The real world abounds with recursively self-improving systems, but one in particular deserves attention: Science, modeled as a system (perhaps even as an agent, with goals and resources). If you want to really understand AI RSI, science should be your reference point.

Science is an intelligent system, and it is obviously recursively self-improving:

1. Scientific discoveries unlock new technology that helps build better experimental tools. This is a top driver of progress in nearly all fields.
2. They unlock new conceptual advances (ideas, theories) that help solve more problems.
3. They increase society's economic output, leading to more resources flowing into science.
4. They unlock better faster tooling (e.g. more compute via better chip & networking technology).

As a result, many measures of scientific *input* grow exponentially:

1. Headcount (doubles every ~15 years)
2. Global R&D spending (doubles a bit faster, every ~13 years)
3. Papers and patents (technically this is a measure of headcount)
4. Compute dedicated to science (doubles every ~2 years)

But is scientific progress exponential? Historically, the rate of scientific impact over time has remained roughly constant since the start of the industrial revolution (i.e. scientific progress is *linear*). 1850-1900 was about as dramatic as 1900-1950 or 1950-2000.

1850–1900: Evolution, germ theory & antiseptic surgery, thermodynamics, electromagnetic field equations, the periodic table, pharmaceuticals, electricity, telegraph and telephone, internal combustion engine, skyscrapers, mechanized agriculture...

1900–1950: special and general relativity, quantum mechanics, nuclear fission & atomic energy, antibiotics, genetic theory, electronic computers, information theory, synthetic polymers and plastics, the transistor, aviation...

1950–2000: DNA, genetic engineering, integrated circuits, microprocessors & personal computing, the Internet, crewed spaceflight, moon landing, satellite communications & GPS, standard model of particle physics...

In real terms, like life expectancy, which has increased in a remarkably linear fashion of roughly 3 months per year since 1840, progress is a straight line. This is especially apparent for fields where impact is easy to measure, like biology, medicine, and agriculture.

I first wrote about this phenomenon and its causes in 2012, and a steady stream of research has confirmed it in the years since. Examples include the 2018 paper by Nielsen and Collison, "Science Is Getting Less Bang for Its Buck," and the 2020 economic paper, "Are Ideas Getting Harder to Find?" (In fact, I believe the Nielsen paper stemmed from a conversation I had with him about this exact idea six months earlier)

In short, the primary cause is that research solves the highest-impact, easiest problems first, and every subsequent problem is either harder or lower-impact. Exponentially so. The paper that presented information theory wasn't very hard to write (single author!) but you'd have a hard time ever writing a CS paper that beats it in impact.

This is why science as a system requires exponential resources (input) to produce linear impact (output). It gets exponentially harder over time.

Worth thinking about if you're pondering RSI for AI. I fully believe AI RSI is already happening and will accelerate in the future. But I do not believe this leads to an "intelligence explosion" -- that would fly in the face of everything I know about intelligence and everything I know about recursively self-improving systems.