We read it against our axiomatic monetary theory (MoMaT). Where Snoyman argues normatively and theologically, we argue formally and institutionally — and the structural parallels run deeper than the difference in idiom suggests.

Michael's framework in brief​

At the root sits ratzon lekabel — the desire to receive. Creation, on this reading, is built from want, and the spiritual task is to move toward giving. That is hard precisely because receiving is where everyone starts.

Michael grades this into four levels (action × intent):

From there he diagnoses three macro systems:

1. Violence — receiving-to-receive. Theft, conquest, slavery. Destructive; few defend it openly today.
2. Free markets (idealised) — giving-to-receive. Voluntary exchange, full information, fair courts, hard money. Productive, but cannot by itself produce selflessness.
3. Socialism — aims at giving-to-give, but in practice reverts to receiving-to-receive under coercion: forced transfer is still taking.

His conclusion: selflessness cannot be imposed at gunpoint. Let selfishness run the macro engine, and cultivate giving in the micro — family, close community. He closes by likening the Kabbalistic masach (the screen that defers immediate gratification) to low time preference, and warns that inflation pushes the other way.

Capitalism in MoMaT: the A–R–G core​

MoMaT does not define capitalism by ideology or morality. Its core functionality is A–R–G — three coupled forms of sharing (German: Arbeit, Risiko, Gewinn):

A (labour sharing): No household produces everything it consumes. Work is specialised, and coordination runs through contracts, wages, and the credit that pre-finances production before any sale returns.

R (risk sharing): Risk never disappears — it is absorbed up a hierarchy. Workers and suppliers prefer stable income and pass production risk to entrepreneurs; entrepreneurs pass credit and liquidity risk to banks; banks pass systemic risk to the central bank. Interest is the insurance premium for that absorption, not a rent on idle metal.

G (profit sharing): Profit appears only when invested production meets real demand and closes the cycle. In the market reading it is the return to those who pre-financed and bore the risk — a risk premium, not evidence of exploitation. But profit is more than a risk reward: it is a share of the common product created by the division of labour, and how that share is cut is a separate, explicit institutional choice.

And here MoMaT makes a claim we do not make lightly. For the first time, profit sharing has an explicit algebraic handle — not only as the reward for risk absorption inside a firm or up the banking hierarchy, but as a calculable share of the common product of shared labour. The accounting layer is built as the coproduct of three Lawvere theories, T_DEB + T_Val + T_QEB: double-entry debit/credit (T_DEB), mark-to-market valuation (T_Val, quantity × price), and the bilateral quadruple-entry bookings (T_QEB). Crucially, equity splits as EK = FE + RE: Financial Equity, a model of T_DEB that stays invariant under any change of valuation (the gauge invariance of the books), and Real Equity, a model of T_Val that depends on the chosen valuation functor.

Distribution lives entirely in the valuation theory and is orthogonal to the settlement invariants. That is what makes the old "dividing the cake" problem — the socialist and Marxian question of sharing the social product, GDP — a well-posed, computable object rather than a slogan. Different valuation regimes (historic cost, fair value, market prices, even plan prices) are different models of the same theory T_Val; each is a different cut of the same cake without enlarging or shrinking it. The GDP split itself is an aggregation–disaggregation adjunction (Σ ⊣ Π) with an explicit distribution vector whose shares sum to one. So the classical dream of sharing the common product is expressible in MoMaT: as an explicit, auditable valuation choice on books that balance under any gauge. MoMaT does not decree the split — it makes the split calculable, bookable, and open to institutional design. (Worked out in the distribution chapter of the monograph.)

Capitalism, on this reading, is the machinery that makes A–R–G composable, bookable, and learnable — from a household ledger to central-bank settlement. Markets are one expression of it: voluntary exchange as giving to receive, routed through typed debt and accounting invariants.

The capitalist cycle as hylomorphism​

What ties A–R–G together over time is a hylomorphism — the composition of an unfold and a fold. In the semantics of programming languages and category theory (familiar ground for Michael's Haskell readers):

Unfold (coalgebra / anamorphism). A coalgebra γ sends a current state S to a one-step extension F S — a possible next shape. Iterating γ unfolds a tree of futures. In MoMaT this is credit-financed investment: from today's balance sheet, contracts and credit entail wages, inputs, production steps, and payment obligations branching forward in time. Production stays speculative until it is tested. Marx's G → W → P (money → commodities → production) lives on this side.

Fold (algebra / catamorphism). An algebra α sends a composite F A back to a result A — it collapses structure into a value. In MoMaT this is demand and settlement: sales revenue, profit or loss, debt repayment, and cash settlement fold the production tree back onto the books. Marx's W' → G' (realised commodities → more money) closes the arc. Demand validates investment — ex post, never by decree.

Hylomorphism h = (α) ∘ ⟨γ⟩ is the full loop: unfold a promise into the future, then fold reality back onto it. Failed validation writes off (the fold returns a loss); successful validation closes the books and funds the next unfold. That is how the system learns, cycle by cycle. The wage is paid before the sale (unfold); the sale decides whether the unfold was justified (fold). Risk sharing (R) lives between the two phases; profit sharing (G) is the reward of a successful fold.

Michael's masach — deferring immediate receiving — has a structural echo here: the unfold defers gratification, the fold defers judgment until demand speaks. But MoMaT reads this as mechanics, not moral psychology. It is the typed chronomorphism of a credit economy: promises into the future, validated when settlement arrives.

MoMaT top-level structure: AccCat, DecCat, GovCat​

Above A–R–G and the hylomorphism sits MoMaT's top-level architecture — three coupled categories that share one topos (a single institutional world, not three siloed tools). The triangle below is the canonical MoMaT picture; Magic Sauce shows how it is glued together from local open games. Related research maps it onto Ostrom's three institutional layers, and the engine preview renders the same stack as an interactive 3D scene.

The global Topos triangle — Governance, Decisions, Accounting (GovCat / DecCat / AccCat) — coupled by three adjunctions. Local open games compose along their interfaces to build this institutional geometry; see Magic Sauce for the full picture.

AccCat is the substrate. Quadruple entry and cash as terminal settlement are not optional add-ons to price theory — they are the coordinate system every behavioural theory has to pass through. Nothing in DecCat or GovCat can override arithmetic.

DecCat is the field of play. Firms, banks, and households act as compositional open games — locally egoistic lenses (Smith's bakers and butchers) that learn from forecast errors via Sim ⊣ Est against the realised accounts in AccCat.

GovCat is the rule layer. Loan, wage, and settlement contracts type which games and postings are allowed to run at all. Institutions learn over their rules through Constrain ⊣ MechDesign with DecCat — mechanism design meeting constitutional constraint.

Two adjunctions — and the third they imply​

The triangle carries two genuine learning loops, one fast and one slow. The third edge — GovCat ↔ AccCat — is not a third loop but their composition: the round trip that makes audit well defined.

Top-down (Push): Gov → Dec → Acc. A rule becomes a decision, a decision becomes a booking — each step adds detail (covenant → journal entry). Bottom-up (Pull): Acc → Dec → Gov. Books roll up into decisions and then into a governance verdict — each step summarises and drops detail. DecCat sits inside; GovCat and AccCat face the boundary — contracts on one side, cash and balances on the other.

The GovCat ↔ AccCat edge is that same chain read as a single arc:

1. Down: contracts mandate what must be booked — what the rule layer requires to appear in the ledger.
2. Up: the books reveal whether compliance was achieved — and here the audit gap is measured.

That gap — what contracts require booked versus what is booked — surfaces only on this Gov–Acc round trip. It is the core audit quantity, and it decomposes into two causes:

• Wrong execution (right rules, wrong decisions) → fix the operational loop (Dec ↔ Acc).
• Wrong rules (rules that cannot be executed, or no longer fit reality) → fix the systemic loop (Gov ↔ Dec).

One number, two causes. Audit is then not a separate department sampling vouchers after the fact; it is the composed adjunction pointing to where the institution must learn next. It also settles what data to gather between governance and accounting: not everything twice, but the mandated booking set (from Gov, pushed down) against the realised posting set (from Acc, pulled up), with DecCat as the channel where execution variance shows up.

Michael's macro/micro split has a direct homologue: selfish play in DecCat, rule-bound settlement in AccCat, admissibility in GovCat. His worry about coercion is a GovCat pathology — forced identification of agents, rules that cannot glue local action to global demand. His idealised market is a DecCat achievement under GovCat rules (voluntary contract, fair courts), with outcomes booked in AccCat — and the audit loop is where you see whether the three still compose.

Elinor Ostrom's constitutional / collective-choice / operational stack is the same trinity under another name — see the table in Related research. Compositionality across the three layers is exactly what lets polycentric governance work without a single planner.

Where MoMaT agrees​

Want as the starting point​

Michael's ratzon lekabel matches our core dynamic once you strip the theology: agents want, scarcity persists, and demand validates investment. The capitalist cycle is the hylomorphism above — credit and contracts unfold (coalgebra), sales and settlement fold (algebra). Failed validation writes off; successful validation closes the books and funds the next cycle. Want is not a moral defect but the driver the institutional geometry has to absorb.

Free markets as "giving to receive"​

Michael's idealised market — no coercion, voluntary trade, honest information — maps cleanly onto the A–R–G core: labour is specialised (A), risk is borne by those who pre-finance (R), and profit rewards validated production (G). His apple seller and our baker are the same figure: the act is giving, the intent stays self-interested, and the system channels that interest productively through the A–R–G machinery.

We say the same in categorical language: Smith's invisible hand as local egoistic lenses in DecCat, and capitalism as a decentralised macro-learning system — agents update from forecast errors while institutions adapt on two levels, within rules and over rules in GovCat.

Selfishness is channelled, not abolished​

Michael is explicit: charity and volunteering in market societies are rarely "pure" in the Kabbalistic sense — status, tax relief, and feeling good all count. Markets do not try to eliminate selfishness; they redirect it.

MoMaT does not moralise this away either. The three-category stack replaces intent-typing altogether: AccCat asks whether the books balance, DecCat models what agents do strategically, GovCat holds the rules. The question is never purity of intent but whether demand validates investment and who bears which risk in the hierarchy (firm → bank → central bank).

Socialism: right goal, wrong mechanism​

This is the strongest overlap.

Michael argues that socialism aims at giving-to-give but delivers receiving-to-receive: people "give" at gunpoint. Scarcity remains, "need" stays undefinable, production incentives weaken, and status competition simply moves to non-monetary channels.

We reach the same conclusion structurally rather than mystically. Central planning fails as a knowledge and coherence problem — Hayek's point, which in our framework is a sheaf pathology: local information does not glue into a global plan. When a central organ cannot see real demand, even well-intentioned intervention misallocates — the historical "ton ideology," where the plan counts tons instead of useful nails. Central-bank liquidity is necessary but never sufficient; production must still find real demand. Forced identification of agents in the macro game is the categorical counterpart to Michael's coercion diagnosis.

Capitalism is not intrinsically evil​

Michael does not demonise markets. They are productive but, in his framing, do not fulfil "the purpose of Creation."

We push further toward demoralisation: capitalism is the A–R–G system — labour, risk, and profit sharing made explicit in the books. Exploitative systems are built by people, not by the mathematics of accounting. Distribution (G) and stability (R, settlement) are orthogonal in MoMaT: once quadruple entry and gauge invariance are in place, the split of the common product becomes an explicit, computable valuation choice — the dividing-the-cake question made well-posed — rather than something smuggled inside a single word, "money."

Where MoMaT diverges​

Hard money​

Michael's ideal market assumes hard money — money that privileged parties cannot create cheaply. He ties the masach to low time preference and faults inflation for pushing toward immediate consumption.

We argue the opposite on structural grounds. Gold- and scarcity-backed regimes live in a finite initial algebra: reserves deplete and stabilisation turns brittle (gold-depletes in our stability proofs). Fiat systems, by contrast, are a final coalgebra of the central bank: liquidity can be emitted to meet settlement need — the institutional reading of "whatever it takes." We share Michael's worry about privileged cheap money creation; our answer is institutionalised central-bank elasticity under accounting invariants, not a retreat to commodity scarcity as the stability anchor.

Interest is not time preference​

Michael treats saving as low time preference — deferring consumption, "giving to your future self."

In MoMaT, interest is not time preference. Interest payments are insurance premia for risk absorption along the hierarchy: firms pay banks for portfolio and liquidity risk, banks pay the central bank for lender-of-last-resort insurance. Deferral (Verzicht) does appear — but in the hylomorphism (invest now, validate later), not as a psychological screen laid over desire.

Inflation​

Michael treats inflation as something that discourages holding cash and encourages near-term consumption.

We treat it primarily as a valuation phenomenon — input prices, wages, resources — read through the valuation algebra, not as a purely monetary phenomenon in the Friedman sense. Central banks do not "control inflation" by rationing reserves alone; taking every price movement for a liquidity problem is itself a category error.

Moral intent vs typing​

Michael's four levels are ethical: action and intent, pure and mixed motivation.

MoMaT replaces that grid with typing: giral money, reserves, and cash (G → R → C); claims versus terminal settlement; quadruple entry across paired double-entry systems. Charity may be impure in Michael's sense — for us the only diagnostic is whether the catamorphism of demand validates the anamorphism of investment, and whether the institution learns from the result.

Teleology​

Michael's telos is selflessness and affinity with the divine. Ours is Oikos: continuity, learning, institutional coherence — Aristotle's household law made reflexive through accounting. The guiding motif of our program is a place where want and reality speak the same language, reached when dreams have become bookable — validation through demand and balance sheets, not refinement of the soul.

Charity is a public good — the missing Ostrom step​

This is where we think Michael's argument takes a wrong turn — and where MoMaT quietly supplies what he is reaching for.

Michael wants giving-to-give: charity, selflessness, care beyond self-interest. In the language of economics that is not a private good traded in a market — it is a public good, non-rival, hard to exclude, and chronically under-provided by self-interested exchange. His own framing half-concedes it: markets are the macro engine for selfishness, while giving has to be cultivated separately in the micro.

Yet he still asks the free market to carry giving — "giving to receive." That is precisely the step an economist would not take. Markets allocate private goods well and provide public ones poorly; the free-rider problem is not a moral failing but the incentive geometry. Pure market dynamics under-provide charity for the same reason they under-provide clean air or flood defence.

The economist's answer to public goods is neither "let the market do it" nor "let the state command it." It is Elinor Ostrom's answer: polycentric governance — many overlapping centres of authority, local rules that compose, with neither a single market price nor a single planner in charge. Ostrom showed empirically that commons and shared provision are sustained this way, in the space between market and state.

And Ostrom's institutional stack is already MoMaT's stack:

This is not an analogy imposed after the fact; it is the same three-layer geometry — governance, strategic decision, operational accounting — that A–R–G and the audit loop already run on. See the mapping in Related research.

So the argument closes on itself. Polycentrism is what actually delivers Michael's charity — public-good provision between market and state. But polycentrism only works if the three layers compose: overlapping jurisdictions are coherent only when GovCat, DecCat, and AccCat glue level by level (household → association → municipality → state), and only when the same stack carries both private market production and public-good production on one set of books. That compositionality is exactly what MoMaT provides — the sheaf-gluing of local open games into a global institution, shown in Magic Sauce.

Read this way, MoMaT does what Michael wants — but by the route he rules out. Giving-to-give is not something free markets secrete as a by-product; it is a public good that has to be institutionally engineered, and the engineering is polycentric composition of exactly the governance / decision / accounting layers MoMaT makes formal. His telos survives; only the mechanism changes — from "the market will provide" to "compose the institutions that provide."

One sentence each​

Michael: Markets are the right macro engine for selfishness; selflessness is micro-work; state coercion perverts the goal.

MoMaT: Agreed on the engine — but it runs on typed debt-accounting with a fiat liquidity coalgebra, not hard money, and giving-to-give is a public good, delivered by Ostrom-style polycentric composition of governance, decision, and accounting rather than secreted by markets; the decisive question stays whether demand validates investment and whether institutions learn.

Understand it first, then use it for good​

There is a bigger point underneath all of this. Capitalism is one of the great achievements of humanity — a sophisticated machine for sharing labour, risk, and profit at planetary scale, learning cycle by cycle from whether demand validates investment. Treating it as intrinsically evil is as unserious as treating it as automatically just. Both moves skip the only step that matters: understanding what the machine actually is.

Most of the disappointment with markets comes from asking them to deliver what markets structurally cannot — public goods, charity, kindness, the giving-to-give that Michael rightly prizes. Markets are magnificent at allocating private goods and hopeless at provisioning public ones; blaming them for the second is like blaming a ledger for not being a prayer. Stop bashing capitalism for failing at a job it was never the right tool for, and a different possibility opens up: keep the engine for what it does superbly, and compose it — polycentrically, à la Ostrom — with institutions that provide what markets cannot.

That is the whole point of MoMaT. First understand capitalism precisely — not as sin and not as salvation, but as a typed, bookable, learnable architecture of labour, risk, and profit sharing, with distribution a computable choice rather than a hidden fate. Then, on that understanding, design it for the purposes we actually want it to serve. Once the books balance under any valuation gauge, once the three layers compose, once distribution is an explicit dial rather than a buried assumption, kindness and charity stop being sentiments we hope survive the market and become institutions we can engineer on the same foundations. Understand the achievement first; then use it for good. MoMaT is built to do exactly that.

Further reading​

• Michael Snoyman — Kabbalah and Economics
• OiC.OS — Magic Sauce — Topos triangle and local open games (the TikZ figure above)
• OiC.OS — Engine preview — interactive 3D view of the same three layers
• OiC.OS — Money Theory — shortest summary of the axiomatic framework
• OiC.OS — Technology — three layers for CFOs and treasurers
• OiC.OS — Related research — Ostrom ↔ GovCat / DecCat / AccCat
• OiC.OS — MoMaT — the research program and open questions
• OiC.OS — Axiomatik der Ökonomik (PDF) — working draft of the German monograph

Comments and collaboration: contact@oicos.systems.

Our answer is now online as a working draft (PDF): Axiomatik der Ökonomik — Von Schuld- und Erfüllungsverträgen mit Geld, Zinsen und Lernen zum Topos der Wirtschaftspolitik. Citation: MoMaT-A.

This is the German monograph of the MoMaT program — Monetary Macro Accounting Theory. It builds on forty years of Renée Menéndez's work on credit-money capitalism, work by Viktor Winschel since 1996 on monetary theory, compositional game theory, and categorical semantics, and about a decade of joint development since 2018.

The idea in one sentence​

Accounting is not an appendix to price theory. Double and quadruple entry, gauge invariance, and the three languages AccCat (accounting), DecCat (decisions), and GovCat (governance) are the geometry in which economic behaviour must live — from a household ledger to central-bank settlement.

Ten structural results​

1. A universal economic space. The axiomatics defines a minimal space — analogous to a Riemannian manifold — through which every behavioural theory must factor. Consistency of the books is not one constraint among others; it is the coordinate system of economics.

2. Noether's theorem of accounting. From symmetry follows invariance. At the micro level every entry balances: debtor and creditor T-accounts must match across quadruple entry (QEB) over paired double-entry (DEB) systems. Aggregated to the macro level, the same law says that the world as a whole is not indebted: the sum of all claims equals the sum of all obligations, because every claim is someone else's liability. There are no net financial positions in a closed economy.

3. Gauge invariance. A gauge structure formalises coordinate and unit independence — the freedom to re-express accounts in another currency or valuation without changing their economic content. This is where Hellwig's type error becomes visible: "euro" and "unit" are not strings but objects of different types.

4. Profit and earnings sharing. With gauge invariance and quadruple entry in place, a division of profit and of results appears as coherent institutional design — not as an afterthought bolted onto marginal productivity.

5. Distribution becomes discussable — on a firm footing. Only after QEB, gauge invariance, and the accounting Noether theorem are established can distribution questions be posed rigorously: wages, profit, risk premia, product shares. The framework separates what the books require from any particular distributional ideology.

6. Three types of money and the absorption hierarchy. Money is not homogeneous. Typed as giral (book) money, reserves, and cash (G → R → C), it reveals the risk-absorption ladder of the economy: firms absorb risk first through retained earnings, then commercial banks, then the central bank as lender of last resort.

7. Endogenous interest. The interest rate is endogenous — a risk-insurance premium, not a policy dial and not a rent on idle gold. Interest bans and "money breeding money" without production become empty categories in this geometry.

8. Fiat money is inherently stable. Money backed by institutional invariants is not merely "more stable than gold" — it is stable by construction, through quadruple-entry closure. Commodity money carries no such guarantee. Stability is an institutional invariant, not a scarcity of metal.

9. Cash as terminal settlement. In the axiomatics there is no untyped "money". Cash (C) is the terminal object — the settlement standard that discharges debt relations. Clearing and settlement are primary; exchange is secondary. A barter market with a Walrasian auctioneer has nothing to settle.

10. Financial and real endowment together drive the dynamics. Neoclassical equilibrium theory lets the real endowment alone determine outcomes. Here the cycle is generated by financial and real endowment together: there is no production without prior financial endowment — credit, contracts, booking. The dynamics is a hylomorphism. Investment unfolds (a coalgebra: it opens a tree of production, credit, and contracts into the future); demand and settlement fold it back (an algebra: revenue, profit, or loss). Demand validates investment, ex post. Failed validation writes off and constrains the next cycle; successful validation closes the books and funds the next unfold. That loop is how the system learns — cycle by cycle — and why market economies, for all their faults, remain the most adaptive institutional setup humanity has built: they let promises be made into the future, test them against reality, book the result, and begin again.

Where to read next​

• MoMaT-A — References — citation key and PDF
• Money Theory — shortest summary of the framework
• MoMaT — title pages and the fourteen open questions the program answers
• Announcement on LinkedIn — the ten results in short form (German)

Comments and collaboration: contact@oicos.systems.

The page is available in two formats:

• Podcast — listen to the full speech on the page (English audio)
• Slide deck (PDF) — the presentation as a downloadable deck

Why this matters​

Classical interest compensates the lender in a rigid way, largely independent of whether the financed project succeeds or fails. That mismatch shows up again and again in history — in debt crises, in shifts of regime when policy rates move, and in the social cost of guaranteed returns on money while borrowers carry the downside alone.

Our axiomatic money theory starts from quadruple-entry invariance and cash as the terminal object of debt relations. Monetary Architecture asks what a financial order would look like if risk were shared explicitly — through pools and success-dependent mechanisms rather than a one-sided interest contract.

The new page is the bridge: theory on one side, four millennia of institutional experience on the other, and a concrete proposal for a more stable architecture in between.

Endogenous interest and the central bank​

The historical experience over the centuries is consistent with our finding of an endogenous interest-rate theory. The central bank's task is not to artificially restrict liquidity provision as an unjustified lever for steering the business cycle. Liquidity should follow the needs of the contracts to be cleared and then settled — that is, the demand for cash as the terminal means of performance.

In our framework the interest rate is endogenously derivable. It is not a policy dial for macroeconomic fine-tuning; it is a measure of risk. Lending rates are insurance premia on investment — compensation for bearing uncertainty that is realised through write-offs in a pool, not a guaranteed rent on money regardless of outcome. Deposits are insured on the same logic: the system mutualises loss, rather than pretending that fixed nominal returns can be promised without regard to solvency.

Central banks should therefore stop acting as if they controlled inflation and the cycle by rationing reserves and chasing a single policy rate. They do not control inflation in the Friedman sense. Inflation is not a purely monetary phenomenon. It is driven by input prices — labour wages, resources, and real estate — reflected through the valuation algebra of a labour- and risk-divided economy. Monetary policy that treats every price movement as a liquidity problem misidentifies the mechanism and invites the overreach we have lived through in one interest-rate regime after another.

The historical slide through regimes — and the podcast on Monetary Architecture — makes that visible in plain language. The theory in Money Theory states the structure; the new page shows why a different architecture follows from it.

Links​

• Monetary Architecture — full text, audio player, and context
• Money Theory — shortest summary of the axiomatic framework
• Slide deck (PDF) — presentation download

We are building the community around compositional finance and the OiC.OS engine — liquidity pools, supply-chain finance, and organisational forms. GITEX is a great place to meet partners, projects, and investors who want to work on one engine instead of reinventing reconciliation every quarter.

Contact at the fair: contact@oicos.systems

Links​

• GITEX Europe 2026 exhibitor list — these are the exhibitors (search for BVAA / Executive Deal Lounge).
• BVAA — Bundesverband Auswanderungsberatung & Auslandswirtschaftsförderung e.V. (Daniel ten Brinke, board).
• BVAA at GITEX Berlin 2026 — Executive Deal Lounge, packages, and registration (30 June–1 July 2026).

Flyers (BVAA)​

• GITEX Messe 2026 (DE)
• GITEX Berlin (EN)

See you in Berlin.