I didnt read your draft paper, but your premise in HN sounds a bit off to me. AGI does not assume the ability for finding or learning an optimal solution to every problem (with that assumption it would be trivial to prove it impossible in many different ways). Independent of the exact definition, a system of intelligence that is better or equal to the best human in any domain would be at least termed AGI. (If there exist a couple incompressible problems along the way you can memorize the human solution.) If you proved AGI impossible under such a (weaker?) definition you would prove that humans can no longer improve in any domain (as the set of all humans is a general intelligence). Or you would need to assume that there is something special inside humans, which no technology can ever build. I disagree with both premises.
AGI Is Mathematically Impossible (3): Kolmogorov Complexity
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Re: AGI Is Mathematically Impossible (3): Kolmogorov Complexity
#22Okay, read the abstract and Intro. Recently, in the paper
"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
Re: AGI Is Mathematically Impossible (3): Kolmogorov Complexity
#23I think that any paper that argues something is impossible is fundamentally flawed, particularly when there are examples of it being possible. 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?
You might want to check out the works of that buzzkill that Gödel is ^^ https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_... " The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.e. an algorithm) is capable of proving all truths about the arithmetic of natural numbers. For any such consistent formal system, there will always…
> You might want to check out the works of that buzzkill that Gödel is ^^
Please explain why do you believe this is relevant to the points I've made.
Re: AGI Is Mathematically Impossible (3): Kolmogorov Complexity
#24Re: AGI Is Mathematically Impossible (3): Kolmogorov Complexity
#25AGI Is Mathematically Impossible
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. :-(
Re: AGI Is Mathematically Impossible (3): Kolmogorov Complexity
#26The human brain does not have perfect memory. It is not always logical. And more often than not it is motivated and influenced by "external" forces - health, hunger, sex drive, environmental conditions, luck, spiritual inspiration, or whatever. The perfect worker is purely logical and has perfect memory and no external influences - never gets hungry or sick or wants to be the boss themselves. The AI race is funded by folks interested in creating the perfect worker, not a human. I have to agree with the conclusions of this paper that they won't be able to make humans. (But they don't really want to.) The Vatican has also published interesting works on this idea. The question is - if you take out everything that makes it human, can you call it intelligent?
Re: AGI Is Mathematically Impossible (3): Kolmogorov Complexity
#27How is your brain doing it then?
The "A" stands for "Artificial" in contrast to what our brains do.
If you want to argue for a fundamentally non-material mind (ie, that human cognition happens in a physically impossible, spiritual plane), then cool. Though you might want to give some consideration to how much it seems like physical processes on the brain can demonstrably affect cognition.
If you aren't arguing for a non-materialist position, then the distinction between "artificial" and human intelligence isn't meaningful. A powerful enough computer could simulate the material processes in your brain. If as the OP claims it is mathematically impossible for a computer to generate intelligence, no matter how powerful that computer, then it is impossible for your brain to do so (via material processes).
Re: AGI Is Mathematically Impossible (3): Kolmogorov Complexity
#28How is your brain doing it then?
Wouldn’t it be possible that not all brains can do it all, but some can specialize in certain problems. But when combined with everyone else’s we can approach general intelligence?
Re: AGI Is Mathematically Impossible (3): Kolmogorov Complexity
#29How is your brain doing it then?
Doing artificial?
The brain still exists in the same universe running on the same mathematical laws. The A adds no constraints that can make anything impossible. There is nothing that the brain is doing that we cannot also replicate, we just cannot get to the same scale yet.
Re: AGI Is Mathematically Impossible (3): Kolmogorov Complexity
#30I didnt read your draft paper, but your premise in HN sounds a bit off to me. AGI does not assume the ability for finding or learning an optimal solution to every problem (with that assumption it would be trivial to prove it impossible in many different ways). Independent of the exact definition, a system of intelligence that is better or equal to the best human in any domain would be at least termed AGI. (If there e…
Independent of the exact definition, a system of intelligence that is better or equal to the best human in any domain would be at least termed AGI.
Exactly. There's this "thing" you see in certain circles, where people (intentionally?) mis-interpret the "G" in AGI as meaning "the most general possible intelligence". But that's not the reality. AGI has pretty much always been taken to mean "AI that is approximately human level". Going beyond that is getting into the realm of Artificial Super Intelligence, or Universal Artificial Intelligence.