# laplace — RSS Amplifier Recent posts from the 3 feeds in the RSS Amplifier directory that cover laplace. Page: Feed: --- ## [But what is cross-entropy?](https://3blue1brown.substack.com/p/but-what-is-cross-entropy) _2026-07-16 · Grant Sanderson · 3Blue1Brown mailing list_ Compression is Intelligence Part 2 ## [On monthly puzzles](https://3blue1brown.substack.com/p/on-monthly-puzzles) _2026-06-17 · Grant Sanderson · 3Blue1Brown mailing list_ And the plan for their solutions ## [Reinventing Entropy](https://3blue1brown.substack.com/p/reinventing-entropy) _2026-06-07 · Grant Sanderson · 3Blue1Brown mailing list_ Compression & Intelligence Part 1 ## [Escher's most mathematically interesting piece](https://3blue1brown.substack.com/p/eschers-most-mathematically-interesting) _2026-03-22 · Grant Sanderson · 3Blue1Brown mailing list_ The Print Gallery, and the tour of complex analysis it invites. ## [The most underappreciated formula](https://3blue1brown.substack.com/p/the-most-underappreciated-formula) _2026-02-27 · Grant Sanderson · 3Blue1Brown mailing list_ Exploring spheres in higher dimensions ## [The Hairy Ball Theorem](https://3blue1brown.substack.com/p/the-hairy-ball-theorem) _2026-01-31 · Grant Sanderson · 3Blue1Brown mailing list_ A few surprising applications of one of the most absurdly named theorems in topology, together with a beautiful proof for why it is true. ## [SoME4 Prizes](https://3blue1brown.substack.com/p/some4-prizes) _2026-01-16 · Grant Sanderson · 3Blue1Brown mailing list_ Winners of the supplementary "helpful for teachers" prize we set up for the 2025 Summer of Math Exposition ## [Recruiting, both for myself and for other companies (potentially yours)](https://3blue1brown.substack.com/p/recruiting-both-for-myself-and-for) _2025-12-04 · Grant Sanderson · 3Blue1Brown mailing list_ I have two small requests, both of which I’ll elaborate on further down in this post. ## [How Laplace transforms solve differential equations](https://3blue1brown.substack.com/p/how-laplace-transforms-solve-differential) _2025-11-05 · Grant Sanderson · 3Blue1Brown mailing list_ Studying the forced oscillator ## [But what is a Laplace Transform?](https://3blue1brown.substack.com/p/but-what-is-a-laplace-transform) _2025-10-12 · Grant Sanderson · 3Blue1Brown mailing list_ Visualizing the most important tool for differential equations. ## [PixelRift — Platforming with Level Editor (Sponsored)](https://crawlproof.com/a/8zPABoxriBSX) _2025-10-12 · **Sponsored**_ Includes a built-in level editor, campaign with elemental heroes, and boss encounters. ## [Why complex exponents matter](https://3blue1brown.substack.com/p/why-complex-exponents-matter) _2025-10-05 · Grant Sanderson · 3Blue1Brown mailing list_ Laplace Transform Prelude ## [Why Ruler and Compass?](https://3blue1brown.substack.com/p/why-ruler-and-compass) _2025-09-18 · Grant Sanderson · 3Blue1Brown mailing list_ The fifth and final guest video ## [Exploration & Epiphany](https://3blue1brown.substack.com/p/exploration-and-epiphany) _2025-09-07 · Grant Sanderson · 3Blue1Brown mailing list_ A guest video about Sol LeWitt's incomplete open cubes, and the group theory behind it. ## [Simulating Phase Change](https://3blue1brown.substack.com/p/simulating-phase-change) _2025-08-28 · Grant Sanderson · 3Blue1Brown mailing list_ Guest video by Vilas Winstein ## [The AI that solved IMO Geometry Problems](https://3blue1brown.substack.com/p/the-ai-that-solved-imo-geometry-problems) _2025-08-17 · Grant Sanderson · 3Blue1Brown mailing list_ Guest video by Aleph0 ​ ## [Solving Linear Equations Modulo a Composite Number](/solving-linear-equations-modulo-a-composite-number/) _2025-07-26 · Alex Dowad · Alex Dowad Computes_ Alternative Title: Put a Ring on It: Solving Matrix Equations Over Z/NZ Recently, I implemented the index calculus algorithm for computing discrete logs (i.e. solving a=bx mod N), in order to understand it better. The trickiest part, by far, was figuring out how to solve systems of linear equations modulo N, where N is an arbitrary integer which may not be prime. Web search turned up a number of… ## [But how do AI videos actually work?](https://3blue1brown.substack.com/p/but-how-do-ai-videos-actually-work) _2025-07-25 · Grant Sanderson · 3Blue1Brown mailing list_ Guest video by from Welch Labs ## [Understanding Manger’s Padding Oracle Attack on RSA Encryption](/understanding-mangers-rsa-attack/) _2025-05-14 · Alex Dowad · Alex Dowad Computes_ The previous article discussed Bleichenbacher’s 1998 attack on RSA encryption, which relies on access to a PKCS#1v15 padding oracle. Just a few years later, in 2001, James Manger published details of a different padding oracle attack on RSA encryption. Manger’s attack is similar to Bleichenbacher’s attack, but relies on a different type of padding oracle. Manger’s paper is shorter and easier to… ## [Summer of Math Exposition #4](https://3blue1brown.substack.com/p/summer-of-math-exposition-4) _2025-05-05 · Grant Sanderson · 3Blue1Brown mailing list_ Teachers, I'd love to hear from you ## [Where my explanation of Grover’s algorithm failed](https://3blue1brown.substack.com/p/where-my-explanation-of-grovers-algorithm) _2025-05-04 · Grant Sanderson · 3Blue1Brown mailing list_ Addressing some viewer questions from the most recent video ## [8.1% APY Plus Free Stock (Sponsored)](https://crawlproof.com/a/t89JKA53hGGb) _2025-05-04 · **Sponsored**_ Claim 8.1% APY and up to $1,030 in SK hynix and Nvidia stock. ## [But what is Quantum Computing?](https://3blue1brown.substack.com/p/but-what-is-quantum-computing) _2025-04-30 · Grant Sanderson · 3Blue1Brown mailing list_ Building up to Grover's Algorithm ## [Revisiting those colliding blocks that compute π](https://3blue1brown.substack.com/p/revisiting-those-colliding-blocks) _2025-03-13 · Grant Sanderson · 3Blue1Brown mailing list_ Happy pi day! ## [Understanding Bleichenbacher’s CRYPTO’98 Padding Oracle Attack on RSA Encryption](/understanding-bleichenbackers-crypto98-rsa-attack/) _2025-02-12 · Alex Dowad · Alex Dowad Computes_ In 1998, Daniel Bleichenbacher published a method for cracking RSA encryption with PKCS#1v15 padding, given access to a “padding oracle”. I learned of this attack via the cryptopals challenges, where it is featured in challenge #47 and #48. The instructions for the challenge state: “We recommend you just use the raw math from the paper and not spend too much time trying to grok how the math… ## [Fast Bulk Record Updates in Rails](/bulk-record-update-in-rails/) _2024-11-28 · Alex Dowad · Alex Dowad Computes_ Today I investigated a performance issue in a client’s Rails application. The problem code was taking about 40 seconds to create and/or update several thousand database records, resulting in HTTP request timeouts. After taking some measurements, reorganizing the code a bit, and applying some standard optimizations, that went down to 8 seconds. A 5× speed boost isn’t bad, and the client would… ## [Stuff I Have Learned: Transmit records in column-major order for better compression](/json-arrays-column-major-order/) _2024-11-09 · Alex Dowad · Alex Dowad Computes_ The other day I achieved a 25% reduction in load time for a single-page application which requires a large amount of initial data, with just a few lines of added code. If the technique described below seems obvious, well… sorry. I’m writing it down in case it’s interesting to some readers. The web application in question needs many records from a back-end database, which are serialized to JSON and… ## [Solving Laplace’s Equation](/solving-laplaces/) _2024-09-22 · Alex Dowad · Alex Dowad Computes_ (This article is the 4th in a series on differential equations. The previous installments were 1) Understanding the Heat Equation, 2) Understanding the Wave Equation, and 3) Understanding Laplace’s Equation.) The previous article explained the meaning of Laplace’s Equation. We saw a couple examples of equilibrium heat distributions in a piece of heat-conducting material, including this one: Those… ## [Understanding Laplace’s Equation](/laplaces-equation/) _2024-09-17 · Alex Dowad · Alex Dowad Computes_ (This article builds on two earlier ones, Understanding the Heat Equation and Understanding the Wave Equation.) Having explored the meanings of the Heat Equation and Wave Equation together with you, I now want to tell you about a third differential equation, also highly significant, and closely connected to the other two: Laplace’s Equation. Here it is: ∇2F=0 In his excellent text Calculus, Gil… ## [Another Lesson From My First CVE: Use Assertions to Guard Against Infinite Loops](/guard-against-infinite-loops/) _2024-08-25 · Alex Dowad · Alex Dowad Computes_ (This article follows on the previous one about lessons from CVE-2024-2757.) After going through the experience of accidentally introducing a denial-of-service vulnerability into PHP (due to an unintentional infinite loop), I adopted a software development practice which I haven’t seen others write about. The short version is: use assertions to ensure that non-trivial loops terminate. The rest of… ## [A Lesson From My First CVE](/lesson-from-my-first-cve/) _2024-08-22 · Alex Dowad · Alex Dowad Computes_ In May 2024, for the first time (to my knowledge), a CVE ID was created for a security vulnerability which I accidentally introduced into a high-profile software project. This is it: CVE-2024-2757. I took some scant comfort in the fact that it was a denial-of-service vulnerability and not something worse, such as arbitrary code execution. Even so, this was unpleasant and I don’t wish to repeat the…