Tootfinder

The replies to these posts fell into three groups:
1. Cyclists who’ve never had a severe crash involving their head but are happy to wear a helmet
2. Cyclists who’ve had a severe crash involving their head and are happy to wear a helmet because it saved their life
3. Cyclists who’ve never had a severe crash involving their head and are happy •not• to wear a helmet because they insist it doesn’t make a difference
One quadrant is notably absent.

"Every morning, a spider rebuilt its web on my car mirror, only for the wind to destroy it again. Watching that tiny creature taught me something about toxic cycles, misplaced resilience, and the quiet courage it takes to stop rebuilding in the wrong place."
"True resilience isn't about stubbornly withstanding the storm; it's about having the wisdom to find a new foundation."
This piece of writing hits like a gut punch.

What a Spider Taught Me About Resilience and Letting Go
Every morning, a spider rebuilt its web on my car mirror, only for the wind to destroy it again. Watching that tiny creature taught me something about toxic cycles, misplaced resilience, and the quiet courage it takes to stop rebuilding in the wrong place.

Lots of inner city streets could run smoothly at 30kph
https://www.theguardian.com/environment/2025/oct/15/switching-50kmh-speed-limits-to-30kmh-would-protect-cyclists-while-barely-…

Switching 50km/h speed limits to 30km/h would protect cyclists while barely affecting commutes, research finds
One expert says a cyclist hit by a car travelling 50km/h has about a one-in-10 chance of surviving, while at 30km/h it is a nine-in-10 chance

📉 Either too little or too much: Report finds world's water cycles are getting more erratic
#climate

Either too little or too much: Report finds world's water cycles are getting more erratic
The water cycle has become increasingly erratic and extreme, swinging between deluge and drought, according to a new report from the World Meteorological Organization (WMO). It highlights the cascading impacts of too much or too little water on economies and society.

An elementary derivation of 3-cycles for a quadratic map
Arpad Benyi, Ioan Casu
https://arxiv.org/abs/2510.12558 https://arxiv.org/pdf/2510.12558

An elementary derivation of 3-cycles for a quadratic map
We present an elementary derivation of the period-three cycles for the real quadratic map $x\mapsto x^2+c$, a fundamental model in one-dimensional discrete dynamics. Using symmetric polynomials, we obtain a complete algebraic characterization of 3-cycles and determine explicit conditions for their existence and stability, without reliance on computer algebra. Through conjugacy with the logistic map, we recover the classical threshold values of the logistic parameter corresponding to the emergen…

🇺🇦 #NowPlaying on KEXP's #ElSonido
Foudeqush:
🎵 CUCHILLOS
#Foudeqush
https://foudeqush.bandcamp.com/track/cuchillos-prayers
https://open.spotify.com/track/3y8OsvL4IaMqfIVvPXCqQU

Embedding finitely generated free-by-cyclic groups in {finitely generated free}-by-cyclic groups
Marco Linton
https://arxiv.org/abs/2510.10178 https://arxi…

Embedding finitely generated free-by-cyclic groups in {finitely generated free}-by-cyclic groups
We refine Feighn--Handel's results on subgroups of mapping tori of free groups to the special case of free-by-cyclic groups. We use these refinements to show that any finitely generated free-by-cyclic group embeds in a {finitely generated free}-by-cyclic group. When the free-by-cyclic group is hyperbolic, it embeds in a hyperbolic {finitely generated free}-by-cyclic group as a quasi-convex subgroup. Combined with a result of Hagen--Wise, this implies that all hyperbolic free-by-cyclic groups ar…

A look at efforts in Sweden to make its banking systems and payment networks resilient to hybrid warfare attacks; 90% of Sweden's transactions are digital (Evelina Youcefi/Bloomberg)
https://www.bloomberg.com/news/articles/20

Labelled growth rates of $\omega$-categorical structures and applications in choiceless set theory
Bertalan Bodor, Samuel Braunfeld, James E. Hanson
https://arxiv.org/abs/2509.12656

Labelled growth rates of $ω$-categorical structures and applications in choiceless set theory
We study the labelled growth rate of an $ω$-categorical structure $\fa$, i.e., the number of orbits of $Aut(\fa)$ on $n$-tuples of distinct elements, and show that the model-theoretic property of monadic stability yields a gap in the spectrum of allowable labelled growth rates. As a further application, we obtain gap in the spectrum of allowable labelled growth rates in hereditary graph classes, with no a priori assumption of $ω$-categoricity. We also establish a way to translate results abou…