AGI Is Mathematically Impossible (3): Kolmogorov Complexity

Also, what's the point of telling others you believe what they are doing is impossible, specially after the results we are seeing even at the free-tier, open-to-the-public services?

But I take that to mean there's no general, universal algorithm to tell us anything we want to know. But that's not what intelligence is, we're not defining some kind of absolute intelligence like an oracle for the halting problem. That definition would be a category error.

"What Has a Foundation Model Found? Using Inductive Bias to Probe for World Models"

your thesis of Ai's lack of capacity to abstract or at least extract understanding from noisy data was largely experimentally confirmed. I am uncertain though about the exact mechanics b/c as they used LLM's, its not transparent what happened internally that lead to constant failure to abstract the concept despite ample predictive power. One interesting experiment was the introduction of the Oracle that literally enabled the LLM to solve the task that was previously impossible without the oracle, which means, at least its possible that LLM's can reconstruct known rules. They just can't find new ones.

On a more fundamental level, I am not so sure why these experiments and mathematical proofs still are made since Judea Pearl already established about seven years ago in "Theoretical Impediments to Machine Learning " that all correlation based methods are doomed as they fail to understand anything. his point about causality is well placed, but will not solve the problem either.

The question I have though, if we ignore all existing methods for one moment, then what makes you so sure that AGI is really Mathematically impossible? Suppose some advancement in quantum computing would allow to reconstruct incomplete information, does your assertion still holds true?

https://arxiv.org/abs/2507.06952 https://arxiv.org/abs/1801.04016

Unless you believe in magic, the human brain proves that human level general intelligence is possible in our physical universe, running on a system based on the laws of said physical universe. Given that, there's no particular reason to think that "what the brain does" OR a reasonably close approximation, can't be done on another "system based on the laws of our physical universe."

Also, Marcus Hutter already proved that AIXI[1] is a universal intelligence, where it's only short-coming is that it requires infinite compute. But the quest of the AGI project is not "universal intelligence" but simply intelligence that approximates that of us humans. So I'd count AIXI as another bit of suggestive evidence that AGI is possible.

Using Kolmogorov complexity, we show that many real-world problems—particularly those involving social meaning, context divergence, and semantic volatility—are formally incompressible and thus unlearnable by any finite algorithm.

So you're saying the human brain can do something infinite then?

Still, happy to give the paper a read... eventually. Unfortunately the "papers to read" pile just keeps getting taller and taller. :-(

[1]: https://en.wikipedia.org/wiki/AIXI

Then I started to read the paper, and it's worse.

Every one of his 'examples' would not just be 'solved' by any existing LLM, even a 'dumb' system that just spits out a random sentence to any question would pass his first 2 'tests' with flying colors. I'm not kidding, he accepts "Leave the classroom and stop confusing everybody with your senseless questions" as a good solution.

In fact, the only system that would fail is this hypothetical AI he imagines that somehow gets into infinitely analyzing loops.

Then his 3rd test, an investment decision, gives the same outcome as himself up until the point he draws in extra information not available to the AI, after which he flips his 'answer' which he then labels as 'correct' and the previous answer based on the original info as 'false' because he made some money on the bet a few weeks later, seriously?

I think for your theory to hold up, you would need to show that physics cannot, even in principle, be simulated mathematically at sufficient scale (the number of interacting subatomic particles). That would be surprising.

At the moment it seems like your results contradict reality, meaning your starting assumptions cannot all be true.

Then I understood why not. Your paper proves that I am unable to understand your paper. It also proves that you are unable to understand your paper.

Like eval/apply under Lisp. Or Forth.

If you solve a problem "by accident", there are very many other people who make foolish decisions daily because they do not think. Some of those pan out too and lead to understanding. A resource-bounded agent can also maintain a notion of fuel and give a random answer when it has exhausted its fuel.

The structural incompleteness mentioned isn't really meaningful. Humans have not demonstrated the capacity to make epsilon-optimal decisions on an infinite number of tasks, since we do not do an infinite number of tasks anyway.

K-complexity, and resource-bounded K-complexity are indeed extremely useful tools to talk about generalization, I'd agree, but I think the author has misunderstood the limits that K-complexity places on generalization.

I would politely suggest that until you do that and then come up with a convincing rebuttal for every point they make that is not self-evidently wrong, you shouldn't be wasting humans' time.

I’ve now had time to read through the thread properly, and I appreciate the range of engagement—even the sharp-edged stuff. Below, I’ve gathered a set of structured responses to the main critique clusters that came up.