Theorizing Protocolization II: Atomic Protocol Questions
Solving real coordination problems to discover the formal laws of protocols.
In the first installment of Theorizing Protocolization, we introduced protocolization as a progressively developing planetary transformation, that is, the metabolization of technologically-mediated behaviors into reliable coordination infrastructure at every social scale. From the highly cost effective and beneficial promotion of hand hygiene, to the simple yet powerful standardization of shipping containers, to the heady mixture of institutions, laws, and norms that form rules-based international order, protocols grow, rhizomatically, into what Venkatesh Rao coined as New Nature – a pervasive yet nearly imperceptible artificial lawfulness.
This combination of ubiquity and invisibility creates a peculiar methodological quandary. Protocols permeate a multitude of technical substrates, institutional arrangements, and social realities, operating simultaneously at hyperlocal and global scales. Even so, it can prove difficult to locate protocolization precisely. What does it look like to theorize such a thing? How can we identify formal models that describe the common, generalizable features of protocols which can be reliably applied across contexts? If we manage this at all, how can we tell if we’re doing it well?
This time, we’ll explore one of our early responses to the challenge of conducting a generative collective research program for protocol formalization. In particular, we will introduce a new top-level research track built around specific, well-posed problems that we call Atomic Protocol Questions. We’ll explain what they are, why we think they’re a promising approach, and how you can contribute.
Join us at the next Special Interest Group in Formal Protocol Theory (SIGFPT) call in Discord on March 6 if this idea interests you.
Birds, Frogs, and Atoms
The physicist Freeman Dyson, in his 2009 Einstein Lecture given to the American Mathematical Society, divided mathematicians into two species: birds and frogs.
“Birds fly high in the air and survey broad vistas of mathematics out to the far horizon. They delight in concepts that unify our thinking and bring together diverse problems from different parts of the landscape. Frogs live in the mud below and see only the flowers that grow nearby. They delight in the details of particular objects, and they solve problems one at a time.”
Fields Medalist Timothy Gowers, riffing on the famous “Two Cultures” divide between academics in science and the humanities, similarly drew a distinction among mathematicians between theory-builders and problem-solvers.
Setting aside the apparently common impulse to bisect mathematicians, both reached the rather common-sense conclusion that a healthy intellectual climate requires individuals of both temperaments, for each complements and builds on the other. In Dyson’s words:
“Mathematics is rich and beautiful because birds give it broad visions and frogs give it intricate details. Mathematics is both great art and important science, because it combines generality of concepts with depth of structures.”
It seems quite natural to think that theorizing protocolization would entail primarily a theory-building approach. One might envision, for example, articulating an abstract general notion of a Protocol, audition or invent various formal systems in search of one that best captures it, and then set about applying that framework to protocols out in the real world. In fact, this has been the character of most of SIGFPT’s pathfinding investigations thus far, and will likely always form a major track of study; there is immense value in creatively bringing diverse domain knowledge to bear on shared formal questions.
But it also comes with several challenges, largely due to the difficulty of enumerating in advance a set of necessary and sufficient features of a successful formal modeling framework to this domain. Protocols are unusually resistant to analysis through any single descriptive lens. Even when a formalism is expressive enough in principle, it is often unclear how to apply it across domains without either flattening the phenomena that matter or rebuilding large amounts of domain knowledge inside the model itself. Several of the SIG’s early discussions revolved around issues of this nature.
Therefore, as a complement to the top-down, avian theory-building, we’ve introduced a research track for bottom-up, froggish theorization: enumerating small, well-scoped research questions about specific protocolized contexts: Atomic Protocol Questions (APQ).
The spiritual forebear of the APQ is David Hilbert’s famous list of 23 unsolved problems presented at the 1900 International Congress of Mathematicians in Paris. Hilbert’s problems ranged across the foundations of mathematics, number theory, algebra, and geometry, and came to define much of the research agenda for twentieth-century mathematics. In several cases, individual problems motivated new branches of mathematics entirely: his second problem, on the consistency of arithmetic, led to Gödel’s incompleteness theorems and the field of proof theory; his tenth, on solving Diophantine equations algorithmically, was eventually resolved through computability theory. In this vein, our ultimate goal is to pose and then attack a set of open questions that captures protocol studies in both conceptual and disciplinary breadth.
Subatomic Particles
“Atomic” is meant in several senses:
Self-Contained: Each problem is intelligible and evaluable on its own, without requiring deep background in other APQs or specialized disciplines.
Indivisible: Each problem is framed at the lowest level of abstraction needed for its bearing on protocol studies – not decomposable into simpler protocol questions.
Heterogeneous: The problems collectively span a wide variety of subject matters, disciplines, and scales to avoid overfitting to a small set of favored contexts.
Representative: The problems collectively cover as many dimensions of protocolization as we can identify— learnability, evolvability, tensions, coordination costs, and many more.
The first two properties make each APQ tractable in isolation. The second two ensure the collection functions as more than a grab-bag of puzzles – it becomes a map of the protocol landscape.
Each APQ has three essential constituents: an empirical context (a real-life, observable protocolized system), a key dimension of protocolization (a theoretically significant concept or aspect of protocolized systems), and a sufficiently precise research question (crisp enough to admit evaluable answers). Moreover, answering it should require one not simply to lean on the prior research of the particular field in which it originated, but to say something new about it qua protocol, and thereby demonstrate the value of this unique perspective.
Keeping Apart
Consider a familiar urban frustration: bus bunching. Buses, of course, are meant to adhere to a consistent schedule with a regular interval between arrivals (ideally both at once). In real life, buses tend to cluster together because of compounding delays: a delayed bus will arrive at a stop with more passengers waiting to board, who then take more time to board, delaying the arrival at the next stop, and so on. The trailing bus, meanwhile, will be in the opposite situation, picking up fewer passengers until eventually it catches up to the first. This problem, called “bus bunching” is a well-studied positive feedback loop.
It’s also a protocol problem. The issue isn’t what technology buses should use, but what rules should govern their coordination behavior. There are a number of common approaches to the overall problem, but the most basic interventions are to disrupt the feedback loop by making buses that are “ahead” wait at stops longer, have delayed buses skip stops, or have trailing buses overtake leading buses. The optimization objective is not necessarily a given – one can prioritize schedule adherence, for example, which tends to work best in lower-frequency routes where travelers plan based on the timetable, or optimize for headway between adjacent buses which tends to produce better outcomes on high-frequency routes where passengers arrive randomly. In practice, it is likely that a system in a realistic urban context would need to combine several strategies to flexibly manage the various causes of bunching.
Recent work has focused on dynamic control designs that integrate real-time information on various contributors to bunching and make adjustments automatically. For example, reinforcement learning systems trained in simulation can develop policies that dynamically adjust, such as holding times based on traffic conditions and demand, outperforming more conventional analytical or optimization-based methods. Separate lines of research approach the issue from the demand side, providing information to passengers about current wait times and bus congestion, in the hope that some passengers will make the decision to wait for a less crowded bus. Perhaps more drastically, real-time data can be used to update the bus schedule itself dynamically, with the obvious drawback of making the system less legible to would-be passengers.
The progressive integration of dynamic information and automation raises several interrelated issues with the relationship between these systems and the humans who participate in them – as drivers, dispatchers, or passengers. It turns out that deployment of real-time systems are hindered by various meatspace practicalities that are not typically modeled in simulation. One factor is variation among drivers, who each drive a bit differently, and in particular have different propensities to comply with the holding control guidance. This is double-edged: naive non-compliance tends to degrade the effectiveness of the overall fleet control, but human operators might also be able to react to conditions that are not easily observed through the data pipeline, due to cost or difficulty. Similarly, exposing information to passengers indeed allows them to make informed decisions about which bus to board, but there is a reflexivity problem; passengers may end up inadvertently coordinating so as to cause crowding on the previously-empty trailing buses!
The APQ approach attempts to sharpen such concerns into more tractable research questions about protocols:
What operational discretion should a dynamic bus dispatch protocol preserve for human agents? When does human judgment improve versus degrade the protocol’s coordination performance?
What non-invasive data sources can capture sources of user heterogeneity that influence demand?
What ludic elements for drivers and passengers encourage aligned participation in the protocol?
Each of these examples is meant to conform to the APQ specification. The empirical context and research question aspects are obvious, but more subtly each question is targeted towards the intersection of current research on bus bunching and ideas of interest in protocol studies (key dimensions). The first question bears on concepts such as stewardability, invisibility, and legibility. How much can and should participants steer a protocol? In what ways must it be limited? When is active awareness of, and intervention into, protocols helpful or hindering? The second is a question of constraint and observability, from the system’s perspective. Can we improve the responsiveness and dynamism of protocols without overreaching or creating protocol failure surfaces and vulnerabilities? The third is ludicity, that is, how to support the protocol’s functioning and legitimacy via game-like and strategic elements.
The questions are also deliberately posed at a moderate level of abstraction. Protocol Studies is not, at present, suited to admit capital-P Problems that are well-posed in the sense that is typically expected in formal mathematics or other formally rigorous disciplines. On the other hand, it is not so broad (“What’s the best bus system?”) as to render any attempt at an answer indeterminate. It is also agnostic to the specific academic lineage or technical tools that one may use in subsequent research. Bus bunching itself ties together research in, at a minimum, control theory, urban planning, operations research, economics, and machine learning. A good APQ should invite a variety of possible approaches from a variety of possible perspectives. This diversity both within and between questions is in fact a load-bearing feature of APQs envisioned as an overarching research program.
Jumping Together
The key wager behind the FPT effort is that “protocols,” over and above a striking set of terminological convergences, are something like what the philosophy of science calls a “kind”, or at the very least, exhibit the sort of structural unity that licenses productive cross-domain theorizing. We are not merely asserting that protocols are important but conjecturing something formally unified beneath the surface diversity. The APQ project operationalizes this with a sort of wisdom-of-the-crowds logic applied to consilience – a “jumping together” of independent streams of evidence to a unified explanatory framework across disciplines. APQs are an attempt to enable such convergence in protocol studies.
Individually, questions are designed to encourage concrete, independent investigations into pressing practical issues in technology and society. An APQ is falsifiable in the sense that it shifts debate from abstract questions about which formalism(s) might comprise the “right” foundation to empirical and technical questions about fit: what traction does each provide on this concrete question, and what are its limitations?
In aggregate, the APQs must be sufficiently diverse to span the conceptual space of protocol studies across their constituent contexts and dimensions. The hope is that though approaches to different problems may initially appear disparate, the character of their solutions will reveal similarities and differences that interfere constructively or destructively. When multiple formalisms attack the same underlying phenomena, their idiosyncratic commitments tend to wash out, while shared structure is reinforced.
APQs, then, enable comparison at two levels. Within a single problem, multiple formalisms can be evaluated adversarially. Across problems, the more telling comparison emerges: do solutions to different APQs sharing a protocol dimension reveal common structure? If “evolvability” means something formally similar whether we’re studying bus networks or robot swarms – despite different researchers, methods, and vocabularies – that’s evidence the dimension names something real.
The history of science is rich with examples of consilience, when it works. One such example is the notion of computability. In the 1930s, mathematicians from around the world invented precise, independent definitions of what it means to be computable. Alan Turing developed abstract machines. Alonzo Church created the lambda calculus. Stephen Kleene formalized recursive functions. Emil Post devised production systems. They each worked from different starting points with different motivations, often unaware of each other’s efforts. All four formalisms turned out to define exactly the same class of functions. This striking convergence – proven rapidly once the systems were compared – is substantial evidence that “computable” captures something true about the underlying nature of reality.
Or consider entropy. Carnot’s 1824 question about engine efficiency was purely practical – “What’s the best a heat engine can do?” This led to Clausius’s thermodynamic formulation, then Boltzmann’s statistical interpretation decades later. Yet they proved mathematically equivalent for macroscopic systems at equilibrium – evidence that entropy named something real.
In both examples, specific problems came first and the unifying concept emerged from comparison. Neither Carnot nor Turing were attempting to architect entropy or computability from first principles. Carnot was trying to understand engines. Turing was trying to answer the Entscheidungsproblem. The generality emerged from specificity. This is one aspect of the symbiotic dance between frog and bird.
In these cases, of course, this convergence was also uncoordinated – researchers weren’t necessarily comparing notes. APQs are a bit different: a deliberate invitation for multiple formalisms to attack shared problems. Convergence here wouldn’t inherently prove that protocol as a concept “carves nature at its joints”, but it would demonstrate something nearly as valuable: that the abstraction does productive, non-redundant work across domains that previously had no common vocabulary.
Convergence Not Guaranteed
Of course, this all assumes that there is some sort of kind upon which methods can converge in the first place. The history of science also shows that that is not necessarily the case, either. Cybernetics and the complexity science of the Santa Fe Institute, for example, are two intellectual movements that share affinities with protocol studies. The cyberneticists generated fundamental insights into what would become control theory, information theory, and artificial intelligence, but did not achieve their goal of unifying the behavior of all goal-oriented systems. Complexity science has made enormously productive contributions through agent-based modeling, network analysis, and related methods, yet cannot really be said to have converged on a formally precise definition of complexity itself.
This is not a particular criticism of those programs’ approach or, say, bird-to-frog ratio. We can’t know whether different approaches would have or will someday yet yield some more unified frame. They’re simply reminders that convergence isn’t guaranteed, even with world-class talent, real research traction, and genuinely promising phenomena. Importantly, even without achieving some kind of “grand unification,” both lines of research produced lasting value, impact, and influence on later technical thinkers.
Perhaps, after all, “protocol” is more useful for pointing at phenomena than predicting or engineering them. We should find that out too. APQs are designed so that even if convergence doesn’t come, we’ll have produced something worthwhile: well-posed problems, cross-disciplinary vocabulary, and concrete progress on specific systems. But we believe that if there is indeed a fruitful underlying logic of protocols waiting to be unearthed, this direction will bring us closer to doing so.
Join Us in the Mud
That’s all well and good, but how does one actually create an Atomic Protocol Question? A great place to start is Protocol Watching. Once you learn to see protocols, you will find them in every corner of our modern world: your airplane boarding group? Your daughter’s LEGO set? Your laptop’s charging cable? Each offers a myriad of protocol puzzles waiting to be honed into an APQ. Timber Stinson-Schroff offers a handy guide, complete with tools and tips to help you get started.
You might also seek the guidance of the LLMs. In addition to the human audience, this essay also functions as a piece of intelligence media to provide a specification of Atomic Protocol Questions for ingestion into your model of choice. Armed thusly with your protocol bicorder, you’ll have the elements to contribute to our project well in hand, no matter your technical background.
David Hilbert perceived clearly that the articulation of a problem itself is a generative act of taste. More than a list, his problems were a challenge and invitation to a global network of talented researchers to participate in an ambitious collective research program. As Dyson observed,
“Hilbert himself was a bird, flying high over the whole territory of mathematics, but he addressed his problems to the frogs who would solve them one at a time.”
In this spirit, be you bird, frog, hedgehog, or fox, we encourage you to join SIGFPT and help expand, refine, and prune the APQ set. Bring a problem you know well – from your domain, your city, your organization, your frustrations – sharpen it into an atomic question, and let it enter the comparative surface. Problems shape the future of research programs, and, eventually, entire fields. In helping to pose and attack APQs, you can help set the agenda for ours – perhaps for years to come.
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