Remembering Pierre Kabamba

I think it was sometime in 1998 or 99. I was walking down the hallway of the faculty floor of the Aerospace Engineering department of the University of Michigan, where I was a graduate student at the time. One of the professors had tacked a recently published paper by his door, as professors like to do. It was something about computing asteroid rendezvous orbits, and it used some rather pretty continued-series approximations of a sort that were popular in the 19th century. The professor in question was chatting with another, Pierre Kabamba, and was making some sort of self-deprecating remark about his paper (though he was clearly pleased with it), but Pierre was having none of that.

He exclaimed with a characteristic ebullience, “But this is wonderful! You’re doing ROMANTIC mathematics!”

The remark made me smile, and put me in an unreasonably cheerful mood for the rest of the day. At the time, I was working with another professor, and growing increasingly depressed and jaded (I was too inexperienced at the time to recognize a fundamental incompatibility). I didn’t know it at the time, but I would go on to switch topics and advisors, and complete my PhD with Pierre. I would spend a wonderful three years in his company, rediscovering, as an adult, the spirit of romanticism in engineering that had me memorizing airplane silhouettes in high school.

Last week, I learned, much to my shock, that Pierre passed away just over four years ago, in 2014, of lung cancer. He was only 59, and the last time I saw him, in 2011, he had been his usual cheerful and energetic self. We had last collaborated in 2006, on a course we co-developed and taught in parallel (me at Cornell, Pierre at Michigan).

The easiest way to describe Pierre is this: he was a real-life Hercule Poirot, and in many ways, the person who taught me to think in the ways I still try to practice on this blog. So let me tell you about Pierre and what I learned from him.

Other than the fact that he was African, and a professor of aerospace engineering rather than a detective, Pierre might have stepped straight out of a Hercule Poirot novel.

Like Poirot, Pierre was Belgian (his family had moved there from Kinshasa when he was a child). Like Poirot, he was a devout Catholic of the old-school sort: absolutely principled and with an unwavering sense of justice, fairness, and personal integrity. Like Poirot, he maintained perfect order and method in his life and habits.

Like Poirot, he had an egg-shaped head (but no mustache), a bright smile, and a deceptively comical French manner (complete with occasional interjections of French in conversation) behind which lurked a wonderfully perceptive mind that was at once inventive and imaginative, and impossible to bullshit.

The first time I met with him, I did some wild ranting about stuff I wanted to work on. He listened patiently, then asked the exact uncomfortable question I needed to be asked: “Are you looking for feedback, or are you looking for validation?”

He didn’t shut down my bullshitting or judge it. He recognized it as part of my own process. But he made sure I was being self-aware about everything I was doing, and owned the choices I was making.  He was highly self-aware himself, and expected no less of his students. That’s what made him interesting.

Most academics at top universities are very smart, but very few are interesting. Pierre was easily one of the most interesting human beings I’ve ever met.

Over the weekend, I spent several hours gathering my memories of Pierre and making notes about how he shaped my thinking. I was hoping to write a more comprehensive appreciation of his life, but that will have to wait for my memoirs. There’s too much to say, and too much of it is way too entangled with how I see myself and the world, in ways that I can’t untangle right now.

But let me try to offer a few small glimpses.

One time, we were talking about the divide between the theoretical and experimental sides of our discipline, systems and control engineering, and he said something that stuck with me: “I don’t think of it as theoretical versus experimental, I think of it as practical versus impractical.”

It took me years to unpack what he meant, and imbibe the underlying philosophy myself. Here’s a little exegesis of what I believe he meant.

Systems and control theory is something of a field that, rather like macroeconomics or physics, lends itself to vast and beautiful grand unified theories based on spherical-cow thinking. At its core is a set of wonderfully general and powerful ideas about stability, feedback, controllability, observability, information, and uncertainty. If you have the right kind of crackpot sensibility, it is an ideal subject for going psychotically and mystically crazy with (think John Nash).

For most “classical” control practitioners (and here I’m referring to the spherical-cow aesthetic rather than the technical subset of the subject that is also referred to as classical) the holy grail is inventing a controller that can control absolutely any system while knowing absolutely nothing about it, based purely on feedback. It is our equivalent of the AGI problem in AI or quantum relativistic gravity in physics.

The way control theorists approach it, this problem is an exercise in applied mathematics and information theory, rather than something concerning messy real-world physical systems.

The classical aesthetic is also the dominant aesthetic in systems and control theory, and the one people have in mind when they say somebody is a “systems” thinker (which is as much of a red-flag for me as the word “Singularity”). Model it all to death in one grand model. Then control it like a communist economy.

But this wasn’t Pierre’s paradigm. That isn’t to say he was “practical” in the sense of working on roll-up-your-sleeves real-world problems. No, he was too much of an unapologetic ivory-tower academic for that. Rather he was practical in eschewing vast spherical-cow grand-unified theories of control, and drawing his inspiration instead, from small messy realities.

Pierre liked to make the spherical cow a little less spherical, one leg, snout, or tail at a time. One small patch of practical beauty discovered in messiness at a time. Not always in a way that a practitioner would appreciate or value, but invariably in a way that would reveal the presence of the romantic within the banal. A hard kernel of pleasing mathematical structure within a little patch of squishy, superstition-inducing phenomenology.

Here’s an example.

One class of problems Pierre worked on extensively throughout his career was aircraft and missile maneuvering under various difficult conditions, often drawing inspiration from problems faced by real pilots.

One such problem is landing an airplane safely under conditions requiring “microburst avoidance” (small, sharp downdrafts that can lead to crashes). Working with a student, he found some rather charming solutions that revealed interesting things about the structure of the problem. Later, a fellow graduate student, and licensed pilot, grumbled to me that they weren’t actually practical maneuvers a pilot would use.

But that wasn’t the point.

Pierre wasn’t necessarily trying to teach birds or pilots to fly. He was, instead, looking for that tiny gem of romance and poetry that can be found within the phenomenology of even the ugliest, jankiest engineering problem, if you know how to look for it. And they don’t come any uglier than microburst avoidance.

That was the signature Pierre move (another trait that reminded me of Poirot), the unerring eye for small, hidden elegances, the music in the jankiness. The thing that didn’t fit and therefore destroyed the grand unified spherical-cow narrative. The thing that prompted a search for solutions that were perhaps more modest in scope, but more humbly respectful of reality. Even if they didn’t always succeed in wrangling that reality into submission.

Pierre’s work was reality-aware in a way I find a lot of engineering, both academic and in industry, is not. He paid attention. He picked up on what was actually important. And he tried to find the beauty and music within it, rather than start from abstract beauty and make it important by force of spherical-cow ideology.

He was best-known for his work on several such seemingly ugly problems that spherical-cow theorists like to avoid. His most famous paper was probably the one that dealt with what are known as generalized hold functions.

Here’s the problem in lay terms. A control system — like an autopilot, a thermostat, or a driverless car steering system — is typically mathematically modeled using continuous mathematics. But the solutions, in practice, are implemented as real-time algorithms on digital computers.

These computers take a feedback signal (say velocity) and then manipulate a control signal (say a brake or steering angle). The input and output signals are discrete: they are “sampled” data systems. To apply the continuous mathematical models, you need some sort of discretization hack.

One aspect of the hacking is interpolating the signals in the system. The simplest way is using what’s called a zeroth-order hold. You simply pretend the signal doesn’t change between samples (think of this as the numerical integration method you might have learned in college, where you essentially fit a bar chart under a curve).

Pierre showed that you could “hold” the signal in generalized ways, using the underlying continuous model for guidance, in order to get much better performance out of the system. And it wasn’t just an elegant bit of practical hacking of spherical-cow math. It also made an important — and romantic in a certain sense — philosophical point (that problems of modeling and estimation are coupled; never mind if you don’t get what that means).

You don’t need to appreciate the technical contribution to appreciate the aesthetic point. For most students of control engineering, hold functions are an ugly real-world bit of jankiness that intrude on all the lovely spherical-cowness of the pretty math. I hated the ugliness so much, I avoided taking the discrete control course in graduate school.

To get over what you might call a sort of mathematical disgust response, and go looking for beauty in hold functions, takes a particular kind of romantic engineering sensibility. The kind that might go looking for the prettiest piece of trash in the dumpster (which is the sort of thing Sarah Perry likes to do, and the reason I like her writing).

This is what I think of as romantic engineering. Pierre’s well-known paper, Control of linear systems using generalized sampled-data hold functions, found the beauty in a patch of important real-world apparent ugliness. It has been widely cited, and was the work for which he was recognized as a Fellow of the IEEE.

The classical aesthetic in engineering is driven by the classical aesthetic in the more familiar cultural sense: a belief that reason can and should rule over both the world and the mind. The result, in science and engineering, is often spherical cow ideological blinders. The romantic aesthetic, by contrast, is marked by a mix of humility and genuine curiosity about the world in the form it actually exists, rather than in the form we hope to see.

Work shaped by a romantic aesthetic seems to begin with the assumption that the mysteries of the universe are far richer than our overweening classicist hedgehog imaginations, that reality contains a surprising amount of detail. Pierre’s romanticism wasn’t of the turbulent Sturm und Drang variety (except to the extent that it dealt with literal turbulence in aircraft control). It was of a quieter, more contemplative sort. Of the sort alluded to in the quote attributed to Newton:

I do not know what I may appear to the world; but to myself I seem to have been only like a boy playing on the seashore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.

(It is perhaps worth noting here that Newton’s own work, despite the grand unifications it led to in the hands of others, was also marked by a profoundly romantic scientific sensibility).

In terms of a pair of archetypes I reference a lot on this blog, most systems and control theorists are hedgehogs. Pierre was a true fox. And he was the one who taught me that it was okay to be a fox.

The aesthetic of foxy romanticism shone through in all his work. One more example.

One of last major pieces of work was on quasilinear systems.

Here’s one way to understand those. If [aesthetically] classical control theory is about spherical cows, the most important spherical cow is what is known as a linear system. The most powerful theories and models apply primarily to linear systems. But many real-world systems of practical interest are only approximately linear, with a bunch of janky nonlinearities tacked on. The core system is linear, so well-behaved, but the instrumentation and control you have to wrap around it in order to control it is often nonlinear in annoying ways.

Classically oriented theorists react to this situation in one of two ways. They either stick with expanding the theoretical scope of the linear-systems spherical cow, or try to find some smaller nonlinear spherical cow that has its own internal elegance. What they typically don’t do is actually take on the cruft.

The real-world common problem, of what you might call crufty linear systems, turns theorists off.

It’s the kind of practical ugliness they’d rather leave to engineers in industry.

Not Pierre. He went in, with a merry band of his usual-suspect collaborators, and found the poetry in the cruft. The result was a very Pierre, very foxy synthesis: a textbook on quasilinear control.

It is this romantic sensibility that I imbibed from Pierre. It is the reason I pick the things to think about that I do.

My own PhD, though unremarkable and unexceptional in the broader scheme of things, was something of a training course in romantic idea engineering: start with real-world inspiration, look for the patches of romantic elegance that you can detect in the ugly bits others like to hurriedly look away from, build something small and pretty out of it. It’s a sensibility that sticks with you, like learning to ride a bike.

Nearly 10 years after I first overhead his conversation about “romantic math” in the hallway, for example, I made one of my few contributions to industrial research at Xerox (a job I got via his senior students as it happens): solving an optimization problem using pretty continued-series expansions for expressing it.

The “romantic math” sensibility was at the heart of everything he taught me, and has continued to serve me long after I stopped doing hands-on math or control engineering.

I like to think that in return for what he taught me, I influenced him to make the last major course change in his own career. Until he worked with me, Pierre was a traditionalist. He was suspicious of simulations and algorithms. He liked closed-form proofs and theorems (most control theorists are applied mathematicians at heart). But I wanted to use a bunch of techniques I’d picked up from AI and operations research, and convinced him that interesting things could come of that. One of the papers I wrote with him was about a class of scheduling algorithms.

With typical Pierre panache, he took to the new way of thinking in his own way, devoting a sabbatical year to exploring it. One day, he said he had something to show me relating to thinking he was doing on algorithms. He then proceeded to demonstrate a neat little trick (that I’ve since forgotten), casting the modus ponens operation (the fundamental operation in logical inference) in matrix algebra form (the favorite tool of control theorists). Using that trick, he could work with evolving matrices of 0s and 1s instead of logical propositions.

Cute, I thought, and thought no more of it. I didn’t realize he had built himself a little portal to another world.

A few years later, that line of thinking had morphed into one of his more interesting late papers: a bound he worked out about self-replicating robots, using Von Neumann’s theory of self-replicating cellular automata, one of the foundational ideas in computer science.

At the time, I was at Cornell, working as a postdoc, and one of the young faculty members there, Hod Lipson, had just published some interesting results on self-replicating robots. Over the phone, Pierre told me about his result, but then added, with the same cheerful excitement I’d heard in his voice that day in the hallway when I first noticed him, “Hod Lipson has scooped us!” He was genuinely excited to have the company on his bunny trail, rather than jealously protective of it as many academics tend to be.

Within just a few years of me getting him interested in computer science problems, he’d made a fascinating, imaginative, and original contribution.

He didn’t care about credit. He didn’t care about joining bandwagons, he didn’t care to be known as the conquerer of big spherical cows, he didn’t care about disciplinary boundaries. He wasn’t one of the flash-and-bang big-keynote-delivering celebrities of our field (he had nothing against them; he just didn’t care for that sort of thing himself). But he commanded both respect, and what is more important for a scholar, interest among peers. People always perked up with curiosity when talking about him. Those who knew him were always happy to talk about his work. That’s the mark of an interesting mind.

He was practical beyond technical matters too, but he didn’t have much to say about publish-or-perish, or getting a tenure track position. He wasn’t a master string-puller capable of opening big, important doors for his students.

Instead, he liked to offer “practical” advice in his sense of the term, designed to keep romanticism of the spirit alive.

His parting advice to me, the day I graduated, was much more philosophical than what I got from anyone else, “you have one rare quality, imagination, but to become established, you have to find the one thing that people come to identify you with, so you can then be free to do what you want to. Early in my career, I became ‘the sampled-data guy’. You have to become some sort of ‘It’ guy. You have to find that ‘It’.”

It was the one time in our relationship that he offered validation, rather than feedback. And without being asked.

It was typical of Pierre to find the philosophical insight in what many would consider a burdensome risk of professional scholarly life: being pigeonholed for one thing. He saw it differently. He spotted the interesting romance of it, refactored the meaning of it, and owned it. That people saw him as the “sampled-data guy” was not a burden.

It was a helpful narrative entry point into the thought spaces he liked to explore, but it didn’t constrain him. And he wanted me to build a doorway like his into my own head-spaces.

It was advice that served me well far beyond the limits of academic control theory. Today, I’m the “Gervais Principle guy.” If I hadn’t imbibed Pierre’s way of thinking about such things, that would bother me. Instead, it delights me. To be firmly put in a box is, paradoxically, to gain the freedom to wander anywhere you like, with foxy lightness.

Pierre didn’t want to tame spherical cows, and nor did he want to teach birds to fly. He just wanted to find the romance in the banal. The small signs of divine music in messy realities. And he crafted for himself the freedom to do that.

I suspect there was an element of religion there for him, looking for small bits of the divine. In his private life, he was an accomplished musician, and composer of a large repertoire of gospel music. A familiar sight on the engineering campus was Pierre randomly playing the piano in the Pierpont Commons building. Often, people would stand and listen for a while, having no idea who he was. It’s not the sort of thing famous professors do. It’s the sort of thing interesting professors do.

I’m going to miss Pierre. I’m going to miss hearing the music of the world through him.

But I’m going to continue practicing that wonderful way of being in the world that he taught me, romantic, foxy, practical, always looking for the beauty in the mess, and the music in the friction.