function composition

3Blue1Brown visualizes the Riemann zeta function and the analytic continuation that extends it beyond where its series converges, building toward the Riemann hypothesis.

Robert Miles explains reward modelling, in which an AI learns what humans want from their preference comparisons instead of a hand-written reward function. He walks through the 2017 paper on deep reinforcement learning from human preferences.

Martin Donald explains the Wave Function Collapse algorithm using Sudoku-like constraint solving and shows how he implemented it with Blender and Godot. It links demos and reference articles.

Mathologer examines the infamous Numberphile claim that 1+2+3+... equals -1/12, explaining what is wrong with the calculation and how it connects to real math like the zeta function and analytic continuation.

A step-by-step animated explanation of how SHA-256 works, from padding and message schedule to the compression function and final hash, with source code for the animations.

Kaze Emanuar searches for the best sine approximation for the Nintendo 64, comparing the lookup tables in Mario 64 and Ocarina of Time with polynomial alternatives. It walks through numerics and 3rd, 4th and 5th order approximations.

An animated visualization of basic quantum mechanics using a free particle, with simulations based on the actual equations. It covers waves, particles, and how measurement collapses the wavefunction.

An Every Frame a Painting video essay on how Akira Kurosawa used movement, weather and composition to tell stories. It draws on clips and interviews with other filmmakers.

3Blue1Brown's second neural network chapter explains cost functions and gradient descent, showing how a network learns by minimizing error during training.

Tom Scott features Kurtis Baute inside a sealed homemade biodome as carbon dioxide builds up, showing how stale air with elevated CO2 affects cognitive function. Sources include studies on CO2 and cognitive scores.

A short Art of the Problem clip explaining Diffie-Hellman key exchange, using a paint mixing analogy for one-way functions and touching on modular arithmetic and discrete logarithms.

A short How to ADHD explainer, featuring Brendan Mahan, on why simple tasks can feel impossible for people with ADHD. It introduces the 'wall of awful', a pile of past failures, shame and anxiety that builds up in front of a task and blocks starting it.

Mathologer examines how identities like 1+2+3+... = -1/12 arise in Ramanujan's work, starting from his 1913 letter to Hardy. The video explains the rules for summing infinite series and why such results are meaningful but not naive sums.

Tom 7 (suckerpinch) delivers a long, comedic digression on gradient descent and floating-point imprecision. He shows how rounding behavior can supply the nonlinearity needed to build a neural network.

Veritasium explains the many-worlds interpretation of quantum mechanics, drawing heavily on Sean Carroll's book. It walks through the Schrodinger equation and why wave collapse may be unnecessary if the universe keeps splitting.

Vsauce's roughly 24 minute explainer on the Banach-Tarski paradox, building from infinity and set theory to the decomposition of a sphere into pieces that form two spheres.

3Blue1Brown introduces Fourier series, from the heat equation to drawing arbitrary shapes with rotating circles. It builds a visual intuition for decomposing functions into sine waves.

An Every Frame a Painting video essay on Michael Bay's style, 'Bayhem', covering his camera movement, composition, color and editing. It argues that even if you dislike his films, they teach something about visual perception.

Huygens Optics explores the idea that space is a non-linear elastic medium, and uses simulations to show how wave energy might be confined locally into particle-like objects. It touches on inertia, the Schwinger limit and the vacuum as a medium.

A short cartoon explaining how language models like ChatGPT work, from autocomplete and conditional probabilities to neural networks, gradient descent and backpropagation. It shows how networks act as universal function approximators.