Paul Fabel

Malignant narcissists experience increased paranoia, denial, and rage as death nears. They often externalize these experiences through destruction and abuse of others in an effort to maintain a sense of control.

I suspect all of these wars are in part related to Trump’s awareness of his mortality.

War or Nothing A tale across the years; seven lessons learned from a quarter-century in a war-oriented society, where the greatest crime is any opposition to killing.

Seven lessons learned from a quarter century in a war-oriented society.

It's 2001—the year the movies promised we'd make contact with aliens—and the United States has rather recently been attacked by terrorists who flew passenger planes into buildings.

www.the-reframe.com/war-or-nothi...

Yes, despite pragmatic rarity of checking off conditions.

Metrizability demands monoid of additive non-negative reals.

Origin stories of latter highly nontrivial, done carefully.

First class examples of limits, colimits, and monoid quotients emerge, done with care.

Reusable tools writ large.

Hating the Game The cooperation game, the murder game, and acting in good faith with people you know are acting in bad faith.

Today I wrote about the racist accommodation to the racist response to Bad Bunny's Super Bowl show; the moral hazard of extending good faith to those who act in bad faith; and how alienating white bigots is actually part of the solution, not a part of the problem. www.the-reframe.com/hating-the-g...

For cancellative abelian monoids, a nontrivial quotient map can have trivial kernel.

Map the free monoid F(C) over Cantor space C onto the additive non-negative reals, so that the right-shift map of F(C) represents halving.

Knowledge of the kernel of a quotient map is NOT one stop shopping.

AI is getting good at math, but USING it still feels like looking up the answers in the back of the textbook.

Useful as a sanity check but generally hopeless as one stop shopping for understanding.

Exploring, developing tactics, finding examples and counterexamples, is not replaceable by AI.

Unlike groups, point preimages need NOT all have the same size under monoid epimorphisms.

There is an M_3-->M_2 counterexample with trivial kernel.

Let AAA=A and BB=B, in the domain and codomain.

Map A to B and id to id.

Want to localize your favorite monoid M?

Define all arbitrary quotients of M.

Then show that the quotients of M form a thin category with all joins and meets.

Mod M by the universal group kernel, so that the quotient M1 is cancellative.

Now Mod M1 x M1 by the diagonal.

Substituting x=7 certifies or refutes a random trig identity, armed with a scientific calculator, working in radians.

The finite discrete space F is orderable but most automorphisms h:F-->F are NOT order preserving.

Same holds if we replace F with Cantor space C.

However each order preserving h:C-->C quotients to
h^:[0,1]-->[0,1] preserving the `dyadic rationals'

And vice versa, each h^ lifts to an h.

Opinion | State Terror Has Arrived

Explore this gift article from The New York Times. You can read it for free without a subscription. www.nytimes.com/2026/01/24/o...

Or a first.

Looking forward to it!

the not-so "golden age," one year on Expo, a Swedish antiracist magazine that I contribute to, asked me to write a personal reflection how researching and reporting on the far right has felt during the first year of Donald Trump's return...

I wrote about how fucked up the past year has been as a person who's covered the far right for over a decade and who lives in DC. The guardrails are gone, and everyone knows it.

Everything those of us on this beat warned about happened, and then some. postsfromunderground.ghost.io/the-not-so-g...

A Shining Mausoleum on a Hill Life, death, and the rampage of ICE.

New article! On life, death, and the rampage of ICE.
sarahkendzior.substack.com/p/a-shining-...

Testing our sanity

María Corina Machado says she presented Trump with her Nobel peace prize medal

5-panel comic showing what appears to be an athlete accepting a gold medal and obnoxiously celebrating. it isn’t until the final panel that we see he’s on the last place podium and celebrating a fake win.

😒

Breaking Bad Redux.

In a talk called "A reintroduction to proofs"

emilyriehl.github.io/files/reintr...

I've speculated about teaching an undergraduate level introduction to proofs course but using dependent type theory as the implicit formal system in place of set theory and first order logic.

YouTube video by Sheafification of G Some things are MORE EQUAL than others??

New Sheafification. Holidays will be ok.

www.youtube.com/watch?v=GX5C...

nonexample ,Update from 10 months ago. Deepseek just nailed the same question.

Does there exist an infinite abelian group such that each proper subgroup is finite?

(10 months ago) Hey Deepseek! Does there exist an infinite abelian group such that each proper subgroup is finite?

Deepseek. No...

In reality:

For an example consider a colimit indexed by the natural numbers, of cyclic groups of order 2^n, under monomorphic bonding maps. (Prufer group).

Strong Floor, No Ceiling, Can't Leak!

Dibs.

Strong Floor, No Ceiling, Can't Leak!

S: In a Manger (Ippolitov-Ivanov)( Civ V)
A: Fairytale of New York (The Pogues)
B: Run Rudolph Run (Chuck Berry)
C: Please Come Home for Christmas (Don Henley)
D: Santa Claus is Coming to Town (Bruce Springsteen)
F: I saw Mommy Kissing Santa Claus

Watch it cold.

Lots to like, the music alone is enough.

This looks great! Nice collection of topics and you can't beat the price.

Lol. Sorry for not seeing the joke.