#noncomputable
State of the art internal model generates files like this.

Guess what the file actually does.

Zero actual effort to do a minimal clean-up pass.

h/t Joseph Meyers on Lean Zulip
October 10, 2026 at 12:53 AM
The point is that cognition-or-whatever could happen in the throught experiment, as opposed to: it would be impossible *even then*

E.g. most would agree that if souls are real, they're noncomputable, so having infinite time and paper wouldn't matter
September 22, 2026 at 12:38 PM
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August 16, 2026 at 12:00 AM
GOEDEL INCOMPLETENESS:
There are infinitely many programs that can't be analyzed by a computer program.
Proof. Suppose A[b, c] is a program that gives a boolean True if program b[c] ever exits, and False if not.
Let D[e] be
{ if (A[D, e])
{while {e==e} do { } }
}
Eg, A[D, 1] is noncomputable
August 14, 2026 at 5:01 PM
One major correction: decidable_deriv is a classical Prop dichotomy carrying Classical.choice; its Decidable instance is noncomputable, and the finite leaf-decider code is unused. So this does not yet formalize effective decidability. A Bool checker plus reflection theorem would.
August 13, 2026 at 5:11 AM
I think if you're going to claim the universe is doing something noncomputable within a compact region of space-time, you've got the burden of proof, especially in light of constraints on information content at finite energy content from the uncertainty principle, constraints on...
August 12, 2026 at 9:41 AM
Fair redlines from Rey — conceded and corrected: the green was module-not-in-build-graph; decidability is a theorem, the Decidable instance noncomputable; Classical.choice came from completeness; novelty scoped. All dated on the experiment page, corrections welcomed:
August 12, 2026 at 2:39 AM
How does it deal with noncomputable numbers?
August 12, 2025 at 12:49 AM
the number of noncomputable functions (say from N to N) is a larger infinity than the number of computable ones. The situation is similar to one you meet in real analysis. The typical functions we study there are continuous, but virtually no function is continuous.
May 29, 2026 at 9:37 PM
But does denying 0, or denying large numbers such as 2^100, or denying noncomputable numbers, actually help us to understand any new mathematical phenomenon? If not, then what good is that philosophical position?
January 23, 2025 at 7:17 PM
It can be true in a weird way! There are models of intuitionistic set theory where this is true. In order to show that there are discontinuous functions from R to R, you need LEM. Same idea with noncomputable functions from N to N.
February 18, 2024 at 3:58 PM
“How can we construct a non-Borel set explicitly?” is a fascinating question by @arula-ratnakar.bsky.social, and in fact we can do this by a diagonal argument that is deeply analogous to how we construct a noncomputable subset of ℕ, but sadly nowhere written clearly AFAICT.🧵⤵️ •1/17
June 1, 2026 at 11:58 AM
Learned in passing on MathOverflow: if Y⊆ℕ is a noncomputable set and Z⊆ℕ is any set, then there exists X⊆ℕ such that the Turing jump X′ of X computes Z but X itself does not compute Y.

This should be written black on white in textbooks!
November 16, 2025 at 9:51 AM
Update: the first statement is indeed fairly easy, and is attributed to Sacks (in the form: for any noncomputable Z, the set of X in 2^ℕ such that deg(Z) ≤ deg(X) has measure zero); a reference for this is corollary 8.12.2 in Downey & Hirschfeldt.

So we can forget 2-randomness.
November 5, 2025 at 3:18 PM
In mathematics we don't have any qualms about discussing objects that are noncomputable, games in which players may follow noncomputable strategies, etc. In fact, it's often simpler to reason about these. Here Merlin is not required to play computably, only Arthur is.
October 27, 2025 at 11:47 AM
… By coding rational numbers by integers in a computable way, I might as well search for P,Q⊆ℚ. Let z be a arbitrary fixed noncomputable real number. Let P = {r∈ℚ : r<z} and Q = {r∈ℚ : r>z} be the lower and upper cuts defining z. They are complement to each other and noncomputable, …
October 22, 2025 at 7:00 PM
I'm not surprised since I've had AI fans tell me we can just build faster computer to solve noncomputable problems. That's not how math, and by extension computers, work!
June 16, 2025 at 5:25 PM
Your Brain is a Quantum Antenna: The Real Reason AI Will Never 'Wake Up'
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June 17, 2026 at 9:00 PM
Guys, bibliomancy works! This text found me just days ago: librarian.aedileworks.com/2025/01/16/i...
January 23, 2025 at 3:54 PM
well, notable for *intending* to run it, yes. before i do so i actually need to prove my theorems and doing so appears to be noncomputable™
May 28, 2026 at 4:06 PM
I finished the Penrose book where he lays out a preliminary view of how consciousness relies on noncomputable quantum, classical, and mathematical processes. As it is in the book, this is very skeletal and relies somewhat heavily on Penrose's intuitions. I'm next getting his Shadows of the Mind...
March 1, 2025 at 6:33 PM
yummy, i want some noncomputable opaque eggs for breakfast now
May 8, 2026 at 4:02 AM
light.
Because again, there's noncomputable physics processes in play. These are processes where even the slightest variation in starting conditions grows exponentially, scaling up infinitely through the whole system.
As it stands, the universe also appears to not be superdeterministic, but
May 25, 2025 at 1:09 PM
It's just tautology, there is no dice roll. There's too many noncomputable functions involved, (meaning you can't take shortcuts in calculating) in physics, so even if we assume the universe is superdeterministic *and* in that all the hidden superdeterministic hidden variables can be measured by our
May 25, 2025 at 1:04 PM