AGI is Mathematically Impossible 2: When Entropy Returns
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AGI is Mathematically Impossible 2: When Entropy Returns
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Re: AGI is Mathematically Impossible 2: When Entropy Returns
#2This paper presents a theoretical proof that AGI systems will structurally collapse under certain semantic conditions — not due to lack of compute, but because of how entropy behaves in heavy-tailed decision spaces.
The idea is called IOpenER: Information Opens, Entropy Rises. It builds on Shannon’s information theory to show that in specific problem classes (those with α ≤ 1), adding information doesn’t reduce uncertainty — it increases it. The system can’t converge, because meaning itself keeps multiplying.
The core concept — entropy divergence in these spaces — was already present in my earlier paper, uploaded to PhilArchive on June 1. This version formalizes it. Apple’s study, The Illusion of Thinking, was published a few days later. It shows that frontier reasoning models like Claude 3.7 and DeepSeek-R1 break down exactly when problem complexity increases — despite adequate inference budget.
I didn’t write this paper in response to Apple’s work. But the alignment is striking. Their empirical findings seem to match what IOpenER predicts.
Curious what this community thinks: is this a meaningful convergence, or just an interesting coincidence?
Links:
This paper (entropy + IOpenER): https://philarchive.org/archive/SCHAIM-14
First paper (ICB + computability): https://philpapers.org/archive/SCHAII-17.pdf
Apple’s study: https://machinelearning.apple.com/research/illusion-of-think...
Re: AGI is Mathematically Impossible 2: When Entropy Returns
#3So does the human brain transcend math, or are humans not generally intelligent?
Re: AGI is Mathematically Impossible 2: When Entropy Returns
#4So does the human brain transcend math, or are humans not generally intelligent?
I think the latter fact is quite self-demonstrably true.
Re: AGI is Mathematically Impossible 2: When Entropy Returns
#5Without reading the paper how the heck is agi mathematically impossible if humans are possible? Unless the paper is claiming humans are mathematically impossible?
I’ll read the paper but the title comes off as out of touch with reality.
Re: AGI is Mathematically Impossible 2: When Entropy Returns
#6Re: AGI is Mathematically Impossible 2: When Entropy Returns
#7So does the human brain transcend math, or are humans not generally intelligent?
Humans do a lot of things that computers don't, such as be born, age (verb), die, get hungry, fall in love, reproduce, and more. Computers can only metaphorically do these things, human learning is correlated with all of them, and we don't confidently know how. Have some humility.
Re: AGI is Mathematically Impossible 2: When Entropy Returns
#8So does the human brain transcend math, or are humans not generally intelligent?
My take is that it transcends any science that we'll understand and harness in the lifetime of anyone living today. It for all intents and purposes transcends science from our point of view, but not necessarily in principle.
Re: AGI is Mathematically Impossible 2: When Entropy Returns
#9So does the human brain transcend math, or are humans not generally intelligent?
I think the latter fact is quite self-demonstrably true.
Colloquially anything that matches humans in general intelligence and is built by us is by definition an agi and generally intelligent.
Humans are the bar for general intelligence.
Re: AGI is Mathematically Impossible 2: When Entropy Returns
#10So does the human brain transcend math, or are humans not generally intelligent?
I think humans have some kind of algorithm for deciding what's true and consolidating information. What that is I don't know.