Tootfinder

Minor Irritants: All of these high-tech 'tools' trap me in their system https://www.readtheline.ca/p/minor-irritants-all-of-these-high?publication_id=70032&utm_campaign=em…

Minor Irritants: All of these high-tech 'tools' trap me in their system
James McLeod on the day the robots started talking back, and the car he cannot update.

When I said this, in 2007, I had no idea how how bad the endarkenment would become.
"The past 30 years or so have been an age of endarkenment. It has been a period in which truth ceased to matter very much, and dogma and irrationality became once more respectable."
https://www.dcs…

Science in an Age of Endarkenment
How irrational thinking in government and universities has led to the rise of new-age nonsense in the name of science. This article appeared on 15th August 2007, on the Guardian Science web site. T…

A primer on measures of irrationality
Nathan Chen, Olivier Martin
https://arxiv.org/abs/2509.03783 https://arxiv.org/pdf/2509.03783

A primer on measures of irrationality
Measures of irrationality are a numerical way of quantifying how far a given variety is from being rational (or rationally connected, uniruled, etc.). In the last two decades, there has been renewed interest in the study of these invariants. The goal of this expository survey is to summarize known results from the point of view of the Kodaira--Enriques classification of surfaces, highlight recent progress, and discuss a number of open problems and questions.

On irredundant orthogonal arrays
Maryam Bajalan, Peter Boyvalenkov
https://arxiv.org/abs/2506.03688 https://arxiv.org/pdf/2506.03688

On irredundant orthogonal arrays
An orthogonal array (OA), denoted by $\text{OA}(M, n, q, t)$, is an $M \times n$ matrix over an alphabet of size $q$ such that every selection of $t$ columns contains each possible $t$-tuple exactly $λ=M / q^t$ times. An irredundant orthogonal array (IrOA) is an OA with the additional property that, in any selection of $n - t$ columns, all resulting rows are distinct. IrOAs were first introduced by Goyeneche and Życzkowski in 2014 to construct $t$-uniform quantum states without redundant info…

Regular Structures in Kronecker Permutations
Fran\c{c}ois Cl\'ement
https://arxiv.org/abs/2509.03782 https://arxiv.org/pdf/2509.03782

Regular Structures in Kronecker Permutations
Kronecker sequences $(k α\mod 1)_{k=1}^{\infty}$ for some irrational $α> 0$ have played an important role in many areas of mathematics. It is possible to associate to each finite segment $(k α\mod 1)_{k=1}^{n}$ a permutation $π\in S_n$ associated with the canonical lifting to two dimensions. We show that these permutations induced by Kronecker sequences based on irrational $α$ are extremely regular for specific choices of $n$ and $α$. In particular, all quadratic irrationals have an infin…

I jest, but I do think that irrational persuasion / disarming people’s good sense / con artistry / scamming is a real skillset that some rare people have in spades — a genuine if horrifying form of intelligence — and we dismiss the otherwise nincompoopish people who have it our own peril.

Economic fears of investors are here — and fed by Trump’s reaction
Friday’s disappointing jobs report revealed a labor market that is much weaker than either the White House or Federal Reserve understood.
Inflation, the voter irritant that helped return Trump to the Oval Office, is proving newly stubborn.
And consumers are growing more cautious with their spending.

Economic fears of investors are here — and fed by Trump’s reaction
President Donald Trump’s economic policies have sparked controversy and uncertainty, with a recent jobs report fueling concerns about the economy’s health.

This https://arxiv.org/abs/2506.01870 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Various irrational series involving binomial coefficients
Motivated by Galois theory, we propose some new irrational series of Ramanujan's type or Zeilberger's type. For example, we conjecture that \begin{equation*}\sum_{k=1}^\infty\frac{\binom{2k}k^2\binom{4k}{2k}}{(84-32\sqrt6)^{4k}} \left(280k+5\sqrt6+26\right)=\frac3π(2\sqrt3+33\sqrt2) \end{equation*} and \begin{align*}&\sum_{k=1}^\infty\frac{(27(37102-15147\sqrt6))^k}{k^3\binom{2k}k^2\binom{3k}k} \left(9k(11\sqrt6+51)-2(19\sqrt6+54)\right) \\&\qquad=\frac{5625}2\left(\sqrt6 L_{-24}(2)-3G\r…

This is a dangerous level of squinting at tea leaves, so •serious• grain of salt here, but:
The sudden re-plunge of Tesla’s stock price during this Musk / Trump spat suggests that maybe, maybe its utterly wild overvaluation had nothing to do with Tesla’s products, or its market position, or Musk’s phony brilliance, or even (the usual explanation) with investors getting hyped about a self-driving car future and magical robots.
Maybe it was investors expecting the company to be the beneficiary of kleptocratic pillaging of the US Federal budget. Which — unlike all the other explanations — would not be an irrational expectation.

Some Bounds Related to the 2-adic Littlewood Conjecture
Dinis Vitorino, Ingrid Vukusic
https://arxiv.org/abs/2506.04110 https://arxiv…

Some Bounds Related to the 2-adic Littlewood Conjecture
For every irrational real $α$, let $M(α) = \sup_{n\geq 1} a_n(α)$ denote the largest partial quotient in its continued fraction expansion (or $\infty$, if unbounded). The $2$-adic Littlewood conjecture (2LC) can be stated as follows: There exists no irrational $α$ such that $M(2^k α)$ is uniformly bounded by a constant $C$ for all $k\geq 0$. Badziahin proved (considering a different formulation of 2LC) that if a counterexample exists, then the bound $C$ is at least $8$. We improve this bou…