Technical Writing

Neural networks as compositions of differentiable layers, gradient descent and backpropagation, embeddings as learned geometry of meaning, the transformer architecture and self-attention, the full training pipeline (pre-training, fine-tuning, RLHF), scaling laws, and why prediction is compression and compression requires understanding.

Framebuffer memory layout, GPU architecture and scanout, kernel graphics drivers, display servers and compositors, the GPU rendering pipeline and shaders, and every level of graphics API from raw framebuffer access through Vulkan, OpenGL, and Canvas.

From ENIAC's 500 FLOPS in 1946 to exascale computing, a survey of every major class of computing hardware—CPUs, GPUs, NPUs/TPUs, ASICs, and FPGAs—and the fundamental constraints that shape each.

From keypress through USB interrupt and OS event handling, network stack (DNS, TCP, TLS), datacenter routing and query processing, to browser rendering—dense with technical detail at every stage.

Linux powers most of cloud infrastructure. OpenSSL secures HTTPS. PostgreSQL stores most data. This article surveys the critical layers, the funding crisis, and the risks of depending on unpaid infrastructure.

Immutable objects (blobs, trees, commits), content-addressed storage via SHA-1, and a directed acyclic graph of commits—how Git manages branching, merging, and distributed collaboration.

BIOS/UEFI firmware, GRUB bootloader, kernel initialization, initramfs, and systemd—each stage of the boot sequence, with modern boot optimizations.

Both protocols are electromagnetic waves at 2.4 GHz, governed by Maxwell’s equations and constrained by Shannon’s theorem. GFSK and frequency hopping for Bluetooth, OFDM and MIMO for WiFi—every design difference traced back to tradeoffs between bandwidth, power, and complexity.

Types, control flow, structs and methods, implicit interfaces, goroutines and channels, generics—and what Go leaves out on purpose, and why.

Dynamic typing, data structures, comprehensions and generators, decorators, classes with dunder methods—and what Python trades away for its elegance.

Dynamic typing, closures, the event loop, promises and async/await, classes, modules—and JavaScript’s infamous quirks.

Pointers and pointer arithmetic, dynamic memory allocation, the compilation model, undefined behavior—and why C remains essential after 50 years.

Vectorized operations, data frames, the apply family, the tidyverse—a language built by statisticians for statisticians.

Newton's laws, Maxwell's equations, general relativity, quantum mechanics—all consequences of requiring the action to be stationary. The Lagrangian, the Euler–Lagrange equations, worked examples including the double pendulum, and Noether's theorem.

Bisection and Newton's method for root finding, Gaussian elimination, Jacobi/Gauss-Seidel/SOR, and Euler through Runge-Kutta 4—each method with the mathematical idea, convergence properties, and working Python implementations.

P vs NP, the Riemann Hypothesis, Yang–Mills and the mass gap, Navier–Stokes, the Hodge Conjecture, Birch and Swinnerton-Dyer, and the Poincaré Conjecture—formal statements, intuition, and the state of the art.

Orthogonal projection as the core engine, the algorithm with full proofs, the connection to QR factorization, and applications across least squares, quantum mechanics, and statistics.

Epsilon-delta limits versus infinitesimals, and how Abraham Robinson proved infinitesimals rigorous through non-standard analysis and hyperreal numbers.

Peano axioms, Euclidean geometry, and set theory—how axiomatic thinking extends from mathematics to law, science, and reasoning generally.

Peano arithmetic, Euclid's postulates, ZFC set theory, Kolmogorov's probability axioms, group axioms, and worked proofs—then the philosophical question of what an axiom actually is.

Seven proposed axioms—least action, the quantum postulate, Poincaré invariance, the equivalence principle, gauge invariance—and what they can and cannot explain.

From Planck's quantum hypothesis through Schrödinger’s equation to the measurement problem, decoherence, and the major interpretations (Copenhagen, Many-Worlds, Pilot Wave), plus Bell's theorem and quantum computing applications.

The formal statement, the history from de Moivre through Lindeberg-Feller, three angles on why it works, when it fails, and applications across statistics and machine learning. Links through to the interactive CLT demo elsewhere on this site.

Kolmogorov's axioms, the frequentist/Bayesian/formalist interpretations, the quantum measurement problem, Shannon's information theory, and Kolmogorov complexity—probability, information, and computation as one problem.

Risk-neutral pricing, the Greeks, implied vs. realized volatility, where the model breaks down, and five systematic strategies for exploiting mispriced options.

The transform's key properties, worked ODE examples, the s-plane and pole locations, transfer functions, and exponentials as eigenfunctions of LTI systems.

The major carriers, the world's busiest ports, how shipping actually works, and why maritime is far cheaper than air freight. Includes an interactive map of major routes and chokepoints.

Why currencies have different values, how the market physically operates, key historical events (Bretton Woods, Soros breaking the pound), the carry trade, and how exchange rates affect ordinary life.

Spot markets, forward contracts, grid operators, and speculators—how modern economies coordinate complex energy systems in real time.