AGI is Mathematically Impossible 2: When Entropy Returns

Care to elaborate?

A lot of people see a title that is "subject I want to discuss" and jump to the comment section without even bothering to look at the link. There has been a lot AI hype, so counter-hypists are starved from content and just jumped on the first "confirmation bias title" they could find.

Thank you for the comment, "typical crackpot" feels a bit light considering how unhinged that is.

"emergent superintelligent AI" is as much superstition as believing in imaterial souls. One company literally used the term "people spirits" to refer to how LLMs behave in their official communications.

It's a cult. Like many cults, it tries to latch on science to give itself legitimacy. In this case, mathematics. It has happened before many times.

You're trying to say that, because it's computers and stuff, it's science and therefore based on reason. Well, it's not. It's just a bunch of non sequitur.

While I'm constantly disappointed by self driving cars, I do get the impression they're better at navigating the world than I was when I was four. And in public roads specifically, better than when I was fourteen.

No problem here is you proof - although a bit long:

1. THEOREM: Let a semantic frame be defined as Ω = (Σ, R), where

Σ is a finite symbol set and R is a finite set of inference rules.

Let Ω′ = (Σ′, R′) be a candidate successor frame.

Define a frame jump as: Frame Jump Condition: Ω′ extends Ω if Σ′\Σ ≠ ∅ or R′\R ≠ ∅

Let P be a deterministic Turing machine (TM) operating entirely within Ω.

Then: Lemma 1 (Symbol Containment): For any output L(P) ⊆ Σ, P cannot emit any σ ∉ Σ.

(Whereas Σ = the set of all finite symbol strings in the frame; derivable outputs are formed from Σ under the inference rules R.)

Proof Sketch: P’s tape alphabet is fixed to Σ and symbols derived from Σ. By induction, no computation step can introduce a symbol not already in Σ. ∎

2. APPLICATION: Newton → Special Relativity

Let Σᴺ = { t, x, y, z, v, F, m, +, · } (Newtonian Frame) Let Σᴿ = Σᴺ ∪ { c, γ, η(·,·) } (SR Frame)

Let φ = “The speed of light is invariant in all inertial frames.” Let Tᴿ be the theory of special relativity. Let Pᴺ be a TM constrained to Σᴺ.

By Lemma 1, Pᴺ cannot emit any σ ∉ Σᴺ.

But φ ∈ Tᴿ requires σ ∈ Σᴿ \ Σᴺ

→ Therefore Pᴺ ⊬ φ → Tᴿ ⊈ L(Pᴺ)

Thus:

Special Relativity cannot be derived from Newtonian physics within its original formal frame.

3. EMPIRICAL CONFLICT Let: Axiom N₁: Galilean transformation (x′ = x − vt, t′ = t) Axiom N₂: Ether model for light speed Data D: Michelson–Morley ⇒ c = const

In Ωᴺ, combining N₁ and N₂ with D leads to contradiction. Resolving D requires introducing {c, γ, η(·,·)}, i.e., Σᴿ \ Σᴺ But by Lemma 1: impossible within Pᴺ. -> Frame must be exited to resolve data.

4. FRAME JUMP OBSERVATION

Einstein introduced Σᴿ — a new frame with new symbols and transformation rules. He did so without derivation from within Ωᴺ. That constitutes a frame jump.

5. FINALLY

A: Einstein created Tᴿ with Σᴿ, where Σᴿ \ Σᴺ ≠ ∅

B: Einstein was human

C: Therefore, humans can initiate frame jumps (i.e., generate formal systems containing symbols/rules not computable within the original system).

Algorithmic systems (defined by fixed Σ and R) cannot perform frame jumps. But human cognition demonstrably can.

QED.

BUT: Can Humans COMPUTE those functions? (As you asked)

-> Answer: a) No - because frame-jumping is not a computation.

It’s a generative act that lies outside the scope of computational derivation. Any attempt to perform frame-jumping by computation would either a) enter a Goedelian paradox (truth unprovable in frame),b) trigger the halting problem , or c) collapse into semantic overload , where symbols become unstable, and inference breaks down.

In each case, the cognitive system fails not from error, but from structural constraint. AND: The same constraint exists for human rationality.