What is Formal Protocol Theory?
Issue #45: An Introduction to the Ongoing Work of SIGFPT
For the past three months or so, a group of us have been meeting every other Friday for an hour (10 AM PT, 5PM UTC), on the Summer of Protocols Discord, to talk about how to build rigorous foundations under the currently gooey subject matter of protocol studies. This is a brief overview and reflection on our work so far. Our next meeting will be on Friday 22nd, on Impossibilities and Symmetries. If this overview interests you, do join us.
Our group is also the host for the upcoming Protocol Foundations Workshop (September 12–14). The deadline to apply to that is also Friday, 22nd, so if you’re interested in a taste of what we might get into in the workshop, attend our Friday call.
Our group is called SIGFPT (Special Interest Group in Formal Protocol Theory). So what do we mean by Formal Protocol Theory (FPT)?
Well, how do you go from Jerry Seinfeld’s stand-up bit on the complexities of shaking hands to a formalized description that logicians and mathematicians can use to probe the deeper subtleties beneath both human and computer handshakes?
That’s FPT.
Or: How do you turn the bickerings among nations at climate summits into rigorous model-based predictions of how well climate protocol compliance will work?
That’s also FPT.
Or: Whether one blockchain is more censorship-resistant than another in some rigorous sense?
That’s FPT too.
FPT seeks general unifying principles, concepts, and methods across a vast scope of cultural and technological phenomena and across a wide range of scales, from micro to macro. From handshake-scale to planet-scale. In this, our ambitions are comparable to economics.
We have held six meetings so far, devoted to the following topics (notes, references, working documents, and transcripts are available to group participants):
Session 0 (May 28): Initial survey. At our kickoff session, (in-person at Edge Esmeralda), we held an initial discussion of the possible range and scope of FPT, domains of interest, and explored what sorts of unification and formalization might be possible.
Session 1 (June 13): Prototypical toy examples. In our warmup session, we discussed handwashing and handshaking to develop our initial intuitions. These have since emerged as the main throughline toy examples in our discussions. They have proved to be useful in the same way E. coli and fruit flies are useful examples for biologists, or “guns vs. butter” for economists.
Session 2 (June 27): Observability. In our second session, we discussed the question of observability of protocol systems, using climate protocols as the focal example. We considered concepts of observability from control theory and computer science, and discussed what it might mean for a protocol to be observable.
Session 3 (July 12): Notation. In our third session, starting with Ken Inverson’s Turing-award lecture, Notation as a Tool for Thought, we explored how we might develop an expressive, yet elegant language for talking about protocols formally.
Session 4 (July 25): Paper-napkin math. Drawing on the long tradition of quick-and-dirty, yet rigorous, calculation and design in sciences and engineering, inspired by the methodological approaches of Enrico Fermi and Freeman Dyson, we explored what it might take to develop FPT as a field that’s equipped with tools you can calculate with. Using ideas from Abhishek Mahajan’s famous MIT course on Street-Fighting Math, and examples drawn from traffic protocols, we explored how FPT might build bridges between abstract symbols and real numbers.
Session 5 (August 8): Process calculi. In this first of our deeper dive sessions we explored the world of process calculi, pioneered by scholars like Tony Hoare and Robin Milner, and considered how well the tools apply to the problems of working with protocols.
Session 6 (August 22 — upcoming). Impossibilities and Symmetries. In our upcoming session, we will start with the influential Witsenhausen counterexample and explore a core concern of any field dedicated to formal investigations – impossibilities and symmetries (or equivalently, conserved quantities).
We have several other topics lined up to look at – statistical physics models (such as spin-glass models), stock-flow models from system dynamics, unusual flavors of game theory, modeling formalisms underlying software systems such as game engines or CAD tools, and empirical techniques such as the construction of the consumer price index (CPI) in economics or epidemiological models in public health.
As you can see, we aim to stay grounded in real examples (both toy and complex), observable and empirical modeling approaches, and tractable computability, even as we explore some pretty rarefied abstractions.
If this scope sounds intimidating, don’t worry. Though we are not afraid of exploring hard and complex ideas, sometimes requiring advanced mathematics or logic/foundations ideas, our guiding principle so far has been to try and rely on each other’s expertise, (and support from LLMs!) to bring the subject matter down to the simplest, most elemental level possible – ideally, paper-napkin level, and requiring no more than high-school mathematics to navigate.
We can’t always get to ELI5 of course, but we can get surprisingly close. And even when we don’t have someone with relevant deep expertise on the call, able to guide us, we don’t let that stop us. Thanks to LLMs and “vibe-coding” sensibilities, we are able to make progress where in the past we might have faltered.
So even if you have no STEM background, but have cultivated a taste for formal thinking in some other domain (for example, through classical music, chess-playing, or poetry) you should be able to follow along and contribute. In our session on notation for example, musician (and current SoP fellow), Ben Zucker joined us and we had a fascinating discussion of music notation, as well as other examples like dance notation.
Our goal is to establish a track of discussion of value across a range of skill and expertise levels, and across a wide range of domains. Whether you simply enjoy playing with platonic abstractions and symbol systems, or itch to turn quick and dirty formulas into rough-and-ready estimates and designs for use in engineering work, or have Godelian ambitions to discover logico-mathematical profundities beneath familiar everyday phenomena, SIGFPT should be fun for you.
Right now, we’re running this group for six months as a pilot effort, but we hope to build up enough critical mass of both ideas and regular participation to keep it going as a sustained research conversation. The mission is not only to advance the research agenda at the Summer of Protocols, but provide interesting fuel for the personal research and work agendas of participants, in their day-to-day work. So we hope participants’ individual projects – whether in academic research, or building engineering tools and products, or simply pursuing a personal interest in a formal thinking challenge – will benefit from participation.
So if you’re interested, join us this Friday on our next call!
Last chance to apply for 2025 Protocol Symposium attendance
This Friday, August 22, is your application deadline for attendance at the flagship annual event of the Summer of Protocols program. The theme of the symposium is the same as this year’s program: Accelerating Order: exploring protocols as an emerging new world logic, through education, research, and scene-making activities.
2025 Protocol Symposium
We are excited to announce the second annual Protocol Symposium, the flagship annual event of the Summer of Protocols program. The theme of the symposium is the same as this year’s program: Accelerating Order: exploring protocols as an emerging new world logic, through education, research, and scene-making activities.