bróráni, Bribri, and Cabécar territories. Their externalities — intensive water use, agrochemical contamination, pressure on adjacent lands — operate as mechanisms of environmental and economic dispossession on indigenous communities.

    16
    Indigenous territories of five different peoples situated inside the PILA Biosphere Reserve — appropriated without prior, free, and informed consultation.

    Recovering What Was Lost — and Dying for It (2011–Present)

    Faced with the persistent failure of the state to enforce legally recognized rights, indigenous movements launched what they call recuperaciones de facto: community-led recoveries of territories formally inscribed under the ADIs but materially usurped by non-indigenous occupants. Beginning in 2011 in places like Salitre, Cabagra, and Térraba, these recoveries triggered the organized, violent reaction of ranchers determined to suppress them.

    The consequences have been lethal. On March 18, 2019, Bribri leader Sergio Rojas Ortiz was assassinated. On February 24, 2020, Brórán leader Jethy Rivera was killed. Both murders occurred despite the existence of precautionary measures from the Inter-American Commission on Human Rights (Measure 321-12, issued in 2015). The impunity has been near-total: the Rojas case was archived in January 2024 with no detained suspects. In the Rivera case, the material perpetrator was initially convicted in February 2023, but the appellate court in Cartago reversed that conviction in July 2023, and in a second trial in August–September 2024, the accused was acquitted — despite his confession — under the principle of in dubio pro reo.

    The UN Special Rapporteur on the Rights of Indigenous Peoples documented that these attacks remain unpunished, with Costa Rican authorities failing to investigate even when perpetrators are known to the community. The cycle of dispossession–resistance–repression, the article argues, reveals that the de facto recoveries are not isolated incidents but the empirical manifestation of an ongoing class struggle over the means of production, mediated by a persistent colonial condition.

    “The contemporary accumulation by dispossession requires the same extra-economic violence that Marx identified in primitive accumulation.”

    A Broader Pattern: The State Always Chooses Sides

    The indigenous story does not exist in isolation. The article places it within a broader pattern of how the Costa Rican state has responded to rural land conflicts throughout its modern history — and the answer is consistent: it favors capital.

    The 1983 crisis is emblematic. When United Brands announced it was leaving, the state bought its land at $35,000 per hectare — a price that demonstrated the state’s weakness vis-à-vis transnationals. Standard Fruit demanded $200 million in credits and fired 700 workers. In the first eighteen months of the Monge administration alone, 185 rural conflicts were registered. In July 1983, 3,500 hectares of United Brands land were occupied by union militants and campesino federation members — and they were evicted by 600 police officers.

    Land occupations surged across administrations: 70 under Trejos, 500 during the Figueres (second) and Oduber governments, 120 in Carazo’s first year alone. The “land question” was never limited to Guanacaste, where cattle-ranching concentration had always been extreme and conflictive — it was a national structural feature.

    Rebuilding Political Categories from the Ground Up

    Here is where the article makes its most ambitious theoretical move. Rather than importing Marxist categories as ready-made tools, Gómez Julián claims to reconstruct them inductively from the historical evidence itself. The sequence is deliberate: facts first, categories second, return to facts with new interpretive power third.

    The State, in class societies, is the social organization of the political power of the economically dominant class. Law is the system of enforceable norms established by state power — it is the legal organization of that political power. Government is the administration of state institutions, and crucially, the economically dominant class is not necessarily the governing class: those who hold power are not always those who administer it, but the governing class is factually subordinate to the dominant class.

    Democracy, in its most general sense, is the government of the majority over the minority. But this concept was coined in slave-owning Athens of the 5th century BC, where only adult male citizens could vote, excluding women, slaves, and foreigners. The democracy of adult male citizens was a dictatorship for everyone else — the overwhelming majority. This dialectical relationship extends to all class societies: every democracy is a dictatorship for those systematically excluded from the majority’s will, and every dictatorship preserves an internal “democracy” for the class that imposes its hegemony. The relationship is dialectical, not identical.

    The Rule of Law (Estado de Derecho) is the idea that the state’s power is regulated and guaranteed by law — meaning the state creates law and then voluntarily submits to its own creation. But the article argues this is a sophism: states do not create law to submit to it; they create it as a regulatory framework founded on the interests of the politically and ideologically dominant class. As evidence, the author points to Article 105 of Costa Rica’s own Constitution, which prohibits referendums on budgetary, tax, fiscal, monetary, credit, pension, security, and administrative matters — that is, on virtually every fundamental issue of national social life. The validity of any referendum result is ultimately subject to the decision of the Legislative Assembly. The state, in other words, has structurally exempted itself from popular will on every matter that counts.

    And corruption? It is not an aberration. Defined as the practice in which a public official formally deviates from the functions for which they were entrusted with power, corruption “formally” (not factually) departs from stated commitments. Why is the deviation formal rather than factual? Because, within this framework, corruption is a necessary mechanism for the interests of the dominant class to impose themselves over the rest of society while electoral democracy reigns — one of several mechanisms that enable factual dictatorship through the alienation of the dominated classes.

    Three Processes, Two Levels of Abstraction

    The theoretical heart of the article lies in the way it reconstructs the relation among primitive accumulation, accumulation by dispossession, and what it calls acumulación entrelazada. In this post, I translate the latter deliberately as intertwined accumulation. The choice matters because it allows us to distinguish the concrete process reconstructed in the Costa Rican case from the broader concept of entangled accumulation developed by Guilherme Leite Gonçalves and Sérgio Costa.

    The distinction is not merely terminological. At the level of objective historical processes, primitive accumulation and accumulation by dispossession can possess relative autonomy: they are distinguishable mechanisms with their own immediate forms, temporal locations, and material effects. Relative autonomy does not mean isolation. It means that one can identify each process in reality without denying that, under concrete historical conditions, they coexist, penetrate one another, and alter the conditions under which the other operates.

    Primitive Accumulation

    Marx’s original problem: the violent historical separation of producers from their means of production and the construction of the property relations required for capitalist production. In the Costa Rican sequence, this includes colonial dispossession, Carrillo’s 1841 abolition of communal tenure, the 1882 decree that treated Maleku territory as vacant land, and the Soto-Keith concession of 1883. These are not simply old events remembered by a later capitalism; they establish legal and material conditions that subsequent accumulation inherits.

    Accumulation by Dispossession

    David Harvey’s formulation identifies the continuing and contemporary use of expropriatory practices: privatization of land and common goods, suppression of collective rights, commodification of previously non-commodified spheres, colonial or neo-colonial appropriation of assets, and the use of credit, law, and state power to transfer resources. In the Costa Rican case, this logic appears in contemporary territorial occupation, conservationist appropriation, environmental-service markets, and other mechanisms that convert collectively preserved resources into fields of accumulation.

    Intertwined Accumulation

    As reconstructed here from Gómez Julián’s Costa Rican case, intertwined accumulation names the concrete relation of mutual conditioning and reinforcement among relatively distinguishable accumulation processes. It is the point at which an earlier expropriation creates the legal, spatial, or social conditions for a later dispossession; the later dispossession reproduces or deepens the effects of the earlier one; and both become connected to new fractions of capital, state institutions, and wider circuits of accumulation. In this sense, intertwined accumulation is not a synonym for either primitive accumulation or accumulation by dispossession, nor does it abolish their analytical distinction.

    Relative Autonomy Does Not Mean Separation

    This way of reading the historical record avoids a false choice. We do not need to say either that primitive accumulation is a closed episode belonging only to the birth of capitalism, or that every later dispossession is simply the same phenomenon under a new name. A concrete process may be identified as primitive accumulation when it restructures property relations by separating communities from the conditions of their reproduction. A contemporary process may be identified as accumulation by dispossession when already existing rights, assets, commons, or public resources are transferred into circuits of capital. And a third analytical problem appears when the effects of these processes become causally linked.

    That third problem is what intertwined accumulation captures here. The relevant relation is not merely chronological succession. It is a material interaction: one process changes the conditions of possibility of another. Earlier legal destruction of communal tenure can make later private occupation easier; later occupation can normalize and reproduce the property regime created by the earlier rupture; state regulation can connect both to transnational commodity chains, tourism, conservation finance, or carbon markets. The processes remain distinguishable, but their effects are no longer additive. They become synergistic.

    Concrete analytical structure
    Primitive accumulation + accumulation by dispossession → mutual conditioning → intertwined accumulation

    The arrow does not mean a rigid historical sequence. It represents a causal relation that may operate across different periods, regions, and institutional forms.

    The Costa Rican mapping makes this visible. Carrillo’s abolition of communal tenure created a legal environment within which the Huetar coffee-frontier dispossession could advance. Decree XIV of 1882 converted Maleku territory into legally available space and enabled its appropriation by ranchers and settlers. The Soto-Keith concession connected territorial dispossession in Talamanca to transnational banana capital. PILA and the PSA later inserted ancestral territory into conservationist and environmental-value circuits, linking local territorial conflict to tourism, state administration, and global carbon capital. The post-2011 de facto recoveries reveal the contemporary collision between the collective indigenous regime and the individual capitalist regime produced through this long history.

    Entangled Accumulation: The Broader Category

    This is where Gonçalves and Costa’s concept of entangled accumulation becomes especially useful. Their 2019 formulation is deliberately broader. It seeks a comprehensive category for the interdependencies that have structured capitalist expansion across history: exploitation and expropriation; wage and slave or otherwise unfree labor; state power and illegal violence; capitalist and non-capitalist economies; different geographical scales; different historical periods; and intersecting social hierarchies such as class, race, ethnicity, and gender.

    In that broader framework, primitive accumulation, accumulation by dispossession, financial expropriation, superexploitation, and other forms do not follow a rigid chronology. They may coexist in the same period and space, disappear and re-emerge, and become connected through law, politics, corruption, culture, discourse, and the changing boundary between state and market. Entangled accumulation therefore operates at a higher level of abstraction: it is a general category for the historical interpenetration of multiple mechanisms and dimensions of capitalist accumulation.

    The two concepts can therefore be related without collapsing them into one another. Intertwined accumulation, as used in this post to interpret the Costa Rican article, is the more concrete category: it identifies a specific process of causal articulation and synergy among distinguishable modes of accumulation inside a determinate historical formation. Entangled accumulation, in Gonçalves and Costa’s sense, is the more general category under which such concrete articulations can be theorized together with many other forms of interdependence.

    Relationship between the concepts
    EintertwinedEentangled

    This set-theoretic expression is an interpretive shorthand used in this post, not a formula stated verbatim by either paper. It means that the specific Costa Rican process can be treated as one concrete determination within the wider family of interdependencies captured by entangled accumulation.

    This distinction also clarifies why the Costa Rican article can speak of the convergence of primitive accumulation, accumulation by dispossession, and intertwined accumulation without reducing all three to one undifferentiated process. The first two refer to mechanisms that can be identified with relative autonomy; the third refers to their concrete articulation when they coexist and reinforce one another. At the same time, that entire configuration can be located within Gonçalves and Costa’s more encompassing theory of entangled accumulation. What looks like a terminological inconsistency at a purely abstract level thus becomes, at the level of historical reality, a useful distinction between mechanisms, their interaction, and the general category capable of containing both.

    The key distinction is between a mechanism and a relation among mechanisms: primitive accumulation and accumulation by dispossession can be identified separately, while intertwined accumulation names the historically concrete synergy through which they condition and reproduce one another.

    A Timeline of Dispossession: Key Milestones

    1542–1880

    Laws on baldíos, early decrees (e.g., Guatuso). Legal-administrative dispossession: Crown → State → Private hands.

    1830–1890

    Coffee boom and beneficio system. Concentration via processing and credit. Huetar resistance in Orosí (c. 1860). Dissolution of communal land regime.

    1870–1910

    Banana concessions (Keith/UFCO). Bribri-Cabécar displacement. Atlantic enclave; corporate spatial control; dispossession in Sixaola.

    1933–1940

    Coffee regulatory bodies (Instituto de Defensa del Café). Crisis management without reversal of concentration.

    1950s–1970s

    Internal colonization (ITCO/IDA). Convention 107. Law 2825. Partial titling; insecurity and frontier appropriations persist.

    1977

    Indigenous Law 6172. Formal recognition vs. persistent non-indigenous occupation.

    1982

    Creation of Parque Internacional La Amistad (PILA). State-conservationist appropriation of Bribri-Cabécar ancestral territory.

    2011–present

    De facto recoveries in Salitre, Cabagra, Térraba. Community reoccupation. Threats and attacks intensify.

    2019–2024

    Assassinations: Sergio Rojas (March 18, 2019), Jethy Rivera (February 24, 2020). UN/IACHR: impunity. Rivera conviction reversed; Rojas case archived.

    Why Land Is Not Just Land: The Question of Rent

    The article introduces one more theoretical tool that deserves attention: the Marxist concept of ground rent — both natural and differential. Contemporary indigenous struggles, the author argues, cannot be explained solely by the seizure of land as a means of production. They also revolve around the natural resources those lands contain: water, forests, biodiversity, scenic beauty, carbon sequestration capacity. The yield from these resources can be converted into rent that is appropriable by various fractions of capital — agroindustrial, extractivist, touristic, conservationist (private or state-run).

    The PSA inside indigenous territories, the nature tourism surrounding national parks created on ancestral lands, the monetization of environmental services in the carbon market, and adjacent agroindustry are all concrete devices through which capital captures or redistributes rents whose material base is precisely the territories that indigenous peoples have preserved through their historical struggle. Indigenous territorial defense is therefore simultaneously defense of communal use-value against capitalist exchange-value, and a material obstacle to the full realization of differential rent by capital.

    What This Means — and Why It Matters Beyond Costa Rica

    The article’s conclusions are blunt. The “White Legend” of Costa Rican democratic exceptionalism does not survive contact with the evidence. A country where nearly three-quarters of the peasantry is landless, where the Gini coefficient for land ownership approaches 0.8 nationally and reaches 0.9 in cattle regions, where over 90% of farms in some zones lack legal titles, and where indigenous leaders are assassinated with impunity for reclaiming territories that the state itself has legally recognized as theirs — that country is not a democratic anomaly in an unequal region. It is a case study in how formal democracy and extreme agrarian concentration coexist, and how the latter is structurally enabled by the former.

    The argument is not that Costa Rica is uniquely evil. It is that the myth of its exceptionalism serves a function: it legitimizes the very regime of accumulation that makes extreme inequality possible. The “White Legend” is not a miscalculation or a public-relations excess. It is, in the article’s framework, an ideological device that is functional to the system it obscures. As long as Costa Rica believes it is democratic and equal, the structural mechanisms that produce dispossession operate without scrutiny.

    And the final, perhaps most unsettling implication: the article concludes that non-indigenous civil society participation is essential to defend rights that are “fundamentally irreconcilable with the needs of accumulation.” The rights of indigenous peoples over their territories, in other words, cannot be secured within the existing accumulation regime without a political rupture that extends beyond indigenous communities alone. This is not a call for charity or solidarity in the conventional sense. It is a structural observation: the system that dispossesses indigenous peoples is the same system that produces landlessness among non-indigenous peasants, and their interests converge at the point where the logic of accumulation is challenged.

    §

    A Note on the Source

    This post is primarily a reading of José Mauricio Gómez Julián, “Acumulación por despojo y el mito del excepcionalismo democrático costarricense: el despojo indígena como rasgo estructural de la concentración agraria,” Revista de Historia, No. 93 (January–June 2026), pp. 1–45, published by the Universidad Nacional de Costa Rica. The article is available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International license. The author is an independent researcher specializing in political economy and statistical methodology, with a degree in Economics from the Universidad Latina de Costa Rica.

    The conceptual clarification developed above also engages Guilherme Leite Gonçalves and Sérgio Costa, “From primitive accumulation to entangled accumulation: Decentring Marxist Theory of capitalist expansion,” European Journal of Social Theory (2019), DOI 10.1177/1368431018825064. To keep the analytical levels distinct, this post deliberately reserves entangled accumulation for Gonçalves and Costa’s broad category and uses intertwined accumulation for the more concrete process reconstructed from the Costa Rican case. That terminological distinction is an interpretive choice of this post rather than a claim that the two papers themselves explicitly establish the same hierarchy in those exact words.

    The article is explicitly situated within Marxist political economy and historical materialism. It does not claim neutrality: it argues that the theoretical framework it employs has superior explanatory power for the phenomena it documents, and it reconstructs its core political categories (State, Law, Democracy, Rule of Law, Corruption) inductively from the historical evidence rather than importing them as axioms. Readers who disagree with the theoretical framework may still find the empirical documentation — drawn from census data, property records, legislation, UN reports, Inter-American Commission records, and direct indigenous testimony — valuable in its own right.

    The data referenced throughout — Gini coefficients, titling statistics, acreage figures, occupation percentages — are drawn from the sources the article cites (Seligson, Edelman, Brockett, Dunkerley, Paige, Guevara and Chacón, Vargas Mena, Zúñiga et al., and others). No figures have been invented or extrapolated beyond what the article itself presents.

    “The history of the communities indigenous from the conquest to the present reveals not an exceptional democratic inclusion but a systematic dispossession as a structural feature of capital accumulation.”

  • SOME REFLECTIONS ON MARX’S PRICES OF PRODUCTION

    SOME REFLECTIONS ON MARX’S PRICES OF PRODUCTION

    Was Marx Wrong About Prices of Production? — A 260-Page Investigation Says No

    Political Economy • Econometrics • Marx

    Was Marx Wrong About Prices of Production?
    A 260-Page Investigation Says No.

    How one researcher spent years showing that the most famous critique of Marx’s economics rests on a mistake Marx never made.

    Based on: Gómez Julián (2026), “Some Reflections on Marx’s Prices of Production” — Introduction, Conclusions & the Formal-Empirical Chapter · DOI 10.5281/zenodo.21842251

    A Fatal Flaw, or a Fatal Misreading?

    For over a century, a single mathematical argument has been wielded as the definitive proof that Karl Marx’s economics doesn’t work. It goes like this: Marx claimed that the value of goods is determined by the labor that produces them, and that market prices eventually gravitate toward “prices of production” — modified versions of those labor values, adjusted for how capital-intensive each industry is. But when you try to verify this with a system of simultaneous equations, the numbers don’t add up. The sums of values don’t equal the sums of prices. The theory, critics have said since the early 1900s, contains a fatal algebraic error.

    This paper — spanning 260 pages and drawing on philosophy, history, sociology, and statistics — argues that the error was never Marx’s. It was the error of the people who checked his math using a method he never used.

    The Photograph vs. the Movie

    Imagine you’re trying to understand a river. You could take a photograph of it — capturing one frozen moment — or you could film it as a movie, watching how the water flows over time. For over a hundred years, the economists who criticized Marx took a photograph of his theory and then complained that it didn’t look like a movie.

    Here’s the specific issue. Marx described a two-step process: first, a general rate of profit forms across the entire economy; then, each industry’s price deviates from its pure labor value according to how much capital it ties up relative to the average. The standard critique — originating with Ladislaus von Bortkiewicz in 1907 and repeated ever since — takes all of Marx’s accounting identities and solves them simultaneously, as if input prices and output prices were determined at the same instant. Under that framework, Marx’s three aggregate equalities cannot all hold at once.

    The “inconsistency” that has been attributed to Marx for over a century is the inconsistency of the simultaneous-dualist framework that was imposed on him, and it dissolves as soon as time is restored. — Gómez Julián, summarizing the central thesis

    But here’s the catch: solving everything simultaneously is equivalent to assuming that the economy is a photograph — that there is no time. And Marx’s entire framework is built on the opposite premise: that the economy is a process, an unfolding sequence in which the prices that exit one period become the input prices that enter the next. Once you restore that temporal dimension, the “inconsistency” vanishes. The three equalities hold simultaneously — not because Marx was secretly consistent in some miraculous way, but because the contradiction was an artifact of the framework imposed on him, not of his own logic.

    The paper calls the simultaneous approach “Walrasian Marxism” — a phrase that captures the irony: economists imported the logic of Léon Walras’s general equilibrium theory and used it to read Marx, then blamed Marx when the result didn’t work.

    In Plain Language

    Marx was accused for over a century of getting the arithmetic wrong. What actually happened is that someone redid his arithmetic under an assumption he never made — that the prices of things you buy to produce and the prices of things that come out of production are the same prices, set at the same time. If you assume that, Marx’s accounts don’t close. But that assumption is equivalent to saying the economy doesn’t happen in time.

    But Was the Movie Real?

    Pointing out that Marx’s logic works when you read it correctly is necessary but not sufficient. The “temporalist” school has been making this argument for nearly fifty years. But the author noticed a critical gap: nobody in that school had ever taken real-world data and actually estimated the three types of prices Marx described — direct labor values, prices of production, and market prices — and then tested whether market prices actually gravitate toward prices of production as the theory predicts.

    This matters because, as the paper puts it, leaving the correct reading of Marx “in the territory of conceptual argumentation while the incorrect reading occupies alone the territory of measurement” is a strategic vulnerability. If you can’t show that real prices behave the way your theory says they should, your theory remains a philosophical argument, however internally consistent.

    But before presenting any numbers, the paper devotes substantial space to establishing that the process Marx described actually happened in history. This is not an appendix; it’s a foundational part of the argument.

    Before Capitalism

    In pre-capitalist societies, exchange was regulated by labor time — not because someone enforced a theory, but because the material conditions made it so. Barter was dominant, inflation did not exist, and prices could only reflect production costs given available technology. Evidence from anthropology (Malinowski’s Trobriand Islands studies), sociology (Mauss on gift exchange), accounting history (Kula’s analysis of feudal estate records), and even paleogenomics all converge: objects were valued in proportion to the labor they embodied.

    The Transition

    The dissolution of feudal relations, the monetization of exchange, and the destruction of pre-industrial normative frameworks created the conditions for capital to move freely between industries. Thompson’s work on the “moral economy” documents how the new free-market ideology had to be violently imposed, destroying customary protections and creating an unprecedented relationship of exploitation.

    Capitalism Established

    Once barriers to capital movement were destroyed, capital flowed from commerce to industry chasing higher profits, and generalized competition forced a redistribution of total surplus value across sectors. The crisis of 1873 — which destroyed nearly half the blast furnaces in major iron-producing countries — is presented as concrete evidence of the mechanism: firms whose costs were still based on older, individually more labor-intensive methods went bankrupt when they couldn’t compete with prices of production dictated by modern technology.

    In Plain Language

    Prices of production didn’t appear the day someone wrote an equation. They appeared the day capital could freely move from one industry to another chasing the highest profit — which didn’t happen until legal, moral, and political barriers were destroyed. Before that, things were exchanged roughly according to the labor they cost, and there is more than enough evidence — ethnographic, accounting, archaeological, and genetic — to show it.

    What Is a Production Price, Exactly?

    This is where the paper moves into its most technically original territory. The author carefully separates two things that must not be confused:

    What a production price is (the explanandum): it is the expected value, over the distribution of economic perturbations, of the long-run time average of market prices. In plain language: it’s the center of gravity around which actual market prices keep spinning. Not the price they arrive at and stay at (that would be equilibrium), but the average around which they never stop oscillating.

    Key Concept

    The production price is neither an eternal, timeless equilibrium (the error of the simultaneous approach and of Walrasian economics, which takes the law as such for the whole and eliminates time) nor a chaos of prices without law (the error of empiricism, which stays at the level of individual prices and loses the law). It is the law of the whole realizing itself through the contingency of the parts.

    How each step of the process works (the explanans): a rule that determines this year’s market price from last year’s market price and last year’s latent production price, and nothing else. This is modeled as a hierarchical Ornstein-Uhlenbeck process — a three-level cascade in which the production price is itself a latent state with its own dynamic gravitating toward value, and market prices gravitate toward that latent state rather than toward a fixed, noisy index.

    The uncertainty is built into the model explicitly: uncertainty in the average rate of profit, uncertainty in the advanced capital, uncertainty in the disaggregation of national accounts into 37 sectors (handled through multiple imputation with 25 imputations combined by Rubin’s rule), and parametric uncertainty estimated through Bayesian Markov Chain Monte Carlo methods.

    One crucial point: no magnitude is obtained by solving a simultaneous system. Value is constructed empirically and directly as $V = c + v + p$ (cost plus surplus value), and production price as $\Phi = c + K \cdot G’$ (cost plus capital times the general rate of profit). There is no Leontief inversion, no simultaneous algebra, anywhere in the construction.

    In Plain Language

    Think of a production price as the “gravitational center” of a spinning object. The object (a market price) never stops moving — it wobbles, it swings, it drifts — but over time its average position is pulled toward that center. The math describes both what the center is and how each wobble happens, and it does so while honestly accounting for all the uncertainty in the measurement.

    The Defining Equations: (9) Through (11)

    Here is where the metaphor turns into mathematics. The paper writes the definition of a production price in three successive steps — each one making explicit an assumption the previous step left implicit — numbered (9), (10), and (11) in the original text. None of the three generates a trajectory by itself; together they define the explanandum — what the object is — that the cascade below then generates.

    Equation 9 — What a Production Price Is
    $$ \lim_{t\to\infty} E\!\left[\varphi^i_t\right] \;=\; k^i_t + K^i_t\, E\!\left[G'(t,X)\right] \;=\; \Phi^i_t $$

    Here $\varphi^i_t$ is sector i’s market price at time $t$, $k^i_t$ is its cost price (constant capital consumed plus variable capital), $K^i_t$ is the total capital advanced, and $G'(t,X)$ is the general rate of profit — itself a stochastic process indexed by a perturbation $X$ that bundles the exodus of capital between branches and technological innovation.

    In words: a production price is the long-run limit of the average market price. Not the price itself at any instant — that keeps oscillating forever — but where its time-average settles as the horizon stretches out. Notice the object on the right-hand side, $k + K \cdot E[G’]$: it is the same accounting identity introduced earlier (cost price plus the average profit rate applied to capital advanced), except the profit rate is now written as an expectation, because it fluctuates.

    Equation 10 — Making the Averaging Explicit
    $$ \Phi^i_t = \lim_{t\to\infty} E\!\left[\varphi^i_t\right] = \int_{-\infty}^{\infty} \!\left(\lim_{t\to\infty} \varphi^i_t(x)\right) f_X(x)\, dx \;=\; k^i_t + K^i_t \int_{-\infty}^{\infty} G'(t,x)\, f_X(x)\, dx $$

    $f_X$ is the probability density of $X$. The equation says the expectation is an average over every possible state $x$ of the system’s turbulence, weighted by how likely that state is.

    Equation (10) earns its keep by making a subtle move legitimate: swapping the order of the limit and the expectation. That looks harmless, but it hides a real question — does the market price $\varphi^i_t$ even converge to anything as $t \to \infty$? The paper’s answer is no: a capitalist system doesn’t settle into a fixed point, it settles into a limit cycle — perpetual oscillation. So the convergence the argument needs isn’t of the instantaneous price, but of its cumulative time-average. That average does converge, for almost every state of the world, precisely because the system is ergodic — the fraction of time the cycle spends in each region of its orbit stabilizes. This is the Birkhoff ergodic theorem doing, in mathematical language, exactly what Marx says in economic language: the production price isn’t the value the market price reaches and stays at, it is the average around which it never stops oscillating. The oscillation isn’t an obstacle to the average — it is the average’s condition of existence.

    Why the Order of Operations Matters

    The paper invokes Lebesgue’s Dominated Convergence Theorem to justify swapping “limit of the average” for “average of the limit.” This requires bounding market prices by some integrable envelope — economically, that no price can grow without limit, which technological ceilings and competitive pressure guarantee — and, crucially, it does not require that the convergence be uniform across sectors. Uniform convergence would mean competition equalizes profits instantly and identically everywhere, with no room for a shock to hit one industry harder than another. Marx’s theory says the opposite, and the math is built to allow it.

    Equation 11 — When the Capital Base Is Also Uncertain
    $$ \Phi^i_t = \lim_{t\to\infty} E\!\left[\varphi^i_t\right] = \int_{-\infty}^{\infty}\!\!\int_{-\infty}^{\infty} \left[k^i_t + K^i_t(y)\, G'(t,x)\right] f_{X\mid Y}(x\mid y)\, f_Y(y)\; dx\, dy $$

    Equation (10) still treated the capital base $K^i_t$ as known exactly. Equation (11) drops that simplification: $Y$ is a second random variable carrying the estimation error in $K$, with density $f_Y$, and $f_{X \mid Y}$ lets the profit-rate perturbation depend on which realization of that error occurred. The object is the same double average — only now uncertainty is propagated from two sources instead of one.

    This last equation is not a mathematical flourish; it is the reason the empirical section spends so much effort on multiple imputation. National accounts don’t hand anyone a clean measurement of capital advanced by sector — it has to be reconstructed from incomplete data, and that reconstruction carries its own error. Equation (11) is the license to treat that error as a random variable to be averaged over rather than a nuisance to be ignored. The uncertainty is propagated externally — by a generator outside the statistical model itself — rather than estimated as an internal parameter of the dynamic model: estimating $K$’s error inside the model would confound it with the model’s own measurement-noise term, opening a ridge of non-identification between two magnitudes that the data alone cannot tell apart. Kept external, twenty-five complete reconstructions of the data are generated first, each respecting the Marxian aggregate identities to machine precision, the dynamic model is fit on each, and the twenty-five fits are combined by Rubin’s rule. That is the outer average of equation (11), computed by literally drawing from the distribution of $Y$ instead of assuming it away.

    The Engine: A Three-Level Ornstein–Uhlenbeck Cascade

    Equations (9)–(11) define the target; they don’t generate a path toward it. The explanans — the mechanism that actually produces a year-by-year trajectory consistent with that target — is a hierarchical Ornstein-Uhlenbeck process with up to three nested levels, fit as a single Stan program (the same program handles one, two, or three levels, which guarantees that adding levels can never silently break the simpler cases nested inside them). All series enter standardized; time is discretized one year at a time using the Euler–Maruyama scheme.

    Level 1 — The Market Price
    $$ dev_{t,s} = \varphi_{t-1,s} – \Phi_{t-1,s} $$
    $$ \kappa^m_{t,s} = \kappa_{\mathrm{cap}} \cdot \mathrm{invlogit}\!\left(\kappa_s + \beta_1\, z^{TMG}_t\right) $$
    $$ \Delta\varphi_{t,s} = \kappa^m_{t,s}\!\left(-\,dev_{t,s}\right) \;+\; a_{3,s}\, dev_{t,s}^{\,3} \;+\; \gamma\, COM^{std}_{t,s} \;+\; \varepsilon_{t,s} $$

    Subscripts $s$ (sector) and $t$ (year) run throughout. $dev$ is last year’s gap between market price and the latent production price. $\kappa^m$ is the sector’s reversion speed, passed through a logit link that caps it inside $(0, \kappa_{\mathrm{cap}})$ and lets the general rate of profit ($z^{TMG}$) modulate it without ever pushing the system out of the stable region of the discretization. $\varepsilon$ is a fat-tailed (Student-t), stochastic-volatility innovation, so volatility can cluster in time without destabilizing the mean.

    Read the Level 1 line as a spring. The term $-\kappa \cdot dev$ is the restoring force: it pulls the market price back toward the production price with a force proportional to how far it has drifted. The cubic term $a_{3,s} \cdot dev^3$, with $a_{3,s}$ constrained negative by construction — not estimated, imposed — makes that restoring force grow faster than proportionally once the deviation gets large: the further the market strays, the harder it snaps back. This is a declared stability assumption, not a discovery: it guarantees the model can never generate an explosive regime, at the real cost that if such a regime existed in some sector of the actual economy, this particular specification could not detect it.

    Levels 2–3 — Where the Latent Center Itself Reverts
    $$ \mu_{s,t} = m_{0,s} + m_1\, G’_t + m_v\, V_{s,t} $$

    The production price $\Phi$ is not treated as a fixed, observed index; it is itself a latent state that reverts — more slowly, with its own sector speed $\kappa_p$ — toward this mean $\mu$. $m_1$ is the channel running through the general rate of profit; $m_v$ is the coefficient measuring how strongly the production price tracks the directly-constructed value $V_{s,t} = k + p$ (Level 3, and the reason the cascade goes up to three levels rather than stopping at two).

    This is the bridge back to the abstract equations above, term by term. $\mu_{s,t}$ is the estimable stand-in for the right-hand side of (9): $m_{0,s} + m_1 G’_t$ plays the role of $k + K \cdot E[G’]$, and $m_v V_{s,t}$ is the specific functional form chosen for the value-tracking channel that the abstract definition deliberately leaves open (the paper is careful to say that capitalist competition as a function of the value structure is declared at the level of equations 9–11, not derived; giving it the concrete shape $m_v V$ is a modeling choice made at the cascade level, defended by how it performs under validation rather than deduced from the definition). And the expectation of $G’$ from equation (9) has its operational counterpart in the profit rate averaged across the twenty-five multiple imputations — the mechanism equation (11) licenses.

    The coefficient $m_v$ carries real theoretical weight: it is the empirical stand-in for Chapter 9’s claim that prices of production gravitate around values. It is given a neutral prior, $m_v \sim \mathcal{N}(0,\, 0.5)$ — centered at zero, symmetric, assigning equal plausibility to $m_v > 0$ and $m_v < 0$ before seeing any data. That matters for the same reason a fair coin matters in a coin-flip experiment: if the data carried no signal, the posterior would sit wherever the prior put it, hugging zero. It doesn’t. It lands at $m_v \approx 1.0136$ with $P(m_v > 0) = 1$ — evidence that the data moved it there, not the prior. The anchoring to value is found, not assumed into the setup.

    In Plain Language

    The cascade is three springs stacked on top of each other. The market price is tied by a spring to the latent, unobserved production price. The production price is tied by its own, slower spring to a moving target that blends the general rate of profit with the directly-measured labor value. Pull any one spring and let go: it doesn’t snap to a fixed point, it settles into the kind of perpetual, decaying oscillation that equations (9)–(11) describe as an average. The springs are estimated from sixty-one years of real U.S. data, not assumed; the coefficient tying prices of production to values, specifically, could have come back negative or zero — the model gave it every chance to — and it didn’t.

    What the Numbers Say

    The empirical core of the paper is a panel of 37 productive branches of the United States economy over 61 years, from 1960 to 2020. The hypothesis tested encloses three distinct relationships, and the paper is meticulous about not conflating them. Each is stated, tested, and reported separately.

    Market Prices ↔ Prices of Production: The Strongest Link

    This is the relationship with the firmest statistical support, confirmed through six independent lines of evidence:

    Central Finding

    Gravitation exists, and it is slow. The median speed across sectors is $\kappa_m = 0.0770$, equivalent to a half-life of approximately 9 years. Market prices take about a decade to cover half the distance toward their production-price center. This is consistent with Marx’s characterization of gravitation as a tendential, mediated regulation, not an instantaneous fit.

    The number is remarkably stable under stress tests:

    • Removing five of the six productive blocks from the panel barely moves the estimate — it shifts in the third decimal place. The sixth, which gathers 18 of the 37 sectors, does produce a shift (from 9 years to 6 years), and the paper decomposes it: about half the acceleration is the generic effect of halving the panel — removing 18 sectors at random already gives 0.0929 — and not the block itself.
    • Dismantling the value anchor in three different ways — including permuting surplus value across spheres — moves the speed in the third decimal place. This is significant: it means the conclusion about market-to-production gravitation does not depend on the less robust production-to-value link.
    • The market deviation has its own dynamic signature. Compared against a random walk matched in variance, three out of six test statistics separate cleanly (the weighted-sum convergence reaches a tolerance of 0.01 while the null never reaches a tolerance ten times more lenient; recurrence analysis laminarity triples the null; recurrence entropy doubles it). The ones that don’t separate are recurrence-analysis determinism and the two deterministic-chaos invariants — the Lyapunov exponent and the correlation dimension — which the paper never claimed to find.
    • The estimate is invariant to secondary methodological choices. Sweeping the latency regularizer across three values produces life medias of 9 years in all three arms (speeds of 0.0774, 0.0770, 0.0772).
    • The known bias of disaggregation pushes against the result. Splitting a national figure among 37 branches is underdetermined and biases speed estimates downward — meaning the true half-life is probably 7–8 years rather than 9. A bias that works against your conclusion is one you can live with, because the result holds despite it, not thanks to it.

    Prices of Production ↔ Values: The Thinnest Leg

    This is the weakest part of the empirical argument, and the paper states so with complete transparency. The problem is not a defect of the instrument but a property of the object:

    Methodological Transparency

    The coupling coefficient estimated within the dynamic model is $m_v = 1.0136$ with a 95% credible interval of $[1.0096,\; 1.0176]$ — but the same procedure returns 1.0365 when surplus value is permuted across spheres, preserving all annual aggregates. Why? Because production price and value share the cost price, which explains 66.1% of the variance of the former and 72.0% of the latter, and their correlation in levels is 0.9987. The coefficient would land near one even if the law of value didn’t hold at all. The paper therefore reports it as a consistency check, not as evidence.

    The real support for this relationship comes from cross-sectional tests, not from the dynamic coupling. When temporal common trends are removed and analysis is conducted within-year, the slope of the markup on own surplus value is 0.675 with the true data versus 0.090 under permutation, with intervals that don’t come close to overlapping. The sectoral ordering of the wedge between $\Phi$ and $V$ has an inter-annual rank correlation of 0.986 and a 60-year value of 0.558 — highly persistent structure, not noise.

    A collateral finding worth noting: the coefficient of variation of sectoral profit rates is 0.669 — meaning profit rates across industries show considerable and persistent dispersion. Far from contradicting the theory, this dispersion is the condition of existence of the mechanism: if profit rates were already equalized, there would be no differential to drive capital migration, and gravitation would have nothing to operate on. Marx postulates equalization as a tendency, not an accomplished fact.

    Market Prices ↔ Values: Sustained in Form, Adjusted in Existence

    The structural modification across sectors exists and is nonlinear (the nonlinearity step holds comfortably at 6.8 null deviations). But the existence step is adjusted: 44% of its gain is obtained equally with sectoral characteristics unpaired from their spheres, and the gap against the maximum null is on the order of one paired standard error. The coefficients survive a deliberately severe correction for serial dependence (tripling the error).

    The Instrument Behind That Number: A Nested Ladder in gdpar

    That test is a small ladder of nested distributional-regression models, fit with gdpar (Gómez Julián, 2026b), the author’s own R package for generalized distributional parameter regression, published on CRAN on July 15, 2026. The ladder climbs from a bare model — “the market-to-value ratio has no sector-specific correction at all” — through a model where organic composition, wage share, and sector size shift that ratio linearly, up to a model where the correction is a flexible spline rather than a straight line. Two gains matter, measured in units of predictive density: adding the linear correction buys 207.3 units; letting it curve buys another 215.1. Both were checked against a control built to be hard to pass — shuffling which sector gets which characteristics 99 times, refitting each time, with the spline’s knots held fixed across every shuffle so the comparison can’t be won by a better basis alone. The curvature gain clears its null with room to spare (6.8 null standard deviations; the best of 99 shuffles reaches only 114.8 against 215.1 observed). The existence gain is honestly reported as thinner: shuffled sectors still buy about 44% of the real gain merely by having some characteristics to fit — three covariates and an intercept give a model room to accommodate noise even when it is being told nothing true — so the genuine margin over the null sits at about one paired standard error (23.2, against a gap of roughly 24 units). Both numbers are reported together, precisely so the large one isn’t read alone.

    A companion specification, estimated in the same gdpar fit, asks the same question about dispersion rather than location: not where the market-to-value ratio is centered, but how tightly it clusters. Larger sectors and sectors with higher capital composition show systematically less relative dispersion — elasticities of $-0.226$ and $-0.104$ — consistent with equalization operating more effectively where capital is more concentrated. Both effects clear a “breaking factor” (the multiple of the standard error at which the 95% interval would first touch zero) north of six and four respectively, past the 2.94 ceiling reached anywhere else among this paper’s location coefficients, and the finding reproduces under a completely different likelihood family (a gamma distribution on the price ratio) to within 5.2%.

    Three Failures That Confirm the Theory

    One of the most intellectually striking features of this paper is how it handles results that, at first glance, look bad for its thesis. There are three, and the paper reports all of them without softening — then shows deductively why each one was expected if the theory is correct.

    Negative Result No. 1

    The model does not out-of-sample predict better than a random walk. But this was deductively implied by the slow form of the thesis. At a horizon much shorter than the half-life, a mean-reverting process is, to first order, a random walk. If something takes a decade to get halfway back, looking at a single year won’t let you see it return.

    Negative Result No. 2

    The value term is predictively indistinguishable. Again, this follows from the slow coupling between prices of production and values: with half-lives on the order of decades and only 61 years of data, univariate root-unit tests are structurally underpowered.

    Negative Result No. 3

    No univariate test separates the true wedge from its permuted placebos. But this was predicted before measuring, by the persistence of sectoral ordering itself (inter-annual rank correlation of 0.986). A highly persistent time series is hard to distinguish from its permuted version using tests designed for shorter memory.

    Finding these signatures is corroboration of the slow form of the thesis, and not finding them would have been the real problem. — Gómez Julián, on the negative results

    The paper’s stance on this is worth highlighting: “Lejos de refutar la tesis, los tres están deductivamente implicados por su forma lenta” — far from refuting the thesis, all three are deductively implied by its slow form. A single mechanism (slow gravitation) explains both the substantive thesis and all the apparently negative results, and it also survives in the validated posterior. “That a single cause explains the thesis and all the apparently negative results, and that it additionally survives in the validated register, is the opposite of a petitio principii: it is a unified, falsifiable, and internally validated narrative.”

    Temporalism Isn’t a Preference — It’s a Condition of Measurement

    Perhaps the most consequential result in the entire paper is not a number but a statement about what can and cannot be measured. It concerns the “modulator” — the component of Marx’s argument in which the general rate of profit enters into the structural modification of each sphere, meaning the deviation of each sphere is not independent of the reference but generated by it.

    The Identifiability Argument

    When the model was run with a single, fixed general rate of profit for all 61 years (as a simultaneous approach would require), the posterior exhibited a flat ridge: two completely different functional bases (a degree-two polynomial and a spline basis) produced the same pathology to the third decimal place, with an effective sample size of only six draws. The diagnostic got worse with more sampling (R-hat rising from 1.33 to 1.73). This is the unmistakable signature of a direction in parameter space along which the likelihood does not change.

    The cause is theoretical, not computational. With one fixed reference, the modulator can only be identified evaluated at that single point — a single number, not a function over the space of references. You cannot estimate three coefficients from a polynomial if you have one data point.

    When the reference was allowed to vary year by year (61 different general rates of profit), the model converged within minutes, with a large improvement in both time and effective sample size, and zero divergences.

    Named, Not Improvised: Theorems 1A and 1E

    This diagnosis isn’t an ad hoc read of a misbehaving sampler. gdpar (Gómez Julián, 2026b) — the same package behind the nested ladder above — ships a formal identifiability result for exactly this situation. Its Theorem 1A establishes that, with a single fixed reference point, a distributional modulator is identified only at that point: as one number, not as a function over the space of possible references. Theorem 1E is the positive counterpart: letting the reference vary restores identifiability of the modulator as a function. Fitting a degree-two polynomial (three coefficients) or a five-knot spline basis (five coefficients) against one single, unmoving reference asks for more than a single data point in that dimension can support — which is exactly what a flat likelihood ridge looks like from the sampler’s side.

    The figures behind the improvement, precisely: a fixed reference with a degree-two polynomial gives an R-hat of 1.7333, an effective sample size of 6, and 8 divergent transitions in 39 minutes; a one-knot spline basis reproduces the same pathology — R-hat 1.7335, effective sample size 6, 14 divergences, 5.6 hours. Letting the reference vary year by year (61 distinct annual values of the general rate of profit), centering the additive component and raising the sampler’s adaptation parameter to 0.99, gives an R-hat of 1.0035, an effective sample size of 1332, and zero divergent transitions — in 2.9 minutes. That is the 115-fold improvement in time and 222-fold improvement in effective sample size referenced above, and it is a theorem, not a tuning trick: no amount of additional sampling closes that gap under a fixed reference, because the object being asked for — the modulator as a function — simply is not there to find.

    The consequence is stated precisely: with a single fixed general rate of profit obtained by solving the system simultaneously, the claim of Chapter 9 of Volume Three of Capital is unverifiable by construction. It is not that the data are insufficient — the object is not identified, and no amount of data would identify it. The argument does not establish that simultaneism is false as a description of capitalism (that is established by historiography and sociology); it establishes that a simultaneous procedure cannot, even in principle, empirically verify the specific part of Marx’s argument that this work estimates.

    In Plain Language

    Marx says: first a general rate of profit forms, then each industry deviates from it according to how capital-intensive it is. To check whether the deviation depends on the general rate, you need to see what happens to the deviation when the general rate changes. If you calculate one general rate for the entire 61-year span, it never changes, and there is nothing to observe. That is exactly what happened: the model with one fixed rate doesn’t converge — not because of computational limitations, but because it is being asked to measure a relationship with a single observation of one of the two variables. Calculating one rate per year — which is what the temporal reading says you should do — the same model converges in three minutes.

    What This Is, and What It Isn’t

    The paper is careful, almost painstakingly so, about the limits of what it claims. This section matters because a reader coming from the “pro-Marx” or “anti-Marx” side might be tempted to over-read the results. The author doesn’t let you.

    What the evidence authorizes: In the United States between 1960 and 2020, market prices gravitate toward prices of production with a decadal half-life that is sectorially heterogeneous, and this speed survives three independent assaults (removing five of the six productive blocks, destroying the value anchor, varying secondary methodological decisions). This is a measured, calibrated, and falsifiable fact.

    What the evidence does not authorize:

    • It does not claim superior predictive power (the model does not out-predict a random walk, which was expected).
    • It does not claim that univariate root-unit tests confirm gravitation (they are structurally underpowered at this time scale).
    • It does not claim uniqueness or categorical novelty. The contribution is the explicit integration and canonization of a slow gravitation cascade with value anchoring, measured on real data, with propagated uncertainty, validated, and subjected to a diagnostic whose unfavorable results are reported alongside the favorable ones.
    • It does not claim that this statistically demonstrates the law of value, “and not for rhetorical prudence but because it would be false: a price series can show that a magnitude behaves as the law predicts, and cannot explain why that magnitude exists or whether the category with which we name it is the correct one.”

    That last point is the paper’s deepest epistemological commitment. Questions about whether “value” is the right category for what prices ultimately measure are not answerable by any price series, no matter how long. They are answered by history, sociology, and philosophy — and the firm answer is the one obtained when all four disciplines (those three plus statistics) point in the same direction. The four-dimensional convergence is the argument, not any single leg of it.

    The paper also addresses the homology that unifies its seemingly disparate halves — the historiographical-filosofical first chapter and the econometric second chapter. The relationship between necessity and contingency that governs the transition from feudalism to capitalism (where the same demographic shock produced opposite outcomes in different regions of Europe) is structurally identical to the relationship between prices of production and market prices. A law determines the center; circumstances determine each particular outcome. Neither fact negates the other, because they describe different levels of the same reality.

    What It All Adds Up To

    Here is the simplest version of what this 260-page paper establishes:

    Marx was reproached for a century for having done an arithmetic calculation wrong. What happened is that his calculation was redone under an assumption he never made: that the prices of things bought to produce and the prices of things that come out of production are the same prices, fixed at the same time. If you assume that, Marx’s accounts indeed don’t close. But that assumption is equivalent to saying the economy doesn’t happen in time. As soon as you accept that what exits the factory this year is what enters the factory next year, the accounts close without anyone having to fix anything. — Gómez Julián, Summary for the Reader

    But recognizing the conceptual error was only the first half. What had been missing — and what this paper contributes — is doing those accounts with real data instead of with fictitious numerical examples, which is what the school that had the correct conceptual reading had never done.

    The empirical results show that prices in the U.S. economy over six decades do behave as the theory predicts: they gravitate, slowly, toward prices of production calculated with Marx’s theory and no other. This finding survived every attack the author could devise — removing productive sectors, destroying the value anchor, permuting surplus values, varying methodological decisions, and running diagnostics whose unfavorable results are reported in full alongside the favorable ones.

    The part of the argument linking prices of production to labor values is also supported by real evidence, though less firmly, and the paper says exactly where the weak points are and why they are properties of the object, not defects of the instrument.

    And the paper does not claim to have demonstrated the law of value with a series of numbers, because “questions of that kind are not answered with numbers: they are answered with history, with sociology, and with philosophy, and the firm answer is the one obtained when the four things (the previous three, together with statistics) all point in the same place.”

    That convergence doesn’t make the result eternal — better evidence can overturn it tomorrow. But it makes it, for now, “our best possible approximation to the truth.”

    — — —

    “In science as in life, overcoming adversity is what makes us truly strong.”

    This post summarizes the introduction, conclusions, and the formal-empirical chapter (§2.4) of Gómez Julián, J. M. (2026). Some Reflections on Marx’s Prices of Production: Historicity of the Law of Value, Dialectical-Materialist Foundation, and Dynamic Formalization Under Uncertainty. Zenodo. https://doi.org/10.5281/zenodo.21842251. The full paper spans approximately 260 pages across two chapters covering philosophy, historiography, mathematical formalization, and empirical econometrics. Equations (9)–(11) and the model specification cited here reproduce that chapter’s notation; gdpar is cited separately as Gómez Julián (2026b).

    Written for the curious. An invitation to read.