Yesterday’s pre–intermission piece was Haydn’s Symphony No. 93, which reminded me of something funny: Beethoven wrote 9 symphonies, Mozart around 50, Tchaikovsky 6… and Haydn wrote 104. Composers by number of symphonies by inclassicalmusic Haydn’s “London Symphonies” (Nos. 93–104) were written for his two London trips in the 1790s. The London audience loved Haydn, his music during that time was all charmingly lovely. No. 93 is especially fun — elegant, bright, and just cheeky enough. My friend was like, “I can totally picture people in wigs dancing minuets.” ...

Tonight Honeck conducted the CSO in Mozart’s Requiem: CSO and the Chicago Symphony Chorus Honeck’s arrangement wove together Mozart’s Requiem (K.626) with several of his earlier funeral works, linked by backstage Gregorian chants: Special Mozart Requiem program from CSO’s official program book. It clarifies the interesting history untangle the complicated authorship of Requiem. CSO’s really got amazing people writing program notes. ...

The luminous Serenade for Strings (Op.48) by Tchaikovsky pairs beautifully with the choreography of one of his biggest fan, George Balanchine. Near the end of the first movement, as the sweeping orchestral line descends, the corps marches in orderly formation offstage, leaving the solo ballerina alone—poised in stillness—until her partner moving in counterpoint towards her. This moment (exactly 10:00 below) always gives me goosebumps:

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 $$ \begin{align} \max_{\lbrace c_t, x_t, k_t\rbrace_{t\ge 0}}& \int_0^\infty e^{-\rho t}U(c_t)\thinspace\text{d}t\cr \text{s.t.}& \ \dot k_t = x_t -\delta k_t, \forall t\cr & \int_0^\infty p_t(c_t + x_t)\thinspace\text{d}t = \int_0^\infty p_t(w_t + v_tk_t)\thinspace\text{d}t \cr&\text{where, } p_t :=\exp{(-\int_0^\infty r_{\tau}\thinspace\text{d}\tau)}. \end{align} $$ ...

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. ...