Artifice @ArtificeNotes

Explore the Reality. Everywhere Joined November 2024

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Artifice @ArtificeNotes

3 hours ago

@ARIKAHENRY Adjacent to this, if one treats their mind as a precious resource, how does committing attention to stuff with no importance (internet slope) devalue the important stuff?

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10% of the population holds 90% of the polynomial understanding. Inside the 10%, 1% hold 81% of the power law understanding. If the the quote tweets continue to infinity it becomes exponential understanding.

Danielle Fong 🔆 @DanielleFong

20 hours ago

even inside of the 10%, 81% of the total power law understanding is held inside the 1%

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Artifice @ArtificeNotes

4 hours ago

@WesRoth Seems biased.

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Artifice @ArtificeNotes

7 hours ago

Taken to the extreme, one might consider installing mass drivers on the moon.

Beff (e/acc) @beffjezos

17 hours ago

The thing about Elon is he is often not the very first in a space bur he always frontloads solving the mass production challenges and then has an unbeatable ramp that always wins asymptotically and crushes competition

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Artifice @ArtificeNotes

7 hours ago

@WesRoth

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Artifice @ArtificeNotes

7 hours ago

@elonmusk Most likely outcome is Dems let Musk do his thing so they can take credit for economic prosperity.

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Artifice @ArtificeNotes

7 hours ago

From my dilettante perspective, I was thinking that what AI does when solving hard math problems is similar to the EML function. Here is Claude’s take: The analogy holds, and eml is a sharp case of it. In eml, every expression becomes a binary tree of identical nodes, with a grammar as simple as S → 1 | eml(S,S). That gives you total generative power and almost no legibility. Ln x is already three nested calls. Run it backward, from data to formula, and exact recovery only worked at shallow tree depths up to 4. Building trees is trivial. Looking at a big one and seeing "oh, that's arctan" is the hard part. I'd refine one piece of your picture. Language models don't work at the eml level. They're trained on human vocabulary, so they chain named lemmas and standard techniques, not raw primitives. So they can use abstractions; what they rarely do is mint new ones. A model may define a helper lemma inside a proof, but it doesn't become a reusable object. The next problem starts from the same vocabulary as the last. That's why machine proofs often read as correct but unidiomatic: the reasoning works, but nothing in it got a name. The deeper reason is that a chain earns a name by recurring. "Group" and "eigenvalue" became concepts because the same structure kept showing up across unrelated problems, and naming it shortened all of them. A model solving one problem in isolation has no cross-problem view in which a pattern can recur. Some of its odd chains may also deserve no name at all: one-off routes that happen to work. The test of a new function is whether it compresses other things, not whether it was clever once. There's a research line aimed at exactly the step you're describing. DreamCoder-style library learning solves a batch of problems, mines the solutions for repeated subprograms, and promotes them to new primitives, which makes later solutions shorter. That is your "condense the chain into a function," made mechanical. It works in narrow domains and hasn't scaled to frontier math. The condensing step is also harder than it looks, not just neglected. By Richardson's theorem, deciding whether an expression built from x, a few constants, arithmetic, sin, exp and abs equals zero is undecidable. So no general algorithm can always tell you that a long chain simplifies to something short. Simplification runs on recognition, and recognition comes from having seen the pattern before. That's the very cross-problem experience the current setup lacks. So in your terms: a proof is a program that runs once, and a concept is a subroutine. AI has become good at the first and is still mostly missing the second. Sources: - [All elementary functions from a single binary operator (arXiv)](arxiv.org/abs/2603.21852)

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Artifice @ArtificeNotes

18 hours ago

@chasedownleads Did you guys wear socks?

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Artifice @ArtificeNotes

18 hours ago

Is X becoming more civil or am I just hanging out with the wrong crowd?

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Artifice @ArtificeNotes

18 hours ago

@NotPolemicist @scs_real My dad could beat up your dad. Just kidding...my dad's dead.

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Artifice @ArtificeNotes

18 hours ago

@DanielleFong This is at least the second thing that is false by at least a smidge. What could it mean?

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Artifice @ArtificeNotes

20 hours ago

@beffjezos @ashebytes Looks kinda dumb. But it seems like a lot of fun.

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Artifice @ArtificeNotes

20 hours ago

@ChrispyLispy @flowersslop @RLParadoXxx That's from inbreeding. I think you proved her point.

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Artifice @ArtificeNotes

21 hours ago

The Janssen effect: in a tall silo full of grain, the pressure on the floor stops rising as you add more grain, unlike water, where it keeps climbing with depth. H. A. Janssen, an engineer in Bremen, measured this in 1895 using wheat in wooden bins. Friction against the walls turns part of each layer's weight sideways, so the walls carry it instead of the floor. Floor pressure levels off toward a ceiling set by the silo's radius and how much friction the walls have, and once the grain is a few diameters deep, adding more mostly loads the walls. The same physics still sits behind modern silo and hopper design codes. It also helps explain why dangerous overloads often happen while the silo is emptying, when the grain shifts and the walls stop holding the load the same way.