Even a superintelligence has to wait for some answers

The astronomer Jacques Laskar worked out how fast that happens to the Earth's own orbit: "an error of 15 meters in the initial position of the Earth gives rise to an error of about 150 meters after 10 Ma, but the same error becomes 150 million km after 100 Ma" 2, where Ma means millions of years. The error grows roughly tenfold every 10 million years, so past about 100 million years no amount of computing can tell you where the Earth will be.

The air above us does the same thing on a much shorter clock. In 1963 the meteorologist Edward Lorenz showed that in a simple model of moving air, two almost identical starting points drift apart until the runs look nothing alike. His conclusion still stands: for something like the atmosphere, "prediction of the sufficiently distant future is impossible by any method, unless the present conditions are known exactly" 3.

Tiny errors in where you start grow until they swamp the forecast. A 2019 study by Fuqing Zhang and colleagues put numbers on it for the weather. Today's useful forecasts reach "around 10 days," and "the ultimate limit of midlatitude day-to-day weather predictability is about 2 weeks." Even cutting the uncertainty in today's measurements tenfold buys only "up to 5 days" more 4.

To be fair, that limit is being tested right now. A 2026 preprint (a study shared before peer review) using an AI weather model with carefully tuned starting conditions reports forecast skill "lasting beyond 30 days," though its authors say it's still an open question whether such starting conditions can be found in real time 5.

A superintelligence would forecast better than we do, maybe much better, and yet somewhere out past the edge of chaos the details are gone for any mind, because the starting information was never there to begin with.

In 1936 Alan Turing proved something that still surprises people: there is no general method that can look at any program and decide whether it will eventually stop or run forever. In modern terms the question is called the halting problem, and "the halting problem is unsolvable" 6. That holds for any mind that computes, however fast.

My favorite illustration is a contest called the Busy Beaver. Take every possible tiny computer program of a given size and ask which of the ones that eventually stop runs the longest. For programs with five instructions, an online collaboration finished the search in July 2024 7 and proved the answer with a computer-checked proof: 47,176,870 steps 8. Getting there meant checking more than 181 million machines.

For six instructions, the answer may never be known. One six-instruction machine, nicknamed Antihydra, behaves like a famous unsolved math puzzle known as the Collatz problem, and settling it means solving "a Collatz-like problem" 9. The Busy Beaver numbers grow faster than any function a computer can calculate 10, so every new step up eventually outruns every mind.

Five years before Turing, Kurt Gödel found a deeper crack. Take any consistent system of rules F (consistent meaning it never proves a contradiction) that is powerful enough to do arithmetic. Gödel showed that "there are statements of the language of F which can neither be proved nor disproved in F," and that such a system "cannot prove that the system itself is consistent" 11.

Mathematics is built from axioms, the starting rules everyone agrees to assume, up to theorems, with conjectures sitting off to the side as statements nobody has proved yet. Gödel guarantees that the side pile never empties. A superintelligence would prove a staggering number of theorems, and it would still face true statements its rules can't reach.

The last wall is subtler. Some processes, Stephen Wolfram argues, are "computationally irreducible": "there can be no way to predict how the system will behave except by going through almost as many steps of computation as the evolution of the system itself" 12. The only way to see the end is to run every step. How common that is remains Wolfram's conjecture, but if he's right, a lot of the world can only be watched step by step as it unfolds.

A related open question asks: "If it is easy to check that a solution to a problem is correct, is it also easy to solve the problem?" 13. Mathematicians call it P versus NP, and it's one of seven million-dollar Millennium Prize problems. Nobody knows the answer, and most of the cryptography protecting your bank account rests on unproven bets that some problems really are hard 14.