Is There an Upper Limit to AI Intelligence? Physical Limits of Computation and Self-Improvement (Part 1)

If an AI keeps improving itself, how far can its intelligence go? Could the speed of light or the amount of matter in the universe set the ceiling? This piece is a Q&A built from a conversation the author had with an AI assistant, with the questions reorganized. Part 1 takes five questions on the upper limit that physics sets on computation and on when self-improvement levels off. Part 2 will look at where today's AI has passed humans and where it has not. Every figure used in the answers was rechecked against the original papers or the primary announcements of research groups and companies, as of October 4, 2026.

Q1. If an AI keeps improving itself, does its intelligence grow without limit? Has anyone shown an upper bound?

Upper bounds have been argued for, but "upper bound" comes in three layers, and they are not equally solid.

The first layer is a limit on computation itself, and it is well established physics. In 1998, Margolus and Levitin showed that the number of times a physical system can switch to a new state per second is capped by its energy. Add one joule to a computer and its processing rate can rise by at most about 3×10³³ operations per second. In 1981, Bekenstein argued that the amount of information that fits in an object of given size and energy is also capped (Page later questioned how widely that bound applies).

In 2000, Seth Lloyd at MIT combined these limits to estimate the performance of an "ultimate laptop" with a mass of one kilogram and a volume of one liter. Fixed only by the speed of light, the quantum of action and the gravitational constant, it comes to about 5.4×10⁵⁰ operations per second on roughly 10³¹ bits. In 2002 he applied the same reasoning to the whole universe: over its history it can have performed at most 10¹²⁰ operations on 10⁹⁰ bits (10¹²⁰ bits if gravitational degrees of freedom are included). Krauss and Starkman added that the accelerating expansion of the universe caps the total amount of information that can ever be processed in the future. These papers answer the question "could the amount of matter in the universe be the ceiling?" directly.

The second layer is a ceiling inside a formal definition of intelligence. In 2007, Legg and Hutter defined intelligence as a number measuring how well an agent achieves goals across many environments. Under that definition intelligence has a maximum, reached by a theoretical agent called AIXI. But AIXI is incomputable: no physical computer can actually run it. Mathematically there is a ceiling, but it cannot be reached.

The third layer is a claim that links the first two. In a 2015 paper on the limits of self-improving AI, Yampolskiy wrote that because computation has physical limits and more complex systems need more matter, the matter available in the universe sets a theoretical upper limit on achievable intelligence. That is an argument resting on the assumption that intelligence is a function of computation and matter, not a proof. The same paper also presents the opposing view: since problems can always be made harder, intelligence may have no upper bound.

Q2. If self-improvement levels off, what stops it?

Slowing down is not the same as having a ceiling. If gains grow logarithmically, each step adds less, yet the total keeps rising forever. A ceiling appears when each round of improvement shrinks by a fixed fraction. In 2016, Toby Walsh gave the example of each generation improving by half as much as the one before: the system can improve itself infinitely many times and still never more than double its intelligence. Yampolskiy cites a similar case: run a program-optimizing compiler on its own code again and again, and the gains go from 20% to 3% and then settle at zero.

For human research, these diminishing returns have actually been measured. In 2020, Bloom and colleagues showed that the number of researchers needed to double chip density is now more than 18 times what it was in the early 1970s, and that for the U.S. economy as a whole, research productivity halves roughly every 13 years.

Whether AI self-improvement will follow the same path is still open. In 2025, Eth and Davidson compressed the question into one number, the "returns to software R&D", r. If r is below 1, each doubling of software performance needs more than twice the research effort of the last, and progress fizzles. If r is above 1, progress accelerates. A follow-up model by Davidson and Houlden assumes r falls as software approaches its "effective limits", and puts the distance to those limits at a median of about 11 years of recent AI progress (6 at the low end, 16 at the high end). Both are research reports, not peer-reviewed papers.

So there are two kinds of ceiling, one set by physics and one set by where improvement converges, and whichever is lower bites first.

Q3. If computation could reach the physical limit, how much power would that be?

As an amount of computation, it can be estimated. There is no formula that converts it into a level of intelligence.

Start with the human brain. In 2020, Joseph Carlsmith concluded it is more likely than not that 10¹⁵ floating-point operations per second (FLOP/s) are enough to match the brain's task performance, and less than 10% likely that more than 10²¹ FLOP/s are needed. Taking Lloyd's ultimate laptop at 5.4×10⁵⁰ operations per second, one kilogram of matter is worth roughly 10²⁹ to 10³⁵ human brains. A FLOP and one of Lloyd's elementary operations are not the same unit, so read this as an order of magnitude only.

Two cautions. First, this is not a practical machine: Lloyd notes that, seen from outside, it would look like matter at about a billion kelvin. Second, it is a limit on parallel computation. Each bit can flip around 10¹⁹ times a second, but signals crossing the device are held to the speed of light. What physics allows looks less like "one very deep mind" and more like "an enormous number of thoughts running side by side". In 2012, Marcus Hutter argued that thinking faster and thinking better should be kept apart.

There is one careful measurement of how compute turns into skill. In 2021, Andy Jones trained AlphaZero agents on the board game Hex at several board sizes and found that each tenfold increase in compute adds about 500 Elo points; an agent with twice its opponent's compute wins roughly two games in three. Applied naively, 10³⁵ times more compute would mean stacking that two-in-three edge about 120 times. But playing strength saturates at perfect play, and in Jones's experiments the compute needed for perfect play grew about sevenfold with each step up in board size.

The most concrete picture comes from asking which problems could be solved outright. Checkers, with about 5×10²⁰ positions, was solved in 2007: perfect play by both sides is a draw. For chess, Shannon's 1950 lower estimate of the number of possible games is about 10¹²⁰, the same order as the universe's total operations. Brute force is out of reach even for the whole universe, but the number of positions (about 10⁴³ by Shannon's estimate) is far smaller, so a smarter method could still solve it. Go has about 2×10¹⁷⁰ legal positions, far beyond the 10⁹⁰ bits the universe can hold. Even at the physical limit, Go remains a game to be mastered approximately, not solved.

Q4. How far is that limit from the compute behind a recent "AI solves a hard problem" result?

The September 2026 Navier–Stokes computation is, against the physical limit, over in an instant.

On September 8, 2026, OpenAI announced that an internal AI system had produced a proof, together with a formal verification in the Lean proof assistant, that the Navier–Stokes equations (which describe the flow of water and air) can develop a singularity, a point where speeds grow without bound, in finite time from a smooth starting state. The proof covers the case where a smooth external force acts on the fluid throughout. According to OpenAI, on the order of 10,000 agents ran at once and reached the result about 88 hours after launch, using about 130 billion output tokens on this problem alone. OpenAI says it will not claim the Millennium Prize, and as of October 2026 the Clay Mathematics Institute still lists the problem as "Active".

OpenAI did not publish a FLOP count. Assuming each generated token costs about twice the model's parameter count in FLOP, a model of 100 billion to 10 trillion parameters, and adding the cost of reading inputs, we get roughly 10²⁴ FLOP (somewhere between 10²³ and 10²⁵). This is our own rough estimate.

Set against different yardsticks:

• For a human brain at 10¹⁵ FLOP/s, it is about 30 years of thinking.
• For all the world's computers (about 10²¹ operations per second, per Lloyd and Reilly's 2025 estimate), it is about 17 minutes.
• For a one-kilogram ultimate laptop, it is about 2×10^-27 seconds. Given the same 88 hours, that laptop could repeat the whole search about 10³² times.
• For the entire history of the universe (10¹²⁰ operations), it is 10⁹⁶ repetitions.

This only compares amounts of computation. Having 10³² times the compute does not mean solving problems 10³² times harder.

Q5. Then will superhuman intelligence emerge?

Physics does not forbid it. That alone does not mean it will happen.

With the brain at around 10¹⁵ FLOP/s, human-level compute is a waypoint, not a ceiling. But a high ceiling is only a necessary condition. Whether AI actually gets there depends on two empirical questions, not on physics: how efficiently compute turns into capability (if it grows only logarithmically, as in Q3, headroom does not translate into fast gains), and whether the returns r from Q2 stay above 1.

The sequence "first human-level general AI (AGI), then superhuman AI (ASI)" is not a given either. Walsh argues that human intelligence is one point on a continuous scale running from cockroach to mouse to human, and there is no reason to think it is a special tipping point beyond which runaway growth begins. Where real AI systems have passed humans, and where they have not, is the subject of Part 2.

What we know, and what we don't

What we know: computation has an upper limit set by the speed of light, quantum mechanics, gravity and the amount of matter in the universe, roughly 10²⁹ to 10³⁵ human brains per kilogram and 10¹²⁰ operations over the history of the universe. Even the much-discussed computation behind a recent hard-problem result is a blink against that limit. A ceiling on intelligence exists inside a formal definition, but the agent that attains it cannot be computed. The claim that finite matter means finite intelligence appears in the literature, but it assumes intelligence is set by the amount of computation.

Two things remain unknown: how efficiently compute turns into capability, and whether the returns r stay above 1. Physics does not rule out superhuman intelligence. Whether it arrives depends on these two questions, not on physics.

Part 2 looks at where today's AI has actually passed humans and where it has not, including AI that acts in the physical world. Research on what goes on inside AI models is covered in this earlier article.