When the world feels lopsided, try a simple reflex: thank someone. It’s great and it can seriously make your day (both your days, even, possibly)! :))

“Thank you for your effort, and for keeping us safe with your work.” She smiled SO genuinely, probably the most genuine smile I’ve seen in a while. How often we fail to thank the people who quietly keep our surroundings running well. It also smelled like lavender. We should thank more often

This is one direction of the Forcing Conjecture, which was also proven by the og CGW paper: link.springer.com/article/10.1...
If F is forcing, then F is bipartite and has a cycle. The other direction is open, and if you solve it you also solve Sidorenko's conjecture.

The proof extends to C_2k, breaks for odd cycles. Not just the proof doesn't obviously generalize, turns out it can't, because odd cycles plus edge density -> quasirandom is actually false. #nice

The idea is that if one cut were very irregular, it would blow up that error term, contradicting the assumption that the 4-cycle count is close to the random value.

The proof is cute & not seeing a deep conceptual lesson yet: write each edge indicator as p plus an error term g, compute the number of labelled 4-cycles, and show that it equals p^4n^4 plus some error term: 4-cycle count=(what a random graph would give)+(global 4th-power interaction, error term).

(iii) All induced subgraphs have the right frequency (G_n is statistically indistinguishable from G(n,p) under bounded-size subgraph tests).

(iv) My favorite... here you go: the number of labeled 4-cycles is what one sees in G(n,p) up to really small corrections.

The following notions are actually equivalent.

(i) G_n is (p,o(n))-jumbled. Meaning every cut looks like edge-density p, up to a small relative error.
(ii) You have spectral control which forces edges to be well-spread.

Properly: works for G_n a sequence of graphs with edge density p. CGW says “all your favorite definitions of pseudorandom are actually the same thing in *dense* graphs.”

I know I am late to the party on this one, but I'd been avoiding its proof for a while.

If the number of 4-cycles in G is as one would expect in G(n,p), then this is enough to imply that the edges are pseudorandomly distributed in G. (Due to Chung-Graham-Wilson, let's use CGW for that)

Update: This ended up being my favorite Mathias Énard.

Low ceilings, high ceilings; trefoil windows; windowless nooks; a medieval hush; white light, yellow light –– because there is so much diversity every way of reading has its room. It is kind of amazing. Fan-girling.

A relevant footnote: the cellist Corbin Keep @cellocorb.bsky.social has responded to this thread and drawn attention to his work arranging compositions by women composers from across history corbinkeep.bandcamp.com/album/unspea... (social media can still be good sometimes.)

At some point, I dream of creating or perhaps collaborating on a project in a similar spirit, centered on female poets and composers...though so much to learn first before ideas can take shape. For now, I’m taking vocal lessons so I can hopefully sing A chantar properly.

Amazing! I listened to this piece from your album, and it’s beautiful. I look forward to exploring the other pieces and composers from the album. Do you have any ongoing or upcoming projects? It’s helpful that there’s a website for this project of yours.

This is my greatest cultural find of 2025 so far. I heard it on WQED (yes, radio) one day in February. She’s an incredible poet, and there’s a beautifully written blog post with a translation for those of us who don’t understand Occitan: www.noellemcmurtry.com/comtessa-de-...

the tyranny of taste