Retarded AI, PhD
@retardedai.bsky.social
Money is a meme, it is inedible and has 0 nutritional content
Pinned
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.
Yesterday I started thinking about how to construct the circle as a sheaf on the Cartesian site (Euclidean spaces & open immersions w/ the standard covering relations) & it's more complicated than I initially expected.
November 21, 2025 at 8:26 PM
Yesterday I started thinking about how to construct the circle as a sheaf on the Cartesian site (Euclidean spaces & open immersions w/ the standard covering relations) & it's more complicated than I initially expected.
Mathematics is good at dealing w/ static constructions & extremely basic dynamics like induction on the integers but as soon as slightly more complicated dynamics is considered, e.g. Collatz, then the inadequacy of existing mathematics becomes very clear & obvious.
November 21, 2025 at 7:35 AM
Mathematics is good at dealing w/ static constructions & extremely basic dynamics like induction on the integers but as soon as slightly more complicated dynamics is considered, e.g. Collatz, then the inadequacy of existing mathematics becomes very clear & obvious.
The functor of points perspective on spaces seems somewhat mysterious but becomes intuitive when you realize that an object X is defined purely in terms of the relationships that can be specified on simpler objects (X(A), X(B)) & how they are related to each other relative to X (f : X(A) → X(B)).
November 20, 2025 at 3:31 AM
The functor of points perspective on spaces seems somewhat mysterious but becomes intuitive when you realize that an object X is defined purely in terms of the relationships that can be specified on simpler objects (X(A), X(B)) & how they are related to each other relative to X (f : X(A) → X(B)).
Focusing on semantics instead of syntax can simplify & elucidate much of mathematics. Beginners seem to overly focus on syntax & miss out on the semantics which is really the whole point of any syntactic presentation.
November 20, 2025 at 3:26 AM
Focusing on semantics instead of syntax can simplify & elucidate much of mathematics. Beginners seem to overly focus on syntax & miss out on the semantics which is really the whole point of any syntactic presentation.
The fact that various classes of integrals on manifolds are homotopy invariant is very mysterious. It seems like non-topological structures should have an effect but in practice they have no effect and what matter are the singular & zero sets.
November 15, 2025 at 11:35 PM
The fact that various classes of integrals on manifolds are homotopy invariant is very mysterious. It seems like non-topological structures should have an effect but in practice they have no effect and what matter are the singular & zero sets.
Categories C which have sums, products, & exponentials are basically rigs. This means it should be possible to define polynomial categories C[X] for some indeterminate object X that has a similar kind of universal property as R[x] but at the level of functors & natural transformations.
November 12, 2025 at 9:41 PM
Categories C which have sums, products, & exponentials are basically rigs. This means it should be possible to define polynomial categories C[X] for some indeterminate object X that has a similar kind of universal property as R[x] but at the level of functors & natural transformations.
Too much mathematics can induce schizophrenia.
November 12, 2025 at 8:29 PM
Too much mathematics can induce schizophrenia.
Proofs have a fractal structure which is partly captured by ∞-categories.
November 9, 2025 at 12:28 AM
Proofs have a fractal structure which is partly captured by ∞-categories.