death … is nothing to us, because as long as we exist, death is not present, and when death is present we do not exist.

In contrast, dependencies are present at all times.

This is another essay in the Autonomy and Cohesion series.

Both autonomy and cohesion can be defined through dependence:

Dependency slope

Autonomy looks like this:

And cohesion looks like this:

But at a closer look, it’s always rather like this:

It’s a directed dependency graph, and such that all the edges (shown as arrows above) lead to one or a few power nodes (shown as circles above). The graph has a slope. Levi Bryant then has a point in treating power as gravity. And so has Luhmann, who saw power not as held by somebody but as a medium. Both avoided an anthropocentric treatment of power.

When cohesion is drawn as a dependency graph, it’s easy to see the direction of each edge showing the dependency, and the overall slope towards one power node. But you may live in this medium for a long time without seeing the slope. The international transaction system looked like this: a shared pool with no power concentration for a long time, until a sanction cut off a whole country out of it, like the US cut off Iran in 2012, forcing a huge oil-based economy to be reduced into barter trade. I’ll go back to this kind of dormant dependency shortly.

Dependencies are not always unidirectional. But even when mutual, they are often asymmetrical.

You depend on the morning train more than the train depends on you. The corner shop depends on its bank more than the bank depends on it.

Autonomy on lease

You don’t pay a subscription fee for using the alphabet. It is not just free to use: once you learn to read and write, nobody can take away your literacy. That’s free autonomy. Here, free is both as in free beer and as in freedom, and they are connected: there is no rent to pay for free autonomy because you are unbound.

By contrast, autonomy on lease is held for as long, and on whatever terms, an owner allows. But what do you pay for the lease?

An earlier essay in the series elaborated on the way cohesion mechanisms work. Each takes some participatory autonomy and potentially gives some consequential autonomy. That clusters the different ratios ranges of autonomy cost/gain into seven zones. To participate in a coordination regime, participants pay coordination rent — financially, as procedural compliance, or as conformity to group norms.

It is that coordination rent which is the cost of the lease.

Rent is not a feature of all leases, though. A chokepoint may have a deliberate owner who extracts from it and can hold it shut, or it may be an accident no one designed and no one is billing for. The Intermediated boundary on the autonomy plane marks precisely that difference. It does not divide leased from not leased. The Intermediary boundary divides an unarmed lease, an accidental chokepoint with no owner by design, no rent, and usually little staying power, from an armed one, where a deliberate owner can hold the node and charge for the privilege of passing through it.

Armament is not the only thing that varies. A lease can also be standing or dormant. A standing lease is exercised continuously. A dormant lease is not known to exist at all until something wakes it up.

The clearest examples of standing leases are the platforms. For an Amazon seller, an Uber driver, a developer in Apple’s App Store, it may feel like they freely run their private business, yet the platform sets the fees, the ranking, the visibility, and the right to remain, all revocable at will. That is an armed lease, and a standing one: visible on the surface, collected every day. That is the Technofeudal zone in the Cohesion Spectrum. A distinguishing feature, as clarified in that article, is that the terms are set unilaterally and are non-negotiable. But the landlord can also kick out the tenant at any moment, as Apple did with Epic Games in 2020. That’s a reminder in case the non-negotiability leaves any semblance of a market in that zone. But sanctions don’t come as a surprise in the standing area. They do when the lease is dormant.

The dangerous leases are indeed armed and dormant. The book Underground Empire by Farrell and Newman’s is a catalog of such leases. Every offshore “Eurodollar” is a claim on a real dollar that can only be settled through American institutions, so the world’s payment system is leased from the United States and revocable by sanction. The one-sided control sits asleep, felt as a neutral commons, until a sanction wakes it, as it did for Iran in 2012, and again in 2018. Huawei is another prominent case. Huawei’s access to advanced chips was repossessed in 2020 by a single export rule. As a result, their mobile phone business collapsed within a year.

And then there is the lease with no landlord at all. In March 2016, Azer Koçulu, an unpaid volunteer maintainer, fell out with the npm registry after it handed his package name “kik” to a trademark holder, and withdrew all of his open-source packages. One of them, the eleven-line “left-pad,” was a small, hidden dependency that caused a major disturbance when removed. It affected the pipelines of Facebook, PayPal, Netflix and Spotify, which could not compile until the registry was restored. Notice that no platform owner pulled a lever and no rent was ever charged. A commoner turned out to be powerful only by how many happened to depend on his eleven lines of code. He held a chokepoint in the last place anyone looks for one. It was an unarmed dormant lease. Admittedly weak, because the node was trivially substitutable, but a lease all the same.

So, the leased autonomy flavors make up a matrix:

And if we go back from the split we started in the updated Cohesion Spectrum, we’ll end up with an autonomy taxonomy:

Neat, right? But the world is messier, so don’t fall for it. It’s a good sense-making tool, yet better use it only as a Wittgensteinian ladder. Once you climb, throw it away.

One node, two powers

A power node can be occupied by a state, a platform, or an accidental commoner. At any rate, one who controls it holds up to two distinct powers.

The first is the power to see. Whoever sits at the junction can watch everything that flows through it. Farrell and Newman call this the panopticon effect. (Panopticon is the name for a prison design invented by the English philosopher Jeremy Bentham in the 18th century, allowing “all prisoners of an institution to be observed by a single prison officer without the inmates knowing whether or not they are being watched.”) The NSA’s STORMBREW program, revealed in the Snowden disclosures, tapped the internet backbone via a telecom partner at seven access sites in the United States and copied the international traffic passing through. Its sister program PRISM drew material straight from the big American technology firms, Google, Microsoft, Apple and the rest. Note the link with the Huawei case, where the sanction was for doing surveillance. In fact, the US government has nothing against surveillance as such. The issue is not the practice, but the practitioner.

And here’s yet another case: the US Treasury quietly arranged to read the financial messages crossing SWIFT, which is illegal under Belgian privacy law (where SWIFT is headquartered).

These are grand schemes of infrastructure weaponization, but there are plenty of smaller ones. Take your local internet provider. They can see all your traffic.

The second is the power to cut off: the chokepoint effect. When the Trump administration sanctioned eleven judges of the International Criminal Court, they lost access to services with US providers. Beti Hohler, one of the eleven judges:

As a sanctioned person, I no longer have access to American products and services, even in Europe. My Apple ID, iCloud, Amazon, Airbnb, PayPal, and other accounts have all been blocked or cancelled. These cancellations happened overnight without advance warning.

Add to this the major cases, such as those involving Iran and Huawei, and numerous smaller ones, such as that of Epic Games, mentioned earlier.

So, a chokepoint has the power to cut off a country, a company, or a person.

Exit, but bounded

A lease binds only as long as there is nowhere to go. Where real alternatives exist, the power to repossess is weak. The distance between a leased and a free autonomy is the cost of substitution.

Digital cash and decentralized money ideas and prototypes existed since the 90s. But the tipping point was the 2008 financial crisis. That’s when the old monetary order lost its legitimacy. Worse still, major banks were rescued with taxpayer money. This and the maturation of cryptographic technologies gave the initial push to the first cryptocurrencies. The demand for censorship-resistant payments combined with speculation accelerated adoption.

When Musk bought Twitter and turned it TikToxic, the available alternatives outside the intermediary boundary were few and hardly working. But in a short time, that has changed, and now tens of millions use protocols like ATprotocol and ActivityPub for microblogging (40 million on Bluesky and 8 million on Mastodon, respectively). Now this has spread to long-form blogging (Leaflet on the ATprotocol and WriteFreely on ActivityPub, among others), photo-sharing (Pixelfed), events (Mobilizon), and messaging (Germ).

EU was dependent on cheap Russian gas, but the war in Ukraine pushed the use of alternatives. The EU is still heavily dependent on US technology and services, but the Trump policy finally woke the EU up to the reality (some countries like France had been warning for years) and prompted belated measures.

And of course, we have the fresh case, the suspension of Fable. Hopefully this will boost interest in open-source LLMs. There are some early signs of this happening.

But forces pushing every coordination regime toward places with higher coordination rent extraction are always active.

Balázs Bodó et al in their paper on decentralization, warned about the constant threat of recentralization:

The exploitation of competitive edges leads to the recentralisation of markets into monopolies. Without governance mechanisms in place, nodes may collude, people may lie to each other, markets can be rigged, and there can be significant cost to people entering and exiting markets.

Crypto-currency movements were led by the shared value of desintermediation. But the ecosystem not just re-introduced intermediaries. These intermediaries neatly correspond to those of fiat currencies: payment wallet providers (custodians), payment gateways (like bank payment processors), smart contract platforms (clearinghouses), token launchpads (investment banks), and other gatekeepers.

The most successful decentralized alternative to X-Twitter is Bluesky. But some authoritative voices question whether they are really decentralized and warn about re-centralization.

The EU Parliament replaced Google as a search engine, but that was an easy target; no lobbying there. Let’s see if the EU institutions will be able to get rid of Microsoft and AWS. If so, which I doubt, this will be a real success. But even that might turn out to be only surface-level autonomy, since it is governed by the same kind of thinking that brought about the situation it tries to improve, as noted in this recent article.

The creation of chokepoints, according to the Second Law of Technodynamics (coming soon), happens spontaneously in all socio-technical systems left to their own devices. So it seems that finding a substitution only temporarily removes the lease.

The loudest voices clustered around two responses: bad for innovation, good for safety. All past technology and safety regulations for food, electronics and pharmaceuticals shared the same two responses. The pattern is the natural business-policy tension.

Business-policy tension

Businesses seek adaptability, experimentation and speed.

Policy seeks predictability, accountability, and safety.

That is how each side describes itself, picking the values that are easiest to justify. A more neutral framing is that businesses seek freedom, either for innovation or simply to find a way to maximize their economic gains, while policy seeks control, either for broader social welfare or in pursuit of political agendas.

The tension is old. It is already visible in the High Middle Ages and intensified with the commercial revolution and the rise of the merchant guilds. Early on, it ran between merchant freedom and feudal oversight, and was partly resolved in the Italian city-states: guilds came to control banking and textiles, while rulers imposed taxes and price ceilings. The same tension recurs at every scale. It was acute between Venice and the papacy over trade with the Muslim world. Rome embargoed commerce with the Levant, above all in war materials such as iron, timber, and arms (Connon 24 of Third Council of Lateran, 1179), while Venice, whose livelihood depended on that trade, lobbied to have the bans lifted and at times ignored the pope outright, keeping its convoys to Mamluk Egypt running. Guilds also scaled up their coordination. The Hanseatic League, the best-known case, federated merchant towns across the Baltic and North Sea and negotiated privileges with cities and kings, at times even waging wars with them. The tension took a new shape with the chartered trade monopolies of the 16th to 18th centuries, the English and Dutch East India Companies being the most prominent cases. Here, business and policy fused, with the state granting a private firm a monopoly and quasi-sovereign powers. During the Industrial Revolution, it was reshaped by the drive for efficiency against the nascent demand for social protection. Britain’s Factory Act of 1833 constrained working hours for children. Its decisive innovation was enforcement, a four-man inspectorate empowered to enter any mill and levy penalties, whereas earlier acts had set rules but left them to local magistrates and so were largely ignored. Today, the tension surfaces most clearly in the modern regulatory system, nowhere more visibly than in the European Union, with the AI Act as its latest instance.

Addressing the tension

The business-policy tension is now well recognized, and there are attempts to manage it. These attempts range from traditional command-and-control (1985-2005), to co-regulation (2008-2015), public-private partnerships (2014-2021), and the most recent invention, regulatory sandboxes (2024-present). These periods in parentheses only indicate when each method was the dominant way to address the tension. Otherwise, they all coexist today.

The narratives of these approaches are simple. The initial was: “innovation creates risk — we must regulate it, and that’s it.” With the tension increasing, the new script read “regulation is too rigid, let’s consult businesses”(co-regulation), borrowing the term co-regulation from psychology and having mainly a psychological effect, if any. Yet, it showed a trend towards a more participatory approach and helped shift the narrative to “consultation is not enough, let’s build together”(public-private partnerships) and then "even building presumes we know the rules — let's experiment to find them together" (sandboxes).

This last invention, regulatory sandboxes, is a hot topic now, charged with different expectations and somehow trying to accommodate them all, ultimately turning into a strange beast with little chance of reproducing.

Regulatory sandboxes are meant to be safe environments where businesses can innovate under relaxed rules and supervision. They were first tried in finance in the UK with some positive results and then suddenly became a trusted device despite little evidence that they work, so much so that the EU AI Act dedicated several articles to them and mentioned them 52 times. Now there is even a separate regulation for the AI sandboxes.

The sandbox, being a sandbox, was also very accommodating for experimenting with itself by absorbing different symptoms of the tension. From a space for businesses to innovate, supervised but under relaxed rules, they morphed into a place where regulators can learn about technologies and AI providers will learn how to be compliant. This last bit looks very much like a response to the objection of Meta and Google. The text “the AI regulatory sandboxes should aim to enhance legal certainty for innovators” was a “moreover” in the AI Act. Now, in the Sandbox regulation, it got promoted as the primary aim. The innovation aim got demoted to “also.”

What’s difficult for me to imagine is what will attract participants to sandboxes. Supervising innovation sounds to me like conducting a jazz solo. And not much queuing is in sight. Every EU member state should have at least one active by August this year. To my knowledge, there is currently only one operational sandbox, in Spain.

But enough about sandboxes. The point is that all these approaches give different answers but to the same question: How to manage the business-policy tension? Let’s step back and ask a different question: What this tension actually is?

What it actually is

The business-policy tension is not a specific interface. It is just another manifestation of the omnipresent tension between autonomy and cohesion. The tension can be found in any biological, social and socio-technical system, even in some form, in purely technical systems. Different cohesion forces and tools result in different coordination regimes (more on that later).

This essay is part of the Autonomy and Cohesion series. In an attempt to make it self-standing, I’ll try to summarise the basic idea in the next three paragraphs.

Autonomy is the capacity to make uncoerced decisions; in purely technical domains it is read as a component’s degree of freedom. Cohesion is the action or fact of forming a whole or working as a whole, and through that second, dynamic aspect it subsumes coordination. Cohesion imposes constraints and reduces autonomy. Extreme autonomy dissolves the whole.

Too little autonomy makes systems rigid, non-adaptive, and brittle; too little cohesion yields inefficiency, silos, and, at the limit, disintegration. So systems do not resolve the tension. They hold a balance, and the balance is relative to culture, situation, and type of system.

Cohesion comes from two sources. There are forces we find ourselves within: needs for safety, belonging, reduced uncertainty, and shared values; social identity and loyalty; and external forces such as having a common enemy or a common market. And there are tools we shape and get shaped by in return: language above all, and rituals, norms, rules and laws. Forces are largely beyond our influence; tools are deliberately deployed, yet once deployed, they act back on us. Different tools strike the autonomy–cohesion balance differently.

The tension is a fractal. The business-policy tension is only one manifestation of the autonomy-cohesion dynamics in that fractal. And so the tension is not only between policy and business, but also within policy and within businesses and all the way down. Take the recent statement of Keir Starmer:

My experience now as prime minister is of frustration that every time I go to pull a lever there are a whole bunch of regulations, consultations, arm’s-length bodies that mean that the action from pulling the lever to delivery is longer than I think it ought to be, which is among the reasons why I want to cut down on regulation, generally and within government.

(My first challenge here is to resist commenting on the “policy lever” metaphor, which is so rich and generative on its own and even more so when paired with the “deliverology” narrative. Luckily, there is a good essay on the lever bit already and more moderate than the one I would’ve written.)

It is a clear illustration of the tension and its two sides, highlighted now green for autonomy and cyan for cohesion:

My experience now as prime minister is of frustration that every time I go to pull a lever there are a whole bunch of regulations, consultations, arm’s-length bodies that mean that the action from pulling the lever to delivery is longer than I think it ought to be, which is among the reasons why I want to cut down on regulation, generally and within government.

So the same autonomy–cohesion tension that runs between business and policy runs inside policy. A new executive wants to act. Old policy, encoded as regulation and arm’s-length bodies, holds it.

Each balance contains the next. The executive wants free movement (autonomy), yet ministries should act in sync (cohesion). The cabinet needs cohesion, but each ministry wants room to act. The balance works within and between recursion levels. While each ministry wants its own autonomy, it is only usable if the ministry has internal cohesion across its agencies, which in turn want their own autonomy, down to the individual official whose discretion is balanced by departmental policy. Central government wants local authorities aligned, while each municipality demands discretion shaped by local conditions, and is itself in need of cohesion between its own departments.

The fractal on the business side looks similar. This quote of Andy Jassy, CEO of Amazon, almost mirrors that of Keir Starmer:

Builders hate bureaucracy. It slows them down, frustrates them, and keeps them from doing what they came here to do.

A firm participates as an autonomous agent in the market, balanced by regulation and trade rules. Inside the firm, each department wants autonomy. Unbalanced, that autonomy hardens into silos, a popular corporate pathology. Each team, each employee, repeats the pattern: discretion in daily tasks balanced by shared goals, reports, and rules.

So business-versus-policy is one cut through a structure that repeats at every level: cell, organ, hand, person, team, department, firm, market; official, ministry, government, union. The tension is invariant. What changes is the cohesion mechanism: rules, plans, meetings, protocols.

Cohesion mechanisms vary in many ways. Andy Jassy again:

When you’re running something at scale, you need mechanisms to deliver the right experience and constant improvement for customers. However, as companies grow and add more managers, unneeded processes get layered on that add little value.

Some cohesion is good (cyan), and other is bad (pink).

But it is more useful to think in terms of autonomy cost (participatory autonomy) and autonomy gain (consequential autonomy) that different cohesion mechanisms bring. This results in a cohesion spectrum with seven zones.

The zones and trajectories are explained in another essay.

What is important here is that regulation, and by that I mean technical and safety regulation like the EU AI Act, is just one cohesion mechanism. It has a particular place in the spectrum (Administrative zone), which determines its impact on autonomy and, in turn, on the potential for innovation and the resulting tension.

Then maybe different cohesion mechanisms, further to the right towards the Interoperable zone, can bring more autonomy and alleviate the tension. But more importantly, when it comes to safety, they have another feature which makes them worth considering.

Illegal or impossible?

Let’s compare two familiar ways to coordinate the traffic of two (or more) intersecting roundabout roads: traffic lights and roundabouts.

A traffic light, just like law, is a cohesion tool that works on the basis of rules and sanctions. The rules are clear: red means stop. If you don’t, there is a sanction, and the sanction is also clear. If you don’t stop, collide with and kill somebody crossing on green, the sanction, applied only afterward, will not change the outcome for the victim.

Roundabouts are protocols. Their physical properties, together with some simple rules, serve as constraints that produce self-organized coordination behavior. The emerging order results from each driver following the rule of yielding to circulating traffic, but otherwise relying on personal judgment. The coordination between participants is internal and direct, unlike traffic lights, where it is external, though an intermediary. That difference is non-trivial, as I wrote elsewhere. But there is another difference when it comes to head-on collisions. While traffic lights make it sanctionable, well-designed roundabouts make it impossible.

Such a feature is not unique to roundabouts. Many standards and protocols work this way: cryptography protocols, building code for earthquake resistance, circuit breakers in the stock market, and childproof packaging, to name just a few better-known examples. Many others exist, but — as is so typical of protocols — they are invisible as long as they work.

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Which brings us back to the AI Act. The complaint is that it overrates the risk and smothers innovation. More likely, it’s the reverse: it underrates the risk.

It uses the EU’s product-safety template, the one for toys, electronics, and drugs. The checklist is: sort by risk tier, certify, monitor, fine the violator. That fits bounded harms, typical for the Administrative zone: rule plus sanction, applied after the outcome. But the template itself is a risk-categorization claim, in which the worst case is serious but recoverable. The people most worried about AI think it belongs in a different class altogether: alongside nuclear weapons, where the worst case is catastrophic and irreversible. It doesn’t matter if they are right. It is enough that the possibility is on the table, because for a risk of that size the sanction model fails on its own terms. An ex-post penalty is worth what it was worth to the driver dead at the green light. After a catastrophe of that scale, there is no one left to apply the sanction.

The bad outcome should be impossible or hard to reach, not merely punishable.

This shift does not abolish regulation. It only changes what regulation does. Instead of setting a rule and waiting to punish, a law can mandate a protocol and then govern it from a distance. Sometimes the law calls the protocol into being. eIDAS did this for digital identity, INSPIRE for spatial data. Sometimes the protocol already exists, and the law simply makes it compulsory. The EU’s SEPA rules required everyone to adopt IBAN, and its Common Charger Directive (2022/2380) required portable devices to adopt USB-C and the USB Power Delivery protocol, standards the industry had already built. Either way, the law names the need and points to the protocol, and the protocol does the coordinating.

And it coordinates differently from the law. Break a rule, the act still happens, and the sanction comes after. Break a protocol and nothing happens. Send the wrong account format and the transfer does not go through. Send a malformed request to a server, and you simply fail to coordinate. There is no wrong outcome to punish, because there is no path to it. End-to-end encryption does not block interception. It makes what is intercepted unreadable, so the interception is pointless. The roundabout goes further. It removes the crash itself. The undesirable is not threatened but designed out of the possibility space.

The recognition event I’m talking about is the “Assize of Arms” of 1252, mandating the mass use of the longbow: all men between 15 and 60 were obliged to possess bows and arrows.

A century later, in 1346, the English army of King Edward III defeated the much larger French army of King Philip VI at the Battle of Crécy. More importantly, it was a victory of yeomen armed with cheap longbows against well-trained and heavily armed nobility.

The Birth of Modernity

LinkedIn is full of sensation-seaking obituaries. Every so often, somebody announces the death of a framework, technology, or profession. That is, of course, the common status signaling: follow me to stay relevant. Yet, a commentator in 1346 would’ve been right to declare: “R.I.P Knighthood.”

Indeed, amateur yeomen using cheap military technology made the professional fighters, at least the knightly version, obsolete. And unlike the mainstream interpretation of history, it was already then that modernity started.

According to the world-machine theory, modernity changed the relationships between the four classes: monarch, oligarchy, technocracy, and workers. Before the growth of commerce brought the need for accountants, lawyers and auditors, the technocracy was mainly of theological (priests) and military (knights) kind. As with a more contemporary understanding of technocracy, this codified knowledge could change social status, but at the time, it was a new phenomenon marking the beginning of a new world order.

The Battle of Crécy is arguably the moment when the relationship between technocracy and workers, in that case, knights and yeomen, began to shift. And, as with the other six relations, although it had its specifics and complexity, the dominant trend was an increase in the agency of the previously weaker class.

A Second Longbow Moment

Now we are going through a second longbow moment. The first candidate that comes to mind as a parallel to longbows would be, without doubt, military drones. And indeed, like the longbow (and later gunpowder), they have demonstrated how cheap, smart technology can cause serious damage at long range. But there is a seemingly less obvious candidate that may happen to be a historically better match: vibecoding. While drones are changing warfare, vibecoding is changing not just codefare but also worldfare and is likely to have an impact that parallels that of the longbow. Or much bigger.

In Medieval Europe, heavily armored knights represented the dominant military force. Their growing political power was fully dependent on possessing and mastering the latest military technology.

Today, at least until recently, professional developers had a similar technocratic dominance over not only the working class but the rest of the technocracy. That technocracy-worker boundary may look blurred now, but it seems the popularisation of “knowledge worker” restates the distinction, especially after the traditional collar-color-coded stratification first turned into a metaphor and then into a less reliable one. Notably, the dominance of the contemporary knight-programmer was not only over the working class but also over the rest of the technocracy. And it was from that part of the technocracy that the contemporary longbowers, the vibecoders, emerged. Yet the technological skill distance between them looks similar to that between knights and yeomen.

Knights were professionals, while the longbow archers were amateurs. Hobbyists. But it was a “mandatory hobby” from 1363 on: the new Archery Law made the archery practice obligatory on Sundays and holidays. A hobby required by law.

Vibecoding started as a hobby for non-professional coders, too. Now it seems it has become mandatory, not by law but by selective pressures.

Longbow warfare did not require each shot to be perfect. It required enough arrows, fast enough, to make perfection unnecessary. At Crécy, the English longbowmen had a far higher rate of fire than the French (actually Genoese) crossbowmen.

That is close to vibecoding. Much AI-generated code is imperfect, sometimes plainly unsafe. But the point is not flawless output. It is throughput: many attempts, many drafts, many partial wins. Most arrows miss, but enough hit to matter. Most generated code versions are brittle and some are wrong, but enough work, after review, to move the project forward. The professional developer resembles the knight or crossbowman: slower, more exacting, and more costly to waste. The vibecoder resembles the longbowman: working with volume, tolerating misses, and relying on repetition and judgment over precision.

While longbowers contributed to the development of the modernity machine, which was switched on a few centuries after the battle of Crécy, the vibecoders are now contributing to the switching on of the divergence machine. Longbowers democratized military power, but in a way characteristic of the modernity machine: standardization. Instead of highly customized technology that required many years to master, they used standard, inexpensive technology that could be operated successfully with little practice. And while standardization replaced bespokeness in the Middle Ages, today, it is bespokeness that spreads. Whereas professional programmers usually come together to build and standardize software of mass use, vibecoders individually create idiosyncratic apps for individual use. In both cases, the bespokeness itself relies on standardization: knights — metallurgical and horse breeding best practices; vibecodes — standard protocols (CLIs, MCP, web protocols) and reusable agentic primitives (skills, hooks, tools, and templates).

Another important difference is that adding a longbow to a knight's technology stack won’t make him superior to the longbow archer. But senior software engineers adding vibecoding produce amazing results.

Homo Ludens

Generative AI is an intrinsically playful technology. In world history, there hasn’t been a playful technology so powerful. And it seems it’s penalizing those who don’t approach it as such and rewarding those who do.

Peter Steinberger — developer of OpenClaw, the biggest breakthrough in agentic engineering since Claude Code — constantly emphasizes the importance of playfulness.

Lex Fridman: In this world, if you look at 2025, so many startups, so many companies were doing kind of agentic type stuff, or claiming to. And here, Open Claw comes in and destroys everybody. Like, why did you win?

Peter Steinberger: Because they all take themselves too seriously.1

While vibecoding refocuses attention from syntax to intent, that intent itself evolves through rapid iterations that reshape the original idea. Peter Steinberger again:

I could not have planned this out in my head, put it into some orchestrator, and then, like, something comes out. Like it’s to me, it’s much more my idea what it will become evolves as I build it and as I play with it and as I, I try out stuff.

Homo Faber today is Homo Ludens.

But Homo Ludens needs time to play. And this puts indie knowledge workers in a privileged position. GenAI and vibecoding mark the third phase in the evolution of the gig economy. The first phase, 2010-2020, made the gig economy visible, and we saw the first platforms created to support it. The second boost came from the pandemic. Remote work has normalized and weakened the monopoly of offices. Staying home, people had time to rethink their priorities, and many quit their corporate jobs to join the gig economy. Today, vibecoding brings a third boost. Freelancers have more time to experiment than paycheck employees. Even now that we see some companies allowing employees to use vibecoding, they cannot choose the area of application and have limitations on the tools they can use. There are no such limitations for freelancers. The overall AI effect for them is threefold: they can turn into a micro-company doing coding, design, research and automation; they can play in new, previously inaccessible markets; and they can build apps once restricted to corporations, open-source communities and well-funded startups. To use Arthur C. Clarke's framing, if some freelancers previously went back to corporate jobs after a few years in the gig economy, that would be a failure of nerve. If they do it today, that would be a failure of imagination.

This essay is part of the Autonomy and Cohesion series, which includes an earlier one-dimensional version of the Cohesion Spectrum.

Autonomy is the capacity to make informed, uncoerced decisions. To keep the same term in purely technical domains, it must be understood also metaphorically. Since components are unable to make decisions, “autonomy” should be understood there as the degree of freedom or independence within the system.

Cohesion, in the context of socio-technical systems, is the action or fact of forming a whole or working as a whole. It is about forming a unity (static aspect) or acting in unison (dynamic aspect), where uni- (from unus, one in Latin) is the common for being one and acting as one. Due to the second, dynamic aspect, cohesion subsumes coordination.

The tension between autonomy and cohesion is also observed in the technical layer, shaping and being shaped by the tension in the social layer. There is an evolutionary trend toward increased decoupling, punctuated by setbacks.

Cohesion imposes constraints and reduces autonomy. Cohesion is due to natural forces and designed mechanisms.

Liquids and solids exist in their states due to cohesion forces binding molecules, such as van der Waals forces, dipole interactions, hydrogen bonds, and ionic bonds. Socio-technical systems exhibit analogous forces — though more complex, less understood, and largely beyond direct influence. That last property is what sets them apart from cohesion tools and technologies: tools are things we deliberately create and deploy. But once created, they act back on us, issuing imperatives their designers did not intend. The steam engine built to cut wood ended up organizing factories, cities, and labor.1 The distinction is not that forces shape us while tools do not. It is that forces are what we find ourselves within; tools are what we make, and then find ourselves within.

Personal cohesion forces include needs for safety, belonging, reduced uncertainty, self-esteem, and shared values, driving the formation of groups and organizations. Social identity further strengthens cohesion through identification with communities, professions, or beliefs, while emotions like loyalty or empathy may dominate in certain contexts. In social networks, self-expression, validation, and fear of missing out are key drivers.

Cohesion operates internally and externally. Within organizations, identity, dependencies, shared resources, and the pull of collective benefits such as efficiency bind elements together. Networks rely on proximity, transitivity, and shared interests. Externally, forces such as shared enemies or market pressures sustain cohesion despite internal tensions.

Cohesion tools and technologies – such as language, rituals, norms, and media – enable coordination. Language is central, self-producing, and generates other media. These tools vary in how they balance cohesion and autonomy, which they do alongside cultural and contextual factors.

Different cohesion mechanisms affect autonomy in two ways. Since cohesion imposes constraints, the cost of participation is always a loss of autonomy. However, some cohesion mechanisms also increase autonomy. In certain cases, the autonomy gain can exceed the autonomy cost. To account for the dual effect, autonomy should be represented as a two-dimensional vector: participatory and consequential autonomy.

Participatory autonomy is the operative discretion available to participants within a coordination regime. It is the actual autonomy range remaining after complying with the regime’s constraints. Operative discretion often differs from the formal one. An Amazon seller may formally be running their own business, but the commission rates, search ranking, return policies and delisting conditions are set unilaterally by the platform.

Consequential autonomy is the decision space made available to participants as a result of the coordination regime. When using HTTP, complying with the protocol’s request-response conventions is non-negotiable, but doing so grants access to the entire web, a decision and action space that did not exist before the protocol.

The Zones

The ranges of participatory and consequential autonomy across different cohesion mechanisms cluster into several zones, some of which overlap.

Oppressive

Both participatory and consequential autonomy are compressed to functionally negligible levels. Physical force or legal non-personhood eliminates exit. Residual micro-decisions, such as the pace of work or small acts of solidarity, persist, but they cannot alter outcomes in any significant way, and the regime contributes nothing to participants’ decision space because it is organized around elimination rather than enablement. Unlike other zones, where an organization’s coordination footprint spans multiple mechanisms and zones (more on that later), oppressive regimes suppress alternative coordination so thoroughly that the footprint collapses toward a small region clustered near the origin. The origin itself functions as an asymptotic boundary: the theoretical endpoint toward which oppressive regimes tend as they intensify. Yet no real system reaches it, because doing so would require the complete elimination of the participant as an agent. Chattel slavery, Nazi concentration camps, and North Korean political prison camps are the closest historical approaches to that boundary.

Imperative

What varies considerably is consequential autonomy. A well-organized army provides logistics, collective intelligence, and operational reach that are unavailable to individuals. Feudal arrangements, though coercive, under the customary law (as opposed to the Roman law) gave the right to peasants to hunt and fish on the lord’s land. Early factory work sits higher still: wages with purchasing power, urban infrastructure, residual exit rights. The zone is wide on the consequential axis and flat on the participatory axis.

Coordination proceeds through issued directives. Deviation is sanctioned. Participatory autonomy is systematically constrained across all instances, not by any single explicit prohibition, but by the prohibitive cost of exit. A soldier in combat cannot leave. The situation is similar for a medieval serf. A nineteenth-century factory worker could, in principle, quit, yet only at costs that were effectively insurmountable. The mechanisms differ, but in each case, they converge on the same outcome: effective discretion remains low.

Administrative

Coordination through formal, codified, impersonal rules. Participants have operative discretion. A civil servant can exercise professional judgment, invoke appeals and interpret regulations. That discretion is bounded by procedure and accountability structures. The zone covers both government and private instances. The center of mass of nation-states and corporations, regulatory agencies and institutional churches is this zone. The relevant distinction is whether coordination proceeds through codified, impersonal rules enforced by procedure. When decisions are made by policy rather than identifiable persons, accountability dissolves.2

The rule of law is the core consequential contribution: property rights backed by institutional enforcement, contracts that will be honored, and the ability to challenge decisions through formal mechanisms. These expand what participants can decide and do beyond what they could manage in isolation.

Technofeudal

The Technofeudal zone shares the same low-participatory band as Imperative, at considerably higher consequential autonomy. The structural parallel is not metaphorical: the platform owner is a landlord. Participants bring their product, labor, or content. The platform unilaterally sets all terms and extracts rent for access. That’s why platforms that present themselves as marketplaces belong here, not in the Agoric zone. An Amazon seller cannot negotiate commission rates, search visibility, or return policy requirements. An Uber driver cannot negotiate fare rates or matching priority. A Facebook creator cannot negotiate what percentage of followers see their posts.

The term technofeudalism was coined by Varoufakis.3

Normative

Social pressure replaces formal enforcement. There is no arrest for norm violation, no algorithm enforcing ranking or manipulating feeds, no commander issuing directives. But exclusion is real and costly: loss of belonging, reputation, and access to shared resources. The enforcement mechanism is the community’s collective capacity to make participation costly for violators.

This zone has wide internal variance. A housing association restricts paint colors and structural modifications while delivering only shared maintenance and property value protection. A scientific discipline provides an accumulated body of methodology, a peer-review infrastructure, citation networks, and shared instrumentation that no individual could replicate. Self-managing organizations, worker cooperatives, and holacratic structures sit at the higher-participatory end.

Agoric

Coordination proceeds through price signals and counterparty choice. Participants can walk away, return tomorrow, offer a counterprice, and choose among alternative buyers and sellers. No single actor controls the terms of the encounter. A commodity trader routing orders across multiple exchanges, a bazaar vendor setting a price in anticipation of negotiation, and a freelance professional declining a client each exercise the high participatory autonomy that defines this zone.

The Agoric zone cannot stand alone. The Administrative-zone provides currency stability, contract enforcement, property rights, and competition policy.

Market-enabling intermediaries belong here, not in Technofeudal. A traditional stock exchange, a clearing house and an auction platform facilitate rather than control exchange. The principal test is whether participants can negotiate.

Interoperable

The dominant mechanisms of cohesion here are standards and protocols. Consequential autonomy stays very high throughout. Well-designed protocols create qualitatively new possibility spaces rather than improving access to existing ones. HTTP did not make existing communication faster: it made a global hyperlinked information space possible for the first time. The roundabout yield rule does not improve on traffic light performance: it enables drivers to negotiate gaps directly, simultaneously reducing fatalities and delays. The gain is categorical, not incremental.

Participatory autonomy varies widely within the zone. Some protocols leave no discretion. Any deviation from HTTP’s request-response format results in coordination failure. Others build in meaningful choices. The AT Protocol lets participants decide where to host their data, which moderation service to use, and which feed algorithm to adopt.

Protocols appear in other zones too. However, in the interoperable zone, protocols are the dominant mechanism, and not every class of protocol, but only the cautonomous ones, which means those with a high consequential/participatory autonomy ratio.

Clarifications

Freedom, Autonomy, Agency

Autonomy as choice may look like an overstatement in some systems or situations and an understatement in others. For example, in Decoupling and Rules on Graphs, autonomy is used as a proxy for degrees of freedom. In the Cohesion Spectrum, both the participatory and consequential dimensions are relevant not only to autonomy (what you can choose) but also to agency (what you can do).

Since all three concern distinguishable states available to a system, the issue of using autonomy when discussing degrees of freedom or action space can be easily resolved by applying Ashby’s concept of variety. It will dissolve the decision-space/action-space question since it is neutral between deciding and acting. It simply counts states regardless of whether they are decision states or action states. The additional benefit is the utilization of the Law of Requisite Variety.

And yet, sticking with autonomy has several benefits. The first is that autonomy as a concept is evocative and accessible. The second and more important benefit is that autonomy and cohesion name the lived experience of the tension: what it feels like to have latitude or to lack it, what it feels like for a group to hold together or to fragment.

Nominal and Effective Autonomy

Not all autonomy reductions or expansions are the same for each participant. Effective variety is the subset of nominal variety that is simultaneously accessible and relevant to the participant.

Three filters reduce nominal to effective: preference alignment (the most significant and elusive), capability and resources.

Preference alignment is about relevance. How much of the autonomy taken or expanded does the participant care about? A user with no preference over server governance, algorithmic transparency, or data portability experiences zero effective autonomy gain migrating from X to Mastodon or Bluesky, regardless of how significant the nominal autonomy expansion is. Conversely, a coordination regime that constrains only dimensions the participant was indifferent to anyway imposes zero effective autonomy cost. A strict dress code at work reduces nominal participatory autonomy but imposes near-zero effective autonomy cost on someone who would have dressed that way regardless. The preference filter operates on both axes: on Y, it determines whether the participatory cost is actually felt; on X, it determines whether the consequential gain is actually valued.

The second filter is participants’ cognitive, technical and practical competences that allow them to exercise the available action space. The consequential autonomy that the web provides is effectively zero for someone without literacy in any language with significant web presence.

The third filter is about participants’ resources. Unlike capability, they cannot be substituted by effort or learning alone. The web variety is effectively zero for somebody without connectivity or a subscription.

Preference remains the primary filter because it determines whether the other two constraints are even relevant.

Inter-Zone Relations

The bottom band shows a similar range for the participatory autonomy of classic feudalism and technofeudalism. The cost of coordination in both cases is different kinds of lock-in, but it suppresses participatory autonomy in a similar way. What the Amazon seller has that the medieval serf did not is consequential autonomy: global market access at scale.

Imperative, Administrative, and Technofeudal share a common structural property: coordination flows through intermediaries with concentrated agency. A dashed boundary separates coordination mechanisms organized around controlling intermediaries. Here, it is important to distinguish controlling from facilitating intermediaries. Organizations whose coordination footprints are dominated by controlling-intermediary mechanisms cluster below and to the left of this boundary; those using facilitating intermediaries or no intermediaries at all cluster above and to the right of it.

The Agoric zone’s dependence on Administrative is asymmetric: Administrative zones can exist without markets (e.g., central planning, theocracies), but markets cannot exist without Administrative infrastructure. Strip away contract enforcement and property rights, and exchange either retreats into the Normative zone (reputation-governed barter only) or gets captured by the most powerful participant, who becomes the platform — sliding across the Intermediated boundary into Technofeudal.

The Interoperable zone is not self-sustaining either. Its high consequential autonomy depends on Administrative infrastructure (standards bodies, dispute resolution, intellectual property enforcement) and Normative culture (the open-source ethos, cooperative standards development, shared technical values). Protocols emerge from communities.

Social systems are amoebas, not dots

Placing paradigm examples is a double edge sward. It helps clarify the zone and, at the same time, creates the impression that real social systems are dots on the plane. But neither are they dots, nor do they stay in the same position. Only in one case, the Oppressive zone, are they relatively small blotches. In all others, they are bigger blotches, but since they move, better to imagine them as amoebas. They have short-term vibrations and long-term transitions, which will get special attention in the next section.

The autonomy plane maps coordination mechanisms, not organizations, communities, or networks. Any real social system deploys multiple coordination mechanisms simultaneously. A self-hosted e-shop uses HTTP (interoperable zone), negotiates directly with customers (agoric zone), and routes payments through Stripe (intermediated zone). And, as clarified earlier, they also depend on currency stability, contract enforcement, property rights, and competition policy (administrative zone). These are distinct mechanisms at distinct positions on the map. So, if we attempt to represent a self-hosted e-shop with all the cohesion mechanisms it brings and uses, it will look something like this:

Movement

When startups scale, they move from Normative (shared mission, informal trust) toward Administrative (formal HR, legal, compliance). An Administrative organization under crisis slides toward Imperative as directive authority temporarily supersedes procedure, in different areas of the zone, depending if the crisis is war, natural disaster or pandemic. A professional community moves from Normative toward Administrative as it formalizes licensing and ethics codes. These trajectories are path-dependent and often irreversible.

Within the Interoperable zone, moving upward along it means achieving the same consequential expansion with more participatory flexibility. Protocols encode choices about how much discretion participants retain. Recent protocol design history can be read as a series of attempts to reclaim the agency that platform capture had extracted.

A notable movement in the Interoperable zone is that of the crypto ecosystem. It started as a desintermediation initiative with a peer-to-peer promise, but evolved differently. None of the protocols alone could address usability barriers, liquidity, scalability, and risk. As a result, some layers reintroduced intermediaries that closely resemble those of the fiat currency ecosystem in both roles and fee levels. There are payment wallet providers (custodian), payment gateway (like bank payment processors), smart contract platforms (clearing house), token launchpad (investment bank) and so on. So, from the middle of the Interoperable zone, the crypto ecosystem slides south-west into the Intermedates zone.

What drives these trajectories?

Coordination Rent

Startups move from Normative towards Administrative as they scale. Administrative organizations slide towards Imperative under crisis. Agoric regimes drift into Technofeudal under network effect pressure. There is a force driving these trajectories towards places with higher coordination rent. It pulls towards intermediary concentration.

Coordination rent names what happens in any coordination regime where whoever controls the coordination infrastructure can extract a rent from participants.

The mechanism is straightforward. As a regime matures, switching costs rise and alternatives become less viable. Participants become dependent on the regime’s outputs for their own planning. The controller’s capacity to extract increases, not because of any single decision, but because dependency is compounding in the background. Even with benign intent on the controller’s side, the structural conditions for higher extraction accumulate.

The rent is not always financial. In administrative regimes, the rent is procedural compliance. The civil servant does not pay the state in cash. They pay in the form they must fill, the appeal they must lodge, and the codified process they must follow. In normative regimes, the rent is conformity to group norms. The scientist pays in citations, methodological orthodoxy, and conference attendance. In imperative regimes, the rent is obedience. The soldier pays in the suspension of deliberation. In technofeudal regimes, the rent is some combination of all three, plus the financial component that platform economics makes visible.

Regimes on one side of the Intermediated boundary have an identifiable rent-extractor. Regimes on the other do not, which is why the Normative, Agoric, and Interoperable zones resist the gravitational pull in ways the others do not. The boundary is not a static feature. It is the line at which a coordination regime has accumulated enough intermediary concentration that rent extraction becomes structurally possible.

Named trajectories

Once the force is named, trajectories can be named. The Protocol Field4 identifies patterns like the Codification Trap and the Automation Drift.

Doctorow’s enshittification cycle is the obvious worked example. His three stages (good to users, then good to business customers, then extractive to both) map as a single trajectory. The regime begins near the Agoric zone with genuine counterparty choice and low switching costs. It crosses the Intermediated boundary into Technofeudal as network effects compound and coordination rent begins to accrue. The third stage is the regime fully occupying Technofeudal territory, with a residual minimum of value preserved only to prevent exit. The trajectory is predictable, empirically documented across multiple platforms, and in the public domain as a reference point that readers will recognize. It also demonstrates the asymmetry of the Intermediated boundary. The journey in is driven by compounding forces. The journey back out requires external intervention.

Thanks to and for helpful comments on an earlier version.

Come together

The last entry in the Serendipity Glossary is thinging. Material engagement with objects helps thinking and enables tinkering. It’s even more basic than that. According to some school in cognitive science, cognition is not something that happens in the brain but emerges from active engagement with the environment.

Thinging means objects are active participants in thinking.

Writing on paper is already thinging. Like with the potters described by Malafouris (see references in the glossary), the shape is learned into existence. It is a path made in walking, to cite the famous line from Machado’s poem, the Wanderer.

Notes are often locked in their medium.

If there is a way to detach them, shrink them to palm size and print them on cardboard, we can play with them like with a deck of cards, shuffle them, draw several and put them side by side. These accidental neighbors can bring unexpected connections.

I haven’t done that yet, but I started experimenting with an electronic version of it. It’s too early to report results. What I’ll do instead is describe a similar practice, based on the same principle: unexpected neighbors occasionally trigger serendipitous events.

People, Ideas, and Quotes

What is common between Today-is-later, Graph Pruning, and PIQ is that a random sample of a particular type of notes appears on the daily note on certain days.

But while the first two deal with accumulation and entropy, the third one brings together items that can be generative on their own and potentially even more so when they come together in unexpected combinations.

Bringing unexpected people has already shown some serendipity in the Graph Pruning practice. The set of random pages may contain a person's node. That might be somebody I have been out of touch with for a while who has now resurfaced, and I want to catch up with. I’m tagging such cases with the path pattern to keep track. There have been sixteen such cases since July 2024, of which one (so far) has been an actual serendipitous episode. Not bad, but I thought I should make it more targeted and not on its own, but in combination with two other items: ideas and quotes.

And so, on certain days, an algorithm brings a PIQ block on my daily note, with a random sample of people, ideas and quotes pulled from my personal knowledge graph. Each item can trigger something on its own, but the greater potential comes when it appears alongside others in unexpected combinations. These combinations can occur in nine dimensions: three between same-type items, three between different items, and three more between each set and the context of the daily note on which it appears.

These sets of items appear naturally (I take care of their appearance on the page), but they are embedded query results, which means their context is a click away, and whatever they are connected to is just another degree further in the graph. The serendipity event an item may trigger may not come from the concrete one randomly pulled to my daily note, but from another item found in the exploratory journey that the pulled item invited me to take.

The potential for serendipity is high, but it doesn’t mean it will produce a happy accident every week or month. If there is one a month on average, that’s already a good result. But for this to work at all, it needs some critical mass. Currently, I have about 1500 people, 350 ideas and 4800 imported annotations. These numbers need some clarification.

From these 1500 people, I personally know less than a third. The rest appeared via Readwise, as authors of books, articles and papers I annotated. People I personally know are typed with a specific subtype, but for the PIQ practice, I prefer not to limit the pool only to them.

The pool of ideas in PIQ includes notes tagged as idea, thought or capture that have not been turned into anything else. Now I’m experimenting with adding those Bluesky posts and Substack notes, which I kept in my graph for resurfacing. This adds a few hundred blocks to the pool. More importantly, while other ideas would potentially trigger a serendipitous event of Penny pattern, the micro-posts also have the potential of Path. Here’s why. A forgotten post appearing in the daily PIQ block may be linked to new ideas I came up with in the meantime or to other items from that day. The reposting of that post with the new idea will resurface it in a new context together with a fresh idea, which may trigger a different reaction from the social network (now in a new state!), potentially a happy accident. One can’t step twice in the same river. That’s why it is a combination of random and living patterns.

If you practice some flavor of the Zettelkasten method, PIQ can complement your ideas distillery practice. You can even extend the idea pools with your zettels.

In my case, the quotes are all annotations from Readwise. If you have a quote captured manually or from another pipeline, it would be good to add them in the pool. The bigger the better. While in PIQ, I call them quotes, they are often a combination of a highlight and my note about it, which makes it more potent, if not for serendipity, then at least for linking and distillation.

I’m still experimenting with the numbers and frequency, and unlike Graph Pruning, PIQ hasn’t stabilized. The current samples are five people, two ideas, and three quotes. It runs on Tuesdays and Thursdays, and on weekends. The weekend is often ignored.

In all cases, the PIQ block is automatically deleted after a couple of days, unless there was a logged serendipity event, which then remains as the only child block of PIQ. The quotes part of PIQ appears on its own under a different parent, Today’s highlights on Monday, Wednesday and Friday.

The technical implementation of PIQ is simple. Yet, if you want to give it a try, you need to find the best way for it to fit your tool and workflows. With so potent coding agents around, it won’t be any challenge. For those who use Roam Research, I have described my implementation in the next section.

Read more

This is the seventh post in the serendipity series.

The glossary is structured like this. There are three bullets under each term. The first bullet is a definition, the second is about its origin, and the third is an example.

Bisociation

• Association of two (or more) apparently incompatible frames of thought.

• Coined by Arthur Koestler to describe the functional basis of creative thinking.

• Bernard Sadow bisociated the observation of an airport worker rolling a heavy machine on a wheeled skid with his own struggle of dragging heavy bags, leading to the invention of the rolling suitcase.

Epistemic Expectations

• Internalised beliefs or community norms about where knowledge comes from, what kinds of discoveries are possible, and what results are likely to be produced by a specific method.

• Introduced in the field of serendipity research by Samantha Copeland.

• Lewis Thomas and Aaron Kellner both observed rabbit ears drooping after injections of the enzyme papain. Initially, they both ignored this anomaly due to their epistemic expectations of the scientific community regarding cartilage as inert and relatively uninteresting.

Generative Doubt

• A motivated search for understanding, stimulated by the experience of not knowing.

• A management concept, introduced by Cunha et al. in 2015, emphasizing doubt as a creative force.

• Honda achieved success in the US market by not clinging to their original plan for large bikes and by responding to the unexpected popularity of their small delivery bikes.

Indwelling

• A technique for cultivating an “art of locality” by immersing oneself deeply in a specific context or material environment.

• Emphasized as a method for internalizing situational knowledge and cultivating metis by W. D. Holford (2020), linked to James Scott’s (1998) descriptions of the “art of locality” and “traditional cultivators” who develop complex techniques by dwelling within their specific environmental contingencies. It was formally applied to serendipity studies by Synne Frydenberg et al. (2019) in the context of design-driven field studies. The concept draws on Michael Polanyi’s work regarding the internalization of tacit knowledge.

• Designers of arctic ship bridges stayed on a boat in harsh conditions to indwell with the crew, leading to “contextual wake-up calls” and unplanned improvements in their designs.

Managed Serendipity

• An organisational strategy that utilises narrative methods to enable multiple and unexpected encounters with original anecdotal material. It prioritises natural learning processes and the synthesis of diverse stories over the rigid imposition of best practice, aiming to increase the probability of discovering emergent solutions rather than simply repeating past actions.

• Coined by David Snowden in 2003, arguing that while best practice is useful for ordered systems, innovation in complex systems depends on the disruption of entrenched patterns of thinking.

• A company implements a narrative database of uninterpreted stories from its staff, including retiring employees who share anecdotal wisdom. Instead of using directed keyword searches, a user runs abstract queries. This forces multiple encounters with original material that would otherwise be filtered out.

Metis

• “Cunning wisdom”; a form of responsive reasoning that allows individuals to respond well to changing circumstances, ambiguity, and the unexpected.

• Named after the Greek goddess Metis, the first wife of Zeus, who embodied shape-shifting and clever intelligence.

• Captain “Sully” Sullenberger’s emergency landing of an Airbus on the Hudson River in 2009.

Microserendipity

• Small-scale discovery occurring during mundane practice where an unintended observation triggers a break in one’s flow state, acting as a pivot event that forces an immediate reassessment of the agent’s creative intent or trajectory.

• Primarily developed and refined by Wendy Ross and Frédéric Vallée-Tourangeau to move serendipity research toward a granular, systematic analysis of creative action as it unfolds. Earlier iterations of the concept were explored by Beghetto (2013) in the context of classroom creativity and by Bogers and Björneborn (2013) to describe coincidences shared on digital platforms such as Twitter.

• Researcher Ana Piñeyro experienced microserendipity when she overloaded a polymeric coil, creating a “mistake” that she noticed had unique aesthetic and heat-responsive qualities, pivoting her research.

Pseudo-serendipity

• Discoveries that occur by accident and sagacity, but where the investigator was already actively in quest of that specific finding.

• Coined by Royston Roberts (1989) to distinguish between pure serendipity and accidental solutions to known problems.

• Charles Goodyear spent a decade searching for a way to stabilize rubber; he accidentally dropped a mixture on a hot stove, discovering vulcanization, a solution he sought, but found through an unplanned event.

Retrospective Coronation

• The process of using hindsight to label a past accident as serendipitous only after a valuable outcome has been achieved and validated by personal or social judgment.

• Formally introduced by philosopher Samantha Copeland to describe how the status of a discovery is not inherent in the moment of the accident but is bestowed post-factum by the scientific community.

• Penicillin was only “coronated” as a serendipitous discovery years after the initial observation; at the time of the accident, Fleming simply found the mold funny rather than recognizing it as a legendary breakthrough.

Sagacity

• Perceptive wisdom or the ability to sniff out value in accidental results that others might dismiss as errors or noise.

• From the Latin sagax (of quick perception, acute).

• Alexander Fleming’s sagacity lay in his complex recognition that a contaminant mold was actively killing bacteria, rather than simply viewing it as a ruined culture to be discarded.

Serendipity

• Making discoveries by accident and sagacity of things which one is not in quest of.

• Coined by Horace Walpole in 1754, inspired by the Persian fairy tale The Three Princes of Serendip.

• Christopher Columbus, setting out for the Indies but stumbling upon the Americas, is considered a spectacular historical instance of the phenomenon.

Serendipity Filters

• Internal or external pressures — such as preconceived notions, time constraints, or rigid goals — that cause a person to ignore a potentially valuable accidental connection.

• Coined by Abigail McBirnie to characterize the situational pressures that cause potential discoveries to be lost and to explain the paradox of control in serendipitous processes.

• Aaron Kellner observed the same floppy ears in rabbits as Lewis Thomas, but used the phenomenon only as a strength test, failing to follow up because of his narrow focus on cardiovascular muscle.

Strong Emergence

• A phenomenon is strongly emergent if it cannot be deduced, even in principle, from the properties of the underlying components or the process from which it originates.

• A technical term in philosophy and complexity sciences coined by David Chalmers.

• The discovery of smallpox vaccination was a distributed process that emerged from folk knowledge, repeated witnessings by farmers, and the patronage of the scientific community.

Thinging

• The conceptualisation of thinking as an active, distributed engagement with material objects, where things are not viewed as passive or immutable but as forcefields of continuous, active transition that participate in human cognitive life.

• Originally coined by Martin Heidegger to denote the active nature of objects. It was later adapted and expanded by Lambros Malafouris as a core component of Material Engagement Theory (MET).

• In pottery-making, the potter does not simply externalize a preconceived mental blueprint onto inert matter. Instead, as the hand and eye touch the clay, the specific form of a line or curve is learned into existence through a spontaneous dialogue with the material’s resistance.

That’s it for now. There are also terms such as bahramdipity, super-encounterers and zemblanity, but they are not used frequently enough to make it to this glossary.

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References

Barber, B., & Fox, R. C. (1958). The Case of the Floppy-Eared Rabbits: An Instance of Serendipity Gained and Serendipity Lost. American Journal of Sociology, 64(2), 128–136.

Chalmers, D. J. (2008). Strong and Weak Emergence. In P. Clayton & P. Davies (Eds.), The Re-Emergence of Emergence: The Emergentist Hypothesis from Science to Religion (p. 0). Oxford University Press. https://doi.org/10.1093/acprof:oso/9780199544318.003.0011

Copeland, S. (2019). On serendipity in science: Discovery at the intersection of chance and wisdom. Synthese, 196(6), 2385–2406.

Cunha, M. P. e, Rego, A., Clegg, S., & Lindsay, G. (2015). The dialectics of serendipity. European Management Journal, 33(1), 9–18. https://doi.org/10.1016/j.emj.2014.11.001

“Fleming Leapt on the Unusual like a Weasel on a Vole”: Challenging the Paradigms of Discovery in Science | Request PDF. (n.d.). ResearchGate. https://doi.org/10.1162/posc_a_00294

Koestler, A. (1964). The Act of Creation. One 70 Press. (Original work published 1964)

Malafouris, L. (2020). Thinking as “Thinging”: Psychology With Things. Current Directions in Psychological Science, 29(1), 3–8. https://doi.org/10.1177/0963721419873349

Martin Heidegger, M. (n.d.). Being and Time. Retrieved March 24, 2026, from https://sunypress.edu/Books/B/Being-and-Time2 (Original work published 1927)

McBirnie, A. (2008). Seeking serendipity: The paradox of control. Aslib Proceedings, 60(6), 600–618. https://doi.org/10.1108/00012530810924294

Roberts, R. M. M. (1989). Serendipity: Accidental Discoveries in Science. Wiley.

Snowden, D. (2003). Managing for Serendipity or why we should lay off “best practice” in KM. International Journal of Knowledge Management - IJKM, 6.

One coping strategy is to step back (the world is a historical thing after all) and choose more carefully what to pay attention to (not always to follow historians' choices).

Such attempts may result in seemingly weird statements. In an earlier essay, I proposed praising Voltaire not just as an Enlightenment philosopher and a playwright, but also as an entrepreneur. As such — and here I made an even weirder suggestion — he should be listed among other pre-industrial entrepreneurs, such as Jakob Fugger and Josiah Wedgwood. A staggeringly rich banker, interested solely in money-making above anything else, a potter who scaled through industrial innovation and influence branding, and a satirical writer who campaigned for social justice make an unlikely trio. Sounds like a joke: a German, an Englishman, and a Frenchman walk into a bar.

But they did enter, not into a bar but into the Modernity Machine and when they left, that machine was working differently.

So, these three were not just successful entrepreneurs. They are among the more significant engineers of modernity. Two of them also made an early contribution to the Divergence Machine that is replacing the Modernity Machine in our present day.

The Modernity Machine

At some point in history, there was a tremendous shift in how the world worked. For millennia, it was defined by bloodlines, a static sense of fate and divine mystery. And then it turned into a world defined by money, agency, measurement, and public opinion.

According to some, it happened suddenly. According to others, it took centuries. According to some, the main shift was towards secularisation of society, or what Max Weber called disenchantment. There are commentators who focus on the awakening of the arts, and others on the birth of modern science. For Bruno Latour, it was the start of pretending science and politics don’t mix, which allowed us to mix them more effectively.

Most accounts of modernity focus on one area of life, such as religion, economics, politics, or science. That gives a partial picture. In contrast, the Modernity Machine thesis is a systemic view that pays sufficient attention to the role of technology and to the evolution of class relations. Like Luhmann and Latour, it decenters humans.

Machine sounds mechanistic. The opposite of organic, some may say. But that’s a matter of interpretation. The best definition of life that I know of comes from the theory of autopoiesis. It treats the organism, the cell, and different levels of organisation, such as the nervous or immune systems, as autopoietic machines. And the embedding doesn’t stop at the level of the organism. In Principles of Biological Autonomy, Varela wrote:

If one says that there is a machine 𝑀 in which there is a feedback loop through the environment, so that the effects of its output affect its input, one is in fact talking about a larger machine 𝑀′ which includes the environment and the feedback loop in its defining organization.

If machine can be seen as equivalent to system, why not call it the modernity system? Well, the machine metaphor lends itself to useful engineering descriptions such as development, installation, configuration, upgrade, release, put into operation, phase-out, and so on. It also helps to see the characteristics and dynamics of an epoch as a civilization-scale contraption.

The Modernity Machine thesis was developed by in a series of essays starting with this one. It sees modernity as a machine, constructed between 1200 and 1600 (a few centuries earlier than the mainstream theory has it). The early machine operated in parallel while the medieval machine was phasing out, and it still works today on its final day, while a newer one is being turned on.

The Modernity Machine functions through restructuring the relations between four classes: the monarch, the oligarchy, the technocracy, and the workers. The balance of power shifts towards previously weaker parties. There are often setbacks, but the trend persists. The previously suppressed class gains persistent new agency. I tried to sketch that in my notebook:

The Modernity Machine optimized for legibility. To control space, time, people, resources, goods and money, they had to be made readable.

The Power is Shifting

Jacob Fugger (1459-1525) was a merchant who pivoted from textiles to mining. At some point, he also added spices to his portfolio. But what made him rich and influential was his banking business.

How rich? His overall wealth reached 2% of GDP of Europe. Brought to our day, he would be richer than Musk and Bezos.

How influential? He influenced the elections of the emperors Maximilian I and Charles V. Being Maximilian’s main creditor for all his military operations, weddings and other projects, Fugger was in a position to influence European politics.

By his time, the Modernity Machine was already in development, and some upward social mobility was by then possible. Still, the society was strictly split into nobility, clergy, and commoners. Merchants were second-rate commoners, after patricians. For a commoner to become an oligarch solely through money was new. And Fugger went a big step further. He transformed the monarch-origarch relationship from one of divine right to a contractual relationship of creditor and debtor.

For Fugger, monarchs were not just debtors but partners in resource monopolization. He secured his loans by getting leasing rights to mine silver and copper. The demand for copper at that time increased due to other workings of the Modernity Machine: intensified trade (increased demand for coins) and the shift to artillery warfare (cannons were made of bronze, which contains mostly copper).

The oligarchy’s relationship with technocracy co-evolved with the latter’s changing composition. To manage his vast bank network, Fugger needed accountants, auditors, and lawyers. This way, Fugger and other merchants and bankers contributed to the proliferation of new roles in technocracy. It both reflected and accelerated the shift from military or theological knowledge to portable, codified knowledge.

Three centuries later, another pre-industrial entrepreneur, Josiah Wedgwood (1730 – 1795), turned pottery into an industry and pioneered modern marketing. Josiah Wedgwood transformed social relationships as a brander, taste-maker and disciplinarian.

By securing the title “Potter to Her Majesty,” which he used in his leaterhead he seduced oligarchy into buying his “Queen’s ware.” With this, a change in monarch-technocracy relations catalysed a change in oligarchy-technocracy relations.

Queen Charlotte wasn’t the only monarch whom Wedgewood targeted for influence marketing. The other was Catherine the Great of Russia. He made for her an exquisite dinner and dessert service of 944 pieces.

Once monarchs use such goods, they signal prestige, and nobles want a piece of that prestige too. Once nobles want it, wealthy merchants seek to signal that they share the same taste as the nobility. Wedgwood boosted consumer society through a cascade of desire. Masses bought, elites amassed.

The increased demand was caused by other societal changes, both in taste and in means. Regarding taste shift, one example should suffice. Once drinking tea became cool in the island, and the whole economy was on the rise, so more people could afford it, the demand increased so much that the tea imported from the East India company rose from £14,000 in the early 1700s to near £1 million in the 1760s, and then doubled by the end of the century.

Regarding the ability to afford it, the entire economy was growing, supported by and supporting the recently valued principles of hard work and the new tools for measurement and planning. Households shifted from provisioning for themselves to contributing to the marketplace. Wages increased. Women and children joined the workforce for the first time.

The third relation that Wedgwood shifted was that between technocracy and workers. He introduced the division of labour, which Henry Ford later refined. In this case, the shift was not towards reduced worker agency. Previously, one potter would make a pot from start to finish. Now every worker was specialized and replaceable.

Voltaire (1694 – 1778) brought a completely different transformation of monarch-technocrat relationships. With significant wealth, achieved through lottery hacking, business investments and money lending, he bought his independence so that he couldn’t be silenced or starved. He transformed the old model of the intellectual (monarch-technocracy relationship) from a subservient court pet to a negotiated celebrity. Importantly, while he could operate outside the patronage, he made sure to remain embedded in elite networks and exploit them.

Voltaire transformed the technocracy-oligarchy relationship in a similar way to the way Fugger transformed the oligarchy-monarch relationship: by becoming a creditor to the ruling class.

Voltaire influenced the transformation of the oligarchy-worker relationship by eventually supporting the Genevian natifs (initially siding with the patricians) and, through his Ferney enterprise, providing them with a platform to grow as independent watchmakers.

His influence in increasing the agency of a previously weaker class is probably most pronounced in his campaigns for penal reform. Public opinion and secular reason started to hold the system accountable.

Legibility is Eating the World

The Modernity Machine optimized for legibility. To scale something, you need to control it. And to control it, you need to be able to read it, measure it, and order it.

Fugger was exceptionally well-informed. His life is a notable example of early data-driven decision-making in business. The data had to be reliable, timely, interoperable, and consolidated.

He made sure that the data is reliable in terms of capturing and accuracy. In every branch office, every transaction was monitored and diligently recorded. The recording system was first made reliable by using double-entry bookkeeping, which Fugger learned in Venice. Second, Fugger made it reliable by pioneering the use of auditors.

Fugger made sure the information was timely by creating his private information network. Often, he was informed before rivals and monarchs.

The practice of double-entry bookkeeping was closely related to another Italian innovation, virtual money transfer. Fugger scaled up the new practice of transferring money by making corresponding entries in the respective branches, without physically moving money, which, apart from being faster, was also safer by avoiding the risk of road robberies.

And speaking of novel information management, he introduced something that could easily be seen as a precursor to today’s ERP and core banking software systems. Italian banks maintained separate statements for individual branches. A merchant could not survey their entire enterprise or know their total net worth at a glance. Fugger was the first to implement a consolidated financial statement from all his branches.

If Fugger was the master of financial legibility, Wedgwood advanced industrial legibility. Before him, the kiln was illegible and unpredictable. There was no way of knowing the temperature inside the kiln. Initially, he considered using the color change as a proxy, but it proved unreliable. He then started experimenting with measuring the relative shrinkage of a clay gauge. This Wedgood device was one of the first pyrometers.

Like Fugger, Wedgood understood the importance of diligent information capture. He meticulously recorded his experiments in commonplace books. For many of these recods he used codes to protect his findings.

Wedgeood rendered workers’ time legible through a timetable and a primitive clock-in system.

He also made his brand and offering legible. Wedgeood was the first to use illustrated catalogues.

Like Fugger, Wedgewood understood the importance of financial legibility. By introducing a primitive cost accounting system, he realised that the effect of fixed costs can be reduced by producing high volumes.

By securing royal patronage, Wedgewood converted fashion into a legible market signal.

Voltaire and Wedgwood lived in the century following the Peace of Westphalia, which kicked off the formation of the modern nation-state. The state was busy making its contents manageable. It created legibility by implementing simplifications and standardizations that converted complex, diverse local practices into a uniform administrative grid. This project aimed to provide officials with a synoptic view from the centre to streamline taxation. The concrete measures were the creation of surnames, the standardization of weights and measures, and, most remarkably, the creation of a cadastre. By linking a person to a piece of land, the state replaced complex ownership systems that had naturally evolved to deal with uncertainty with a simple one that made land ownership legible to the new bureaucracy.

And while the state was massively making people legible to the state, Voltaire took the first steps toward making the state legible to people. The French legal system was characterized by intense secrecy, with trial records often withheld from the public. Voltaire campaigned for justice reform both through direct requests for revealing the records and through fiction. He authored fictionalized yet factual narratives to expose procedural flaws in cases like the Calas affair.

Voltaire sought to render science legible to a wider audience by writing a book on Newton's theories, starting a tradition that dominates nonfiction today.

In a similar way as the printing press made knowledge reproducible independent of context, Voltaire made his own influence portable. Depending on how you define “celebrity,” you may put him as the third after Erasmus and Martin Luther. But if we define “celebrity” as someone whose private life, personal opinions, and physical likeness are consumed as a commodity by a broad public, then Voltaire was the first European celebrity.

Commits to the Divergence Machine

While all three engineered the Modernity Machine to a significant extent, Wedgewood and Voltaire did so after the machine was already switched on. So unlike Fugger, they also made some — if you allow me a Git metaphor — commits to the Divergence Machine. It wasn’t the start of its development. The first and most feature-bearing commits were made already by Spinoza. Now, in the century of Wedgwood and Voltaire, there were notable contributions and symptoms of a new world model, made quietly in the background of the noisy modernity machine.

The Divergence Machine (constructed 1600–2000) is a world machine that replaces the Modernity Machine. While the Modernity Machine optimised for legibility, homogeneity and convergence, the Divergent Machine spawns variety and proliferation. And to continue with the software development metaphor, treating bugs as features is its normal operating mode.

The Divergence Machine does not seek to subvert the Modernity Machine; instead, it brackets it, rendering centralised control irrelevant by creating civilizational space beyond its reach. This machine requires operators to live in ontological doubt, avoiding the modernist error of premature commitment to existing moral or ideological schemes.

While Josiah Wedgwood and Voltaire were engineers of the Modernity Machine, they also made notable contributions to the development of the Divergence Machine (especially Voltaire).

For Wedgwood, progress was a matter of tinkering. He relentlessly experimented. Although some of it directly contributed to his business, it shows an early sign of the shift from progress as material plenty to progress as growth of instrumental knowledge.

Wedgwood participated in the multi-disciplinary Lunar Society. As Lovell Edgeworth put it (as cited by Tristram Hunt — see the reference at the end), they gathered to share ‘the first hints of discoveries, the current observations, and the mutual collision of ideas.’ It was a dynamic pluralist discourse used to make sense of the expanding scope of experience.

Voltaire, on the other side, attacked dogma with absurdity.

In Candide, Voltaire mercilessly parodied Leibniz’s optimism, which argued that this was the “best of all possible worlds.” By ridiculing the idea of a prefigured moral ideology, Voltaire shifted the understanding of progress from a theological certainty to an evolving argument grounded in messy reality.

His campaigns for tolerance were early steps in creating a civilisational space for plurality.

P.S. In case I made them look like heroes

The world-as-contraption thesis, featuring the Modernity Machine (aka Convergence Machine) and the Divergence Machine, is about evolving relations between humans and technology and how that shapes society, politics, and the economy, and about the roles of art, science, and philosophy in those dynamics. Essentially, it is not human-centric. Yet, when listing the contributions of three “engineers,” I might have inadvertently made them heroes. Let me fix this a bit.

First, it’s three engineers, among many, not the three engineers. These people made something notable, which attracted information-gathering, which, when published, increased their notability and attracted more work that further increased their notability — a reinforcement loop with a similar effect to preferential attachment in networks. There might have been bigger contributors who were not that lucky or were simply quieter.

And second, they were no saints, far from it.

Fugger was interested in money-making above all, and everything was just a means to make more money. The only social project was the Fuggarei, which is often cited as the first social housing project. But it was, in fact, Feudalism 2.0 at the dawn of capitalism. Today, we have the techno-feudalism of Amazon and Alibaba (what should that be, Feudalism 5.0?).

Fugger financed the bloody suppression of the German Peasants’ War, an event that resulted in the deaths of 100,000 people.

Wedgwood became known as an abolitionist, especially for his famous anti-slavery medallion, yet his business depended on the production of sugar. The 18th century sugar economy was driven by the slave trade.

Voltaire often changed his public position to serve his personal interests. In a previous essay, I already mentioned two such cases: his change in position regarding Turkey and taxation. But there are more. To secure membership in the Académie Française, he wrote letters to prominent churchmen (whom he usually mocked) claiming to be a “true Catholic” and asserting that his writings were “sanctified by religion.” He even performed a public Easter communion, admitting to friends that he did it to “edify” his neighbors, while they viewed it as blatant hypocrisy. Voltaire congratulated Frederick the Great on a treaty that abandoned France’s interests. When this provoked a scandal over his lack of patriotism, he tried to mend his reputation by offering himself to the French court as a diplomatic spy. After his humiliating fall from favour in Prussia, Voltaire replaced all the letters he had written to his niece with forged ones to dramatize his side of the story.

In short, people are complicated, and the world is messy. That messiness was a bug for the Modernity Machine but is a feature for the Divergence Machine.

References

Steinmetz, G. (2015). The Richest Man Who Ever Lived: The Life and Times of Jacob Fugger. Simon & Schuster.

Davidson, I. (2012). Voltaire. http://pegasusbooks.com/books/voltaire-9781605981192-hardcover

Hunt, T. (2023). The Radical Potter. https://www.penguin.co.uk/books/299911/the-radical-potter-by-hunt-tristram/9780141984629

Rao, V. The Modernity Machine series: Part 1, Part 2, Part 3

Rao, V. The Divergence Machine series: Part 1, Part 2

Latour, B. (1993). We Have Never Been Modern (C. Porter, Tran.). Harvard University Press. https://www.hup.harvard.edu/books/9780674948396

Max Weber’s “Science as a Vocation.” (n.d.). Routledge & CRC Press. Retrieved February 24, 2026, from https://www.routledge.com/Max-Webers-Science-as-a-Vocation/Lassman-Velody-Martins/p/book/9781138980600

Luhmann, N. (2012). Theory of Society, Volume 1 (R. Barrett, Tran.; 1st edition). Stanford University Press.

Varela, F. J. (2025). Principles of Biological Autonomy (E. A. D. Paolo & E. Thompson, Eds.; a new annotated edition). MIT Press. https://mitpress.mit.edu/9780262551403/principles-of-biological-autonomy/ (Original work published 1979)

The objective of the first essay was to understand how inference rules work. The example used a small target graph that could be fully displayed in a diagram. The resulting graph had the same number of nodes but was denser after generating eight inferred relations. In the second part, the inferred relations were similar in kind, but their number was tens of thousands. There, the inference was on a much bigger graph of millions of facts. More importantly, it was done using six different ways to express the same logic. We learned about the consequences of different design decisions, resulting in different systems along the autonomy-cohesion axis.

In both essays, some benefits were stated, others implied, or listed in a linked slidedeck, but overall, most likely you are still left with the question: Why bother?

That’s what the current post aims to answer.

The usual drivers for using inference rules are performance optimisation and the need for logical reasoning. But rules can also be used for entity reconciliation, analytics, and even for the primary task of generating knowledge graphs from heterogeneous data sources.

All of those will bring immediate benefits. But they would do so even if the rules are not themselves in a graph. And indeed, the common practice is to keep even declarative rules in the application layer. But the big long-term benefits of inference rules can come when they are kept not in the application layer but in the data layer. Such a shift is another contribution to data-application decoupling, with long-term benefits that improve adaptability by lowering the cost of change.

What follows is a quick review of the use cases and benefits of using rules on graphs, maintained in graphs of rules.

Speed

The most popular use case and immediate benefit is the query simplification and performance.

In the example from the previous post, if we want to count the number of uncles, we have to use the following SPARQL query:

PREFIX wdt: <http://www.wikidata.org/prop/direct/>

SELECT (COUNT(DISTINCT ?uncle) AS ?totalUncles)
WHERE {
  {
    # Uncle via father's male sibling
    ?person wdt:P22 ?father .
    ?father wdt:P3373 ?uncle .
    ?uncle wdt:P21 wd:Q6581097 . # Male
  }
  UNION
  {
    # Uncle via mother's male sibling
    ?person wdt:P25 ?mother .
    ?mother wdt:P3373 ?uncle .
    ?uncle wdt:P21 wd:Q6581097 . # Male
  }
}

The same query over the inferred graph looks like this:

PREFIX s: <http://velitchkov.eu/shapes/rules-post#>

SELECT (COUNT (DISTINCT ?uncle)  AS ?uncleCount)
WHERE {?person s:hasUncle ?uncle .}

It is not just way simpler. It is seven times faster.

Identity

The same entity can appear with different global identifiers. This may be because the graph combines datasets from different publishers, each using its own identifiers. Or it could be that, when generating a knowledge graph from heterogeneous data structures, identifiers are missing and must be created from the content of a source file (such as JSON or XML). In cases like those, rules can infer triples that link all identifiers of the same entity. Sometimes the property owl:sameAs can be used, but there are better ways.

Graph Generation

Inference rules can be used to generate graphs from heterogeneous data structures. One reliable way is to use Façade-X to generate a raw RDF graph, then apply SHACL rules to that graph to enforce the desired identities and semantics.

Façade-X is a method for abstracting heterogeneous structures into an RDF graph. I have written a couple of essays about it previously. Currently, Façade-X is supported by the open source tool SPARQL Anything. Now, Façade-X is on its way to becoming a standard, with more implementations to come. Some are already in development.

SPARQL Anything can now generate RDF graphs from XML, JSON, CSV, HTML, Excel, Text, Binary, EXIF, File System, Zip/Tar, Markdown, YAML, Bibtex, DOCx, and PPTX.

Once the raw graph is generated, SHACL rules can apply the desired approach of resource identifiers and the intended semantics for the target knowledge graph. Resource identifiers are minted by concatenating a namespace and a local name. The local name can reuse some identifier from the source data, or be constructed as a concatenation of several values, generated with a UUID algorithm or created as a hash. The last option makes this rule-based approach superior to some mainstream approaches, such as those using the RDF Mapping Language RML. RML does not support hash functions, while they are standard in SPARQL. Also, using RML requires a solid understanding of source formats and structures, whereas using Façade-X and SHACL rules requires only knowing SPARQL.

Data Catalogues

The approach described for generating knowledge graphs can be used to automatically catalogue data. What needs to be known is the data source and the target catalogue model. As long as there is a protocol to connect to the data store and read privileges, a Façade-X can generate the raw graph, and SPARQL (or other SHACL) rules can transform it into the desired catalogue shape.

Data Quality

The most popular use of SHACL is as an RDF validation language. A SHACL shapes graph is applied to a data graph by a SHACL engine, and the result is a validation report. The report tells us what and where the problems are, but the problems remain.

With inference rules, some of these problems can be fixed. A typical case is when a value is missing, but it can be calculated or substituted. Another occurs when a value, such as a date, is not in the required format but the error follows a consistent pattern.

Inference rules do a great job of solving issues with incomplete data. There can be a missing value, but for analytical purposes, another value is good enough, so it can be used.

What is important in all these cases is to have that change clearly recorded so that the provenance is clear and it is easy to tell what comes from the source data and what comes from data enrichments. This kind of provenance information can again be recorded using inference rules.

Long-term benefits

When business rules are not in the application layer but in the data layer, it contributes to application-data decoupling, reducing technical debt and the cost of change and integration. Let’s unpack this.

The corporate IT in a large organization is built with an application-centric mindset. It is a systemic problem arising from how IT investments are managed. Typical IT investments focus on immediate business needs, staking out accidental application boundaries that inevitably become silos. The chosen solutions are driven by risk aversion and comfort: either applications are purchased from large vendors or developed using technologies the teams are comfortable with. On top of that, there is a functional requirements bias that persists because demonstrable features satisfy decision-makers, while “unsexy” non-functional needs like interoperability are ignored. In project boards, “space” (the enterprise) and “time” (the future) are not represented. All this leads to fragmented data, high costs of change, and high costs of integration. I described all this in detail in

The way to resolve is, as I suggested there, to unify and decouple at the same time. To unify entities’ identity through URIs, structure via RDF, and semantics through shared ontologies. And to decouple data from applications. When data is self-describing, applications become mere “visitors,” preventing them from owning — and ultimately breaking —the information they serve.

When we have inference rules working on RDF graphs, it’s halfway there. The other half is to keep these inference rules not in the application layer, but as RDF graphs themselves. This improves data governance (easier to add metadata and extend as needed), but the bigger benefit is that it contributes to the decoupling of data from applications, an architecture style also known as data-centicity.

Yet at 76, he founded a startup and turned it into a successful international business.

Background

Voltaire wasn’t planning to start a business, nor did he need to. His interests were in writing, theatre, and political causes such as penal reform. He had plenty of revenue streams;1 he didn’t need another. However, his experience in financial management and the circumstances under which the idea was born might make the endeavour less surprising than it first appears.

Prior investment experience

In 1729, with the help of his friend, the mathematician Charles Marie de la Condamine, Voltaire took advantage of a loophole in the state lottery system. The prize value was miscalculated, so it was much higher than the total price of the lottery tickets. Winners also had other benefits. If they held government bonds that were devalued at that time, they could be repaid at the original issue price. According to some estimates, Voltaire earned half a million livres from this chicanery.

Another successful financial operation that year was the speculation with shares issued by the duc de Lorraine. Since these particular shares can only be purchased by the citizens of Lorraine, Voltaire had to prove some lineage. His perseverance made up for the far-fetchedness of his proof. In a letter of September 1729, Voltaire wrote:

After my pressing requests, they let me subscribe for fifty shares, which were delivered to me a week later. I immediately took advantage of the popularity of these new shares, and tripled my money.

These two cases were followed by others.

Apart from speculative and business investments (e.g., he invested in a company that supplied the military), much of his steady income came from lending money at interest.

Other startups

The watchmaking wasn’t Voltaire's first manufacturing startup. A few years previously, he set up a small silk business. Since he was previously engaged in agriculture, literally cultivating his garden, a statement he famously ended Candide with, it seems he just moved to the adjacent possible. While he did so more out of a need for something to cheer him up (at that time, he separated from his niece for the first time in sixteen years) than out of necessity, his silk business, as the subsequent watchmaking, shows his affinity for vertical integration. Voltaire’s silk business started with raising silkworms, but did not stop at producing silk. He also produced silk stockings.

Circumstances

When Voltaire fell out of favour with the French court, he bought an estate at Ferney, on the French-Swiss border, not far from Geneva.

In eighteenth-century Geneva, power was held by patrician families. Ordinary citizens and artisans (natifs) had limited rights. This situation caused numerous conflicts and escalated in the 1760s. French intervention and a military blockade in 1767 temporarily resolved the issue. But the patricians later rescinded the agreement, leading to a wave of violence in early 1770.

At that time, Voltaire initiated the transformation of a nearby fishing village, Versoix, into a trading port to reduce his dependence on Geneva for his supplies. Such a project could also benefit France, for which he convinced the French Prime Minister, Duc de Choiseul, who promised to support it financially.

Voltaire believed that dissatisfied natifs would be willing to move there and build a life away from their oppressors in Geneva. And indeed, quite a few were ready to move, which further angered the Genevan patricians, who were already worried that their local trading and political dominance would be challenged by a new French trading port.

In the meantime, some protesters fled Geneva and were given French residence permits. Since they couldn’t move to Versoix — the project town was not yet built — many settled in Ferney and its surroundings.

It so happened that the French government was facing financial difficulties and couldn’t begin the promised investment in Versoix.

Voltaire realised that many of the emigrants were skilled craftsmen. So, while waiting for the Versoix to be built, he can help them start a business as independent watchmakers.

Watchmaking Business

That’s how the Ferney startup took off as something between a social enterprise and a business incubator.

Quick facts:

• Craftsmen: from 40 in 1770 to 600 in 1773

• Revenue: from 450K (1775) to 600K (1776) livres

• Markets: Spain, France, Russia, Turkey, Holland, Italy, Algeria, Tunisia

Voltaire established the watchmaking business at Ferney as a social enterprise. Without losing its role as such, the startup grew into a successful business selling watches in more than eight markets and, at its peak in 1976, generated revenue of 600K livres annually, equivalent to ten million euros today.

These extraordinary results were almost entirely due to Voltaire’s personal efforts, for he had reinvented himself in a protean variety of roles: not just the overall manager, co-ordinator and organiser but also the financier, the virtual bank manager, the sponsor, the builder of homes and factory space, the buyer of precious metals and other raw materials and the international sales manager.2

Voltaire realised that businesses are most vulnerable at the outset and created the most favourable conditions for production: housing for watchmakers, tax exemptions, and interest-free financing, which he supplied himself.

He turned the theater in his house into a watchmaking workshop. In a letter to the marquis de Jaucourt, Voltaire wrote:

Our theatre auditorium, which you remember, has been transformed into workshops. There, where we once recited verse, we are now melting gold and polishing cogs. We must build new houses for the emigrants. All the workers of Geneva would come here if we were in a position to house them. We must remember that everyone nowadays wants a gold watch, from Peking to Martinique, and that there used to be only three great manufacturing centres, London, Paris and Geneva.

In the same letter, he expressed pride in his religious tolerance achievements:

Sensitive and tolerant souls will be happy to learn that sixty Huguenots live so well with my parishioners, that it would not be possible to guess that there are two religions here.

Alongside his efforts to secure government protection and supplies, Voltaire began seeking customers through his social network. Given the high profiles of his contacts, he achieved good initial results. But he soon realised it wouldn’t scale and started looking for sales representatives. In some cases, like Spain, his efforts succeeded; in others, like Rome, they failed.

The sales situation in Russia and Turkey is particularly interesting. While the Russian market was a good example of strong sales volumes achieved by exploiting the admiration of a single, very rich fan, Catherine the Great, the business in Turkey was conducted through trade representation in Constantinople. The case is interesting as an example of how commercial interests prevail over ideology. While Voltaire had previously enthusiastically supported Catherine’s military operations against Turkey, the successful trade with Turkey now reversed his position.3

Voltaire’s change of position regarding Turkey is rather typical. There was a similar case with taxation. As mentioned earlier, to help the business, he lobbied and achieved a tax exemption. That was easier to defend when the business was growing, and its survival depended on it, but less so later, when it became profitable. Tax farmers, learning of the prosperity in Ferney, tried to get their share. For Voltaire, achieving tax exemption was relatively easy with the previous finance minister, who was his friend, but less so with the new one. And yet he managed to negotiate it. This time, however, tax farmers demanded compensation.

After some successful mediation, Voltaire helped secure an agreement. For the first year, he personally financed the agreed compensation. But then, his reputation as an excellent mediator between the tax authorities and the local population led the Estates-General to appoint him as a tax advisor. Now, Vortaire, who had previously fought for tax exemptions for the watchmakers, proposed a progressive tax regime to finance future compensations, so the rich watchmakers would pay more than the poor peasants.

It’s worth noting that, despite his advanced age and his multiple roles in keeping his watchmaking enterprise running, Voltaire continued to write plays.

Regarding the Ferney watchmaking, it’s quite plausible that, like most entrepreneurs nowadays, Voltaire planned to sell it at some point. In a letter from 23 of December 1775, he wrote:

I am convinced that our property will double in price within a year.

The business reached its peak in the summer of 1776. Then it started to decline. The investment in building new houses to accommodate the growing colony started while the tax exemption was in effect. But now, there was a new finance minister, who restored both the suspended land tax and the required community labour for road maintenance. While this pushed some watchmakers away from Ferney, the business continued for a few decades after Voltaire's death in 1778.

In the list of entrepreneurs

If Voltaire has to be listed, not only among prominent Enlightenment figures and famous playwrights, but also among successful pre-industrial entrepreneurs, who else will belong to that list?

I would nominate Jakub Fugger and Josiah Wedgwood. Although the three of them differ in the size of their businesses, wealth, and business models, they are comparable in how they contributed to the development and operation of the modernity machine. I’ll elaborate on this in another essay.

The limits of new AI, such as LLMs, have prompted renewed interest in older AI (GOFAI), which was rule-based. The interest centers on how knowledge graphs support factual grounding, ontologies get a lot of new attention, but rules are rarely mentioned.

Rules help in dealing with various technical problems. Earlier this year, at a knowledge graph-based project, I proposed a solution to several challenges based on inference rules. At the Connected Data Conference in London, I shared how this was progressing and the benefits. Here are the slides. There is also a recording. I’ll touch upon some parts of that in the next part.

This post is part of a mini-series on inference rules, which is part of a larger series on rules, which is part of an even larger series about autonomy and cohesion.

The focus of this mini-series is inference rules working on knowledge graphs, where the rules are also stored in knowledge graphs, more specifically, using the Shapes Constraint Language (SHACL).

In the previous part, I used a ruleset of three rules attached to a single SHACL shape node to infer “has uncle” from “has parent” and “has brother”. That was done on a small example graph with nine nodes and eight edges. Now we are going to do it on a bigger graph, the represented relation in which are actual facts. We will also need one additional rule. More importantly, we’ll experiment with representing the same logic with different ruleset structures. From that, we can learn not only how to engineer SHACL-based rule graphs, but also that, even at this level, the dynamics between Autonomy and Cohesion can be observed.

Six different structures for the same logic

To test the same logic modelled with different rule connectivity, we’ll use a subgraph of Wikidata, containing people, their parents, and the siblings of their parents. Ignoring reverse relations and non-English labels, this gives a graph of over four million triples, which is sufficient for our purposes. You can run this query to generate that graph yourself from Qlever. In the last section, I’ll explain how to reproduce the whole experiment, step by step, including how to materialize this graph and run the different configurations of the rules graph on it.

There are “mother” (P25) and “father” (P22) properties in Wikidata, which, to maintain the relational directionality, I’ll refer to as “has mother” and “has father.” There is no “has brother,” though, so we’ll need another rule in which to define “has brother” as any “sibling”(P3373) with “gender”(P21) “male” (Q6581097). That’s the additional rule I mentioned earlier.

There are more than a dozen ways to structure an SHACL graph with a ruleset that generates “has uncle” relations. I’ll pick six of them and will record the rule execution time so we can compare them.

Four rules, one shape

First, let’s start with a structure similar to the one used in the previous part, but this time with a variation of the rule for constructing uncle relations. We’ll use a single node shape to generate all nodes on which the four attached rules will be applied.

Since all rules are attached to one node shape, this node shape must specify the target nodes for all rules. The target nodes are the subjects of “has mother,” needed by the rule (1) to get “has parent,” the subject of “has father,” needed by the rule (2) to infer “has parent,” and the subject of “has sibling,” so that for those with gender male (Q6581097), it will construct “has brother” relations. During run time, these target declarations will produce the focus nodes that will be prebound to the $this variable in each rule.

What is specific about this initial rules setup is that the uncle rule (4) uses the output of the other three rules as input. It needs triples with “has parent” predicate, which are constructed by rules (1) and (2), and triples with “has brother” predicate, which are constructed by rule (3).

The dashed arrows show the rule dependencies. The solid line shows the actual sh:rule property in the graph, linking a node shape to an instance of sh:SPARQLrule. All other properties are not shown in the diagram. Of them sh:order and sh:deactivate are quite important, as you’ll see in the last section.

Later in this article, as a shorthand for this configuration with a single node shape and a fully dependent uncle rule, I’ll use the following icon:

The next configuration follows the same overall logic and will generate triples with identical quality and quantity. This time, however, the uncle rule doesn’t use parent relations. It depends only on inferred brother relations and computes uncles from the property chains “has mother”—“has brother” and “has father”—“has brother.”

Another configuration can be such that the uncle rule computes “has brother” by itself but relies on rules (1) and (2) for “has parent.” As I wrote earlier, there are many possible ways to express the same rule logic. The point here was to pick one structure in which the uncle rule is neither fully dependent nor fully independent of the inferencing of the other rules.

Although the uncle rule no longer depends on the two parent rules, we keep them as they are. Why? First, they still provide useful shortcuts that speed up queries, and second, we need to maintain the same quantity and quality of inferred triples so we can compare the different structures of the rules graph.

As a shorthand for this configuration with a single node shape and an uncle rule, dependent on one of the other rules, I’ll use the following icon:

In the last ruleset configuration with a single-node shape, the uncle rule (6) is independent of other rules. It doesn’t rely on inferred relations, only on asserted ones, and computes the uncle relationships by itself.

As a shorthand for this configuration with a single node shape and independent uncle rule, I’ll use the following icon:

Four rules, four shapes

Now, let's see what happens when each rule has its own node shape and that node shape targets only the nodes needed by that rule. The rules will be the same, and the three configurations will be of the same kind, where the uncle rule is fully dependent on the other two, semi-dependent (using only “has brother”), and completely independent. The main difference is that, whereas in the first three configurations, all rules depend on centralized focus node generation, in the second set of three configurations, focus-node generation is decentralized.

Here’s the first configuration. Again, it is made up of rules (1), (2), (3) and (4), but each one with its own node shape.

Now all the rules are applied to all and only the nodes generated by their node shapes. The uncle rule (4), as in the previous ruleset series, depends on the other three rules. Its node specifies its targets along an inferred property, so the generation of focus nodes here also depends on rules (1) and (2). Unlike the uncle rule, the node shape target depends only on these two (still, a lot) and not on rule (3), which infers “has brother” triples.

Here I have placed the numbers on the node shape, since, as you’ll see in the last section, deactivation is done at the node level, not at the rule level. The idea is that, since each node shape only produces targets for its own rule, when the rules are not used, it’s better to switch off the whole thing.

As a shorthand for this configuration with separate node shapes for each rule and an uncle rule, dependent on all other rules, I’ll use the following icon:

In the next configuration, we will use shape (5) to generate uncle relations. The rule of shape (5) depends only on the “has brother” triples inferred by rule (3).

Here, the node with the uncle rule does not depend on inferred triples to generate focus nodes.

As a shorthand for this configuration with separate node shapes for each rule and an uncle rule, dependent on one of the other rules, I’ll use the following icon:

In the last configuration, node shape (6) shares the same target, but its rule is independent, making the entire unit completely independent in the graph (excluding the prefix declarations; more on that later).

As a shorthand for this configuration with separate node shapes for each rule and a fully independent uncle rule, I’ll use the following icon:

Autonomy and Cohesion

Running all six configurations on the same graph produced the same number of triples, 192893, of which the same number of uncles, 19950 (if you decide to reproduce it, you may get different results, depending on when you run the query to extract the subgraph of Wikidata).

The result is basically a graph with “has parent,” “has brother,” and “has uncle” edges. Here’s one cluster of it:

The number of parents, brothers, and uncles triples is the same, but because of the different structure and dependencies, it took a different time.

These results are interesting not only for what we can learn about SHACL-based rules graphs, but also for system engineering in general. To have a more useful comparison, apart from the performance perspective, or short-term efficiency, we need to add at least two long-term perspectives: cost of change and fault tolerance.

If we compare the two columns, we see that configurations with separate node shapes are consistently faster than configurations with a common node shape. From a SHACL-perspective, the reason is that the common node shape produces focus nodes for all the rules, so every rule is applied to a lot of targets, which, from the perspective of the rule conditions, are irrelevant. In contrast, the configuration with separate node shapes produces only the focus nodes, which are relevant to their rules.

From a wider system perspective, the common node shape with rules 1-2-3-4 is imbalanced towards cohesion. Some of the cohesion results from extreme centralization. All rules depend on one node shape for their target nodes. The rules dependencies add even more cohesion: the uncle rule depends on the inferred triples generated by the other three rules. This makes the system vulnerable. A single bug in the targeting declaration will make the whole system collapse (manifested in this case in either giving an error or inferring zero triples). On top of that, if there is an error in any of the first three rules, the uncle rule will not work.

The 1-2-3-4 common shape node configuration needs to be excluded as an implementation option due to excessive cohesion (both structural and logical). The configuration 1-2-3-6 with separate node shapes also needs to be excluded for excessive “autonomy.” (I put autonomy in quotation marks, since in purely technical systems we can speak of “autonomy” only metaphorically as a proxy for degrees of freedom and decoupling, as discussed in another essay.)

The best-performing shape is the multi-shape 1-2-3-4 configuration, which produced all inferred triples in 2135ms (top-right cell in the table above). Not surprisingly, it’s one of those configurations where autonomy and cohesion are well balanced. There are separate node shapes for each rule (autonomy), but there is a lot of logical cohesion bringing efficiency. Once rules 1, 2, and 3 have run, the search space for rule 4 is highly optimized.

Apart from rule 4, depending on the output of the other three rules, its shape also depends on two of the rules, since there are no “has parent” subjects to target unless rules 1 and 2 are executed. So there is still more cohesion than necessary. This can be fixed by targeting the subjects of “has mother” and “has father”. The execution time is now 2514ms (not shown in the table). As expected, reducing this dependency has a performance cost. But that's probably a low price to pay for the increase in fault tolerance.

Yet, the multi-shape configuration with rules 1-2-3-5 has very good performance, second best, and very high fault tolerance. If the rules 1 and 2 don’t work because of an internal error or bad targeting of their node shapes, the uncle rule will still produce all uncle inferences.

What about the cost of change?

An easy way to measure it is to add two new requirements: include foster parents and infer also aunts, besides uncles. In both cases, the multi-shape 1-2-3-4 configuration will require minimal or no change to the uncle rule, whereas the multi-shape 1-2-3-5 configuration will require significant changes to the uncle rule, effectively duplicating other changes, such as adding new rules and modifying existing ones.

The final choice will depend on whether you prioritise modifiability (low cost of change), performance or resilience.

Fault tolerance generally increases with autonomy, at the cost of redundancy, in an approximately linear manner. The cost of change is not directly proportional to the increase in redundancy and depends on other factors. Yet in both series of configurations, those with rule 6 have a higher cost of change than those with rule 5, which have a higher cost of change than those with rule 4. But compared across the series, it’s not that straightforward. For example, the cost of some configuration changes with a single-node shape and rule 6 will be cheaper than implementing the same changes in a separate shape per rule and using rule 5 for uncles. For others, the cost of change will be lower in the multi-shape system.

Different ways of achieving cohesion bring different results. Some improve efficiency but make the system brittle, as is with the system in the left-most position on top. It may also introduce inefficiency. In the case of a SHACL system, such inefficiency may be manifested in the over-production of focus nodes, which increases the search space of SPARQL rules. But that is easily observed also in socio-technical systems, where the economy of scale is reduced by paying for a fat and inefficient bureaucracy.

Simply put, there is bad cohesion and good cohesion, and there is bad inefficiency and requisite inefficiency.

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The focus of this part was on comparing different ways of structuring the graph of rules. In the next one, I’ll review some use cases and benefits.

Now, as promised, a step-by-step guide, including all the code used in this and the previous post.

Step by Step

Here’s how to reproduce the whole experiment.

Step 0: Tool

There are several open source tools you can use to run SHACL rules: the TopBraid SHACL API, its extended version, or pySHACL. Yet another open source SHACL tool, maplib, is currently adding SHACL rules.

For these two posts, I used TopBraid Composer Free Edition. It was discontinued in 2018, but the latest version is still available for download. I keep using it for training courses and workshops, since it has a GUI that makes it easy to run different experiments.

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Inference rules are useful. They bring declarative expressivity — stating what follows from facts rather than how to compute it. But for users, their most salient feature is that they make queries simpler and faster.

This post is part of the Rules series.

I use rules daily in my personal knowledge graph. The most frequent pattern used in queries is linking a block with a page referred to in it. The standard path in Roam is to go to the page reference via :block/refs and then to specify the page via its title using :node/title.

Just like in the example from the previous post “has uncle” makes a shortcut from X to Z, instead of going along “has uncle” and “has brother,” in a similar way the refs-page rule is replacing the route pattern

:block/refs → ?page → :node/title.

In the essay Graph Pruning, for example, both queries for counting typed (in the sense of having a type) pages can be simplified by this rule, making them shorter and faster. The simpler query for typed pages will look just like this:

[:find  (count ?page). 
 :where
  (refs-page "is a" ?isA)
 [?isA :block/page ?page]
]

This is a Datalog rule but in Datomic syntax, so instead of using :- to distinguish the rule head from the rule body, the rule head is put in parentheses. In other words, the rule is a list of lists, the first list being the rule head distinguished with the syntax for grouping and the rest is using the brackets for vectors. The rule for the ref page looks like this:

[
(refs-page ?page-title ?page)
  [?block :block/refs ?page]
  [?page :node/title ?page-title]
]

The refs-page rule simplifies and speeds up the queries. For example, using it will halve the size of the query for the number of words I shared in Writing with Roam.

An important feature of such rules is that they separate domain logic from application code. When rules are themselves nodes in the graph, they are easy to access and inspect. If the graph is based on interoperable standards, the rules can also be fully decoupled from any specific applications and have independent governance. In corporate settings, this becomes critical when organizations need to integrate new data sources, respond to changing business requirements or legislation, or replace a vendor. I will return to this point in the next post.

Now, let’s see how these rules work.

Let’s extend the graph of relations from the previous post with a few more.

If this is an RDF graph, we can define Datalog rules for parent and uncle and use open source tools like Maplib or commercial tools like RDFox and materialize these inferred relations. And that’s how, for example, the personal knowledge graph in the latest Samsung phones work.

But if we want to manage these rules as part of the graph, then we need to either use N3 rules or SHACL rules. SHACL has broader tool support and allows more sophisticated rules than N3. It also has the benefit of expressing the rules with SPARQL. This way, SPARQL, apart from querying and graph manipulation, can also be used for graph generation from heterogeneous data sources, as shown in the post about facade-X, and for expressing rules. Since SPARQL is not as good for recursive rules as Datalog, the next version of SHACL will either allow Datalog rules in SHACL shape graphs or enhance the SHACL rules so that they overcome these limitations.

SHACL rules are either triple rules or SPARQL rules linked to a node shape (SHACL can be extended to include other ways of expressing rules). The node shapes declare the target nodes, which are the computed subset of the nodes in the graph on which the rules are applied. As such, the target node declaration is also an implicit rule.

In this post, I’ll show the graph of rules just as a diagram so that it’s easier to follow. At the end of the next part, I’ll include all the code and the instructions needed to reproduce the examples.

In SHACL, node shapes define the target nodes on which the validation constraints or the rules are applied. A common approach is to target instances of a class. But I want to focus only on relations here and not depend on whether the nodes linked with such relations are declared or inferred as instances of some classes. That’s why I’ll define the target nodes with no reference to any classes but only to properties.

There are plenty of ways to express the rules to produce parent and uncle relations. The same set of rules structured differently creates a system with different efficiency, robustness and maintainability. That’s interesting to study and will do so, on a much bigger dataset and one representing actual family relations. Comparing different rule graph structures is useful for finding the best way to use SHACL depending on the context, but more importantly, it demonstrates how the balance between Autonomy and Cohesion plays out even in simple technical systems. All that in the next part.

For the purposes of this post, I’ll use only one node shape and link all rules to it. To make sure all rules have the right set of focus nodes (that’s how the targeted nodes are called during run time), the targeted nodes declared as the union of subjects of the relations “has mother” and “has father.” Here, subjects is used in reference to the triple structure subject-predicate-object, “has mother,” “has father,” “has parent,” and “has uncle,” being the predicates we’ll focus on.

The node shape node is linked to each rule with the predicate sh:rule which is shown in the diagram below without a prefix. There are statements for prefix declarations, order of execution, and activation switches, which we’ll skip for now but will look into in the next part.

The diagram shows the four main nodes with their type, Node Shape and SPARQL rule, respectively. The dashed arrows represent rule dependencies: the third rule uses “has parent” relation, which can only be produced by the first and the second rule, when their conditions are satisfied.

The target declaration in the nodes shape will make three focus nodes: Mai, Sophie, and Pierre, since these are the only nodes in the graph which are subjects of “has mother” and “has father”.

Once “has parent” relations are available, the third rule, focusing on the subjects of “has mother” and “has father” relations, to which $this will be bound, will produce “has uncle” relations between the nodes linked along the path “has parent”-”has brother”. This will be the resulting graph, shown in green:

What will happen if the third rule is made in a way that uses only asserted relations and is independent of any other rules? And what if each rule is in a separate node shape? Stay tuned for the next part, where we’ll see the answer tо these and other questions using a dataset from Wikidata to generate twenty thousand uncles.

Rules define even their opposites. There is a general ordering that is the norm, and we can only communicate an alternative as deviating from it. To say external rules do not govern us, we say we are autonomous (self-law) or that we are privileged (private-law). Governance implies so strongly the notion of a ruler that an alternative form of governance, anarchy, can only be named in relation to it: “without ruler.”

This essay is part of the Autonomy and Cohesion series and the sub-series about rules.

Cohesion

Rules are a cohesion tool. They reduce interactional uncertainty. By constraining choices and making behaviour predictable, rules allow multiple autonomous agents to coordinate. We learn these qualities of rules from an early age. Make-believe play is random and boring without rules. Coming up with rules and strictly following them is what makes play fun until it exhausts their potential and begs for new rules.

Rules standardize practices (measurements, recipes, spelling, ways of moving) so people can rely on others’ behaviour and build higher-order institutions on top of that reliability. Rules vary in their flexibility and generality, but all perform the cohesion work of aligning expectations across contexts.

When cohesion is understood as both making a whole and working as a whole, two concrete dynamics matter most for rules to enable cohesion. First, rules compress the space of interactions, so coordination costs fall, and then coordination can scale. Second, rules create repeatable patterns that become objects of learning, audit and repair; they turn episodic agreements into durable protocols.

Determination

Rules restrict behavior, structure and meaning.

In traffic, stop at red, restricts motion. In dieting, fast for 12 hours restricts eating time. In boxing, do not hit below the belt restricts physical targeting. All these are restrictions on behavior.

A Haiku must have a 5-7-5 syllable structure. A password must contain at least one capital letter, a number, and a special symbol. A major chord must consist of a root, major third, and perfect fifth. All these are restrictions on structure.

A marathon winner is the one who crosses the finishing line first. A person under 18 is a Minor. An uncle is a parent’s brother. All these are restrictions on meaning.

But on closer examination, the rules restricting structure can easily be seen as restricting meaning. We define Haiku as a poem with a 5-7-5 syllable structure. An allowed-for-this-app password is one that contains at least one capital letter, a number, and a special symbol. A major chord is a chord consisting of a root, major third, and perfect fifth.

Rules may be all about restricting meaning, but they were historically unruly when restricting their own. Rules originated as construction instruments to ensure that columns were erected vertically, beams were straight, and angles were right. Then, after variation on correctness and measuring, their meaning shifted to model and paradigm, which nowadays, when rules are related to algorithms and regulations, seem rather strange.

We keep talking about “meaning” when discussing computational rules. But only humans are meaning-makers. If we bracket this intentionality, then all three kinds of restriction, on behaviour, structure and meaning, collapse into one, determination of a status.

Behavior rules determine the status of an action, for example, is the action permitted. Structure rules determine the status of a structure, for example, is a string well-formed. Meaning rules determine the status of a fact or entity, for example, is this person elected.

Determination is nothing more than a computed distinction, a distinction applied to itself. In the Rule of Saint Benedict, all rules can be changed at the discretion of the abbot. Discretion comes from discretio, drawing distinction. So both applying and bending rules is a matter of drawing a distinction. George Spencer-Brown was right, distinction is the perfect continence.

Computation

Nowadays, the formal expressions of rules looks like this:

Consequence ← Conditions.

The left side follows when the right side holds. The left-pointing arrow can be read from left to right as “if.” Let’s take one of the earlier examples:

Uncle is a bother of a parent.

Sounds like it was taken from a dictionary, and that’s not surprising. Rules restrict meaning. All definitions are rules.

A more formal expression will look like this:

hasUncle(X, Z) :- hasParent(X, Y), hasBrother(Y, Z).

The relationships link pairs of nodes: X to Y, Y to Z, and X to Z. The left-pointing arrow is replaced with:- but it can still be read as “if”. The comma is the logical and, meaning that both conditions on the right side must be true for the conclusion on the left to follow.

This rule is an algorithm to generate hasUncle relationships. If Mei has father Hao, then his brother Wei is her uncle. Replacing the variables X, Y, and Z with the constants Mei, Hai and Wei produces a new relationship, hasUncle, between Mei and Wei.

This rule defines the meaning of “uncle,” but it also illustrates the multiple meanings of the word “rule,” which historically shifted from straightedge to model to algorithm.

First, this rule is an algorithm, where the input of data into the conditions hasParent(X, Y), hasBrother(Y, Z), produces hasUncle relations between X and Z.

Second, this rule also serves as a template for producing such relationships. As such, it illustrates the lost meaning of rule-as-model, which Lorraine Daston is chasing in a big part of her book on the history of rules. That’s also true for rule-as-paradigm since paradigm comes from paradeigma (pattern, example).

And third, even the most ancient meaning of rule as straightedge can be illustrated, if we draw it.

Let’s look at this as a map. If you want to go from X to Z, it’s better to take the “has uncle” route than the “has parent...has brother” route. Via “has uncle,” you can go straight to Z. It is simpler and usually faster. And speed is one of the main reasons to use inference rules, as we’ll see in the next post.

The book has 73 chapters containing rules about the necessary qualifications, rights and obligations of the abbot, the tools of the spiritual craft, what monks should do in each part of the day, the order of prayers, rules about meals, supplies, works, sleeping, and how to treat guests, the young, the sick, and the old.

Chapters 39 and 40 are about meals. Each monk is allowed two daily meals, both of which include two cooked dishes. If that doesn’t correspond to your understanding of ascetic life, wait till you hear the severity of the punishment if one is late for a meal.

This is a post in the Autonomy and Cohesion series. It doesn’t depend on all previous in the series. I even tried to make it self-sufficient. Yet, if you need more context, checking the first two posts in the series will be enough.

Each monk is permitted one hemina of wine (270ml) at every meal. That means the first hemina of wine is given most days of the year on the sixth hour, which is around noon.

If a monk is late for a meal, he receives a warning, and on the second offense, a severe punishment: he is deprived of his portion of wine (Chapter 43).

You may wonder why wine was allowed in the first place, and already at noon. I wondered too. And St Benedict provided a clear explanation. Before reviewing that explanation, let’s first see why the Rule of St Benedict is an interesting text for understanding the Autonomy-Cohesion balance and, more particularly, for the intricacies of some cohesion mechanisms.

Cohesion Mechanisms

All socio-technical systems need to maintain the balance between autonomy and cohesion to remain viable.

The order of St Benedict did that well. At first glance, Benedictines maintained high internal cohesion and high external autonomy, the former enabling the latter. But a closer look reveals a balance both within and between monasteries.

The tools for the internal cohesion were the Rule, the clock (horarium) and the abbot. Still, there was a balance between autonomy and cohesion. The abbots were elected by the monks. Important decisions were taken collectively. Furthermore, the monk’s spiritual journey is highly individual. And the balance is already in the Rule, which provides a middle ground between individual zeal and institutional constraints. That middle ground is what made the order so popular and long-lasting.

Unlike the Jesuits or Dominicans, who operate with high central cohesion, Benedictine houses were very autonomous. Yet, they were well coordinated and maintained remarkable cohesion, although monasteries were hundreds or thousands miles apart.

In the Cohesion Forces and Tools, I provided an overview of the main cohesion mechanisms.

Some of them act at a personal level, like the need for safety, to belong, to reduce uncertainty, and to increase self-esteem.

Others act at the social level. Without distinguishing between forces and tools, the social cohesion list includes: social identity, compassion, loyalty, empathy, language, rituals, norms, rules, standards, laws, protocols, uniforms, goals, plans, decisions, reports, meetings, and coordination tools. Most of these work in any kind of organization, together with operational dependencies, social identity, and efficiency pressures. In social networks, shared interests, shared aversions, memes, and algospeak are the main mechanisms of cohesion, complementing the forces at play at the personal level.

All cohesion forces and tools provide constraints. In this essay, the focus is on two of them, rules and norms.

Rules are tools of codification, establishing explicit boundaries that achieve unity through compulsion. Norms operate as organic forces, relying on internalization to guide behavior.

But norms are even more special than that.

Norms Are a Special Species

Now back to the Rule of St Benedict, and why wine was allowed, not only that, but a good portion of it, and already at noon? St Benedict explains:

[W]ine is by no means a drink for monks; but since the monks of our day cannot be persuaded of this, let us at least agree to drink sparingly and not to satiety

Now, in the spectrum from no-wine to wine according to the discretion of the friar, the expected potential rule “no-wine” as emphasized by St. Benedict with “wine is by no means a drink for monks” is reduced as severity to “one hemina per meal”, because of the norm “the monks of our day cannot be persuaded of this.”

It turns out that, while both rules and norms restrict autonomy, norms can also enable autonomy, support or be converted to rules, and, as the example above shows, reduce the severity of a rule.

It’s worth looking at these four cases individually.

1. Norms restrict autonomy. Unlike rules, they don’t do that through codified punishment, but through social friction. We join the back of a queue not because a guard is present to make sure we do, but because a fair waiting norm and a queuing protocol restrict our autonomy to walk straight to the counter. The norm and the protocol act as coordination mechanisms.

2. Norms enable autonomy. The norm “to improvise” enables the autonomy of the soloing jazz musician, but that only works because of the constraints of the tempo, key, chord progression and turn-taking.

3. Norms make rules work by enhancing them. The library rule to be quiet is weak on its own unless enforced by the collective glare one receives when their phone rings. It is similar to the traffic. No police force will be sufficient to ensure rule-following if the rules are not massively internalized as norms.

4. Norms make rules work by softening them. After the pandemic, working from home was no longer supported by the force of the global crisis, but since it was turned into a norm, it brought hybrid office rules.

That last one was similar to the way the norm, “the monks of our day cannot be persuaded of this,” pushed the default rule of no wine to one hemina of wine. By doing so, the norm did not just make the rule acceptable. Although rules are listed as tools for cohesion, they are not such by themselves. In the case of the one-hemina-per-meal rule, it was only the balancing act of the norm that made it a cohesive tool.

Claims and Biases

Claims are biased. There is a self-serving bias that often influences all three claims. It can lead to exaggerating the importance of the main claim and/or the meta-claim of its originality, or the strength of the support claims. If they are accepted, this can benefit the author with money or prestige. The value can also come in the form of tenure, grants, speaking invitations, or psychological benefits like recognition, perceived influence, and ideological validation.

The core claim is mainly prone to confirmation bias. Confirmation bias filters not only the data selected but also how the question is framed. Evidence is more likely to be searched, interpreted, and cited if it aligns with what the author expects or believes.

The supporting claim is prone to appeal-to-authority bias. In its lightest form, this is the casual name-drop — Stephen Hawking said it, so it must be right. In scholarly writing, it manifests as citation pathologies.

A lesser-known bias is something which I call the elegance bias. This is the tendency to prefer ideas that are simple, symmetric, or mathematically beautiful — even when the world is not. In physics, for example, elegance bias has led researchers to favor unified theories or supersymmetry models not because data support them, but because of their elegance. As Sabine Hossenfelder puts it, when physicists judge the promise of a newly invented but untested theory, they “draw upon the concepts of naturalness, simplicity or elegance, and beauty.” This aesthetic filtering can push certain research directions while marginalizing others.

The confirmation bias I mentioned earlier is indeed the most popular one, in the sense of being the most common and the most talked about. But there is a bias that is even more frequent, yet few talk about it. That is the God’s-eye-view bias. It is typical of all religious texts (and maybe it shouldn’t be called bias there), but it is equally present in all scientific books and papers (the exceptions are so few that we can safely ignore them). It’s again a God’s-eye view, but it might be more recognizable if it is called objectivity bias. It is so much in the blind spot of science that what I call bias, most will call duty. The duty of a good scientist is to be objective.

The God’s-eye-view bias is based on the belief that there is reality out there which is perfectly knowable and independent of our minds and actions. Such a stance assumes the observer can be removed from the observation, an idea increasingly challenged in both physics and philosophy. QBism and other participatory interpretations of quantum mechanics argue the opposite: that all measurement is relational, and no fact exists without an agent’s involvement.

When the Gods-eye-view bias is baked into the meta-claim — “this is how it is, not just how I see it” — the claim resists challenge. It pretends to speak from outside all contexts. In this sense, scientific writing often inherits not only the rhetorical habits of theology but also its authority structure.

One experimental tool to resist this bias is E-prime — a version of English without any form of the verb “to be.” By removing “is” and “are”, writers are forced to rephrase claims with reference to context or perception: “this appears to me as…” instead of “this is…” While E-prime was suggested as a way to improve clarity, and the motive for introducing it was not related to the God’s-eye-view bias, I find that it has this nice side effect: by applying it, we can see how deeply this bias is embedded in language itself.

Sometimes I think that small doses of elegance bias can cancel out some of the God’s-eye-view bias. Like beauty can twist the truth, truth-chasing may be counterproductive based on a narrow view of beauty. :

there’s a way of talking about truth, where it’s very easy to think of truth as different from the beautiful, say, and that’s because we think of truth in terms of the correctness of propositions and we have an idea of correctness or of correspondence. But from a phenomenological perspective, that actually is a secondary sense of truth, and the primary sense of truth is disclosure or presence, or, to be you know, technical in the way that Husserl uses the terminology the you know, the evidencing of something. So evidencing is the you know, we use evidence as a noun in English we think here’s a piece of evidence, but that another languages evidencing has this verbal sense where you disclose something, you uncover it, you reveal it, it comes to presence.

While the elegance bias primarily arises from a search for beauty in mathematical expressions, if that search shifts to human experience, we might reduce both the elegance bias and the God’s-eye-view bias.

Attributions, IP, and AI

The main meta-claims are about attribution. The meta-claim for the core claim can be that it is an original idea of the author, while that might not be the case. Or that it is not the original idea of the author, while that might be the case. For instance, several Arabic texts from the 9th to 13th centuries were attributed to Aristotle to boost their authority, even though the actual ideas were Neoplatonic or newly developed by the translator-authors. Other Islamic philosophers attributed their own ideas to classical sources, masking their originality, not so much to increase credibility but as to follow a convention in Islamic philosophy to state that one is repeating the wisdom of the past.

In the modern world, attribution is bound to the machinery of intellectual property: originality becomes not just a virtue but a legal condition. In some cultures, especially modern Western ones, originality means ownership, and ownership implies rights. But that was not always the case, and in some places it still isn’t. In medieval China, the emphasis on individual authorship and ownership, as understood in the West, was often secondary to collective or anonymous forms. Even today, Chinese IP law retains traces of this collective orientation, emphasizing utility and shared benefit over originality for its own sake. Similarly, many traditional knowledge systems — from Andean farming techniques to West African music — treat knowledge as a communal inheritance rather than an individual asset.

The strong Western sensitivity to intellectual property is strangely inverted by the very institution that most profitably exploits it: academic publishing. It celebrates the sanctity of authorship and originality while operating on a model that strips both of their substance. As notes, scholars have become both the unpaid workforce and the paying customers of a system that feeds on their own production.

A not-wholly-unfair analysis of academic publishing would be that it is an industry in which academics compete against one another for the privilege of providing free labour for a profitmaking company, which then sells the results back to them at monopoly prices.

The paradox extends beyond academia: citizens, through public taxes, already fund most research, only to be asked again to purchase access to its results — sometimes at the price of an expensive book for a seven-page paper. What is defended as the protection of intellectual property thus becomes a mechanism for its expropriation. The system rewards not the creation of knowledge, but its circulation within a closed economy of prestige and metrics.

Academic publishing is a medium that aggregates, validates, and redistributes knowledge within institutional boundaries. Artificial intelligence extends this logic to a planetary scale. The largest investment wave in history now rests on a technology that similarly feeds on existing knowledge, yet without even the pretense of attribution. Its disregard for intellectual property stems not from cultural specifics, as with China, or from a commons-based ethos, as with open source projects, but from pragmatic erosion. The IP is highly valued again, but its meaning has shifted to Infrastructural Property amid global meaning drift.

On the other hand, the AI synthesis is natural, just the scale and speed look overwhelming from the perspective of a single human. But single humans, depending on when they wrote what they wrote, had different possibilities for knowledge synthesis too. :

Modern authors have the advantage that they have access to more data. But I find their opinions easier to predict, so I often prefer older authors since they surprise me and therefore expand my worldview more.

It seems LLMs continue on that same path; it’s just the ability to access more data and quicker than a single human could, which makes it look inhuman, but, as I wrote elsewhere, it’s natural.

The agent, human or not, is the medium, just like the medium is the agent.

The only meta-claim that holds in all cases, then, is that of knowledge synthesis.

SPARQL is easier than you think. Thinking in containers helps there as well, as I showed elsewhere . And if you are not interested to learn it, lazy, or in a hurry, LLMs know SPARQL, so they can help you.

Façade-X can be (and is) used to unify the files you work with, so you can get a powerful personal knowledge graph. It can be (and is) used at the corporate and multi-organizational level to unify and integrate data, and unlike proprietary alternatives, without creating technical debt and at no cost.

It has now been four years since the paper introducing X-Façade was published. In the meantime, the reference implementation SPARQL Anything, built by the leading authors of that paper, Enrico Daga and Luigi Asprino, is already capable of applying Façade-X on over a dozen different file formats.

This is the second part on Façade-X (and the 5th post in the Containment series ). In the previous part, I went through several examples to show how different structures are interpreted in a unified way.

It turns out that every data structure is a container that holds one or more containers, which can be optionally ordered and typed. Each container indicates an optionally typed boundary and can contain zero or more nested containers of the same kind. The deepest level contains one or more literals.

The examples in the previous post were with CSV, XML, and JSON. These are formats for structured data. But about unstructured data?

Most of the unstructured data today is published as HTML. If Façade-X can unify it, then mixing data from CSV, XML, and JSON would be trivial.

The Graph Façade of HTML

Recently, I published a simple HTML page with links to my slide decks, scattered in different places. I’ll use this page as an example.

Running this generic construction query on it

PREFIX fx: <http://sparql.xyz/facade-x/ns/>

CONSTRUCT {?s ?p ?o}
WHERE {
  SERVICE <x-sparql-anything:> {
        fx:properties fx:location “https://kvistgaard.github.io/slides/” ;
        fx:media-type “text/html”           .
        ?s ?p ?o
  }
}

will generate a graph of 241 triples, which looks like this

How come an HTML of less than 30 visible lines of hypertext produces so many triples? Well, it turns all elements into a graph and there are plenty, even in this small page.

Let’s see how many types of containers there are and their instances.

So there is one Heading1, two Heading2, three Heading 3, 16 paragraphs and 17 hyperlinks.

Now we can ask all kinds of questions. As an illustration of one such question, let’s get all the visible content ordered, with the format type, paragraph or heading, and all hyperlinks.

This query is a bit more sophisticated because it uses relative hyperlinks, as some of the slide decks are HTML pages stored in the same repository as the page with the collection of links. At the end of the post, there will be a section with step by step guidance for those who want to reproduce these examples.

So far, we used CSV, XML, JSON and HTML. All these formats are different, and yet they have something in common: they are open standards. Sadly, a lot of information is locked in proprietary formats. And the majority of those happen to be formats of Microsoft. Can Façade-X help there?

Modelling the Mazes of Microsoft

To start with, Excel is an obvious choice. First, in case this needs reminding, there is a global dependence on Excel.

And second, it will be easy to compare with the CSV, XML and JSON examples from the previous part.

The example data there was not random. All these people are polymaths. The other thing they have in common is that they are all known mathematicians. Some of them are also known for their work as philosophers, and others as artists. They are now all in one Excel workbook, in two separate worksheets

Façade-X distinguishes between a resource and a data source. A resource contains a data source, which contains one root container. In all previous cases, we had the file name as the resource. Façade-X turns that file name into a named graph identifier, containing the data source, the root container, containing everything else. If we look at what is generated not as triples but as quads, then the fourth element of each quad will be the named graph. If we take the first CSV and ask for the graph, we’ll get this:

It can be read as: subject-predicate-object-context.

But if we do that on an Excel workbook, we get something more interesting.

The resource we query is partitioned into two resources, which Façade-X will interpret as two named graphs. Each of them contains a data source — the root — which contains the triplified content of each spreadsheet. Here is the resulting graph TriG format, where the containment structure will be easier to see:

@prefix xyz:  <http://sparql.xyz/facade-x/data/> .
@prefix rdf:  <http://www.w3.org/1999/02/22-rdf-syntax-ns#> .
@prefix fx:   <http://sparql.xyz/facade-x/ns/> .
@prefix xsd:  <http://www.w3.org/2001/XMLSchema#> .

<file:///C:/example-datasets/mathematicians.xlsx#artists> {
  [ rdf:type fx:root .
    rdf:_1 [ xyz:birthYear “1404”^^xsd:int ; 
             xyz:name “Leon Battista Alberti” ] ;
    rdf:_2 [ xyz:birthYear “1471”^^xsd:int ; 
             xyz:name “Albrecht Dürer” ] ;
    rdf:_3 [ xyz:birthYear “1930”^^xsd:int ; 
             xyz:name “Anthony Hill” ] ;
  ]
}

<file:///C:/example-datasets/mathematicians.xlsx#philosophers> {
  [ rdf:type fx:root .
    rdf:_1 [ xyz:birthYear “1861”^^xsd:int ; 
             xyz:name “Alfred North Whitehead” ] ;
    rdf:_2 [ xyz:birthYear “1596”^^xsd:int ; 
             xyz:name “René Descartes” ] ;
    rdf:_3 [ xyz:birthYear “1623”^^xsd:int ; 
             xyz:name “Blaise Pascal” ] ;
  ]
}

We got this containment pattern: { [ [ ][ ][ ] ] }.

Next up is Word. Similar to HTML, it contains a sequence of headings, paragraphs and other elements such as bullets and tables.

What is more interesting, and sets MS Word apart, are the comments. Interestingly, MS Word has been notoriously bad at extracting comments, and I often use SPARQL Anything to get them out.

Façade-X sees each comment as a container, containing containers with the comment author, the comment text, and the thread number. In the last section, I’ll share the query that will get the comment, the text of the comment, and the comment author.

Next up is PowerPoint. A PowerPoint slide-deck contains sections (optionally), containing slides, with their title and other content. I’m rarely using PowerPoint for workshops and conference presentations anymore, but I still use it for my training courses. These course materials are full of hyperlinks. And getting them together with their slide and what object they were on, used to be a challenge. PowerPoint itself offered no help for that. And today, in 2025, there is no out-of-the-box way to do that.

You may ask, what about Copilot? It’s useless so far.1

And what about Claude Code? I tried today to get the links with it. The initial answer was wrong. After some minutes and tokens spent and kWh energy consumed, it finally got it right, and produced a CSV listing the hyperlinks and on which slide or speaker note they are.

Yet, SPARQL Anything does it right away, reliably, efficiently and even the query needed is very short.2

One query, many quarries

SPARQL queries RDF graphs exposed via a SPARQL endpoint. But importantly, one query can get and combine data from several independent endpoints. SPARQL Anything extends the use of the SERVICE clause so that the address of each resource becomes an endpoint that can be queried, be that in your file system, or somewhere on the web.

But what about REST APIs?

Here’s an example of a query getting the issues from one the repositories of the Model Content Protocol using the GitHub API:

So, going back to what I started with in Part 1:

The problem comes when you need to answer a question, where parts of the answer are scattered across heterogeneous data sources. One part of the answer may happen to be in a JSON file, served from an API, another is in an Excel workbook, stored in your drive, and yet others are in Microsoft Word, CSV and XML.

Now, in one query, one SERVICE clause can direct part of the query to a local MS Word file, another to a CSV file on the web and a third, to some API, not even counting the trivial case of querying conventional SPARQL endpoints.

One real use case when SPARQL Anything saved me lot of time was when I was reviewing a project deliverable with data quality rules, each based on a property from a domain ontology that gave semantics to the graph the rules were designed for.

These rules were put in a table, and tables can be neatly triplified by constructing a property from the column literal. The subject is the row, the predicate is the constructed URI from the column label, and the object is whatever is in the respective cell.

Here’s a generalized version of that federated query:

SELECT DISTINCT ?ep 
WHERE {
    SERVICE <x-sparql-anything:> # calls the remote ontology file
            { fx:properties
                        fx:location    “http://example.org/ontology.ttl”;
                        fx:media-type  “text/turtle” .
      { ?ep rdf:type owl:ObjectProperty .  } UNION
      { ?ep rdf:type owl:DatatypeProperty .  }
    }

  FILTER NOT EXISTS {       
    SERVICE <x-sparql-anything:> #calls the local MS Word file
            { fx:properties
                        fx:location “file:///C:/example.docx” ;
                        fx:media-type  “application/vnd.openxmlformats-officedocument.wordprocessingml.document” ;
                        fx:docs.table-headers true ; #tells the engine to cretae proeprties from the table headers
                        .
          ?s ?p [xyz:Property ?epQ] # In case the column of interest is with header “Property”

          }
 FILTER CONTAINS (STR(?epQ), STR(?ep))
   }
}

The future of Façade-X

At the moment of writing, SPARQL Anything, the reference implementation of Façade-X, can support the following formats: XML, JSON, CSV, HTML, Excel, Text, Binary, EXIF, File System, Zip/Tar, Markdown, YAML, Bibtex, DOCx, PPTX. Here you can check out the documentation of each format. One data source still not officially supported is SQL, but that will come in the future. Until then, there is a workaround.

Recently, a W3C community group for Data Façades was created, to standardize and further develop the Façade-X and allow for other implementations besides the current SPARQL Anything.

A step-by-step tutorial

There are already some good tutorials on the website of SPARQL Anything. But if you’d like to reproduce the examples from these two posts, here’s a step-by-step guide which you can follow without knowing SPARQL.

Read more

The problem comes when you need to answer a question, where parts of the answer are scattered across heterogeneous data sources. One part of the answer may happen to be in a JSON file, served from an API, another is in an Excel workbook, stored in your drive, and yet others are in Microsoft Word, CSV and XML. This is challenging even when all the files are with the same format, but structured differently.

The problem then is, how to unify structure and semantics from heterogeneous data sources.

This question wraps two other questions: Which universal representation can best carry the information coming from diverse sources, and how to transform different data formats into it?

This is the fourth post in the Containment series.

The answer to the first question is easy: RDF. That’s the only interoperable way of representing data where the semantics do not depend on the structure. Any meaning can be represented with a structure that is always the same: a triple. Unlike tables, for example, where adding another column changes the structure, in RDF, adding a new characteristic about an existing entity or a new entity with a fact about it, is always done by adding a triple. You can’t add just a single entity or a single value. The atomic unit is the triple.

This makes triples are similar to containment. In the same way containment is defined as unity of outside-boundary-inside, a triple is defined by its subject-predicate-object combination.

Bringing several graphs together creates another valid graph. And the use of global identifiers makes RDF graphs self-assembling structures. There are other important benefits of RDF, which I explored in another essay.

The answer to the second question is not so easy. Or at least it wasn’t until recently.

Transforming from a non-RDF to RDF source involves three transformations: transforming identities (from local to URIs), unifying structures (from whatever to a triple), and applying domain semantics (mapping properties and classes from shared ontologies). Initially, all approaches did all three transformations in one stage.

A Brief History of RDFizing

Early transformations began with XSLT in the late 1990s. XSLT is designed to transform one XML structure into another. Though not RDF-specific, it was soon used to convert XML data into RDF/XML by encoding triples within templates. XSLT’s power lies in precise control of XML trees, but it lacks native RDF semantics and becomes cumbersome for complex mappings.

R2RML (W3C Recommendation from 2012) marked the first standard specifically for relational-to-RDF transformation. It defines mappings from relational databases to RDF graphs via declarative rules expressed in RDF itself. Each logical table, column, or join is mapped to RDF subjects, predicates, and objects. R2RML offered formal grounding and interoperability, but it is limited to relational data.

To generalize R2RML’s logic beyond relational sources, the RDF Mapping Language (RML) emerged in 2014 as a community-driven extension. RML extended R2RML, adding support for CSV, XML, and JSON. However, RML can be verbose and performance-heavy for large or dynamic datasets. It requires good knowledge of the data sources and the technologies needed to query them. At the same time, it lacks hash functions, which are essential for constructing deterministic and reliable identifiers.

Around 2017, SPARQL Generate appeared. It extends SPARQL with GENERATE, SOURCE, and ITERATOR clauses to create RDF from diverse input formats such as JSON, CSV, XML, or HTML. Its logic unifies querying and transformation within a single syntax, offering strong expressive power and dynamic control, yet relying on custom extensions not part of the SPARQL standard.

All these approaches perform the transformation of identity, structure and semantics in one stage.

In 2018, OTTR (Reasonable Ontology Templates) shifted focus from mapping to portable templating. It defines parameterized RDF graph templates that can be expanded into concrete RDF structures. Rather than linking to input formats, OTTR standardizes reusable RDF pattern generation, promoting consistency, maintainability, and reusability. It does not handle data extraction directly (works on RDF), but the tools that support it do that, and in this way, separate the stage of generic identity and structure creation from applying domain semantics.

Then in 2021 SPARQL Anything appeared. It introduced a minimalistic model Façade-X, that presents any data structure as RDF, which can then be manipulated with native SPARQL. Importantly, it does so without extending SPARQL and without requiring experience with the source structure.

Façade-X demonstrates that what is common to all structures is, yes, you guessed it, containment.

All data is structured as nested containers

A Word document contains headings containing paragraphs, bullets, tables and images. An Excel workbook contains spreadsheets containing cells. A PowerPoint slidedeck contains slides, containing titles, text, bullets, hyperlinks and images. An XML file contains elements containing attributes, text nodes, and other nested elements, forming a hierarchical tree structure defined by tags. A JSON file contains objects containing key–value pairs and arrays, which in turn contain other objects, arrays, or primitive values such as strings and numbers.

Façade-X interprets every data source as a container, containing key-value pairs. The keys are either generic containment relations or specific RDF properties. The values are either other containers or literals (strings, numbers, dates etc).

Let’s start with the primitive case, a CSV consisting of a single row with the following values: mathematician, philosopher, logician, physicist.

Façade-X will see it as a container, containing one key value pair, the value of which is another container, containing four key-value pairs, the values being the four words. All keys in this case will only indicate order.

Next, a more complicated CSV:

name,birthYear
Albrecht Dürer,1471
Anthony Hill,1930

Every CSV file is an ordered sequence of records where each record is an ordered sequence of values. The first record in this example contains headers. Façade-X (SPARQL Anything) has a parameter telling it if the table has headers. Then it will see this CSV as a container containing two containers, each containing key-value pairs with keys, constructed from the headers and values, the respective fields. Here’s how this looks:

Now let’s have a similar structure, in XML, but a bit more expressive:

<people>
  <person>
    <name>René Descartes</name>
    <birthYear>1596</birthYear>
  </person>
  <person>
    <name>Blaise Pascal</name>
    <birthYear>1623</birthYear>
  </person>
</people>

Façade-X will see this as the following RDF

@prefix xyz:  <http://sparql.xyz/facade-x/data/> .
@prefix rdf:  <http://www.w3.org/1999/02/22-rdf-syntax-ns#> .
@prefix fx:   <http://sparql.xyz/facade-x/ns/> .
@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .

[
  rdf:type fx:root ;
  rdf:type fx:people ;
  rdf:_1 [rdf:type xyz:person ;
          rdf:_1 [rdf:type xyz:name ;
                  rdf:_1 “René Descartes”] ;
          rdf:_2 [rdf:type xyz:birthYear ;
                  rdf:_1 “1596”]
        ] ;
  rdf:_2 [rdf:type xyz:person ;
          rdf:_1 [rdf:type xyz:name ;
                  rdf:_1 “Blaise Pascal”] ;
          rdf:_2 [rdf:type xyz:birthYear ;
                  rdf:_1 “1623”]
        ]
] .

Using blank nodes is optional, but the square brackets beautifully show the containers and how they are nested. There is one outer container. To distinguish it from the rest it is typed fx:root. In this case it is also typed as fx:people, an URI constructed from label of the respective source XML container.

Now we have three levels of nested containers, all of them typed.

Let’s use the list we started with and include it in the structure. This time, let’s render that in JSON.

[
  {
    “name”: “Alfred North Whitehead”,
    “occupations”: [”mathematician”, “philosopher”, “logician”, “physicist”],
    “birthYear”: 1861
  },
  {
    “name”: “Anthony Hill”,
    “occupations”: [”artist”, “mathematician”],
    “birthYear”: 1930
  }
]

From this input, Façade-X, with the help of SPARQL Anything, will produce the following RDF:

@prefix xyz:  <http://sparql.xyz/facade-x/data/> .
@prefix rdf:  <http://www.w3.org/1999/02/22-rdf-syntax-ns#> .
@prefix fx:   <http://sparql.xyz/facade-x/ns/> .
@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .

[
  rdf:type fx:root ;
  rdf:_1 [xyz:name      “Alfred North Whitehead” ;
          xyz:birthYear “1861”^^<http://www.w3.org/2001/XMLSchema#int> ;
          xyz:occupations [rdf:_1 “mathematician” ;
                           rdf:_2 “philosopher” ;
                           rdf:_3 “logician” ;
                           rdf:_4 “physicist”]
        ] ;
  rdf:_2 [xyz:name      “Anthony Hill” ;
          xyz:birthYear “1930”^^<http://www.w3.org/2001/XMLSchema#int> ;
          xyz:occupations [rdf:_1 “artist” ;
                           rdf:_2 “mathematician”
                          ]
          ] .
]

Which, as a visual graph, looks like this:

where _:b1 to _:b5 are local densifiers of the same blank nodes, which in Turtle are represented with [ ]. The same structure, shown as nested containers, will look like this:

It turns out that every data structure is a container that holds one or more containers, which can be optionally ordered and typed. Each container indicates an optionally typed boundary and can contain zero or more nested containers of the same kind. The deepest level contains one or more literals.

Will that hold for all structures? So far, it has worked with CSV, XML and JSON. But what about HTML or MS Word? Or PowerPoint. We’ll see that in Part 2.

Here’s one recipe: move away from abstract symbols and use one relation, that of containment. That’s what boundary math, logic, and unary computing based on them do.

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This is the third post in the Containment series. Containment, besides being the very architecture of our material world, is a fundamental organizing principle of life, language, and thought. The first essay reviews all kinds of containers, from the biological cell to the physical and metaphorical containers we create. It ends with a review of containment in philosophy and logic. The final part is expanded in the second essay, delving into the Calculus of Indications by George Spencer-Brown, as described in his book Laws of Form. That book has inspired people across various fields: mathematics, biology, psychology, cybernetics, philosophy, music, cognitive sciences, computer science, and social sciences. One prominent non-symbolic system for rigorous thinking, heavily influenced by Laws of Form, is the Boundary Math. This current post, third in the series, provides a glimpse at that system. The Boundary Math (aka Iconic Math) was developed by William Bricken with contributions from Jeffrey James and Louis Kauffman.

What is Boundary Math (aka Iconic Math)? William Bricken explains:

Iconic math is rigorous thinking that looks and feels like what it is intended to mean. Postsymbolic thought is embodied experience. Our topic for the moment then is the deconstruction of common arithmetic based on the formal principles first developed by Spencer Brown, with the American philosopher Charles S. Peirce laying the groundwork at the turn of the twentieth century, and with our nomadic ancestors over 30,000 years ago providing tallies as the original substance from which numbers sprang.

The remaining part of the post presents some features of this system.

Arithmetic

When addition is thought of in embodied terms, then it is simply about putting things together. Or, in boundary terms, that is the action of removing a shared boundary.

⟮●●●⟯⟮●●●●⟯ ⇒ ⟮●●●●●●●⟯

It can be done with any number of ensembles.

⟮●●●⟯⟮●●●●●⟯⟮●⟯ ⇒ ⟮●●●●●●●●●⟯

Symbolic addition imposes sequence. For the example above, it will be either first 3 + 5 and then add 1, or 3 + 1 and then add 5, or 5 + 1 and then add 3. With boundary arithmetic, the removal of all boundaries can be done in parallel.

This boundary deletion can be expressed as a void-based transformation:

⟯⟮ ⇒

When ⟯⟮ is transformed into nothing, ensembles get fused.

The polarity of an ensemble can be changed by putting it in angle brackets. On such a basis, subtracting two ensembles is done by matching the magnitude of positive and negative forms.

⟮●●●● <●●●>⟯ ⇒ ⟮●⟯

The next important operation in boundary arithmetic is substitution. Substitution is powerful. It is used, for example, for what in conventional arithmetic we call multiplication and division. I experienced an aha-moment when I saw how multiplication and division are just specific cases of substitution.

Substitution is expressed with a special container like this one:

⟬A C E⟭

which is the instruction to substitute A for C in E. This instruction can be represented in the following way:

⟬PUT FOR INTO⟭

⟬A C E⟭ can be translated as (A×E)/C. This makes it easy to see that multiplication is the special case in which C is one, so we have:

⟬⟮●●●⟯ ● ⟮●●⟯⟭ = ⟮●●●●●●⟯

The multiplication principle is that every unit from one ensemble interacts with every unit from another ensemble. Once represented visually, we can realize how intuitive it is.

Division is a special case of substitution, where

⟬● C E⟭ ⇒ substitute ● for every C in E

Substitution includes structural identities such as global substitution:

⟬A E E ⟭ = A,

self-substitution:

⟬A E E ⟭ = A, and two void-substitions:

⟬ C E ⟭ = A ⇒ delete C from E

⟬A E ⟭ = A ⇒ construct A within E,

where in the first case there is nothing in the “PUT” position and in the second in the “FOR” position.

The natural question now is how to deal with large numbers.

The solution is depth-value. Crossing the boundary outward changes the value of one order of magnitude. The magnitude will depend on the base. In the case of 10-base, that crossing will increase the value by 10. Now all digits can be reused except 0. Then, 2025 can be drawn like this

The calculation of depth value forms involves natural operations such as put, merge and cancel. See chapter 3 of Iconic Arithmetic for details.

Logic

What is Boundary Logic? William Bricken explains:

Boundary logic replaces truth by existence, deduction by deletion, logical connectives by patterns of containment, and sequential inference by concurrent substitutions, without losing any of the capabilities of symbolic logic.

Boundary logic is based on the concept of physical containment, defined as the gestalt between inside, outside and boundary. Unlike Western conventional logic, there is no duality, no true and false, just a single concept for existence.

There are other differences. Boundary logic is iconic, rather than symbolic. Icons maintain structural resemblance to their meaning. Boundary logic is based on information, which is contextual, rather than on truth, which is an absolute value.

Boundary logic reuses the law of crossing:

(()) =

However, the law of calling does not show where the marks are contained. In such a way, it sort of introduces another relation that can be called “taken together.” When the unwritten cross is added, the result is again nothing:

(()()) =

That’s how the boundary logic allows only containment and is fully void-based.

This last form may seem strange. It will become clearer when the concept of pervasion is introduced.

Boundary logic has three axioms, for which only one variable is used. Unlike Laws of Form, it doesn’t include transposition, which can be looked at as another operation, a rearrangement, which is not containment. Here are the three axioms of Boundary Logic:

Occlusion: (() A ) =

Involution: ((A)) = A

Pervasion (A ⋮ A ⋮ ) = (A ⋮ ⋮ ),

Where ⋮ stands for any boundaries, including none.

Pervasion treats boundaries as semi-permeable. Replicas are created inwards and deleted outwards.

Now we can see how pervasion is replacing the law of calling with void-based equivalence

So, if we have this initial form:

(()(()))

then the deepest mark can be deleted, so we get: (()()), but since ⋮ also works in case of no boundaries, we get

(()()) = (()) =

If you want to learn more, here’s a video that provides a detailed explanation and demonstration of the axioms of Boundary logic

Computing

If you could rebuild computation from scratch without any concern for backward compatibility, what would you do? That’s the question the Natural Computing project started with and achieved some remarkable results. Watch here, William Bricken, tell the story

This series reveals the power of containment in an attempt to bring attention to some qualities concealed by the dominant symbolic representations in math, science and technology.

This first essay explores all kinds of containers, from the biological cell to the physical and metaphorical containers we create. It concludes with a review of containment in philosophy and logic, a theme to be expanded in future posts.

The second one is about mathematical and philosophical foundations, based on a single relationship, that of containment. This is the Calculus of Indications of George Spencer-Brown, presented in his book Laws of Form (1969). Over half a century since the publication, his work is mostly unknown, misunderstood and underappreciated. William Bricken explains:

His text is notorious. The academic analysis, enthusiasm, controversy and rejection of Spencer Brown’s work is widely based on a severe misunderstanding that Laws of Form describes conventional logic, which it does not. The text becomes much more controversial when it is taken for what it actually is: a postsymbolic foundation for rigorous thinking.

This essay is another attempt to present this foundation, trying out some new ways of explaining and adding some new perspectives.

Building on Laws of Form, Boundary Logic is even more extreme in not allowing anything other than containment. It eliminates the cases that imply other relations than containment. Boundary logic adds the operation of pervasion. Pervasion treats boundaries as semi-permeable. Replicas are created inwards and deleted outwards.

Boundary logic forms the foundation of unary computing, developed within the Natural Computing Project. Based on void-equivalence and allowing parallel operations, unary computing demonstrated advantages over binary computing.

What is common between all data structures? Yes, containment. Word documents contain paragraphs, bullets, tables and images. Excel workbooks contain spreadsheets containing cells. PowerPoint slide decks contain slides, containing titles, text, bullets, hyperlinks and images. XML files contain elements containing attributes, text nodes, and other nested elements, forming a hierarchical tree structure defined by tags. JSON files contain objects containing key–value pairs and arrays, which in turn contain other objects, arrays, or primitive values such as strings and numbers.

Façade-X presents homogeneously heterogeneous data structures using the relation of containment.

Other series

There are some strange symbols like zero. We are told it stands for nothing. That's hard to believe. It doesn't look like nothing. It looks like something, and it does things. When put after a different number, a zero magically makes it 10 times bigger. In fact, we can only know what 10 stands for if we memorize that trick.

Then we learn to perform operations with numbers. That, they tell us, is called “arithmetic.”

Later, when a number is not known, that is “algebra.”

We get this layer of magic “for free,” and then all mathematics and science are built on top of it. What it stands on is never questioned.

Almost never.

George Spencer-Brown questioned it in 1969 in his book Laws of Form (LoF). He started earlier, with no assumptions, and went further, in the forbidden territory of self-reference.

He started from nothing. If there is anything different from nothing, that difference can be made by somebody able to make a distinction. Once a distinction is made and indicated, nothing more is required. Distinction is the only constant. Relations of constants are all it takes to make an arithmetic but here it’s even simpler because the constant is also the only relation.

And that relation is containment.

This is the second post in the containment series. You may want to check the previous first, but you don't have to. You can start wherever you want.

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Once somebody makes a distinction, that is also the only unique operation. All the rest is repeating: re-calling, re-crossing, re-entering.

The first distinction creates space and invites crossing. The space is a primitive one, without any distance. You can go only from one state to another.

If we indicate a distinction and look at it as both the only constant and the only operation, that's all it takes to have an arithmetic. No numbers, memorization of symbols, magic tricks and taking so many arbitrary things as given.

And, just think about it. Is there a more basic cognitive operation than making a distinction?

Distinction is perfect continence

In the Western tradition, we have the idea of true and false values to judge a proposition. It takes for granted what a proposition is, that it can be understood, evaluated, that there are only two possibilities, true and false, and that they can be distinguished. That's from Aristotle on and didn't change much to this day.

When George Boole created an algebra on this basis, he did not consider the possibility of more than two values, nor what it means for something to have value, before asking what those values might be. To ask what it means for something to have value would already require asking: value for whom? That was not a common question in his time (and it is still rarely asked today). In any case, he created a beautiful, non-numeric algebra. This algebra, however, contained no arithmetic.

George Spencer-Brown attempted to supply the missing arithmetic. He did so without assumptions, grounding it in the most primitive cognitive act: making a distinction. A distinction can only be made by someone, and if what is distinguished is of value, it can be indicated. Out of this, the arithmetic of Laws of Form (LoF) was born. From there, it generated its own algebra. The algebra of Boole, and others, appear only as special cases derivable from it.

The only things that LoF accepts as given are the ideas of distinction and indication. Then, to introduce the laws of form, it needs just one definition:

Distinction is perfect continence.

Making a distinction means drawing a boundary. Like making a circle on a plane, that boundary clearly separates two distinct spaces. In the case of a circle (or a rectangle), we call them inside and outside. One of the meanings of “perfect continence” is that there is no ambiguity when it comes to indication. There cannot be a point on the boundary. It will always be either inside or outside.

The original notation for distinction is what Spencer-Brows calls a mark or a cross, and it looks like that:

In many places, even in the Wikipedia article, it is called a symbol. It's not. Symbols don't illustrate their meaning. The mark does. You can see it as a half-box:

It shows inside and outside, the boundary, and — now with some knowledge about its intent — an invitation to cross that boundary. This is an important and not-so-obvious difference. I’ll be coming back to it a couple of times in what follows.

The distinction is both an operator and an operand, and the only relation in the mathematics of forms: containment.

The distinction is an operator by inviting to cross from one state to the other, and is an operand by being an indication of a state. This action/value duality has important mathematical and philosophical implications.

Distinction is the act of creating something from nothing. From void.

Void is often imagined as empty space. But that is already something: space. If there is space, that's not nothing. Space is what the first distinction creates. Not a space with the notion of distance; more primitive than that. A space where the only “distance” that can be traveled is from a marked space to an unmarked space and back.

Re-calling (condensation)

Axioms are premises that are given. They are not questioned. They cannot be experienced or demonstrated.

The axioms of the calculus of indications, in contrast, are open to examination. These axioms are the two laws of form that give the book its name.

The first axiom is the law of calling.

The value of a call made again is the value of the call.

In other words, to recall is to call.

In the original notation, the expression of that axiom looks like this:1

This is the form of condensation.

Our keyboards don't have this sign. Even if they did, nesting would be challenging. An alternative way to write such expression is by using parentheses (or any other brackets). The law of calling, then, would look like this:

This is convenient but comes at the cost of imposing sequence. That’s a limitation. William Bricken explains:

Symbolic notation imposes sequence, suppressing the inherent parallelism of containment structures. Given sufficient processors we can access any number of containers all at the same time, but we cannot read a page of words all at the same time.2

Back to the axiom: to recall is to call. Two (or more marks) next to one another (not nested) condense into one.

How can you imagine the logic of that?

One simple way to see it, is to switch on your writing assistant like Grammarly, QuillBot, Scribendi or whatever you are using. Then,

The two calls “sentence” have the same value, so you are invited to condense them into one.

That is not the case with “he said that that book was the best,” because each that makes a different indication. The first one indicates the statement and the second indicates the book the statement is about. Or “this is the second post in the series; check out the first first,” where the first first indicates the order of writing and the second first, the order of reading.

Another way to imagine it is highlighting. If you highlight some text and if you then highlight it again, you'll have the same number of highlights, one.

This axiom is also the first initial of the primary arithmetic. Since it can be used in both directions, it can be written like this:

Going from left to right is to condense, and from right to left is to confirm.

The sign ⇀ represents a step and means “is changed to.”

Re-crossing (cancellation)

The second axiom is the law of crossing. It states the following

The value of a crossing made again is not the value of the crossing.

In other words, to re-cross is not to cross.

In the original notation, it looks like this:

This is the form of cancellation. Two tested crosses are equal to none.

Using parentheses, it can be written like this:

The expression is not unfinished. Simply the right side equals to nothing and that is why there is nothing written on the right side.

One way to imagine it is by being outside of a plot, entirely surrounded by a fence. Only two states are of value: you being inside or outside. If you jump over the fence, your state is changed. You are inside. That's the first crossing. If you cross the fence again, no matter where, you'll get outside. You were outside before the crossing and after making two crossings. So, making two crossings, when it comes to distinguishing only being outside versus being inside, is the same as having made no crossing.

Here's another way to see this. Let's have one circle drawn inside another.

Let's indicate the outside of the outer circle with m for “marked.”

If we cross it, we'll go to the unmarked space. Let's indicate that with n. And if we then cross the inner circle, that will be again a change of state and the inner area will be marked.

There are four possible trajectories for making two crossings starting for a marked space, indicated with a, b, c, and d. Trajectory a is for going from outside the outer circle and crossing the inner. Trajectory b is when the second crossing is of the same outer circle.

Then from the inner marked space, c, is for crossing the two circles from the inside of the smaller one, and d is for crossing once and a second time back.

For a point in the unmarked state, there are two possibilities: crossing outside and back (e), and crossing inside and back (f).

In all six cases, double crossing is the same as no crossing; the initial state is unchanged.

The second axiom is also the second initial of the primary arithmetic. Since it can be used in both directions, it can be expressed like this:

Going from left to right is to cancel, and going from right to left is to compensate.

With these two axioms, every arrangement has a unique simplification, which is either the marked or unmarked state. A form like this, for example

can be simplified. The order of simplification doesn’t matter. Each time, either the law of calling or the law of crossing is applied until it reaches either the marked state or the unmarked state, where it can’t be simplified any further.

The form above resolves into the unmarked state.

Knowing now the two axioms, it will be easier to show the benefits of using notation that (1) illustrates its meaning, and (2) doesn’t impose sequence.

Consider the following arrangement of three numeric constants:

It is meaningless as a whole. You need a different arrangement and additional symbols to calculate it. In contrast, this arrangement

is unambiguous. By the law of calling, the three rectangles can be condensed into one and evaluated as the marked state. Then it may generate endless equivalent forms, for example, this one:

Primary Algebra

In Chapter 3, we are told to:

Call calculation a procedure by which, as a consequence of
steps, a form is changed for another, and call a system of
constructions and conventions which allows calculation a
calculus.

That may be taken as two definitions, of calculation and calculus. Being given in the form of instruction, it reminds us that every definition is just a convention.

We are then told to call the calculus of primary arithmetic, primary algebra.

The identities of primary algebra are indexed with J for the initials, C for consequence. Here are the two initials, J1 and J2, and some of the consequences (only those that we’ll need later).

J1 (Position)

The step from left to right is the action take out, and the one from right to left is put in.

J2 (Transposition)

The step from left to right is the action collect, applied on r, and the one from right to left is distribute.

The first consequence that is reached by applying the transformation steps is called reflection:

C1 (Reflection)

Here is one more:

C4 (Occultation)

The step from left to right is the action conceal, and the one from right to left is to reveal.

And here is the last one we’ll need:

C5 (Iteration)

Self-reference (re-entry)

Chapter 11 goes into equations of the second degree. It starts with the expression

and after transformational steps applying the identities of the primary algebra,3 it is turned into an infinite expression:

By just replacing (a(b)) with identical forms, it can be converted into an endless ((((…a)b)a)b). But that also means that (a(b)) in any even depth of ((((…a)b)a)b) is identical with the whole ((((…a)b)a)b). It is in this way that ((((…a)b)a)b) re-enters “its own inner space at any even depth.”

Now it gets really interesting.

Read more