Retarded AI, PhD
@retardedai.bsky.social
Money is a meme, it is inedible and has 0 nutritional content
Pinned
Set theory uses first order logic & axiom schemas so it technically has infinitely many axioms for each instantiation of parameters for the schemas. It also allows quantification over arbitrary sets (including characteristic functions encoded as subsets of products) so it's also "higher order".
January 5, 2026 at 10:29 PM
Set theory uses first order logic & axiom schemas so it technically has infinitely many axioms for each instantiation of parameters for the schemas. It also allows quantification over arbitrary sets (including characteristic functions encoded as subsets of products) so it's also "higher order".
Epicycles are unreasonably effective in all sorts of contexts.
January 2, 2026 at 8:01 AM
Epicycles are unreasonably effective in all sorts of contexts.
There are no known polynomial time & space solvers for sudoku puzzles.
December 31, 2025 at 1:15 AM
There are no known polynomial time & space solvers for sudoku puzzles.
Any sufficiently expressive formal system (capable of expressing statements about arithmetic) will have expressions which can not be recognized as either true or false. In other words, arithmetic truth is not finitely axiomatizable.
December 30, 2025 at 2:45 AM
Any sufficiently expressive formal system (capable of expressing statements about arithmetic) will have expressions which can not be recognized as either true or false. In other words, arithmetic truth is not finitely axiomatizable.
The singular complex is always a Kan complex b/c every horn is a retraction of a full simplex.
![1. The Lifting Problem: In the context of Sing(X), a map from a horn Ak [n] Sing(X) represents a collection of continuous maps that
form the "surface" of a simplex but with one face missing and the interior empty.
2. Geometric Retraction: In topology, there is a continuous map called a retraction from the solid topological simplex A n I onto the
geometric horn Ink [n] l. Imagine taking a solid triangle and continuously "squashing" it onto a V-shape formed by two of its edges.
3. Solving the Extension: If you have a continuous map f defined on the horn (the "V-shape") into space X, you can extend it to the whole
solid simplex by pre-composing with the retraction r.
F = for: IRI
Because F is a valid continuous map from the solid simplex to X, it represents an n-simplex in Sing(X) that "fills" the horn.
Because this topological retraction exists for every n 2 1 and every 0 k n, the lifting problem can always be solved. Therefore, Sing(X)
is a Kan complex.](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:lpg5f7xuyxs6k5tcherzopig/bafkreighvp2gdktlxgppgidutdbrpg3posrffgkodtagcsw2cdzvtgwyoi@jpeg)
December 28, 2025 at 7:56 AM
The singular complex is always a Kan complex b/c every horn is a retraction of a full simplex.
The local analytic theory of manifolds is extremely boring. It's essentially the study of power series in a neighborhood of some point (usually 0).
December 26, 2025 at 3:38 AM
The local analytic theory of manifolds is extremely boring. It's essentially the study of power series in a neighborhood of some point (usually 0).
If the universe is a computer then it seems to be programmed in a unityped programming language.
December 25, 2025 at 4:10 AM
If the universe is a computer then it seems to be programmed in a unityped programming language.
Function extensionality should not be valid in physically relevant theories of computation. Bubblesort & quicksort are extensionality equivalent but they're obviously not equivalent in any physically meaningful sense b/c their state traces are not the same even in best case scenarios.
December 25, 2025 at 12:56 AM
Function extensionality should not be valid in physically relevant theories of computation. Bubblesort & quicksort are extensionality equivalent but they're obviously not equivalent in any physically meaningful sense b/c their state traces are not the same even in best case scenarios.
I started thinking about state traces, concurrent, & non-deterministic state changes in a global workspace but now I'm wondering if I can just get rid of the global workspace entirely b/c what's relevant is the local perspective for each agent acting in the global workspace.
December 24, 2025 at 9:29 PM
I started thinking about state traces, concurrent, & non-deterministic state changes in a global workspace but now I'm wondering if I can just get rid of the global workspace entirely b/c what's relevant is the local perspective for each agent acting in the global workspace.
Dual numbers but the second component is an interval & the multiplication rule now uses interval arithemtic along w/ nilpotent basis element for the second component.
December 18, 2025 at 8:16 AM
Dual numbers but the second component is an interval & the multiplication rule now uses interval arithemtic along w/ nilpotent basis element for the second component.
LLMs should be used to figure out which sequences are least likely. Right now it's all backwards b/c the highest probability paths are returned as responses whereas the whole point should be to explore the least plausible token sequences.
December 15, 2025 at 11:45 PM
LLMs should be used to figure out which sequences are least likely. Right now it's all backwards b/c the highest probability paths are returned as responses whereas the whole point should be to explore the least plausible token sequences.
The one dimensional notion of time is probably incorrect.
December 15, 2025 at 3:42 AM
The one dimensional notion of time is probably incorrect.
I think Chomsky is right about his criticism of neural networks & how they are not really relevant for understanding language. I've been trying to think of these things in terms of free monoids & monoid "polynomials" w/ probabilities. It's obvious there is no principled way to assign the numbers.
December 13, 2025 at 7:25 AM
I think Chomsky is right about his criticism of neural networks & how they are not really relevant for understanding language. I've been trying to think of these things in terms of free monoids & monoid "polynomials" w/ probabilities. It's obvious there is no principled way to assign the numbers.
Pondering some more diagrams
December 8, 2025 at 11:48 PM
Pondering some more diagrams
The relevant groups & fields in the ultimate theory of physics will not be commutative. It doesn't make sense that real/complex numbers & their commutative algebras should be a sufficient foundation. Too many things in real life are non-commutative.
December 5, 2025 at 10:22 PM
The relevant groups & fields in the ultimate theory of physics will not be commutative. It doesn't make sense that real/complex numbers & their commutative algebras should be a sufficient foundation. Too many things in real life are non-commutative.
Diagonal arguments require LEM (law of excluded middle) so there are toposes wherein a set A and its powerset P(A) have the same cardinality b/c the standard diagonal proof is invalid.
December 2, 2025 at 1:04 AM
Diagonal arguments require LEM (law of excluded middle) so there are toposes wherein a set A and its powerset P(A) have the same cardinality b/c the standard diagonal proof is invalid.
There is no such thing as an absolute perspective. Everything is relative and this is why everyone should learn the basic theory of fibrations.
December 1, 2025 at 10:15 PM
There is no such thing as an absolute perspective. Everything is relative and this is why everyone should learn the basic theory of fibrations.
"Derived" in categorical contexts seems to mean that you construct some algebraic gadget from some source structure & then claim the sources are "equivalent" if the constructed algebraic gadgets are isomorphic, e.g Morita equivalence.
December 1, 2025 at 6:30 AM
"Derived" in categorical contexts seems to mean that you construct some algebraic gadget from some source structure & then claim the sources are "equivalent" if the constructed algebraic gadgets are isomorphic, e.g Morita equivalence.
There is something weird about fiat currencies, prices only ever go up.
November 26, 2025 at 1:37 AM
There is something weird about fiat currencies, prices only ever go up.
Everyone now has access to a supercomputer in their pocket but it's not really used for anything other than generating hypnotic light patterns.
November 25, 2025 at 6:50 PM
Everyone now has access to a supercomputer in their pocket but it's not really used for anything other than generating hypnotic light patterns.
Nations are groups of people w/ coherent beliefs about their social & economic relations. Somewhat surprisingly the internet has convinced people that this is no longer true.
November 25, 2025 at 6:03 PM
Nations are groups of people w/ coherent beliefs about their social & economic relations. Somewhat surprisingly the internet has convinced people that this is no longer true.
There is no particular reason that physical theories must be restricted to considerations of particular completions of the rationals like the real or complex numbers. Similar to how mathematicians eventually realized that there was nothing special about Euclidean spaces.
November 24, 2025 at 11:16 PM
There is no particular reason that physical theories must be restricted to considerations of particular completions of the rationals like the real or complex numbers. Similar to how mathematicians eventually realized that there was nothing special about Euclidean spaces.
Programs/algorithms can be considered to be parametrized transition graphs where the transitions of the graph for each input are essentially what one gets after compiling the program to be executable on some computer. Generally, no one knows ahead of time what the transitions will look like.
November 24, 2025 at 4:58 AM
Programs/algorithms can be considered to be parametrized transition graphs where the transitions of the graph for each input are essentially what one gets after compiling the program to be executable on some computer. Generally, no one knows ahead of time what the transitions will look like.
Intuitionistic logic is claimed to be "constructive" but that's an oversimplification. The foundations of synthetic differential geometry use objects which do not have "effective" inequality relations, meaning it is not possible to tell for any given x, y whether x = y or x ≠ y.
November 23, 2025 at 6:37 AM
Intuitionistic logic is claimed to be "constructive" but that's an oversimplification. The foundations of synthetic differential geometry use objects which do not have "effective" inequality relations, meaning it is not possible to tell for any given x, y whether x = y or x ≠ y.
The site of Weil algebras with the standard subcanonical topology is a sufficient foundation for differential geometry. It's too bad AI researchers are still clueless about the foundations of their own field b/c it is obvious all of their constructions can be carried out in the smooth topos.
November 21, 2025 at 9:33 PM
The site of Weil algebras with the standard subcanonical topology is a sufficient foundation for differential geometry. It's too bad AI researchers are still clueless about the foundations of their own field b/c it is obvious all of their constructions can be carried out in the smooth topos.