Fermi Estimates and Dyson Designs

A Fermi estimate is a quick-and-dirty solution to an arbitrary scientific or engineering analysis problem. Fermi estimation uses widely known numbers, readily observable phenomenology, basic physics equations, and a bunch of approximation techniques to arrive at rough answers that tend to be correct within an order of magnitude or so. The term is named for Enrico Fermi, who was famously good at this sort of thing.

A particular anecdote is often cited to explain the idea. During the Trinity test in 1945, Fermi began dropping bits of shredded paper in his office near the test site, and based on how far they drifted from vertical, estimated the yield to be equivalent to 10 kilotons of TNT. This was surprisingly close to the more precise measurements.

Cliche consulting interview questions of the “how many ping-pong balls can fit in a 747” are a degenerate form of Fermi estimation without either the physics angle or active empiricism.

It struck me that there is counterpart to this kind of thinking on the synthesis side, where you use similar techniques to arrive at a very rough design for a complex engineered artifact. I call such a design approach Dyson design, after the physicist Freeman Dyson, who was one of the best practitioners of it (not to be confused with inventor James Dyson, whose designs, ironically, are not Dyson designs).

We can identify an origin story for Dyson design similar to the Fermi one. Dyson came up with the idea of nuclear rocketry based on small nuclear explosions launching a payload into space. The basic design concept was was validated by Project Orion in the 1950s and 60s, using conventional explosives. Here is an excerpt from my notes on the book The Starship and the Canoe (about Freeman and his son George), which has an excellent account of the project and Dyson’s role in it.

The Orion rocket idea finesses temperature limitations of metals by having the nuclear explosions kick it up very quickly. 80,000 kelvin for a millisecond. Chemical rockets are continuous 4000k thermal stress. This is not a subtle device 😆.

A heavy lens-shaped aluminum pusher plate greased between 2Hz explosions to drive a vehicle via a pneumatic shock absorber. “Lurches but not unpleasant. Greased like a channel swimmer, Orion would frog-kick through the void.” I sense a contrast to George’s canoes coming soon.

“Orion in its enormous power could haul such excesses of freight that no cleverness was necessary in planning staterooms and storage” There’s the buckyfullerish expansive-abundance thinking. Strategery is for the delta-vee poors. We kinda got there with wasting transistors.

The part in bold is the essence of Dyson design — vastly over-engineer a critical aspect of the design (propulsive power or power/weight ratio in this case) so that you create an abundance that you can waste in other parts of design space. Dyson design tends to be generative, because it creates room to waste in other design variables, which you don’t need to optimize. Instead you can use the free design room to have fun or do derivative design. Dyson design is promethean design. It unleashes larger design energies.

You can find this signature design style in other concepts Dyson dreamed up, such as the Dyson sphere and Dyson tree.

Fermi estimates and Dyson designs are two sides of the same coin, and the combined thing could be called Fermi-Dyson thinking.

When Fermi-Dyson thinking is tractable in a given domain, you tend to get technological revolutions. The early decades of such revolutions are often marked by the presence of many excellent Fermi-Dyson thinkers. The problems in these decades are often characterized by approximation tractability (Fermi estimation gets you roughly right answers easily) and synthesis leverage (there are design variables that yield to Dysonian extremism). Computing is a great example. Moore’s Law is an excellent Fermi estimate — a roughly right solution to an analysis problem using trivial math. Alan Kay’s notion of “wasting transistors” is a Moore’s-Law-specific Dyson design principle.

Other good examples of domains with Fermi-Dyson characteristics include steam power in the early 1800s, steel metallurgy in the late 1800s, electricity and reinforced-concrete based civil engineering in the early 1900s, petrochemistry in the 1950s, and renewable energy technologies today.

All the best living engineers I know share the one key trait — they are intuitively good Fermi-Dyson thinkers within the computing revolution. They are right early, and right a lot about the effects of Moore’s law, at every level from chips to societies, and set out to build very basic things, often building blocks, using those effects. Outside their core domains, they tend to achieve mixed results, which makes me suspect Fermi-Dyson thinking is a kind of advanced, quantitative, situated intuition. It is somewhere between Kahnemann’s System 1 and System 2. Call it domain-adapted System 1.5 thinking.

The interesting thing is, Fermi-Dyson thinking does not call for ultra-high IQ or genius-level skills with physics or engineering mathematics. You need to be reasonably intelligent and have decent mathematical skills, but the more important traits required are taste and boldness. The taste can be cultivated, but the boldness seems harder to deliberately acquire, since attitudes towards risk of any sort seem to be deep-rooted and hard-to-change aspects of personality.

Many people with high IQs and genius-level skills often have neither taste, nor boldness. Worse, they are often so attached to their outlier skills that they are too eager to prematurely venture into Extreme Math™ regimes where lesser minds cannot follow, where they find precise and optimized solutions to the wrong problems. They are more interested in demonstrating their intellectual superiority in timid and tasteless ways than in solving interesting problems. They get stuck quibbling with unnecessary precision about unimportant things.

Fermi-Dyson thinking is intellectual risk-taking with numbers, which can be anathema for people for whom thinking is a low-risk sport aimed at acquiring prestigious credentials, safe careers, or cheap social validation.

This makes Enrico Fermi and Freeman Dyson seem even more remarkable as individuals — not only were they high-IQ genius physicist-mathematician-engineers of the kind institutions easily recognize, they had the boldness and taste to overcome that handicap and do simple thinking and grade-school math when the problem demanded it, despite their ability to do arbitrarily complex thinking too.

I suspect Fermi estimates and Dyson designs are two of three pillars required for so-called “first-principles thinking.” The third is a phenomenological orientation — privileging direct experience of material reality over received authority and social reality.

In Fermi-Dyson thinking, you do not work on an abstruse problem because a famous professor handed it to you for your thesis or because a famous paper suggested it. You formulate your own problems, and rough-carve it into shape using Fermi-Dyson thinking, before getting into the details. You pick your own starting points based on what seems interesting and important in the world, rather than uncritically accepting an intellectual tradition’s priorities as your own.

Fermi-Dyson thinkers avoid shallow distinctions like physics versus engineering, theory versus experiment, or even humanities versus STEM. Those distinctions are for minds trapped by the status distinctions that matter within institutions. Instead they just observe and think in as straightforward a way as possible, using whatever cognitive and material tools are at hand and do the job. This does not mean they eschew complexity, fine distinctions, or subtle technologies, when those are actually called for by the problem. Recall that Fermi was famously both a theorist and experimentalist. He did complex experiments with neutron bombardment as well as simple experiments with bits of paper. Along with Dirac, he came up with the theoretical model — Fermi-Dirac statistics — that describes particles named after him: Fermions. Dyson was as much engineer as physicist.

First-principles thinking is actually a pretty misleading term, and I think what Elon Musk means by it is really Fermi-Dyson thinking. It’s not “first principles” because it tends to start “in the middle” of a problem, using whatever numbers and abstractions seem stable enough to build on. Arguably, the only people actually doing first-principles thinking are the few physicists, metaphysicians, and mathematicians working on the initial conditions that created our universe (“where did space-time, mass, consciousness, and Planck’s constant come from?” sorts of questions). Everybody else is doing middle-principles thinking.

Musk’s disdain for “analogical thinking” is also misleading, since Fermi-Dyson thinking, being a “System 1.5” style of thinking, requires analogical reasoning too. But the phenomenological orientation and bias towards quantification keeps it grounded. I suspect what really creates weak, fragile thinking is not reliance on analogies or distaste for numbers, but reliance on social validation for your psychological payoffs. Where products of thought are merely a way to feed recognition hunger, they tends to be weak and breed timidity and tastelessness instead of boldness and taste.

Analogies and metaphors play a big role in communication, which plays a big part in how humans seek out social validation and recognition. But this does not mean they don’t play a role in thinking about material reality. When you notice that a spring-mass-damper oscillator and an RLC circuit both have similar behavior, and use mass intuitions to think about electrical charge, you’re doing analogical reasoning. In fact, there is arguably no such thing as non-metaphoric thinking (see the various works of George Lakoff).

Fermi-Dyson thinking has turned into one of my lighthouse concepts for navigating the post-Weirding world in recent months. My buddy James Giammona, a physicist, recently started the Fermi Gym, a weekly Saturday morning salon to practice Fermi estimation. We’re a few sessions in, and I’ve really been enjoying them. I highly recommend it. Some STEM background is helpful but not essential — we mostly stick to arithmetic and high-school level algebra and physics. James recommended Sanjoy Mahajan’s book The Art of Insight in Science and Engineering as a good primer, and I’m waiting for my copy to arrive.

I’m trying to practice my Dyson design skills too. This is slightly harder since unlike analysis, synthesis benefits much more from hands-on iterative prototyping and testing, and not many domains lend themselves to amateur gentleman-scientist levels of experimental work on small budgets. But I think you do want to get as close as you can to experimental design work, even if only at the dropping-bits-of-paper level.

In hindsight, my slow build-out of a home lab and workshop over the last couple of years has been about building a space to do Dyson design thinking in, since I haven’t worked in or near an actual lab for over a decade, and it feels like an important enabling condition for interesting thinking has been missing in my environment, and that side of my thinking has gone seriously rusty. You can do many things with just a laptop, but not everything.