The Hourglass: Faye’s Shoe, Our Shoe

Faye bent the left–right line so that the party-state and fascism almost meet. That similarity is real as office, false as theory. He never drew the other pair. Far-left and far-right anarchists also share a lot: they refuse the standing machine, they keep the person as source, and they split on the means of production.

A circle hid Faye’s point. On a clock, 3 and 9 are 180° apart. Horseshoe theory was a claim about proximity. The honest drawing is an hourglass of two horseshoes stacked.

• Wide top: mixed-economy center. The means of production sit mixed — private title and public title sharing the plant.
• Upper waist: party-state ≈ fascism. Stay in Faye’s shoe and the arms pinch here. That is the historical lesson.
• Lower waist: anarchist communism ≈ anarcho-capitalism. They almost touch as anti-office and split on the plant.
• Wide bottom: center libertarianism. The missing bend of our shoe. Opposite mixed. This program’s invention.

Completing Faye’s open horseshoe with that mirror shoe, and seeing the two shoes as one figure, is new. The figure places. It does not tick. Click any system: the card leads with how that system defines the means of production. Two equal warnings sit as sections, not as filters: the Marxist method on Faye’s left arm, the cartel method on Faye’s right arm.

This is a scientific reconstruction of a map, not a manifesto and not a clock. Walking off CenLib does not force a tour through Hitler and Stalin. Walking up from either anarchist horn — taking the office — is the illicit step the other papers already named. That step is the dotted vertical at the waist.

1. Why this shape

The load-bearing claim is proximity. Faye’s pair almost touch because they share the office. Our pair almost touch because they share the anti-office. Mixed sits wide of that pinch; CenLib sits wide of it the other way. The drawing has to make those four facts visible at once.

• A circle puts the two offices at 3 and 9 — 180° apart — and so hides the claim it was supposed to show. Labels also ran off the left of the page; anarcho-capitalism sat on Spooner. A circle is a clock. This is not a clock.
• One horseshoe only has Faye’s pair. It leaves the anarchists with nowhere honest to sit — which was the original puzzle. Anarchists are not the left tip of Faye’s shoe; the party-state is.
• A diamond (mixed at the top, CenLib at the bottom, party-state left, fascism right) repeats the circle’s error whenever the diamond is wide: the offices become the far corners. Pinch the diamond and you have reinvented the hourglass.
• A lemniscate / figure-8 makes the two loops share a point. The shoes do not share a point. The waist is a crossing — take the office, leave our shoe for Faye’s — not an identity.
• An hourglass of two facing horseshoes is the fit. Faye’s own page layout already put “center” at the top and the tips almost meeting below; that is the upper bowl. Mirror it underneath and the anarchist pair pinches as anti-office; CenLib is the wide bottom. The neck is the claim.

Other silhouettes were tried against that list. They failed one of the four facts. The hourglass is not a metaphor we liked; it is the shape that lets the two almost-touches be seen.

2. What horseshoe theory actually claimed

Jean-Pierre Faye, Théorie du récit / Langages totalitaires (1972), then Le Siècle des idéologies (2002). An earlier anticommunist version sits in Eysenck in the 1950s. The claim: the political spectrum is not a line; the extremes bend, so far-left and far-right are closer to each other than to the liberal center. The load-bearing pair is state communism and fascism. What they share is the office: one-party command, the person treated as an organ, terror as method. What they do not share is the property story, the nation/race story, or the 19th-century origin.

This program takes the office-similarity. It refuses Faye’s smear that the theories are the same. Elite theory (Mosca, Pareto, Michels) already explains why popular forms decay into organized minorities without having to equate Marx with Gentile.

Faye’s textbook drawing puts “center” at the top of the page and the tips at the bottom, almost meeting. That is the upper bowl of the hourglass. Mixed at the wide top: the means of production sit mixed. Leave mixed going left and the plant is socialized under an office (Marxist method). Leave mixed going right and private title is kept, the plant is cartelized, then commanded (cartel method). Both arrive at offices so alike they pinch. The lesson of staying in that horseshoe is historical, not a mood: the plant’s title-regime changes in opposite directions; the person as organ does not.

3. Anarchists were never Faye’s left tip

Ordinary speech puts anarchists at the far left of a line, then puts the party-state in the same slot, then wonders why the slot will not hold. Fractures already split the slot: shared 19th-century goal, split method. Applied Marxism staffed an office that did not retire. Anarchists refused that office.

If anarchists sit at a far-left tip, their mirror on the far right is not fascism. It is right-anarchism: anti-office, split on the means of production. Fascism is the mirror of the party-state. Two pairs. One line cannot hold both. Horseshoe “solves” this by putting the two offices at the tips and leaving the anarchists with nowhere honest to sit.

The fix is the lower bowl. Our shoe — this program’s addition, not Faye’s. Anarchist communism and anarcho-capitalism almost touch at the lower waist as anti-office. They split on the plant. CenLib is the wide bottom that joins them without taking the office. Completing his open horseshoe with that mirror, and seeing the two shoes as one figure, is the invention.

4. The other shoe is ours, and why the anarchists share a lot

Left anarchists (Déjacque, Bakunin, Kropotkin; Proudhon’s possession as a neighbor) and right anarchists (Molinari, Warren, Spooner, Tucker, then Rothbard’s named school) share:

• Refusal of a standing public machine beside society.
• The person as the unit that is not an organ of party, Volk, or ticker-as-state.
• Exit and association rather than a night of proprietors as the preferred grammar (with bloody exceptions this paper will not wash out).

They split on the means of production. Occupancy-and-use and the four monopolies versus homesteading of a firm that hires hundreds. That split is the program’s proposition: the conflict is over property. CenLib is the attempt to join them at that joint — keep the Lockean person, refuse title through the scaled firm, change species at hired-labor scale.

Pure Marxism’s stated goal sits on this shoe, not on Faye’s. Classless association of producers; common ownership of the means of production; Engels’s bronze axe. The party-state is the method that did not arrive — the dictatorship of the proletariat that did not wither. Placing “communism” only at Faye’s left pinch is the red-scare capture Fractures already dated.

5. What sits at the two anarchist sides of CenLib

Our left arm, from CenLib toward anarchist communism. That is the file Fractures already named as method, plus the American individualists Rothbard later claimed.

• Agorism (Konkin, 1980) sits first. New Libertarian Manifesto; Movement of the Libertarian Left. Left free markets. The agora is the goal; counter-economics the means; consistency of ends and means; no party road. Capital-statism — the class that takes a net gain from the State’s intervention — is the enemy, not the entrepreneur. Worker/boss is a feudal holdover; the corporate hierarchy imitates the State, not the Market. He sat historically next to Rothbard and then named the Left. He is not a fork inside Rothbard’s tent. CenLib takes the method from that left-market file.
• Benjamin Tucker, Liberty (1881–1908): occupancy-and-use of the means of production; four monopolies (money, land, tariffs, patents). He called the position anarchistic socialism. Free markets to destroy capitalist privilege. Left-market, next to agorism. Rothbard later claimed the names and dropped the four monopolies (“The Spooner-Tucker Doctrine: An Economist’s View,” 1965). That is a documented capture, the cousin of Russell 1955.
• Josiah Warren (Time Store 1827; Equitable Commerce 1846): first American anarchist; cost the limit of price; profit as cannibalism. Individualist and anti-usury. Left-market ancestor, not Rothbard’s horn.
• Carson / C4SS (2007 ff.): Tucker recovered under subjective value. Left-wing market anarchism. Sits with agorism, not with the outer horn.
• Then Proudhon, Bakunin, Marxism’s stated goal, anarchist communism. Still anti-office. The illicit step is the walk up the waist: seize the office as method → socialize the means of production under a dictatorship of the proletariat → in practice, party-state.

Our right arm, from CenLib toward anarcho-capitalism. The file is Foundations of the Right. Compressed so the map can be attacked:

• Lysander Spooner, No Treason (1867): the Constitution binds no one who did not sign. Claimed by both tents. Occupancy sits closer to Proudhon than to joint-stock. On the figure he is a neighbor of CenLib, not a second ancap label.
• Gustave de Molinari, “De la production de la sécurité” (Journal des Économistes, February 1849): first systematic case that police and defense can be produced on a market. The European economic tip. He said liberty of government, not “anarcho-capitalism.”
• Auberon Herbert, 1890s: voluntaryism. Spencerian; refused the anarchist label.
• Rothbard (1962–82) names anarcho-capitalism: proviso dropped, NAP, joint-stock as end-state. Private title in the means of production through the scaled firm, no standing office. The outer horn of our right arm.
• Tannehills (1970) and David Friedman, The Machinery of Freedom (1973): other houses on that horn. Friedman is consequentialist, not natural-rights. Do not flatten with Milton.
• Hoppe (2001): a walk up from the horn toward Faye’s office (covenant communities). Date the fork. A covenant that becomes blood-and-soil has left our shoe.

Agorism is not in the right-anarchist span. On the hourglass he sits on our left arm.

“National-anarchism” is a captured word. It sits on the walk-up toward Faye’s right tip, not at our tip. Placed so it cannot steal the horn.

Anarcho-capitalism is the named 20th-century outer point of the right span of our shoe. It is not the whole anti-office shoe, and it is not agorism. Occupancy and the four monopolies already refuse absentee dominion — that is why Tucker and Warren sit with left free markets, not at Rothbard’s horn.

6. The Marxist method (a section, not a filter)

Faye’s left arm is not a single point called “communism.” Leave mixed-economy center going left and two walks sit on that arm. The board does not force this series onto every selection. It is a historical lesson, dated here and in Fractures. Each system’s card still leads with how that system defines the means of production, then with the historical lesson of that seat.

Parliamentary walk. Social democracy, then democratic socialism. More of the means of production is socialized; the office stays representative. This is the office relaxing from the pinch toward mixed, and also the electoral road toward more socialization. It is not the Marxist method.

Marxist method, a series of steps.

1. Leave mixed. Private and public title in the means of production; a representative office.
2. Socialize the means of production. The Manifesto’s first economic move: abolish bourgeois property in the plant, not in coats. War Communism (1918–21) is the applied form.
3. Dictatorship of the proletariat. Class Struggles in France (1850); letter to Weydemeyer (5 March 1852); Gotha (1875). Stated as a stepping stone. On the theory, the state withers from here.4
4. Intended landing: common ownership of the means of production; classless association of producers; Engels’s bronze axe. That seat is on our shoe, with the left anarchists, not at Faye’s pinch.
5. Applied landing: the office did not retire. Party-state, pinched against fascism as office.

The dictatorship and the party-state are not synonyms. One is the named step. The other is where the step stuck. The goal and the method are different seats. Date both or produce a fake disagreement.

7. The cartel method (the equal warning)

Faye’s right arm is not a single point called “fascism,” and it is not “applied anarcho-capitalism.” Leave mixed-economy center going right and two walks sit on that arm. Conservatism, classical liberalism, minarchism, neoliberal practice are parliamentary cousins — more private title, a standing office, not this series. The board does not force the series onto every selection. It is a historical lesson, equal in status to the Marxist method on the left.

What happens to the means of production. Title is kept. The plant is organized. Then the office commands it. That is the right-hand change of species. The left-hand change of species is the opposite move on title: socialize the plant, then staff a transitional office. Both thicken the office. Both pinch.

Cartel method, a series of steps.

1. Leave mixed. Private and public title in the means of production; a representative office.
2. Cartelize the means of production. Hilferding, Das Finanzkapital (1910): finance capital organizes the plant into cartels and trusts; competition among residual claimants is already suspended in peace. Wartime Wirtschaft (1914–18) made it policy. Germany’s Law for Compulsory Cartels (15 July 1933) is the applied form. The office does not own the plant. It has a counterpart that can be commanded.5
3. Corporatist command. Carta del Lavoro (21 April 1927): syndicates of employers and workers as organs of the state; production directed without abolishing title. Gentile’s ethical state; Mussolini’s 1932 doctrine. The plant serves the nation. The person is becoming an organ. This is the political step — analogue of the dictatorship of the proletariat, not its synonym.6
4. Applied landing: fascism. Cartel plus state. Title on paper, command in practice. There is no bronze-axe landing on this arm. The named destination was the nation as ethical state — which is the pinch against the party-state as office.

Where cartel theory sits. On Faye’s right arm, as this series. Not at the party-state (that is socialized title, unsocialized command). Not at anarcho-capitalism (that is anti-office). Dimitrov (1935) named fascism “the open terrorist dictatorship of the most reactionary… elements of finance capital.” That is a Marxist reading of this arm, and it is the smear that collapses Faye’s pair into one theory. This program takes the economic description — the plant organized, title kept — and refuses the collapse. Same office, different title-regime.

“Cartel theory” is not Katz and Mair’s cartel party (parties as a state-financed cartel). That is a later, different file. It is not on this figure.

8. Two illicit steps, not a clock

An hourglass whose path says “leave CenLib and you go through the two offices back to mixed” is the same geometry error a 1D loop made. Adjacency at the waist is a warning, not a law of return. The dotted verticals are the illicit step: take the office, and you have left our shoe for Faye’s.

The real walks:

• Off CenLib, along our left arm: agorism first, then Tucker, Warren, Carson, Proudhon, Bakunin, anarchist communism, Marx’s goal. Still anti-office. The illicit step is the walk up: seize the office as method → socialize the means of production under a dictatorship of the proletariat → in practice, party-state. That is Fractures. From the party-state the office relaxes toward mixed: democratic socialism, then social democracy.
• Off CenLib, along our right arm: Spooner, Rothbard’s horn, Molinari, then a walk up (Hoppe, minarchism, a pole’s mix). Still anti-office until the walk up. The illicit step is title through the scaled firm as a legislature, then a pole spending that mix. Fascism is not “applied ancap.” It is the landing of the cartel method: organize the plant, fuse the office to the syndicate. Pinochet is the right-hand state version that actually exists — markets as a tool of the junta, not the 1927 Carta.

Polybius’s anacyclosis is already in the corpus as a warning against treating a cycle as a clock. This map is a placement, not a law of return.

9. Why CenLib is opposite mixed-economy center

Ordinary “center” = representative office + mixed property + elite capture. Center already refused Nolan. The name is the join of the two dated libertarianisms at the means of production, not Keynes-plus-markets.

On this map that claim is visible: mixed-economy center is the wide top of Faye’s shoe; CenLib is the wide bottom of our shoe. They sit on the same property midline and at opposite ends of the office axis. Leave mixed along Faye and you climb toward the two offices that pinch. Leave CenLib along our shoe and you stay with the person as source until someone takes the office.

Neighbors of the join, not the join: analytic left-libertarianism (Steiner, Vallentyne, Otsuka — Cohen’s split as a school, often still a state for the equal share); distributism (Belloc, Chesterton — small owners against both offices); Georgism (land as common, a tax office). Taken as cousins on property. Not the stack.

10. What is not on this figure

Game of Empires is another axis. A unipole can sit on any domestic square. A pole can refuse Ostrom 7 from outside. Putting polarity on the hourglass would collapse the lock Synthesis exists to keep visible.

Nolan’s chart (economic freedom vs personal freedom) is not this map. The axes here are the means of production at scale and the office. “Freedom” as a mood does not place Tucker and Rothbard in different seats, and they must sit in different seats.

A finished constitution is not on this figure. Open problems 8, 9, 10, 15, 33 stay open. Placement is not a proof that the stack works.

11. Pressure tests

• “This is just Faye, flipped.” Faye’s pair is kept as office-similarity, drawn so they almost touch. The anarchist pair is the file he did not draw. CenLib is the bend of that file, not a stitch between Hitler and Stalin. Completing his open horseshoe with our mirror shoe is the invention.
• *“Anarcho-capitalism is the far right, so fascism is next.” Only on a line. On this figure they split on the office; the next seat up* from ancap is a walk toward Faye (Hoppe, junta-markets). Fascism is a different species. National-anarchism is the captured word that tries to steal the horn.
• “Tucker is ancap.” He called himself a socialist, targeted the four monopolies, and sat on occupancy. Rothbard’s 1965 essay is the capture. Inner ≠ outer.
• “Marx belongs at the party-state.” His stated goal does not. Method does. The method is a series of steps, in a section, not forced onto every selection. Date the steps or produce a fake disagreement.
• “Social democracy is the Marxist method.” It is the parliamentary walk on the same arm. Mixed title in the means of production plus a welfare office is not socialization of the plant under a dictatorship.
• “Neoliberalism is the cartel method.” It is the parliamentary cousin on the right arm. Pole-enforced private title is not a compulsory syndicate. Date Hilferding and the Carta, or produce a fake disagreement.
• “Cartel theory sits at the party-state.” That is Dimitrov collapsing the two pinches. Socialized title, unsocialized command is the left pinch. Cartelized title, commanded plant is the right pinch. Same office, different title-regime.
• “Leaving CenLib is a slide into anarchy, then into tyranny.” That is Polybius as a clock, and a 1D loop. The stack’s method is a named hybrid that refuses the office as the organ of getting there. The walk up is a choice, not a tick.
• “Why not a circle / a diamond / one shoe?” Section 1. A circle hides proximity; a diamond that is wide does the same; one shoe has no seat for the anarchists; a figure-8 makes the crossing an identity. The hourglass is the shape that lets both almost-touches be seen.
• “The map is the hypothesis.” It is not. Game of Empires and CenLib remain the two hypotheses. This page is where CenLib sits among the systems those papers already named, and where Faye’s lesson about the means of production is finally visible as proximity.

12. The ecological reading (same seats, not a third axis)

The hourglass is office × property. Smash a third axis onto it and the pinches hide again. The honest second figure is a line: mutual aid at one end, struggle at the other, the join in the middle. Every seat on the hourglass sits on that line. Click either figure; the card leads with the means of production, then with how that system pictures agents in a limited-resource environment.

Economic models stem from biological pictures of those agents. They boil down to competitive or cooperative systems. Competition & Mutual Aid is the warrant paper: fitness unrepaired, inheritance unrepaired, Darwin not a neo-Darwinist, Kropotkin against Huxley, Denis and Raymond Noble against gene-centrism as a privileged level. The insight this map now has to show: the models look irreconcilable because those definitions are not closed. Society is proof of cooperation. A garden is proof. Two apples, or an orchard. Scarcity can be fought over or planted past. Nature, seen fully, is both. We do not yet have the biological clarity to pick the economic model that should then reflect the best outcome. Equilibria is why the game you write down is the same fight: PD is the two apples; stag hunt is the orchard; hawk–dove is struggle as a strategy.

Fascism is survival of the fittest at all levels. Race, nation, person as organ of the Volk. Struggle as law. It sits at the struggle pole. That is not “applied anarcho-capitalism.” Ancap is competitive title, voluntary, anti-office. Fascism is hawk as policy.

The party-state argues cooperation. Class solidarity, socialized plant, from each according to ability. It sits on the cooperative side of the join because that is the argument. It pinches against fascism as office, not as ecology. The stated goal — common ownership, bronze axe — sits on our shoe, with anarchist communism. A garden staffed by a ministry is not Kropotkin’s mutual aid. That is the fracture, visible on two figures at once.

CenLib is the attempted bridge on this reading too. Personal title stays. The hired-labor plant is the orchard the occupants work. Neither costume as proof. Mixed-economy center is the other mixed ecology, with an office. Opposite on the hourglass; neighbors on the spectrum. The difference is who gardens, and whether a standing machine gardens for them.

The ecological filter recolors the hourglass by that reading. The spectrum under the roster is the same seats on a line. Placement is an argument. Open problem 40 wants a codebook so the line is not only a drawing.