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AGI Is Mathematically Impossible (3): Kolmogorov Complexity

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Re: AGI Is Mathematically Impossible (3): Kolmogorov Complexity

#81

Hey all, apologies for the delayed response. I was on a flight, then had guests, then had to make some rapid decisions involving actual real-world complexity (the kind that is not easily tokenized). 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.

5. On “Kolmogorov and Chaitin are misused”

It’s a fair concern.Chaitin does get thrown around too easily — usually in discussions that don’t need him.

But that’s not what’s happening here.

– Kolmogorov shows that most strings are incompressible. – Chaitin shows that even if you find the simplest representation, you can’t prove it’s minimal. – So any system that “discovers” a concept has no way of knowing it’s found something reusable.

That’s the issue. Without confirmation, generalization turns into guesswork. And in high-K environments — open-ended, unstable ones — that guesswork becomes noise. No poetic metaphor about the mystery of meaning here. It’s a formal point about the limits of abstraction recognition under complexity.

So no, it’s not a misuse. It’s just the part of the theory that gets quietly ignored because it doesn’t deliver the outcome people are hoping for.

Re: AGI Is Mathematically Impossible (3): Kolmogorov Complexity

#82

Hey all, apologies for the delayed response. I was on a flight, then had guests, then had to make some rapid decisions involving actual real-world complexity (the kind that is not easily tokenized). 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.

6. On “This is just a critique of current models—not AGI itself”

No.

This isn’t about GPT-4, or Claude, or whatever model’s in vogue this quarter. Neither is it about architecture. It’s about what no symbolic system can do—ever.

If your system is: a) Finite b)Bounded by symbols C) Built on recursive closure

…it breaks down where things get fuzzy: where context drifts, where the problem keeps changing, where you have to act before you even know what the frame is.

That’s not a tuning issue, that IS the boundary. (And we’re already seeing it.)

In The Illusion of Reasoning (Shojaee et al., 2025, Apple), they found that as task complexity rises: - LLMs try less - Answers get shorter, shallower - Recursive tasks—like the Tower of Hanoi—just fall apart - etc

That’s IOpenER in the wild:Information Opens. Entropy Rises. The theory predicts the divergence, and the models are confirming it—one hallucination at a time.

Re: AGI Is Mathematically Impossible (3): Kolmogorov Complexity

#83

Hey all, apologies for the delayed response. I was on a flight, then had guests, then had to make some rapid decisions involving actual real-world complexity (the kind that is not easily tokenized). 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.

And finally 7. On “But humans are finite too—so why not replicable?”

Yes. Humans are finite. But we’re not symbol-bound, and we don’t wait for the frame to stabilize before we act.We move while the structure is still breaking, speak while meaning is still assembling, and decide before we understand—then change what we were deciding halfway through.

NOT because we’re magic. Simply because we’re not built like your architecture (and if you think everything outside your architecture is magic, well…)

If your system needs everything cleanly defined, fully mapped, and symbolically closed before it can take a step, and mine doesn’t— then no, they’re not the same kind of thing.

Maybe this isn’t about scaling up? … Well, it isn’t It’s about the fact that you can’t emulate improvisation with a bigger spreadsheet. We don’t generalize because we have all the data. We generalize because we tolerate not knowing—and still move.

But hey, sure, keep training. Maybe frame-jumping will spontaneously emerge around parameter 900 billion.

Let me know how that goes

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