R.Narkaj

Sometime I think; and sometime I am.

[Ulugbek S. Kamilov @prof_kamilov]

PhD teaches you to spend several years working on a problem that almost no one else in the world considers a problem.

It’s either excellent training for independent thinking or a very expensive way to acquire a new hobby.

[R.Narkaj @NarkajR]

@ALinzi41529 @nasqret Hi, you are right there is no tweet about Galois... But I have already a research that you might be interested. Classify G(n,m,k) for every admisible triple (n,m,k). I sent you an email. Grazie mille del tuo tempo .

[R.Narkaj @NarkajR]

@nasqret @ALinzi41529 Hi, from Italy. I m working on this project based on your early tweet about Galois. Can I send you my project on your email? Thank you

[AppleMath @AppleMath7]

I think arXiv should be on hold for a while until further guidelines and do not accept any papers. This is ruining credibility and integrity and indeed many highly respected fields.

[R.Narkaj @NarkajR]

@NHWK Did they use llm without saying It? :)

[R.Narkaj @NarkajR]

@Vieta__jumping Ok then. Your email please. Grazie

[R.Narkaj @NarkajR]

@Vieta__jumping https://t.co/wgOr33alOL this Is my Roadmap. Let me know what do you think. Thank you

[R.Narkaj @NarkajR]

@octonion @royvanrijn Amazing. Are you still working on Frankl congeture? It would be nice to have a chat about It because in working on It. Thank you

[unwrapped ideas @UnwrappedIdea]

The statistical connection graph formed from training data tends to fall into probabilistically selected categories.
That tendency constitutes the essential nature of the “logicality” current transformer-attention LLMs can possess.

Post-training then overlays a frame against contradictions and logical violations onto this probability landscape; that overlay is what functions as reinforced logic.
As a result, when knowledge is retrieved and connected, this statistical form of logicality inevitably submerges even the propagation of errors—until the system reaches a scaling regime in which those errors become rare and far less visible.

Until that point, it remains impossible, within a single generation and without external re-verification, to reliably distinguish error from non-error.

It may eventually become nearly indistinguishable from complete logic across most coverage areas.
Yet the timing will differ by domain, especially in the detailed regions that matter most.

Perfection does not arrive everywhere at once with a sudden flourish; it spreads the way ink blots across paper.

Users of LLMs therefore need to understand this structure.
That understanding supplies a necessary ground for the claim that the systematic teaching of AI use must be introduced across the sciences and the academic disciplines.

[R.Narkaj @NarkajR]

@octonion Perfetto! Thank you

[R.Narkaj @NarkajR]

The hype of doing real math with AI. A new way to waste time and tokens.

[Sridhar Ramesh @RadishHarmers]

Hype from the hype man. Important context below:

[R.Narkaj @NarkajR]

@__paleologo Thefunpartisthat the move set-swap two symbols inthecandidate cipher-turns the problem into a Markov chain on a huge permutation-like space.Thequestion is:when dolocal moves explore the relevant space efficiently,and can we prove a mixing bound rather than just observe success?

[R.Narkaj @NarkajR]

@nitalikmeta Non è un’analisi comparativa, ma una lettura unilaterale.

[R.Narkaj @NarkajR]

@nitalikmeta @granmartello Critica il linguaggio politico…
ma usa linguaggio ancora più astratto per spiegare la realtà.

[R.Narkaj @NarkajR]

@ValerioCapraro @ylecun

[R.Narkaj @NarkajR]

Too little too late

[James Tate @JamesTate121]

ALARM bells people. 🚨🚨🚨

Neoconservative David Brooks wrote this in an OpEd in the NY Times,
"Trumpism… is primarily about the acquisition of power — power for its own sake. It is a multifront assault to make the earth a playground for ruthless men, so of course any institutions that might restrain power must be weakened or destroyed. Trumpism is about ego, appetite and acquisitiveness and is driven by a primal aversion to the higher elements of the human spirit — learning, compassion, scientific wonder, the pursuit of justice. …
What is happening now is not normal politics. We’re seeing an assault on the fundamental institutions of our civic life, things we should all swear loyalty to — Democrat, independent or Republican.
It’s time for a comprehensive national civic uprising. It’s time for Americans in universities, law, business, nonprofits and the scientific community, and civil servants and beyond to form one coordinated mass movement. Trump is about power. The only way he’s going to be stopped is if he’s confronted by some movement that possesses rival power. …
I’m really not a movement guy. I don’t naturally march in demonstrations or attend rallies that I’m not covering as a journalist. But this is what America needs right now."

[Jesús Fernández-Villaverde @JesusFerna7026]

A guide for students of economics: Ten statements that demonstrate that someone does not understand modern economics or what an equilibrium is, and that you can safely ignore everything else they say.

1. “Equilibrium means the economy is stable or at rest.”

Many assume that an equilibrium is a peaceful state with no forces at play. Instead, an equilibrium is just an arrangement of actions and expectations over time that are mutually consistent. It can be locally unstable, explosive, or fragile. Nothing in the definition of equilibrium implies stability.

2. “Equilibrium implies optimality or social efficiency.”

Equilibrium is often conflated with efficiency, but equilibrium merely reflects decentralized consistency, not welfare maximization. Market power, externalities, incomplete markets, nominal rigidities, and frictions routinely produce inefficient equilibria. I often teach a first-year macro graduate course, and not a single one of the equilibria I define is efficient.

3. “Equilibrium is a unique outcome.”

Many often expect models to have one equilibrium. In reality, multiple equilibria arise naturally in dynamic, strategic, and incomplete-market environments. Models of coordination failures, self-fulfilling expectations, bubbles, overlapping generations, and liquidity traps all hinge on the existence of equilibrium multiplicity.

4. “Equilibrium requires perfect foresight or perfect information.”

Equilibrium does not assume agents know the future. In fact, equilibria are often stochastic. The definition of equilibrium only requires that beliefs are consistent with the (perceived) stochastic laws of motion implied by the model. Bayesian learning, noisy signals, ambiguity, and subjective uncertainty all fit well within an equilibrium framework, provided beliefs converge to an internally consistent (but possibly incorrect) distribution.

Bonus point: equilibria are compatible with agents having diverging beliefs that never converge to a single Dirac distribution.

5. “Real economies are rarely in equilibrium, so the concept is unrealistic.”

Equilibrium is not meant to describe the daily state of the world. It is a conceptual device used to understand the outcome of our models under the assumptions we make. Also, see point 1 above.

6. “Equilibrium requires agents to be fully rational in a psychological sense.”

Equilibrium only assumes internal consistency: agents optimize given preferences and constraints. It does not assume realism about human cognition. We can and do define equilibria in models with behavioral biases, bounded rationality, inattention, or rule-of-thumb behavior. We only need to ensure that the resulting actions and beliefs are mutually compatible.

7. “Equilibrium eliminates dynamics or learning.”

Equilibrium is sometimes misinterpreted as a static state in which nothing evolves. In fact, many equilibria are sequences of probability distributions over states driven by shocks, policy rules, and endogenous responses. Learning dynamics (Bayesian updating, adaptive rules, experience-based expectations) can occur within equilibrium if the evolution of beliefs is self-consistent.

8. “Equilibrium renders expectations unimportant.”

A common misconception is that equilibrium mechanically determines outcomes. In reality, expectations are often central: they determine investment, consumption, asset prices, and policy responses. Many equilibria differ only in their expectations. This is why communication, credibility, and forward guidance matter even in fully rational models.

9. “Equilibrium excludes policy intervention.”

Some interpret equilibrium as a laissez-faire concept. In fact, equilibrium analysis is the foundation of modern policy evaluation. Fiscal, monetary, and regulatory interventions work through equilibrium responses (prices, wages, interest rates, quantities) and must satisfy equilibrium conditions to be credible. Equilibrium is a tool for policy design, not a barrier to it.

10. “Equilibriums…”

Aequilibrium is a Latin neuter noun of the second declension, which forms a nominative plural in “a”. It is composed of aequus (equal; the same root as equality or equity) and libra (balance or scales or the name of several currencies over history).

A final thought: “equilibrium” is a term of art. Its meaning in economics differs from its use in the natural sciences or in everyday language. Terms of art are ubiquitous across academic disciplines, and the first act of intellectual diligence when one starts studying a discipline is to learn what they mean.

[R.Narkaj @NarkajR]

Naturalmente, vale anche per l'Europa. https://t.co/rxqQbJzEHU

[Sahil Lavingia @shl]

My experience working as a software engineer for the Department of Veterans Affairs, on behalf of DOGE.

https://t.co/zmvNNgrAW0