Introduction

What is the world? Is it “everything that is the case?” Does it have different strata, whose realities are grounded in mutually incompatible ways, or just one? When we describe the world to each other, don’t our choices of language privilege certain answers to these questions, and foreclose on the possibility of certain others?

I won’t waste much time with monism (i.e. the answer “just one”), even when many fellow Western tech-and-science types seem to take it as not only beyond the pale but actually laughable to quibble with the monistic assumption of rank materialism. As Aristotle saw long ago, “things are said to be in many ways”; pace him, for reasons I can’t so easily explain, the following millennia of careful research into the “ways in which things are said to be” have recently been overwritten with nothing much more than, well…a quick snicker at Cartesian dualism followed by a jump to, at best, Dan Dennett, or maybe early Wittgenstein.

Yet, the simple fact remains that things are said to be in many ways, and eliminativisms and materialisms of all kinds are foolish, harmful when taken seriously, and ineffective in following and influencing the unfolding of the world.

Schopenhauer’s View

A favorite answer of mine to the questions up top is Schopenhauer’s. He says things are said to be in two ways: first, as Will (capitalized á l’Allemand), in which there are no things at all, really, just the surging, chaotic flow of pure existence that lies behind all appearances.

The second, which Schopenhauer calls the world as Representation, is the familiar world of subjects-regarding-objects. What’s interesting is that, even in this world of Representation, Schopenhauer subdivides into four distinct ways in which things are grounded, or in which things can be: cognitive objects, grounded by reason (if all men are pigs and Socrates is a man, then Socrates is a pig), material objects (through causation), moments and places in time and space (grounded by other nearby places and times), and the ground of motive (the connection between intention and action).

Models, for real

Why am I inflicting this recapitulation of Schopenhauer on you? Well, let me get back to that…First: I’m interested in world modeling—what it is, how to do it, and whether AI can help. Here are some examples of world models:

• 
• If , then all in all the economy is doing well.
• God is love.
• The vibes are off with that guy.
• The rich are, by and large, talented, hardworking, and probably way cooler than you.
• The rich are, by and large, greedy, lucky, and probably ugly.

• 

A world model is at bottom nothing more or less than a representation in the sense of Schopenhauer: a network of objects: a subject organizing (part of) the world to itself. Modernity is the state of a civilization that can develop precise language and intrepid norms of discourse to permit more-or-less free competition between publicly expressed world models. Postmodernity is the observation that grand public world models seem to often throw the baby (the illegible, fractally complex, organic system determining individual flourishing) out with the bathwater (naive adherence to tradition).

The fundamental problem of today’s civilization is finding what comes after postmodernity, which correctly teaches that excessive reliance on legible public models leads to runaway harm beyond the edges of the model, but then gets mired in inescapable negativity. Some individuals find a way out of nihilism to what might be called a meta-modern attitude of understanding and using modern systems (plural) without identifying with them, but our civilization hasn’t advanced to this way of being at scale. (If you like this paragraph, you’ll love David Chapman’s writings on meaning and metarationality.)

The World Is Not An Object

My point in juxtaposing Schopenhauer’s metaphysics and the dream of meta-modern world modeling is this: a world model is a claim, made by some particular subject, about what is to be attended to (perhaps, what is to receive care), which is pragmatically indistinguishable from a claim about what is real. The middlebrow attitude is that a model approximates the world. This is wrong, because the world is not an object. There is no “ground truth” to compare models to, not because we’re solipsists, but because the world-in-itself is a chaotic surging mess in which no grounds are admitted.

The world is not an object. The only objects are our models of the world. This doesn’t mean models can’t be wrong—if you believe “vaccines cause autism,” I can produce observations that (defeasibly!) contradict it. But it wouldn’t be by “looking at the ground truth”; I’d observe that your qualitative model is inconsistent with what seem to me to be reasonable quantitative models, and we’d debate, presumably, until exhaustion.

A Story About the Sun

Let me tell a story about a day when Alice and Bob, a couple, were discussing the ideal frequency of sunscreen use. Alice thought people should use sunscreen every day. Bob opposed this, citing studies showing most deadly skin cancer risk comes from childhood sunburns, with moderate sun exposure possibly beneficial (via Vitamin D). Alice responded citing anecdotes of contacts who tanned and later died of skin cancer.

This seemingly rational debate concealed deeper models. Alice’s unstated world model factors included “if Bob really cares about me, he’ll listen without being annoying about statistical details.” Bob’s hidden model factors included “I’m highly sensitive to the perception of being forced into something, even when the point is correct” and deeper still, something like “the Sun is Good”—a quasi-religious view.

This pattern—where legible, objective modeling on the surface masks emotional, relational, and spiritual paradigms below—is not special to small-scale, intimate interactions, but characterizes human disagreements generally. Consider NAFTA debates: quantitative economic models may mask deeper motivations about the decay of childhood hometowns, manufacturing jobs’ reality-grounding nature, or—of course—attitudes toward foreigners.

We often have this cargo cult of public conversation where we, complicated bundles of stories and feelings, drape ourselves in black cloth and hold out crisp graphs as the only focus of discussion, hoping no one will look under the drape at the messy, emotional, willful grounds of our complete world model. One clear sign of reaching into meta-modernity would be when the sad, angry, hopeful creatures under the cloth start explaining their real models in all their incommensurability, and only then seek common ground as necessary.

A case at larger scale: in problems like “design a zoning policy for Berkeley,” I want everyone with a stake to potentially contribute. There are serious challenges:

1. Normal people would rather socialize than specify policy preferences
2. Models range from “Berkeley should never change” to complex quantitative projections
3. There are many stakeholders with stakes of many, contested, sizes

Sortition (jury-duty style participation) could help with problems 1 and 3, but number 2 is deeper. How do you funge the infungible, commensurate the incommensurable? Current options are:

1. Establish a top-down modeling paradigm producing scalar ratings that can be mechanically aggregated
2. Contributions are in plain text, recombined unpredictably and illegibly by decision-makers to produce a conclusion

Both have problems: Option 1 excludes those who can’t express themselves in the approved language, leads to overconfidence, and lacks consensus mechanisms to update. Option 2 determines the course of civilization by who yells loudest nearest the leader.

What Is To Be Done?

People haven’t really learned to communicate their world models to each other; modernity was built on narrow exceptions that postmodernity has shown unsatisfactory. How do we get people explaining honestly, fully, how they see the world? This problem has spiritual aspects—getting people to notice how they see the world may require a lot of meditation, for instance. But that part really isn’t my brief.

What do I offer, then? Structures for models: organizing, translating, comparing them. In the sunscreen example, the conversation would have improved if Alice and Bob had made their models explicit. Both could have seen the sensitive emotional points they were approaching instead of debating factual details. I think this would really help, modulo the UX problem of figuring out how to develop these models in the midst of a real, human conversation.

For those UX problems at the very least, AI support is a critical activator, smoothing over what would otherwise often become a grind of manual model refinement disincentivizing the kind of deep iterated reflection that seems worthwhile even for this kind of quotidian discussion. We need low barriers to entry but high legibility and reliability.

My suggestion, instantiated in the CatColab software being built at Topos and used to make the models shown above, is not to pick a single modeling language but a single way of constructing languages, formal enough to describe translations between approaches. AI can help by scanning possibilities and showing candidate jumps in the space of models. If candidate models have to be expressed in a well-specified language, that solves some AI-slop problems. If humans pick from candidate refinements, rather than relying on the AI to provide a consensus world model out of its broad averaging over humans-whose-writing-is-on-the-internet, that solves more problems.

The key to all this is to use AI to help clarify people’s world models, not press people to align with algorithm-generated models. We must preserve and enrich individuals’ and communities’ abilities to see the world clearly and express their vision as it is, enhanced, never constrained, by new technological affordancesssss

Thumbnail credit: Jan Buchholtz on flickr

If you liked this and want to full-length and slightly unhinged version, including rambling footnotes on the dating of the beginning of modernity and all, it’s here, below the short version.

Philosophy, Ontology, and Design

Technologies are not just the application of scientific knowledge to practical problems. They reshape our space of possibilities, altering how we live, act, and understand ourselves. The design of new technologies is, often quietly, the design of new ways of being human. Our inventions invent us in return.

This insight captures the notion of “ontological design,” introduced by Terry Winograd and Fernando Flores in their 1986 book Understanding Computers and Cognition: A New Foundation for Design. Rapid advances of AI and other technologies today demand that we grapple anew with this startling realization.

Take the smartphone. It didn’t merely make telecommunication more convenient. It placed us into a new condition of constant connectivity—reshaping how we learn about events, navigate the physical world, seek social connection, and even become the people we are. The repercussions of this transformation for our collective well-being are still coming into view.

Today is an exhilarating and disorienting time to be alive, and to be thinking about and building new technologies. Advances in AI have reignited fundamental questions about the human predicament: What is language? Intelligence? Communication? Flourishing? What kind of human beings are we becoming? What understanding of our predicament should guide the design and use of AI and other technologies?

In Understanding Computers and Cognition, Winograd and Flores showed that philosophical questions are always at stake in technological design. Every new system, they argued, carries a tacit or explicit stand on fundamental issues: what cognition is, what agency is, what communication is, and so on.

They named the guiding assumptions of the AI research of their time “the rationalistic tradition”: a view that human intelligence consists in formal operations (such as search and inference over explicit representations); that agency is the solving of discrete problems by selecting between definite alternatives; and that communication is the transmission of information.

Winograd and Flores issued a threefold challenge to the rationalistic tradition: (1) to call attention to the hidden philosophical assumptions shaping AI research; (2) to show how these assumptions can both limit our technological capabilities and thwart our imagination for the possibilities of human-machine interaction; and (3) to offer an alternative ontology to guide future design. The urgency of this threefold challenge has been renewed today.

Understanding Computers and Cognition argued, quite presciently, that computer systems would become woven into human life as conversational technologies. But not all conversations are alike. Sometimes, for example, we are simply speculating about possibilities; other times we are directly coordinating action in requests, offers, and promises.

Adequately designing software to assist in the execution of such conversations for action, Winograd and Flores showed, required rethinking the nature of communication itself—not as the transmission of information, but as the coordination of commitments.

A promise is not a piece of information. It is a way of shaping and bringing forth the future, together. For example, ride-sharing apps work when a request (“pick me up”) and a promise (“driver arriving”) coordinate action; both hinge on mutual commitment, not just clarity of information.

Our Need For Renewed Ontological Reflection

While the AI paradigm has shifted since the 1980s—from symbolic rules-based AI to neural networks and machine learning—the need for the kind of philosophical reflection exemplified by Winograd and Flores has only deepened. Today’s systems operate differently, but often rest on similarly narrow assumptions about human intelligence, communication, and agency.

We must ask: What are the ontological assumptions guiding AI research today? How might they be limiting not only technical development, but also how we live and interact with AI systems? What alternative conceptions of intelligence, agency, and communication might better orient the future?

These are the kinds of questions that animate my research. I am enthusiastic to explore, alongside the Topos community, how philosophical reflection and technological invention can mutually inform each other, especially as we seek to create technologies that expand, rather than constrict, our capacity for shared sense-making in these turbulent times.

Philosophical reflection becomes especially vital in times of transition and upheaval, when our settled certainties begin to fracture. The world needs bold and rigorous philosophical reflection in our times more than ever. Philosophy helps us see the world anew by helping us question what seems obvious.

We live in an era shaped by a largely unquestioned commitment to efficiency, control, optimization, and problem-solving. Human life itself increasingly appears as a series of problems to solve; and instrumental rationality, the capacity to identify and pursue efficient means to an end, is treated as the highest human excellence.

AI systems today reflect and amplify this logic. We see it in the long-running dream that machines might soon automate all human work. We see it in the hope—expressed again and again—that a superintelligent AI might one day answer all human questions and solve all human problems.

Machines will be capable within twenty years of doing any work that a man can do.

— Herbert Simon, The Shape of Automation for Men and Management, (1965)

But in this relentless drive to optimize and solve, we risk forgetting a more basic question: For the sake of what?

Toward an Ontology of Care

This brings us to the human propensity to care. Caring orients us toward questions of worth: What is worth doing? What tasks are worth automating? What kind of life is worth living? What kind of future is worth creating?

These are questions without technical answers.

Caring shows up in our sense of what matters. It draws our attention, solicits our action, and binds our lives to people, places, and projects that hold meaning for us.

Our propensity to care is likely grounded in our fundamental fragility and interdependence as the peculiar social, mortal, and biological beings that we are.

Traditions from philosophy (especially phenomenology), nursing, education, and sociology have long emphasized that we cannot adequately tend to what matters if we try only to optimize or control it. Indeed, one of my sources in thinking about care is Patricia Benner, a nursing expert who put care at the center of the activity and education of nurses.

What if we cannot adequately tend to what matters while trying to optimize and control it?

Think of the breakdowns in friendships or romantic relationships managed as a series of transactions; the ecological damages wrought by industrial agriculture and factory farming; the failures of medical care when patients are reduced to biochemical aggregates instead of being treated as a whole person.

A maniacal apotheosis of efficiency over care lurks behind one of the most famous thought experiments in AI-safety. I am referring to the so-called “paperclip maximizer,” as described in Nick Bostrom’s Superintelligence. Imagine an AI designed simply to produce paperclips as efficiently as possible undergoes an intelligence explosion. Without constraints, it would set about converting the resources of the entire planet (including human lives) into paperclips.

The paperclip maximizer is a monster of unconstrained instrumental rationality! A system relentlessly optimizing but impervious to the question of why its goal matters, or for whose sake it should be pursued.

In this sense, the paperclip maximizer is not a mere fantasy; it is a mirror held up to our own technological age. As Martin Heidegger observed, modern technology tends to reveal the world (and we human beings ourselves) as resources to be optimized, ordered, and consumed.

When care is thoughtlessly subordinated to efficiency, we risk forgetting to ask the questions that make us human and connect us with our care.

How might a closer attention to the dynamics of care—rather than intelligence narrowly understood as efficient problem-solving—help orient the design and deployment of AI systems and other technologies? My work contributes to such questions by retrieving and extending a tradition of thought centered on the embodied, skillful, and caring dimensions of human life, dimensions often overlooked in dominant conceptions of AI.

This tradition runs through the work of Hubert Dreyfus (Alchemy and Artificial Intelligence, 1965; What Computers Can’t Do, 1972), Stuart Dreyfus (Mind Over Machine, 1986, co-authored with Hubert Dreyfus), Patricia Benner (From Novice to Expert, 1984), Terry Winograd and Fernando Flores (Understanding Computers and Cognition, 1986), to my recent piece, “Can Machines Be in Language?” (Communications of the ACM, Feb 2024, co-authored with Peter Denning).

The enduring message of Understanding Computers and Cognition still holds: technology design is guided by often unexamined assumptions about cognition, action, communication, and other fundamental human phenomena. Today, we are called to articulate and explore an ontology of care, and to do so in a dynamic interplay with the design and development of emerging technologies.

This orientation aligns closely with the mission of the Topos Institute, where I am honored to be a visiting researcher. I look forward to collaborating with the team at Topos in their mission to “research new technologies that increase capacity for collective sense-making, while also creating a culture of use that is mindful of where technology cannot substitute for what must be done by people.”

To continue exploring the issues raised in this blog post, see B’s Topos Colloquium talk, “Language, Technology, and Care”.

Library reform

Libraries collect and organize human knowledge, equipping people with the ability to access, learn, and build upon others’ ideas. In turn, today’s society is equipped to handle problems that are more complex than at any point in history. Still, there is more to document and the scope of our libraries could be meaningfully larger. By expanding what we preserve, we could solve even more complex problems than we do today.

A weakness of today’s knowledge systems is their inability to capture and integrate procedural knowledge. Much of it remains undocumented, locked in our minds, or scattered across sources—thereby going to waste. Debugging, the act of fixing an existing engineered system, is a necessary but tedious step of R&D. Debugging is not only about fixing bugs to make the system functional, it’s about inching towards a vision that likely fuzzily exists in our minds. This vision is made increasingly clear and concrete by tinkering.

Additionally, capturing procedural knowledge helps reveal trails of thought, or even better: mechanistic explanations behind a conclusion, gives us the capacity to check conclusions and “choose our own adventure” in trying to arrive to our own conclusions in research. Citation is a virtue in traditional academic research, but means to tracing the provenance of ideas could be far more ubiquitous.

As an example of a unique modern form of “library,” take GitHub. Modern platforms like GitHub demonstrate how libraries can evolve to preserve not just code, but the entire development process. Developed rather recently, it simultaneously serves as a platform, a collaborative development environment, and a history tracker for developers.

Researchers used to solely write papers to present their findings. Now, they may link to drafts, data, and code offering a more complete picture of what it took to arrive at a final set of results. GitHub simultaneously supports both the act of conducting research and our ability to share and communicate it with others. As a reformed library itself, it has expanded our ability to document and share current research processes. We can take GitHub as a model of a new kind of library—one that we can apply in many more contexts to preserve and understand the (uniquely human) path to discovery.

Conserving thought

The challenge of preserving thought extends beyond storing information—it requires capturing the context, reasoning, and evolution of ideas. Moreover, the purpose of documentation isn’t just to share knowledge with future generations or to fortify institutions; it also helps us preserve and build upon our past work, ensuring that human ingenuity can progress and evolve rather than be lost to time. As I’ve edited, copied, pasted, and deleted text from previous versions of this document, even the version history on my text editor (Overleaf) can’t fully capture the context, goals, and nuances that were present when I first engaged with the project. Arguably, neither can the most sophisticated version control systems. In light of this: How can we effectively collaborate on long-term projects if we struggle to understand the intentions driving the artifacts of our own past?

Our memories are the imperfect recall of imperfect snapshots of the past, the “ground truth.” Preserving the integrity and authority of our sources is worth striving for. Doing so will require rethinking the tools that support researchers and developers who value provenance, documentation and then ensuring it is usable and accessible.

To conclude, I will share some questions that emerged from grappling with the points discussed above. I am making them public not only for others with similar curiosities, but also for my own record as I explore them. Together, these questions form an early-stage research agenda.

Directions for future work

1. In his book Libraries of the Future (1965), Licklider presents a vision for a new age of libraries. How do the above ideas align with his vision, and in what ways do they differ?

2. How can we design information storage systems that detect and flag errors without altering the original content, ensuring both historical integrity and clarity for future understanding? How do we decide what and when to correct, and how must these corrections be made? How do we keep track of the edits that have been made in the order they’ve been made? And what storage mechanisms allow us to update works while maintaining cost-effectiveness (e.g., by reducing redundancy whilst keeping accuracy)?

3. At what point do edits transform a source into something fundamentally different, and how do we measure and express this difference?

4. As inspiration for reformed knowledge representations, what analogies can we draw to gain insights from other fields? Biological systems offer powerful models for how knowledge can be preserved and transmitted across generations. As an example, DNA could be considered a generational log of what worked for survival, including the processes and mechanisms for replication for a given cell.

   • Given these analogies (and additional ones we could generate), what can we learn from existing attempts to disclose procedural knowledge in various complex systems?
   • What fundamental properties allow certain systems—biological, cultural, and social—to preserve and transmit procedural knowledge over long periods, even without explicit design?
   • How do different encoding methods (such as physical, procedural, and symbolic) and various forms of media (e.g. written and auditory) work together to enhance our understanding and retention of information?
   • How do these systems balance redundancy with efficiency?

5. How should we catalog know-how? What would a schema or notational system for procedural explanations look like? How could we detail them in a way that includes the necessary context?

6. Just as hashing and checksums—algorithms used to verify data integrity—ensure that a piece of data is accurately copied or downloaded, they’re also a way to verify data integrity. Similarly, when humans reproduce knowledge—whether through paraphrasing or replicating a textbook solution—we perform a kind of mental “checksum” to verify that an idea or concept has been accurately understood and transferred. Given this, can verification-via-reproducibility help us maintain the integrity of information that been passed down over time?

7. How might temporal metadata help us track the continuous evolution of intellectual artifacts and thought processes over time? How do we design identifier systems for the artifacts we develop? How might we move beyond commit-based, discrete-time version control systems?

8. How might the concepts of authorship and contribution evolve when cataloging research artifacts that take unique forms or are in progress? How do we take account of contributions that don’t rise to the level of citation, such as hearing an interesting thought from a friend? Should we broaden our definition of authorship, or should we create more space to cite unplanned, non-traditional, and perhaps informal academic interactions?

9. How can we support the R&D needed to develop these technologies? Would academia be a feasible place for this work? How have relevant research projects been supported in the past?

10. How can we (better) capture the “negative space" of knowledge work: the dead ends, failed attempts, and pivot points that led to final works?

11. What does it look like to have dynamic interfaces that adapt to individuals? What user information is required to achieve this, and how can it be acquired in a privacy-preserving way?

Introduction

Each of us can see problems in the world, cases where something we care about is in need of attention. On the global scale, I am deeply concerned about rampant pollution, countries engaged in hostile acts of aggression, political corruption, cultural fragmentation, the effects of modern technology on human lives and livelihoods, and more. To myself and I believe many other people, the world seems to be cracking under some sort of immense pressure, with “no one at the wheel” to steer the ship.

At the same time, we humans are imaginative. According to historian Yuval Harari, our superpower lies in creating fictions that can become real through our collective belief and action. This manifests in several ways:

• Social constructs: The value of money is a fiction that becomes real because we collectively believe in and act on it.
• Technological innovation: Many ideas from science fiction, such as mobile phones or virtual reality, have eventually been realized.
• Institutional change: New laws or social movements often start as ideas, and gain traction until they are eventually part of the social fabric.

These examples show how our “fictions” can shape the flow of events.

Rather than waiting for someone else to steer our ship, perhaps we can harness this imaginative power to solve our problems. In this post, I’ll begin by considering how it is that what we propose in language can become reality. Then I’ll propose an idea I’m calling plausible fiction, based on this consideration, and how implementing this idea could lead to a good future for humanity.

As we’ll see, plausible fiction is a lightly-structured approach to imagining and implementing viable solutions to real-world problems. It works by encouraging people to outline a path from our current reality to a desired future, and inviting collective effort to fill in the gaps along the way. This collaborative gap-filling process refines and realizes ideas that would otherwise remain abstract or incomplete, and in so doing move them from fiction to reality. I believe that this approach could be applied to a wide range of issues, at a wide range of scales, and potentially lead to a more participatory world.

When are proposals enacted?

Language clearly has the power to shape the dynamics of reality. Indeed, if I say “pass the salt,” it is empirically the case that with high confidence I can expect that some 10^25 atoms of salt-in-shaker will move through space and that subsequently a few grains of salt will land on my soup. At another scale, the symbolic language of DNA nucleotides codes for complexly-orchestrated chemical processes, whereby proteins are made and bodies are formed. It’s clear that language works; if it didn’t do anything in material reality, no one would use it.

So why not solve our problems by saying “abracadabra, microplastics be gone!”? Obviously, not just any linguistic utterance will result in the reality we want. In order to “come true” or obtain, the utterance needs to be part of a process that starts now, proceeds through the outcome, and obeys the laws of nature throughout.

If someone were to say “pass the salt” in an empty room, or with only their cat to hear them, would it work? Maybe the cat knows English and can decode what the person meant, decides to help out, and gets off the comfy couch to slide the salt shaker over with her paw. Yes, maybe, but it doesn’t sound plausible to me. Similarly, when you think someone is very angry at you, you might be less likely to ask them to pass the salt, because you’re less sure they’ll do it.

The better we understand reality as it is, the more we can live in accordance with it. Some might say we “shape it”, but I think it’s important to see that our understanding of “reality” means that something has already shaped us, e.g. how our brains encode our relationship to it. If we understand quantum mechanics well enough, we can invent a laser; otherwise, we simply can’t. Our stories about Edison developing the practical light bulb involve him making hundreds of attempts: only when he sufficiently understood both the material world and the social world did his proposal catch on. Thus “connecting the dots” between what was wanted by society and what was possible with available resources, the lightbulb and the laser could be reified. This ability to connect the dots between have and want arises from the work of attentive proposing and listening, but the connection itself can stand as a path of low resistance for achieving the result.

What I’m suggesting may be reminiscent of “following the Tao,” or listening to the way of things, but it is not meant to be mysterious at all. The nonaction spoken of as “Wu Wei” is probably the noticing of the low resistance that comes from proposing something that is in accordance with how things work naturally. Common law—the codification of what already exists as customary norms—is the easiest for a government to enforce, a friend proposing an activity they know the group enjoys is the easiest way to get its buy-in, and a hypnotist acting with, not against, their subject is the best way to get results. That is, when we act so as to usher in something that is already supposed to happen, by which I mean already poised or potentiated to happen, it is easier to be successful.

This is also reminiscent of active inference or predictive processing. A successful proposal should be pretty close to a prediction. My outsider understanding of active inference is that we can replace “I want X to happen” with something like “given that I exist and have the needs and abilities that I do, and given that the world is the way that it is, I predict that X will happen”. Wanting and guessing come together in a story.

The last image I’ll give is of lightning. Suppose there is a difference of electrical potential between the ground and the sky. Then nature “wants” to—is drawn to—equalize the two sides by making a spark between them. And if we put up a lightning rod, we propose a path of lower resistance, which tends to attracts such sparks to pass through it.

While a lightning rod can be seen as a kind of proposal, the proposals I mostly want to consider here are spoken or written using language. I believe that language attracts activity too, in some ways just like a lightning rod does. Saying “pass the salt” calls up all sorts of neural and then motor activity within my friend. Inventors use notebooks filled with symbols to attract their own attention to useful way points, and they use other semiotic schemas to attract certain behavior by the factory that makes the product, i.e. they lead the factory to successfully follow their design. Computer programs, written in highly-controlled languages, attract the voltage changes that cause all our applications to run.

And mathematics, from which computer science emerged, has for millenia been in the business of creating high-fidelity language for engineering and navigating—attracting outcomes in—our world. It compresses our ideas and makes them legible and unambiguous, and hence attractive to people. As Barry Mazur said in 2009,

Imagination needs something [in order] to apply itself directly to the largest realm it can possibly apply itself, and for that it needs conveyances, like bridges. And perhaps mathematics is that from my point of view: it’s a way of conveying the imagination to its broadest reach.

(Thanks to TJ for directing me to the Mathematics and Beauty roundtable, and for other advice throughout the article, including suggesting relevance with the work of the Frankfurt critical theory and separately of Michael Bratman.)

By naming an idea concisely and then showing how it unpacks, we can attract broader attention to it, enabling coordination among those who think it is worth implementing.

Plausible fiction

Plausible fiction, as I can define it here, is a story that attempts to satisfy the following criteria:

1. It begins with the world as it is now, including all relevant details and without distortion;
2. It ends with a future that the author desires;
3. It follows a trajectory that obeys natural laws and social dynamics; and
4. It is memetically fit, i.e. it invites participation by those who read it.

While it may seem paradoxical to call these narratives “fiction” when our aim for them is to manifest in reality, using the term “fiction” lightens the burden on the author and reminds us that this is an imaginative process of envisioning a future that hasn’t yet materialized. “Pass the salt” exists in our minds as something like “my friend will pass the salt,” and this story still exists in our own imagination—even if it is quite plausible—until it is reified.

Telling plausible fiction is supposed to be a fun and social activity, but with a functional purpose. The way it works is that one crafts a proposal that aims to influence events by supplying a path of low resistance from the present moment to a preferred future.

But what makes a proposal more likely to work is the process of gap-filling. Every plausible fiction has gaps in its narrative, and each gap is either plausibly fillable, or implausible. Once we find an implausible gap, the fiction becomes implausible and we stop working on it. But when the fiction is actually plausible and compelling, the work to making it real is simply to fill in each of its gaps with more plausible fiction: start where the story leaves off, end where the story picks up, and follow a plausible trajectory throughout. The gap-filling process is recursive, like zooming into a fractal, because even a filled gap leaves smaller gaps—more detail—to be filled in. But as smaller and smaller gaps are filled in, real material conditions will start to move. As my brain fills in the fact that you want me to pass the salt, and then fills in how I’m going to maneuver to do it, and then what it’s going to feel like to grab the salt shaker, my muscle cells actually become activated and the salt actually gets passed.

In other words, I’m making the following conjecture:

The only thing it takes to enact plausible fictions is to recursively and plausibly fill the gaps.

Imagine that one person proposes a difficult but plausibly-true math theorem, but that they don’t know a proof. If a few other people suggest plausible results that would combine to prove the theorem, this would be what I’m calling filling the gaps. The biggest gaps get filled first; if people start to think that filling them is implausible, the proposal is dismissed. But as gaps get filled, the theorem slowly becomes proved.

Similarly, imagine that a restaurant chef suggests a meal to be made. Then the sous chefs fill in the details. No one needs to explicitly tell the sous chef “to cut the carrot, move your arm like this”; but their brain does need to fill in that gap. Eventually the gap-filling descends beyond the level humans need to think about, but I claim that creating the meal is gap-filling all the way down.

Very loosely, the mathematical infrastructure I’m imagining to help manage all this collective gap filling is based on applied category theory. Category theory provides a language for describing and connecting diverse mathematical structures, so we may be able to use it to create a formal system for relating and composing different plausible fictions. Exactly how this might work is a gap which remains to be filled within my own fiction here, but luckily creating formal systems to relate and compose things is precisely the kind of problem we try to solve at Topos Institute, so it’s not implausible to me. If a reader has ideas, please let me know!

But supposing we had mathematical infrastructure to facilitate collective gap-filling, then all we’d need are the plausible fiction writers. As long as our vision starts from the present, is compelling as a possibility, and doesn’t require any magical thinking, I believe people will be motivated to fill in the gaps.

A collaborative process of imagining and refining plausible futures, especially one that seeks varied perspectives, could lead to a more participatory world, where more people become inventors of reality. Much like how Edison’s understanding of both material possibilities and social needs allowed him to develop a commercially viable light bulb, plausible fiction aims to bridge our current reality to a desired future. The more people consider and work out what process would actually bring about a good future, the more likely we are to get there. This approach has the potential to democratize the shaping of our collective future, enabling more people to contribute meaningfully to solving global challenges.

Of course, not all proposed futures will be deemed plausible or beneficial, and so we need a process by which people can examine narratives for viability and desirability. In order to steer away from a plausible fiction you don’t like, try to identify a gap you deem either unfillable or for which you can provide a plausible gap-filling story that contains a negative arc. As such a “defeater” fiction gains traction, the original story may become dormant, with fewer people engaging with or developing it, or it could even become a center around which there is active work to counter it.

What I’m proposing is not very different from the situation we have now. We already tell each other plausible fictions in a dialectic of proposing and critiquing that helps refine our collective vision. But I think we can do this more deliberately and effectively. And like our current system, if this system were effective, it would involve risk. As my wife points out, risk is a tenet of life: one cannot truly live without risk. Nevertheless, I believe that clarifying a structure for this ongoing dialogue and refinement of ideas is crucial for the development of robust, well-considered futures.

I imagine a future where humans do labor that is less stressful because it’s closer to the work they want to be doing, and that a good plausible fiction platform might help us get there. In fact, this vision serves as an example of plausible fiction: it starts with our current reality, where work is often stressful, ends with a desirable future where work is more fulfilling, and suggests that a plausible fiction platform makes that trajectory plausible. But there is a big gap, already identified before: realizing this future depends on developing effective mechanisms for collectively sharing and refining such plausible fictions.

So what exactly is a positive future? I’d love to hear your responses and ideas. For example, here are some ways to engage:

• Share a plausible fiction of your own in the comments, starting with a current challenge and ending with a positive future.
• Find gaps in the plausible fictions I’ve presented here, or those in the comments, and possibly propose ways to fill them.
• Offer technical suggestions for how we might formalize the process of connecting and composing plausible fictions.

By collaborating on these plausible fictions, we can cultivate a better future. My proposal is that plausible fiction may offer a functional, memetically-fit system to bring about what I consider a good future.

Epilogue

David: Hi Claude. Please read the above and identify 3 gaps. Then choose one of them and try to fill it with plausible fiction of your own.

Claude: I’ve read the document about plausible fiction by David Spivak. Here are three gaps I’ve identified in the proposal:

1. The specific mathematical infrastructure based on applied category theory that would help manage collective gap-filling.
2. The mechanism for determining which plausible fictions are most beneficial or desirable to pursue.
3. How to incentivize and facilitate widespread participation in creating and refining plausible fictions.

I’ll attempt to fill the third gap with some plausible fiction of my own:

Incentivizing Widespread Participation in Plausible Fiction

In 2025, a group of tech entrepreneurs, social scientists, and game designers collaborate to create “FutureForge,” a gamified platform for developing and refining plausible fictions. The platform combines elements of social media, collaborative writing tools, and prediction markets to engage a wide audience in the process of imagining and shaping potential futures.

Key Features of FutureForge:

1. Intuitive Interface: Users can easily create, view, and contribute to plausible fictions through a user-friendly web and mobile app.

2. Reputation System: Contributors earn “Foresight Points” based on the quality and impact of their contributions, as rated by peers and expert reviewers.

3. Collaborative Editing: Wiki-style tools allow for seamless collaboration and version control of plausible fictions.

4. Visualization Tools: AI-powered visualization tools help users create compelling infographics and animations to illustrate their ideas.

5. Integration with Education: Schools and universities incorporate FutureForge into their curricula, teaching students to think critically about the future and contribute to solutions.

6. Corporate Challenges: Companies and organizations sponsor challenges on the platform, offering rewards for the most promising solutions to specific problems.

7. Prediction Market: Users can invest virtual currency in the likelihood of various plausible fictions coming true, adding a layer of crowd-wisdom to the process.

8. Real-World Impact Tracking: The platform monitors and highlights real-world developments that align with or stem from plausible fictions created on the site.

As FutureForge gains traction, it becomes a go-to platform for policymakers, innovators, and citizens looking to shape the future. By 2030, millions of users worldwide regularly contribute to and discuss plausible fictions, leading to accelerated problem-solving and more participatory governance at local, national, and global levels.

The success of FutureForge inspires similar platforms and methodologies, creating a cultural shift towards more proactive and collaborative approaches to addressing societal challenges. This widespread engagement with plausible fiction helps to bridge ideological divides, as people from diverse backgrounds work together to imagine and create better futures.

This plausible fiction attempts to address the gap of incentivizing and facilitating widespread participation by proposing a gamified platform that makes contributing to plausible fictions engaging, rewarding, and impactful. It starts with our current technological capabilities and social media engagement, and progresses towards a future where collaborative future-thinking becomes a widespread and influential practice.

The fiction aims to be plausible by building on existing technologies and social trends, such as gamification, collaborative platforms, and the increasing integration of technology in education and policy-making. It also addresses potential challenges, such as maintaining quality contributions and ensuring real-world impact.

Would you like me to elaborate on any part of this plausible fiction or discuss how it might be further refined?

This work was funded by AFOSR grant FA9550-23-1-0376, “Structure and dynamics of working language” and a grant from the Mathematics and Metaphysics Institute, “Accountable metaphysics”.

Thumbnail by 愚木混株 cdd20 on Unsplash

Overview

Sam Staton, Paolo Perrone and I organized a small meeting between Topos Institute and the Oxford CS department. It was kind of like a workshop, but because of the short time frame that we planned it on and limited funding, we didn’t invite all the people we’d like to invite or have it open to applications, so we called it a “meeting.” Anyways, we managed to make some good progress on some open problems within categorical systems theory, and it was a lot of fun, so this is a short retrospective on what worked, what didn’t work, and directions to pursue in the future.

The meeting was fairly loosely structured. We had two talks at the beginning, one from David Jaz on double categorical systems theory, and another from Sam Staton on LazyPPL. The rest of the time was spent on:

• Talking in small groups about math.
• Writing up what we talked about on the LocalCharts forest.
• Explaining things we talked about to the whole group.

I opened the meeting by asking participants to do three things.

1. As much as possible, attempt to ground any new theory with concrete examples.
2. Write things down on the forest on the day that you discussed them, so that you won’t forget them, and so that people interested in the topics of the meeting who didn’t attend the meeting wouldn’t be too left out.
3. Be comfortable with the idea that you might spend three hours teaching existing theory to people who aren’t familiar with it yet. Transmitting knowledge is a good outcome of the workshop and not at all a waste of time.

The last request was I think the most successful idea; people were pretty happy at the end of the workshop about things that they had learned. For the second request, I tried to set aside time at the end of each day to write, but it was very tempting to continue conversations into this time instead of writing, and also it was somewhat hard to write at the end of the day, when everyone was tired from doing math all day and looking forward to dinner. The first request I think was a good idea, but very easy to forget when you are a category theorist! So I think that it’s worth asking people to do in the future, even though we weren’t very good at living up to it.

Content

We gathered together things that people wrote at the workshop into Oxford-Topos Meeting 2024 - Outcomes. Some people ended up writing a lot, others none at all. I ended up not writing very much because I was hovering around helping people install forester. Hopefully in future events, everyone will have forester installed and be used to forester syntax before designated writing times.

So my dream of having all of the discussions captured on paper for those who weren’t present didn’t quite materialize. But fortunately I can talk a little bit now about some of the topics of the discussions that I participated in.

Lessons learned

1. When you are organizing something for academics, it’s good to have a half-hour buffer at the beginning and tell people to show up at the beginning of it, so that when they inevitably show up late, the rest of the schedule doesn’t have to be shifted.
2. Keeping to a schedule is hard. But that’s OK: you don’t necessarily need to keep to a strict schedule in order to get things done!
3. Small is powerful. Generally the most productive discussions involved 2-3 participants, even if there were more than 3 in the group. That being said, there is a balance between “everyone contributes” and “people who don’t have the same level of experience get to be a fly on the wall and see how people with more experience handle a subject”, and I think that sometimes it is more productive to slow down a discussion and keep everyone following, to accomplish the “learning things” objective. All that being said, I think that it is very hard to do math in a group of >5.

Overall, people said that they had a good time at the meeting, so I hope to do this again some time. I honestly think both the small discussion groups and the overall small number of people were both assets, and in fact the small number of days was also somewhat of an asset because it forced people to focus. So I think “scaling this up” doesn’t look like inviting more people for a longer time: I think it looks like inviting different groups of people semi-frequently. Of course, this is only practical when the groups of people happen to be in the same place, but perhaps this is possible if small meetings like this can “piggyback” over other events like conferences. And I encourage other people to organize similar small events and not invite me, but still write up the results on localcharts: I think the ideal number of this kind of event is much larger than would be practical for me to attend!

Some vignettes

A few weeks ago, I started at Topos as a postdoc. For the next while I’ll be working with David under a grant called The Structure and Dynamics of Working Language. The mystery at hand is how an abstract specification compiles into a tangible reality. For example, how a high-level recipe for pie turns into a literal pie. One that is created with particular eggs and apples by a particular person who rolls the rolling pin in a particular way. That language really works — in other words, that it is sufficiently useful that its practitioners carry it forward — hinges on a mutual relationship of trust and adaptability between the one who outlines the abstraction (the specifier) and the one who executes it (the reifier). Below is a series of vignettes that elaborate this theme.

Reification and technology

Trustworthy reification is particularly salient at this moment in technological history, because the lesson that I learned in fifth grade about giving computers specific instructions is no longer true. I can give ChatGPT a vague prompt like “Write an algorithm that sorts a list of names by last names” and it produces specific code that respects not only the intentions of my request but also the context of modern day programming. It uses meaningful variable names, adds comments, and flags edge cases.

As technology speeds up the reification process — in large part because it can reify more and more abstract instructions — we (the specifiers) want to be in a virtuous cycle of trust with it (the reifier). These vignettes illustate how developing and maintaining trust relies on:

• Communication and responsiveness between specifier and reifier.
• The nature and dynamics of the shared context.

Mathematical breadcrumbs

As a first-pass at mathematicizing the relationship between high-level specifications with low-level realities, my instinct is to construct a coarse-graining map from low-level to high-level representing which realities implement which specifications. For example, a map that sends collections of pixels to the labels “cat”, “dog”, “sandwich”, etc. From the perspective of this formalism, all low-level implementations of a given high-level specification are equivalent. However, the vignettes show precisely that this is not the case in how we humans expect our instructions to be reified. I wasn’t happy with how Mrs. Parker put the pieces of bread together, even though it strictly adhered to my instructions. And not every interpretation of “keep my baby safe and happy” is how I want my baby to be cared for. These mathematics of coarse-graining fails to capture the shared context and trust between the specifier and the reifier.

In contrast, I am excited about how frameworks like dynamic operads foreground the two way communication between high-level and low-level actors. As David and I delve more into the structure and dynamics of working language, I plan to keep my eye on the idea of shared context, how it directs the way that language is compiled, how it forms the language itself, and how it is the medium upon which trust is built.

Acknowledgements This blog post is the product of a conversation with David Spivak about why I care about working language. Kris Brown helped me see the role of shared context and the fourth vignette is due to Brendan Fong. Thanks!

Part I

Bartłomiej Skowron, David Spivak

According to legend, one of the ancient philosophers gave a public lecture entitled “On the Good”. This topic attracted many listeners, who probably wanted to listen to considerations about how to live a healthy life, earn money successfully, and gain honorable positions. Nevertheless, this philosopher surprised everyone: instead of talking about these essential goods, he spoke of mathematics, numbers, shapes, etc. Few understood, and many lost interest and left. Reportedly, this lecture concluded that goodness is one, further obscuring the whole matter rather than illuminating it. Why was this philosopher talking about mathematical structures when he was supposed to analyze goodness? And why was the story of this lecture recalled in the 20th century by Alfred North Whitehead and later Felix Browder & Saunders Mac Lane? Because doing mathematics can be seen as a path to goodness, and mathematical structures as structures of goodness itself. Strange, isn’t it? Whitehead wrote: “The lecturer was competent - he was Plato.” It is from Plato that the idea that goodness and mathematics have much in common originates.

Aristotle, who disagreed with Plato, pointed out in his major ethical work The Nicomachean Ethics that the good is understood in different ways. Moreover, even the same person can understand the good differently. When a person is COVID sick, good seems to be health; when she is tired, good seems to be rest; when she acts cowardly, good seems to be courage; when she does not understand how to compose morphisms in the category Poly, good then appears to be understanding the simpler cases of natural transformations. But what should we do when the answer to the question of goodness seems so case-dependent? Is it possible to say something that isn’t empty but instead meaningful and relevant about the good? Following Plato’s intuition, we claim that mathematics may help us do this.

Let us assume, laboriously and for a moment, that goodness is not only what, for example, seems good to you, your friend, or me. Let the good be an idea, a term which we don’t intend in the everyday casual sense, but instead along the lines of Plato’s form or more precisely “idea” in the sense of Roman Ingarden: an idea is something that has some content, some rich ontological structure. For example linearity is an idea—a mathematical one—captured by the ontological structure of the category of vector spaces. In the case of the good, this content is whatever structure allows us to classify certain objects (here, you can replace object with action, person, or value; the object need only be an entity with a desired form or manner of existence) as being instances of this idea. You can think of this content as a specific shape, and of instances of the idea, say goodness, as objects in which this shape is present. To put it yet another way, it is a certain pattern of patterns, and as such can be realized in many objects. We want to know what this pattern called goodness—which remains the same, regardless of how many (if any) instances it has—is.

Nevertheless, caution is needed here: ideas are characterized first of all by the fact that they are general entities (sometimes they are called universals, sometimes they are called abstracts), which means that this shape or pattern has many empty slots, which can be filled in various ways. For example, individual actual real objects do not have such gaps. The act of filling in these gaps is called concretizing qualities, but discussing this would take us into too metaphysical an area. So let’s go back to the basic idea: make a working assumption that when we want to talk about the good, we will try to speak in essence about the idea of the good, or more precisely, about the content of the good as an idea. In this view, the mathematics of goodness becomes the mathematical study of the content of goodness: understanding these “shapes,” patterns and their dynamics. For the purposes of this blog post, let’s assume you can make some sense of what’s being said here.

In fact, sense-making is central to our story of how goodness and mathematics are related. To see this, let’s return to everyday life on Earth. When I need to shop, I need to find the right store where I can find the products in question. I can get to that store guided by Google Maps or just glance at the map and use my sense of direction, as long as I have that sense developed. When I stroll through the park, I can distinguish the balmy, woody notes of lavender or the earthy notes of iris, as long as I have my sense of smell sharpened. When I’m feeling lonely, I can use social sense to make some friendships that seem to respond to that loneliness. If I’m doing philosophy, and I don’t want to be naïve, I can use my sense of irony, like Socrates, and thus for an exercise, distance myself from my own philosophical beliefs. When I make a decision, dividing some goods among people, I can do it fairly if I have a sense of justice. In general, when I make a decision of a moral nature, something attracts me approvingly to good choices, and something disapprovingly outrages me when I imagine bad decisions—the moral sense is responsible for this attraction or repulsion. This is probably the case with every sense: good compositions attract us, and bad ones repel us. Fitting things together is, in fact, sense-making. In general, it seems that the art of living is the art of making sense and avoiding nonsense.

Sense-making is multi-sensory, dynamic, and complex. Our senses of things and, above all, the corresponding qualities must fit together in order to for us to act proficiently. Otherwise, there will remain a lack of meaning and an inability to navigate. In order to divide goods equitably, I must be able to both divide and also (sometimes) use my sense of sight to see the objects I am dividing, as well as my moral sense to see the merits of those subjects, which would be the basis for equitable distribution. When experienced florists arrange a bouquet, they compose the qualities of the different senses: both the color of the flowers and their scent must be well composed. These qualities must fit together so that the bouquet is good and so that we can say that this florist is good at being a florist. A good florist is a sense-composer. Certain fragrance notes may not fit together, and such combinations repel us because they don’t make sense together, whereas certain combinations are almost perfect and attract many sense-makers. Sometimes these combinations even intoxicate and please, such as that of orange, grapefruit, nutmeg, and vanilla. One might ask: on what is this sense-making founded? Behind each sense are the qualities of that sense. For example, to the sense of sight, there are qualities such as redness, linearity, and blurriness; to the sense of smell, there are qualities such as the notes of nutmeg and vanilla. The sense of irony includes qualities such as perversity. To the metaphysical sense, there are qualities such as sublimity. And to the moral sense there are moral qualities, such as the quality of justice.

How does all this relate to mathematics? Simple. Certain sense qualities fit together, making sense, and others don’t; they don’t make sense because they don’t fit together well. Sense-makers do the work of finding fitting compositions daily: we compose senses, and as long as we do it well, we make sense of the world. Then, in interaction with other sense-makers, we exchange our notions of sense, influencing and changing each other: sometimes we all match each other perfectly, and sometimes the group can’t make sense of each others’ points of view at all. Sometimes we all find the same qualities, and in this case we hook up and compose our senses together, making a synergistic group sense that allows the group to navigate the situation better than any member alone could have. This is how consciousness—not necessarily experience, but coherent sense—is created with many multi-level interactions, both individual and collective. Individual senses can come together to create a new higher-level sense, and this process is formed through an active and creative process. This way senses combine may be governed by multi-level laws of composition or fitting together. It seems that no one currently knows the general laws of sense composition: they still need to be discovered. But perhaps these laws have something to do with proper accounting, the culmination of which is mathematical and which we can try to approach with category theory.

Plato had the intuition that goodness is oneness and order. To separate good from evil is to separate order, the cosmos, from disorder. We understand order in this sense as meaning structure: that which can be mathematically grasped. This means that our notion of the good could in fact be mathematized by articulating multiscale compositional dynamics that occur within the network of sense-makers immersed in a world of sensory qualities. This way of mathematizating goodness—or at least some nearby notion—means formulating the dynamic process by which sense is made.

Plato assumed that ideas are static—timeless—and that they exist separately from material things. The considerations here indicate that all sense-making is in fact dynamic. Nevertheless, this dynamism still has a mathematical pattern, the stability of which does not consist in being static, as Plato and Ingarden think, but consists in the dynamic structure of how senses are sensibly composed. Thus, although we started from Plato’s intuition, we conclude that Plato’s theory of ideas is like Wittgenstein’s ladder that, having climbed, must be discarded.

You might assume that the good cannot be analyzed because it is simple and thus inaccessible to cognition. Or you might claim that it is a heterogeneous conglomerate without any internal uniformity or structure and that one can only randomly hit parts of it. We do not claim either of these. The shape of the good is cognitively graspable: it can be learned, and it is essentially compositional in nature. To know the good is to understand the laws of composition. All this, of course, does not mean that it is easy to see the good. Nevertheless, it does mean that it can be done in some way, an expression of epistemological, axiological optimism. However, to reiterate, it is not easy and probably will never be complete. The way leads through categorifying the content of goodness, a project which we propose to begin. Does it make sense?

Part II

David Corfield

Thank you both for your reflections on how we might use mathematics to address goodness. There are some helpful ideas contained in your post to get us started. In particular I agree that something like sense-making plays an important role in what we take to be good.

As for my own starting point to approach the question, I’d like to consider first what might appear to be the hardest part of the problem. When Ancient Greek philosophy considers the good, it is always as part of the particular question of what it is for a human to lead a good life. This is a central concern of each of Socrates, Plato and Aristotle. Now of course the good life has you enjoy good things. It can have you appreciating via the senses, say, a florist’s bouquet, the florist having done a good job in composing the scents and colors of the bunch. It can have you appreciating a good coffee at a convenient store. It can have you communing with good friends for an evening. But the good life involves so much more than these. Rather than a series of satisfactory experiences, it encompasses a certain way of living. Naturally it involves a life that makes sense of features of its environment, that allows for a good fit between an individual and their niches. But the good life is a life rich with meaning, and a life full of meaning-making.

‘Making sense of’ is a phrase generally applied to an existing phenomenon, making sense of the scene before you, making sense of what someone is saying to you, making sense of a mathematical argument. Making meaning, on the other hand, is not making meaning of anything, it’s a creative process. It may be the setting up of a project, like we’re doing here. It may be planning to lead a life together with someone and enacting this plan. Leading a good life is living a life full of meaning, following a vocation, sustaining a flourishing community, creating meaning for yourself and others.

Well that only seems to have complicated the problem. Perhaps we might have hoped to be able to say something about how goodness applies to entities of particular types - a good apple, a good book, a good sheepdog, a good soccer match. Now we have to deal with the thorny issue of characterizing the good life, as though there could be something mathematically tractable about this.

Do we see existing work out there to learn from? Well, of course plenty has been said about the good life. Indeed, the wisdom traditions of the world, from the East to the West, have a great deal to say. ‘Know thyself’ advises Socrates. ‘Inculcate the virtues’, says Aristotle. And Eastern traditions of Buddhism and Daoism have their own say: Follow the Noble Eightfold Path, Follow the Way.

So plenty of verbal descriptions of what the good life looks like, and discussion of the means to transform oneself to pursue it. Can we really hope that category theory can have something to say on the subject? Well, there’s plenty of work at the moment from the interface of cognitive science and wisdom studies, which looks to see whether the former can make sense of the Western and Eastern traditions. Here we see a strong convergence at the moment with the following three approaches:

• Predictive processing/active inference on well-being – Mark Miller, Brett Andersen;
• Relevance realization and the meaning crisis – John Vervaeke;
• Hemispherical balance, the left serving the right – Iain McGilchrist.

Notably these people are talking to each other (e.g., here and here). They’re even publishing together, see, e.g., the joint work of Vervaeke with Miller and Andersen. The unanimous conclusion is that we face a problem today and that we need to change the way we live in the world, in particular we need to develop our meta-cognitive capacities to equip us with the ability to apportion wisely appropriate care to our meaning-making projects, and the ability to seek the right challenges to push our boundaries.

These approaches also allow a great deal to be said on what goes wrong in a life. From the predictive processing side, the optimisers that we are get stuck in feedback loops, the loop of addiction, of depression, and so on. Or we rely too heavily on left-hemispherical thinking and become too instrumental in our dealings with the world. Departures from the right balance are involved in mental disorders.

Now perhaps here we have a window of opportunity, since in particular the predictive processing approach commences from an explicitly mathematical point of view in its characterization of the “Bayesian Brain”. To do this there needs to be mathematics that deals with recursive systems. One where layers of the hierarchy adapt according to bottom-up and top-down processing. We need to have our higher-level cognitive systems engage in self-monitoring, modeling the way we model the world to predict if that modeling is working or needs correction. We need the cognitive apparatus to apply itself to itself.

Take Vervaeke’s description of Jung’s idea of the Self:

“What’s the self? Well, it’s kind of the archetype of the archetypes. It’s like Plato’s notion of the good, which is the form for how to be a form. The eidos of the eidos. It is the virtual engine regulating the self organization of the psyche as a whole. It is the principle—the self is the principle of autopoiesis itself. It’s the ultimate virtual engine that constellates all the other virtual engines so that the psyche can continue its process of autopoietic self-organization. Remember when a system is self-organizing its function and its development are completely merged. It develops by functions and it functions by developing.”

Readers of this blog will know that we have at least one claim for a fruitful place where ACT meets such a complex system, and that is in the work of one of us, David Spivak. Another hint that we could take this further is that another Topos Institute member, Toby St Clere Smithe, is looking to use ACT precisely to capture the workings of the Bayesian Brain. Further relevant work on category-theoretic cybernetics may also help us address the question of the well-being of a complex system. My proposal then is that we take up such work and see if ACT can help us articulate what the cognitive scientists are telling us about well-being.

The problem

In scientific applications (biology, ecology, epidemiology, chemistry, physics, economics, etc.) and related engineering domains, full modeling of a complex system frequently involves the following considerations:

1. Multi-disciplinarity. Problems may show up in a certain domain that cannot be solved with the customary mathematical tools and software frameworks of that domain, and the mathematical, scientific, technical, and cultural assumptions of another scientific domain may be illegible from the perspective of the original domain. For instance, modeling hydraulic systems often involves both rigid body physics and fluid physics.

2. Openness. One is not always lucky enough that one part of the world can be fully isolated from the rest. Rather, systems tend to have interfaces or boundaries, on which (and beyond which) one’s model does not make endogenous predictions—but on which its predictions must depend. For instance, this is typically the case of electronic circuits; they have terminals that are intended to be connected to other systems.

3. Continuity in time. The real world is typically not parceled into discrete time steps. While a sufficiently small time step can generally be chosen, this comes at a great computational cost. We would prefer to be able to reason flexibly about timescales, with a guarantee that for any nonnegative rationals , the forward propagation is compatible with in the sense that, for any initial knowledge , .

4. Continuity in space. We often are interested in systems whose states have continuous extent. i.e. electric fields, fluids, deformable bodies, etc., meaning that the state space is naturally an infinite-dimensional function space.

5. Stochasticity. We often observe systems at a scale where many degrees of freedom are not visible, and even when they are visible, it is frequently advantageous to ignore them. However, these hidden degrees of freedom affect the larger scale behavior in the form of noise, and cause the system to behave stochastically rather than deterministically. The weather is one good example of a system which has some amount of regularity, but also a good deal of noise.

6. Nondeterminism. Even stochasticity makes strong claims about uncertain behavior, by asserting precisely known probabilities of any observable. In many cases, we only know that probabilities lie within a certain range, or we do not know them at all. This motivates “imprecise probability,” which we believe is best understood as a monad which naturally generalizes both the probability monad and the nondeterminism monad (such as the monad of convex subsets of probability-distribution space). The behavior of your opponent in chess is nondeterministic; it doesn’t make sense to have a full probability model for the state of your opponent’s brain.

7. Partiality. Probabilistic programs may in general be nonterminating, or they may reject inconsistent inputs; these both motivate a general notion of partiality, or the ability of processes to result in (a state representing that something went wrong). For instance, you might want to sample from the inside of a disk by sampling from a square, and throwing away points not inside the disk.

8. Hybridness. Complex systems often involve interactions between continuous and discrete (or discretely modeled) components. Discrete components may transition on a fixed timescale, or at times generated by a point process that depends on the outputs of continuous components. Continuous components may depend on the outputs of discrete components. A classical example of this is a hybrid digital-analogue circuit.

Many of these considerations greatly enlarge the space of solutions: the space of time-varying probabilitity distributions over piecewise-continuous vector fields on a manifold is incredibly “large”, in the sense that multiple levels of discretization are required to convert this into something that can be represented on a computer.

Analytic or numerical solutions to problems which are “that large” are, in general, intractable. However, a logically-specified “full model” of the situation is still useful, as a ground truth that more tractable approximations can be compared to, or that behavioral guarantees can be extracted from.

It is for this reason that we would like a compositional, formal framework for such systems, which could be used to design and analyze complex models. We expect that category theory is a fruitful method for finding such a framework.

Solving such “large systems” is a problem that has been attacked by brilliant mathematical physicists for generations; the usefulness of our approach is not necessarily predicated on the idea that a compositional framework would significantly advance the state of the art with regard to concrete solutions or theorems for such systems.

However, having a formal framework would organize the field in such a way as to make it easier to produce rigorously verified and interpretable computer-aided analyses. Moreover, organizing software implementation makes it possible to take existing techniques much farther in less time and code.

In the next section, we discuss applications of such a framework, and then in the last section we will discuss some concrete criteria we have for such a framework, as well as tentative approaches we are pursuing.

Finally, we should say that by “formal framework”, we do not mean that all “large systems” will necessarily be captured by a single definition. Rather, we expect that we will capture certain classes of large systems with different definitions, but that we will be able to relate and translate these different definitions formally. The reason this is desirable is that we want to be able to take advantage of the special properties of different classes of system.

For instance, we might have some definition for systems whose solutions are smooth, and be able to prove some theorems that wouldn’t hold for systems with non-smooth solutions. However, we should be able to also translate a smooth system into a more general class of systems, which we might want to do in order to compose it with a non-smooth system or stochastic system.

Some examples of types of systems that we would possibly like to fit within our framework are the following.

1. Differential equations
   • ordinary
   • partial
   • stochastic
   • random
   • jump-diffusion
2. Markov processes
   • discrete-time Markov chains
   • continuous-time Markov chains
   • Markov decision processes
   • open games
   • (open) mean-field games
   • Markov automata
3. “Hybrid systems”
4. Probabilistic models
   • probabilistic graphical models / Bayesian networks / causalgraphs
   • corecursive programs in a functional probabilistic programming language (including, notably, large language models based on Transformer neural networks)
   • generative probabilistic logic programs
   • score-based generative models (including, notably, diffusion models based on U-Net neural networks)

Classically, these are all different paradigms of system. However, redefining these systems categorically will mean that it will be easier to relate them to each other. This doesn’t necessarily mean that there will be categories for each type of system; we don’t yet know the precise type of categorical gadget we will need for modeling. It could be monoidal categories, it could be pseudo lax virtual triple categories (whatever that is). But morally speaking, there should be some sort of functorial interpretation of certain types of systems into others. And additionally, we should be able to “bottom out” out in a behavioral interpretation in which systems are described merely as joint epistemic states regarding their observables, which can be composed by intersection.

Applications

Decision-making in complex environments is often critically dependent on coherent predictions, informed by observational data (), of how actions () affect the probability of queries (each Boolean-valued) pertaining to a future trajectory

Some examples include:

1. Deciding what policy interventions to perform during a pandemic:
   • observations include recorded cases and outcomes
   • the complex environment includes asymptomatic cases, the details of mobility, the virulence of different strains, etc.
2. Deciding when to switch on and off power-generating stations, and when to charge or discharge grid-scale energy storage:
   • observations include voltages (magnitude and phase) and currents
   • the complex environment includes transmission lines, predictable and unpredictable sources of power demand (at various price levels), weather (affecting renewable capacity), etc.
3. Deciding what incentives to provide for reducing the emissions of climate-affecting gases:
   • observations include weather data, sea levels, sea temperatures, energy supply levels, recorded material flows, etc.
   • the complex environment includes atmospheric advection, cloud processes and albedo, radiative forcing, oceanic eddies, etc.
4. Planning a project with many subgoals (and sub-subgoals, etc.) for which various alternative approaches may be viable:
   • observations include status reports, estimates, milestone completion events, etc.
   • the complex environment includes the changing availability of human resources with varying levels of skills and experience, technical risks and uncertain feasibilities, potential synergies between efforts, etc.
5. Deciding which combination of treatments to suggest to a cancer patient:
   • observations include biomarkers, imaging scans, expert assessments, DNA sequencing, proteomics, metabolomics, etc.
   • the complex environment includes the immune system, cellular regulatory networks, the diffusion of blood in and around tumors, etc.

In many of these cases, we need to integrate information from quantitative models across multiple scientific ontologies and scales (in addition to expert opinions where scientific data is sparse) in a computationally tractable way. In the hopes that machine learning may be increasingly able to provide computationally feasible answers to questions that are sufficiently well-defined, our focus here is on being able to make such boundary-transcending questions well-defined, by defining a sufficiently flexible and rigorous meta-ontology that can encompass all necessary ontologies and adapters between them.

The point is not to figure out how to do traditional-style modeling and simulation of complex systems (although that might be a component), the point is for any model (even when highly complex and multidisciplinary) to have a well-defined semantics to which efficient approximation methods can be rigorously compared. This is as opposed to the common state in current practice in which the best known models are only defined by their custom and informal implementations (especially when machine learning is involved), making it very difficult to reason about the model’s behavior on inputs with which it has never specifically been run. If your model is more than 100,000 lines of mathematically ill-specified Python code, it is hard to have confidence in what it is saying, especially when machine learning is involved in any capacity.

Conclusion

What we have outlined in this post is not just a series of conjectures or a simple project outline, but a full research program, which could supply decades of work across a large community of mathematicians, scientists, and engineers. However, that is not to say that we will only see benefits from this research program after decades of work. We expect that progress can be made in many ways along these lines, but more importantly we see that progress is already being made, throughout both the applied category theory and alignment communities, as evidenced by our bibliography.

Finally, there are plenty of mathematical problems that need to be solved in order to lay the foundations that we need for this program. But the larger challenge is to integrate all of the progress being made, not into a seamless edifice, but into a cohesive patchwork whole, where each abstract concept learned is exploited in as many ways as possible across all domains. This efficient use of concepts is demanded by the twin requirements that it is possible for humans to use the fruits of this program, and that this program has a truly global scope. If you have not yet been convinced of the use of category theory, then hear this: Category theory is the only conceptual technology and intellectual tradition of sufficient maturity and breadth to have a chance of solving this larger challenge.

Introduction

At a Computational Theology workshop, held a few months ago in Austin TX, a number of us—Scott Garrabrant, Sophie Libkind (who also helped me refine the ideas for this post), Eliana Lorch, Anna Salamon, and I—spent several hours trying to work out how math and matter relate. How does the math fact that 4+3=7 relate to the paper-and-ink display “4+3=7”, or to some person’s vocal chords vibrating to create the sound “four plus three equals seven”? The math is pure pattern, and the sound, as vibrating air, is pure matter. What’s going on with the link between them?

Eventually, we came upon the transistor as an excellent example of where math and matter meet.

On the left we see the transistor as matter, a thing in the material world. On the right we see the transistor as pattern, a logical idea. John Vervaeke says that the term symbol is appropriate here—that the symbol is not just a signifier of some transformation but also an active participant in materially achieving that transformation, i.e. that it’s both pattern and matter—though I don’t know how widespread that terminology is. It seems a little more on the “pattern” side, but I need a word, so I’ll go with it throughout this post, saying that the transistor is a symbol in this sense. If you think of a better word than “symbol” for referring to the fulcrum or janus-point which, like a transistor, is both matter and pattern, please put it in the comment section below!

It is now believed that all of math can be recorded and developed within a proof assistant like Agda, Coq, HOL, or Lean. These programs run on computers, computers are made of logic gates, logic gates are made of NAND gates, and NAND gates are formed by attaching two transistors like so:

One can imagine the connection between math and matter, via proof assistants that run on transistors, as taking place in a kind of hour-glass shape.

We do math purely conceptually, and yet these concepts need to turn into material action in order to affect the world. The transistor is a symbol that serves in a dual role, as both logic and matter, and happens to be close to the atomic scale in both: it is half of a NAND gate (upon which all the logic necessary for a computer is built), and as of late 2022 it is about 2 nanometers (the size of 10 silicon atoms) in length.

In the next section I’ll discuss other examples of symbols that serve in a dual role of matter and pattern, and that like the transistor are as condensed as possible. Then I’ll say what this has to do with category theory and its role in the world.

Examples

Besides transistors, what other examples can we find of “symbols”: i.e. condensed instantiations of both matter and pattern? And why are they important?

1. DNA. As an acidic molecule in 3D space that acts according to physical laws, DNA is matter; but as an ordered sequence of four letters whose three-letter words code for amino acids, it is pattern. Reading the DNA and elaborating its meaning involves many other parts of the cell, and we could consider that whole complex to be both matter and pattern, but DNA is more condensed, more symbolic. Is DNA matter or pattern?

2. A signature. As the process of moving a pen across paper to form an ink stain, a signature is matter; but as a token of people’s agreement to regulate their behavior, it is pattern. As we sign a contract in good faith, we’ve set up our internal state in such a way that we think it’s likely that our actions in the material world will follow the pattern dictated by the contract. Is signature matter or pattern?

3. Grandma neuron. Neuroscientists say that a single neuron can code for a single concept, e.g. neuron X fires if and only if one recognizes their own grandma. As a carbon-based object, a neuron is matter; but as representing one’s grandma, it is pattern. If we look at just the grandma neuron, would you call it matter or pattern?

There are many examples, and some are clearer than others. But one thing that strikes me in all this is that there is some process by which examples keep being created, symbols keep getting formed and condensed in our world. Probably early life’s control mechanism was far less condensed than “modern” DNA. Whatever happened in that prebiotic chemistry on the early earth, the robust and effective language for building custom proteins must have been repeatedly refined over eons. Similarly, coordination of animal activity is ancient, but the condensation of this coordination into a binding contract, or the symbolic signature itself, is quite new. And a similar thing could be said about the grandma neuron or the transistor. In each case there seems to be some sort of natural push or process urging the formation of smaller, more concentrated symbols to instantiate pattern as matter. More condensed symbols seem to work better.

What is this natural process? How does it work in so many domains and on so many scales at once? And why is condensing and compressing these symbols somehow “preferred” by evolution? I would love to know.

Compositionality and language formation

Transistors wouldn’t be nearly as important in our world today if they didn’t form NAND gates, and hence logic gates, adder circuits, CPUs, etc. But all that is purely conceptual, i.e. pattern. The thing that makes this grammar work is that it simultaneously fits the material embodiment as well. The material transistors can be arranged according to the conceptual pattern and there is a kind of “functoriality” there: just as the matter instantiates the pattern at the lowest level, so does the matter instantiate the pattern at the higher levels too. Logic gates are made of NAND gates wired together, both in pattern and in matter, and this analogy keeps holding all the way up. Your computer has been programmed to run the programs that let you read this, but it is operating on physics in the material world, thanks to the robustness and compositionality of the transistor as symbol.

Similarly, a single contract is important, but an organization works with a whole slew of contracts. When each is being decided upon, the composition of the whole—how all those agreements are going to be carried out in the one organization—requires a conceptual understanding of roles and activities, all of which will be instantiated by human bodies. The composition of agreements within the company reflects the composition of movements by its employees.

The same can be said for DNA or neurons. A single nucleotide does not define DNA, nor does a single neuron define the brain. The organization of nucleotides in DNA or of neurons in the brain is extremely important for determining what the DNA or brain function will actually be. The point is that in each case the function is carried out materially, and this works because the analogy is compositional with respect to the patterns of connection in these organized systems.

So we’re not only interested in the symbol at the center of matter and pattern, but in the compositionality—the grammar—by which the composition of conceptual patterns and the composition of material flows maintain their alignment.

We can see that language occurs materially and affects the material world, and it is also patterned in that it follows conceptual grammatical rules. When I say “pass the salt”, atoms including your arm and a salt shaker move through space, resulting in some sodium chloride crystals arriving in my bowl of soup. Language controls so much of our world, especially if you see things like DNA as language. And just as important as the fundamental symbols at the base of language is the fact that language is compositional.

Thus the drive toward finding symbols, which bridge matter & pattern, and do so compositionally, seems to be the same as, or at least tightly linked with, language formation. So it’s interesting to ask: by what process is language—including the language of thought, the language of computation, the language of life, etc—formed? This formation appears to be a natural multi-scale process, beginning at least as far back as DNA, and continuing to this day.

An applied category theory question

Though I’ve used different terms for it over the years, I’ve been interested in using category theory to study collective intelligence and sense-making for just over 15 years now. A current instantiation of this question is represented in this blog post:

Can we use CT to formalize a process by which language formation, i.e. by which the condensation of compositional matter-pattern symbols, would naturally occur?

I would love to help answer this question.

Recently, Brandon Shapiro and I developed something that might be relevant: a category theoretic framework called Dynamic Organizational Structures, e.g. dynamic operads, dynamic categories, etc. We have four examples: deep learning, prediction markets, non-cooperative strategic games, and (Sophie and I developed the example of) Hebbian learning. In each case, there is a multi-scale system for updating the ways parts interact to form wholes.

Perhaps the sort of natural process by which matter-pattern symbols are condensed is scale-invariant enough that it would fit into this framework. In other words, I’m wondering: is there a dynamic operad for the language-formation process? This is of course a very loose question, but I think that’s ok; it’s only meant to inspire people to consider and work on it. Indeed, the Hebbian Learning example above was only loosely inspired by spike-time dependent plasticity, but it still serves to give us some insight into the grammar of Hebbian learners. Applied category theory is very broad, and there’s no reason one needs to use dynamic operads, though they may be useful or at least inspire a more useful framework. I’m not really hoping for a definitive category-theoretic answer to the question of how language or symbols are repeatedly formed, though it’d be interesting to hear if someone thought they had such a thing; instead, I’m looking to consider it and make progress on it.

Category theory itself is language, and it’s really condensed and powerful. And with tools like Catlab, it’s moving closer to the matter side of the divide: the categorical patterns are being instantiated in silicon and metal. Is it just a coincidence that we see this condensation happening yet again? Imagine how powerful it would be to instantiate a compositional language-formation process within computational category theory software. If it’s true that nature keeps making this sort of thing happen, as though by some “invisible hand”, then such an implementation may well be in our future. The more well-rounded our understanding of it is, the more elegantly the system can be designed, and the more frictionless I imagine the result will be.