Essays – Yuxi on the Wired

Made by GPT, with prompt: 'A shining red five-pointed star on the top left, sending out multiple light rays. It is in the similar style as socialist iconography. In the rest of the image, four candlestick charts overlapping and growing exponentially from the bottom left to the top right. No vignetting. Widest aspect ratio.'.

Structure and Interpretation of the Chinese Economy

China

economics

politics

history

My basic framework for understanding the modern Chinese economy and its growth. Includes brief histories of Chinese, Soviet, and Japanese economy. Framework applied to two case studies on the stock market and the housing market.

2025-06-03

61 min

Banner illustration for an essay on the computational complexity of diffusion models.

Perfect diffusion is TC⁰ – Bad diffusion is Turing-complete

math

fun

An application of computational complexity theory to diffusion language models. Unlikely to be useful for anything, but it is cute!

2025-04-17

33 min

A symbolic representation of the Cyc project. The vanishing point covered by mist represents the project that keeps growing without ever reaching completion, a destination that is a mirage. The rows of pyramids make up a larger pyramid, due to perspective. This creates the sense of a recursive pyramid, a hierarchy of hierarchies, representing the hierarchy of microtheories in Cyc's ontology. The pyramid is also a monument to the dead, of vast ambitions that failed to secure their design purposes. For Egyptian pyramids, the purpose was a good afterlife. For Cyc, the purpose was AGI.
A one-point perspective image of a path towards infinity, banked by two rows of pyramids. The pyramids are stepped pyramids made of concrete. The path fades into a distant mist. The point of view is above the tops of the pyramids. Monochromatic photo. Created by GPT-4o.

Cyc

scaling

history

After 40 years, 30 million rules, 200 million dollars, 2000 person-years, and many promises, Cyc has failed to reach intellectual maturity, and may never will. Exacerbated by the secrecy and insularity of Cycorp, there remains no evidence of its general intelligence.

2025-04-01

148 min

Statistical Mechanics

math

physics

probability

statistics

biology

How to think like a classical statistical-mechanic, with many examples from gas theory, biology, probability, and information theory. Prerequisites: thermodynamics, calculus, probability, and mathematical maturity.

2024-07-04

118 min

Banner illustration for an essay on the hole argument in general relativity and inverted qualia.

Hole Argument and Inverted Qualia

fun

philosophy

math

physics

biology

The hole argument in general relativity is formally analogous to the inverted qualia problem in philosophy. Like how spacetime points have no existence beyond gauge freedom, qualias have no existence beyond their geometric-functional roles, thus dissolving the hard problem of consciousness.

2024-06-18

69 min

A brutalist sculpture representing classical thermodynamics/neoclassical economics: nonlinear (curved surface) constraint (steel cables tying it down) optimization (the surface struggling to fly towards the sun, touching the solar rays at the closest points). Made in Ideogram V1, with prompt 'A stunning conceptual artwork featuring a white sun casting intense white rays of sunlight, piercing through a curved hyperboloid structure made of concrete. The structure is adorned with straight lines of tight steel cables, creating a strong geometric pattern. The white background and high contrast accentuate the minimalistic vector art style. The piece is reminiscent of Chiaroscuro painting in the style of Piranesi, with a monochrome palette that enhances the drama and depth of the scene., illustration'.

Classical Thermodynamics and Economics

math

physics

philosophy

economics

How to think like a classical thermodynamic-economist, delivered with many illustrations and some sci-fi metaphors. Particular emphasis on what traditional pedagogy gets wrong. Prerequisites: multivariate calculus and mathematical maturity.

2024-05-09

127 min

A brutalist representation of the particle-wave duality of the Hamiltonian--Jacobi equation. The stacked platforms represent the Hamilton principal function according to the field-theoretic wave interpretation, and the steel rebars are the characteristic rays, with balls rolling along them representing the particle interpretation. Made in Ideogram V1 with the following prompt: 'A brutalist terraced mountain made of concrete and steel rebar. There are ripples parallel to the ground. The steel rebars go downhill, and many marbles are rolling down along the steel rebars. White background. High contrast, grayscale, black-and-white minimalistic, in the flat style of vector svg art, conceptual art'

Analytical Mechanics

math

physics

philosophy

What every graduate student should know about analytical mechanics, delivered with economic style and many illustrations. Particular focus on particle-wave duality and old quantum theory. Prerequisites: multivariate calculus and mathematical maturity.

2024-05-04

186 min

A metaphor for real-space renormalization, where the building on the left is coarse-grained to the building on right. The facade of a wide brutalist architecture. On the left, the windows are small and the floors are close together. On the right, the windows are large and the floors are wide apart. High contrast, monochromatic, minimalistic, in the flat style of vector svg art., illustration, conceptual art.

How to do Renormalization

math

physics

scaling

Survival guide for renormalization (RN) theory. How to do it in real space and frequency space. What it all means. Should have something for everyone, from mathematicians to physicists to outsiders, from serious series to pretty pictures. Intended audience: those with two years of undergrad mathematics.

2024-04-11

80 min

Mixture of Experts

scaling

How MoE works, its history, and what it is good for.

2024-01-23

14 min

An abstract representation of the Turing test. On the left is a dark city of obelisks over a bright background, and on the right is the same thing, mirrored and inverted, but with subtle differences due to the randomness of the art generator. It represents the abstract idea of the Turing test: duality, subtle differences, same contours, and complex object made of simple parts. High contrast, monochromatic, minimalistic, in the style of vector svg art.

Predicting AGI by the Turing Test

scaling

math

Minimizing log-perplexity loss is equivalent to maximizing survival length in a Turing test. Assuming compute-loss scaling law, a scaled-up GPT that produces human-like science papers would cost ~200 years of global GDP.

2024-01-20

30 min

Brutalist architecture representing a single perceptron. A hexagonal building in the center representing the unit itself, with multiple arc legs representing the input weights, and antennas projecting off the top representing the output. High contrast, monochromatic, minimalistic, in the style of vector svg art.

The Perceptron Controversy

history

Connectionism died in the 60s from technical limits to scaling, then resurrected in the 80s after backprop allowed scaling. The Minsky–Papert anti-scaling hypothesis explained, psychoanalyzed, and buried.

2024-01-01

114 min

Stylized illustration of a computational graph, with gibberish text that resemble vector calculus, thick and thin lines representing the flow of numbers in the graph. In the center of the vaguely octagonal graph is a letter D, D for derivative. High contrast, monochromatic, minimalistic, in the style of vector svg art.

The Backstory of Backpropagation

math

physics

history

Why backprop was resisted for 20 years: assumption of discretely spiking neurons, goal of synthesizing Boolean logic, fear of local optima, and bad luck. Werbos has the best claim for invention.

2023-12-26

64 min