AGI is Mathematically Impossible 2: When Entropy Returns

I would argue that you are not a general intelligence. Humans have quite a specific intelligence. It might be the broadest, most general, among animal species, but it is not general. That manifests in that we each need to spend a significant amount of time training ourselves for specific areas of capability. You can't then switch instantly to another area without further training, even though all the context materials are available to you.

Sure I can (and thanks for writing)

Well, given the specific way you asked that question I confirm your self assertion - and am quite certain that your level of Artificiality converges to zero, which would make you a GI without A...

- You stated to "feel" generally intelligent (A's don't feel and don't have an "I" that can feel) - Your nuanced, subtly ironic and self referential way of formulating clearly suggests that you are not a purely algorithmic entity

A "précis" as you wished: Artificial — in the sense used here (apart from the usual "planfully built/programmed system" etc.) — algorithmic, formal, symbol-bound.

Humans as "cognitive system" have some similar traits of course - but obviously, there seems to be more than that.

Not the person asked, but in time honoured tradition I will venture forth that the key difference is billions of years of evolution. Innumerable blooms and culls. And a system that is vertically integrated to its core and self sustaining.

1. I appreciate the comparison — but I’d argue this goes somewhat beyond the No Free Lunch theorem.

NFL says: no optimizer performs best across all domains. But the core of this paper doesnt talk about performance variability, it’s about structural inaccessibility. Specifically, that some semanti spaces (e.g., heavy-tailed, frame-unstable, undecidable contexts) can’t be computed or resolved by any algorithmic policy — no matter how clever or powerful. The model does not underperform here, the point is that the problem itself collapses the computational frame.

2. OMG, lool. ... just to clarify, there’s been a major misunderstanding :)

the “weight-question”-Part is NOT a transcript from my actual life... thankfully - I did not transcribe a live ChatGPT consult while navigating emotional landmines with my (perfectly slim) wife, then submit it to PhilPapers and now here…

So - NOT a real thread, - NOT a real dialogue with my wife... - just an exemplary case... - No, I am not brain dead and/or categorically suicidal!! - And just to be clear: I dont write this while sitting in some marital counseling appointment, or in my lawyer's office, the ER, or in a coroners drawer

--> It’s a stylized, composite example of a class of decision contexts that resist algorithmic resolution — where tone, timing, prior context, and social nuance create an uncomputably divergent response space.

Again : No spouse was harmed in the making of that example.

;-))))

Correct: Shannon entropy originally measures statistical uncertainty over a fixed symbol space. When the system is fed additional information/data, then entropy goes down, uncertainty falls. This is always true in situations where the possible outcomes are a) sufficiently limited and b)unequally distributed. In such cases, with enough input, the system can collapse the uncertainty function within a finite number of steps.

But the paper doesn’t just restate Shannon.

It extends this very formalism to semantic spaces where the symbol set itself becomes unstable. These situations arise when (a) entropy is calculated across interpretive layers (as in LLMs), and (b) the probability distribution follows a heavy-tailed regime (α ≤ 1). Under these conditions, entropy divergence becomes mathematically provable.

This is far from being metaphorical: it’s backed by formal Coq-style proofs (see Appendix C in he paper).

AND: it is exactly the mechanism that can explain the Apple-Papers' results

Interaction is just another computation, and clearly we can interact with computers, and also simulate that interaction within the computer, so yes Turing machines can handle it. I'll check out Wegner.

I like the distinction you made there. My observation that when it comes to AGI, there are those who are saying "Not possible with the current technology." and "Not possible at all, because humans have [insert some characteristic here about self awareness, true creativity, etc] and machines don't.

I can respect the first argument. I personally don't see any reason to believe AGI is impossible, but I also don't see evidence that it is possible with the current (very impressive) technology. We may never build an AGI in my lifetime, maybe not ever, but that doesn't mean it's not possible.

But the second argument, that humans do something machines aren't capable of always falls flat to me for lack of evidence. If we're going to dismiss the possibility of something, we shouldn't do it without evidence. We don't have a full model of human intelligence, so I think it's premature to assume we know what isn't possible. All the evidence we have is that humans are biological machines, everything follows the laws of physics, and yet, here we are. There isn't evidence that anything else is going on other than physical phenomenon, and there isn't any physical evidence that a biological machine can't be emulated.

Hang on, hasn't everyone spent the past few years complaining about LLMs and diffusion models being very fallible?

And we can get LLMs to do better by just prompting them to "think step by step" or replacing the first ten attempts to output a "stop" symbolic token with the token for "Wait… "?

Let me steal another users alternate phrasing: Since humans and computers are both bound by the same physical laws, why does your proof not apply to humans?

The point is that if it's mathematically possible for humans, than it naively would be possible for computers.

All of that just sounds hard, not mathematically impossible.

As I understand it, this is mostly a rehash on the dated Lucas Penrose argument, which most Mind Theory researches refute.

TFA presents an information-theoretic argument forAGI being impossible. My reading of your parent commenter is that they are asking why this argument does not also apply to humans.

You make broadly valid points, particularly about the advantages of embodyment, but I just dont think theyre good responses to the theoretical article under discussion (or the comment that you were responding to).

Taking GLP-1 makes me question how much hunger is really me versus my hormones controlling me.

We don’t even know how LLMs work. But we do know the underlying mechanisms are governed by math because we have a theory of reality that governs things down to the atomic scale and humans and LLMs are made out of atoms.

So because of this we know reality is governed by maths. We just can’t fully model the high level consequence of emergent patterns due to the sheer complexity of trillions of interacting atoms.

So it’s not that there’s some mysterious supernatural thing we don’t understand. It’s purely a complexity problem in that we only don’t understand it because it’s too complex.

What does humility have to do with anything?

This paper is about the limits in current systems.

Ai currently has issues with seeing what's missing. Seeing the negative space.

When dealing with complex codebases you are newly exposed to you tackle an issue from multiple angles. You look at things from data structures, code execution paths, basically humans clearly have some pressure to go, fuck, I think I lost the plot, and then approach it from another paradigm or try to narrow scope, or based on the increased information the ability to isolate the core place edits need to be made to achieve something.

Basically the ability to say, "this has stopped making sense" and stop or change approach.

Also, we clearly do path exploration and semantic compression in our sleep.

We also have the ability to transliterate data between semantic to visual structures, time series, light algorithms (but not exponential algorithms, we have a known blindspot there).

Humans are better at seeing what's missing, better at not closuring, better at reducing scope using many different approaches and because we operate in linear time and there are a lot of very different agents we collectively nibble away at complex problems over time.

I mean on a 1:1 teleomere basis, due to structural differences people can be as low as 93% similar genetically.

We also have different brain structures, I assume they don't all function on a single algorithmic substrate, visual reasoning about words, semantic reasoning about colors, synesthesia, the weird handoff between hemispheres, parts of our brain that handle logic better, parts of our brain that handle illogic better. We can introspect on our own semantic saturation, we can introspect that we've lost the plot. We get weird feelings when something seems missing logically, we can dive on that part and then zoom back out.

There's a whole bunch of shit the brain does because it has a plurality of structures to handle different types of data processing and even then the message type used seems flexible enough that you can shove word data into a visual processor part and see what falls out, and this happens without us thinking about it explicitly.

I guess so too... but whatever it is: it cannot possibly be something algorithmic. Therefore it doesn't matter in terms of demonstrating that AI has a boundary there, that cannot be transcended by tech, compute, training, data etc.

I would really like to see your definition of general intelligence and argument for why humans don't fit it.

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.

How so?

As a somewhat colorblind person, I can tell you that the "actual green" is pretty much a lie :)

It's a deeply philosophical question what constitutes a subjective experience of "green" or whatever... but intelligence is a bit more tractable IHO.

I don't think it would be unfair to accept the brain state of green as an accurate representation of green for all intents and purposes.

Similar to how "computer code" and "video game world" are the same thing. Everything in the video game world is perfectly encoded in the programming. There is nothing transcendent happening, it's two different views of the same core object.

Fair enough. But then, AGI wouldn't really be based on math, but on physics. Why would an artificially-constructed physical system have (fundamentally) different capabilities than a natural one?

Stochastic parrots all the ways down

https://ai.vixra.org/pdf/2506.0065v1.pdf