AGI is Mathematically Impossible 2: When Entropy Returns

The difference between human and artificial intelligence (whatever "intelligence" is) is in the following: - AI is COMPLICATED (e.g. the World's Internet) yet it is REDUCIBLE and it is COUNTABLE (even if infinite) - Human intelligence is COMPLEX; it is IRREDUCIBLE (and it does not need to be large; 3 is a good number for a complex system) - AI has a chance of developing useful tools and methods and will certainly advance our civilization; it should not, however, be confused with intelligence (except by persons who do not discern complicated from complex) - Everything else is poppycock

Oh no, I am not at all trying to find an explanation of why this is (qualia etc.). There is simply no necessity for that. It is interesting, but not part of the scientific problem that i tried to find an answer to.

The proof (all three of them) holds without any explanatory effort concerning causalities around human frame-jumping etc.

For this paper, It is absolutely sufficient to prove that a) this cannot be reached algorithmically and that b) evidence clearly shows that humans can (somehow) do this , as they have already done this (quite often).

Very good point.

I in fact had thought of describing the problem from a systems theoretical perspective as this is another way to combine different paths into a common principle

That was a sketch, in case you are into these kind of approaches:

2. Complexity vs. Complication In systems theory, the distinction between 'complex' and 'complicated' is critical. Complicated systems can be decomposed, mapped, and engineered. Complex systems are emergent, self-organizing, and irreducible. Algorithms thrive on complication. But general intelligence—especially artificial general intelligence (AGI)—must operate in complexity. Attempting to match complex environments through increased complication (more layers, more parameters) leads not to adaptation, but to collapse. 3. The Infinite Choice Barrier and Entropy Collapse In high-entropy decision spaces, symbolic systems attempt to compress possibilities into structured outcomes. But there is a threshold—empirically visible around entropy levels of H ≈ 20 (one million outcomes)—beyond which compression fails. Adding more depth does not resolve uncertainty; it amplifies it. This is the entropy collapse point: the algorithm doesn't fail because it cannot compute. It fails because it computes itself into divergence. 4. The Oracle and the Zufallskelerator To escape this paradox, the system would need either an external oracle (non-computable input), or pure chance. But chance is nearly useless in high-dimensional entropy. The probability of a meaningful jump is infinitesimal. The system becomes a closed recursion: it must understand what it cannot represent. This is the existential boundary of algorithmic intelligence: a structural self-block. 5. The Organizational Collapse of Complexity The same pattern is seen in organizations. When faced with increasing complexity, they often respond by becoming more complicated—adding layers, processes, rules. This mirrors the AI problem. At some point, the internal structure collapses under its own weight. Complexity cannot be mirrored. It must either be internalized—by becoming complex—or be resolved through a radically simpler rule, as in fractal systems or chaos theory.

6. Conclusion: You Are an Algorithm An algorithmic system can only understand what it can encode. It can only compress what it can represent. And when faced with complexity that exceeds its representational capacity, it doesn't break. It dissolves. Reasoning regresses to default tokens, heuristics, or stalling. True intelligence—human or otherwise—must either become capable of transforming its own frame (metastructural recursion), or accept the impossibility of generality. You are an algorithm. You compress until you can't. Then you either transform, or collapse

> Why? 1. Basically because physical laws obviously allow more than algorithmic cognition and problem solving.

You seem to be laboring under the mistaken idea that "algorithmic" does not encompass everything allowed by physics. But, humoring this idea, then if physical laws allow it, why can this "more than algorithmic" cognition not be done artificially? As you say - we can obviously do it. What magical line is preventing an artificial system from doing the same?

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