Tchaikovsky’s 18 Morceaux (Op. 72) were his last works for solo piano, completed April 1893 (Tchai passed away Nov 6 1893, his last work is the Symphony Pathetique, which is Op. 74). He thought himself that this was kinda doing “homework” composing these pieces: I’ve been performing my duties very punctiliously, and each day a musical offspring is born. However, these offspring are very much immature and insubstantial; I have no inclination whatsoever to create them, and do so only for the money. I’m only trying to ensure that they don’t turn out too badly. ...

More drama! Recently, Apple and Tencent reached a deal: WeChat Mini-Programs on iOS must now pay a unified 15% “Apple tax” on virtual goods. Basically, Apple gains a 30% commission rate for digital good sold on its ios platform (15% for <1-million business). In China, more than 92% people use WeChat. WeChat is not only a chat app but essentially a mega app where you can do EVERYTHING in it because of its mini program design — merchants can built their app API within WeChat and user (used to be able to) access service — and pay — indirectly using WeChat pay hence bypassing the Apple Commission. ...

Disclaimer: This post provides a factual summary and commentary on publicly available analysis. It does not constitute legal advice, institutional representation, or formal evaluation. All interpretations are solely my own. Drama! Here’s a brilliant article publish in WeChat platform written by Fudan University’s undergrads. Now this is what our future economist should look like: 168的后悔药，复旦年销多少份？基于教务数据的期中退课规模、结构与影响因素分析 The 168-Yuan Regret Pill — How Many Doses Does Fudan Sell Each Year? An Analysis of the Scale, Structure, and Determinants of Midterm Course Withdrawals Based on Academic Affairs Data ...

Here’s how to make Hugo PaperMod landing page (the main page) minimalistic, yet fancy. Inspired by Apple Tahoe OS’s liquid glass aesthetic, on top of PaperMod’s minimalistic design, I added (i) round corner for blog post boxes and (ii) interactive color change. In Hugo, aesthetic configs (e.g. page margins, text box colors) are ultimately controlled by CSS. Even better, PaperMod already has a built-in way to add custom CSS without touching the theme files: any CSS one put in assets/css/extended/*.css in the project gets bundled automatically. So, just create one assets/css/extended/margins.css and paste the following CSS configurations (or, DIY yourself): ...

7 weeks into a quarter, I am now allergic to the word “interest rate” “saddle path” and “EIGENVALUES”. This note presents a continuous-time neoclassical growth model, deriving household and firm optimality conditions, characterizing the steady state, and analyzing the resulting saddle-path dynamics. On top of which, per-household productivity $A$ is left out, which makes it extendable. Consider continuous time model $t\in[0, \infty)$. (Representative) Household’s Problem $$ \begin{align} \max_{\lbrace c_t, x_t, k_t\rbrace_{t\ge 0}}& \int_0^\infty e^{-\rho t}U(c_t)\thinspace\text{d}t\cr \text{s.t.}& \ \dot k_t = x_t -\delta k_t, \forall t\cr & \int_0^\infty p_t(c_t + x_t)\thinspace\text{d}t = \int_0^\infty p_t(w_t + v_tk_t)\thinspace\text{d}t \cr&\text{where, } p_t :=\exp{(-\int_0^\infty r_{\tau}\thinspace\text{d}\tau)}. \end{align} $$Now, plug $(2)$ into $(3)$ and do intergration by part on horizon $[0, T]$, we obtain ...

The theoretically optimal way to board passengers onto a plane has been studied by Jason Steffen in his paper Optimal boarding method for airline passengers. The following YouTube video explains the algorithm and also, briefly touches on why it’s not actually implemented. The math is super elegant, the problem is practical, and gives a bit of an economic design insight (that you don’t always get the theoretical perfect design) Reference: Steffen’s papers: ...

I was feeling a bit nostalgic (and hungry) today after the weekly Friday macroeconomic discussion session, that suppose to end 11:20 but stretches all the way towards noon. There happened to be an AI seminar right after, with lunch — I grabbed a sandwich, fully expecting myself to sit in the back, eating my feelings while absorbing some comforting high-level vibes. Instead, it turns out to be one of the most interesting theoretical advances at the forefront of self-supervised learning. ...

I’ve always thought the Chicago Symphony Orchestra has one of the most insane string sections on Earth—versatile, responsive, laser-precise, and somehow still warm. Tonight, concertmaster Robert Chen led the strings in Vivaldi’s Four Seasons, and… they’re good. So good. 😙🤌🏻❤️🎶 The Chicago audience really enjoys standing up! Technically, The Four Seasons is a set of four concertos, but somewhat it works even better without a conductor—especially when Chen is steering the ship. He carried the dual role of leader and soloist like it was nothing. The orchestra was tight down to microscopic detail, the phrasing felt alive. And Chen’s solo lines are GORGEOUS. The kind of sound that makes you forget it’s the 7th week of the quarter and final exams are coming close. ...

OMG: We analyzed 47,000 ChatGPT conversations. Here’s what people really use it for. Washington Post. https://www.washingtonpost.com/technology/2025/11/12/how-people-use-chatgpt-data/ Methodology: The Post downloaded 93,268 conversations from the Internet Archive using a list compiled by online research expert Henk Van Ess. The analysis focused on the 47,000 chat sessions since June 2024 in which English was the primary language, as determined using langdetect. A random sample of 500 conversations in The Post’s corpus was classified by topic using human review, with a margin of error of plus or minus 4.36 percent. A sample of 2,000 conversations, including the initial 500, was classified with AI using methodologies described by OpenAI in its Affective Use and How People Use ChatGPT reports, using gpt-4o and gpt-5, respectively. ...

Mendelssohn himself resisted attempts to interpret the songs too literally, and objected when his friend Marc-André Souchay sought to put words to them to make them literal: “What the music I love expresses to me, is not thought too indefinite to put into words, but on the contrary, too definite”. (Wikipedia) For (popular) piano works, people LOVE discussing about fav recordings: (Talk Classical) Any recommended recordings? I bought Barenboim’s set in the early days of CDs. https://www.talkclassical.com/threads/mendelssohn-songs-without-words.60895/ ...