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royvanrijn

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Vibe-mathing: the Generalized Vanishing Conjecture

I am a developer . Right now it is difficult to ignore the argument around “ vibe coding .” People who could not have written an application in the traditional way are describing what they want to an AI, running the result, reporting what broke, and iterating. Some of the resulting software is fragile . Some of it is surprisingly capable. Either way, the phenomenon is real . The uncomfortable part…

The Anatomy of an LLM

I think I’ve finished something I’ve been building for a while: The Anatomy of an LLM It is a visual, interactive walk-through of the main machinery inside a large language model. Not just “it predicts the next token”, but what actually happens before that: How text becomes tokens How tokens become vectors How neural networks process those vectors How attention works How transformer blocks are…

Introduction to Java Notebooks

Java Notebook is a new and exciting way to explore the Java programming language. It works a lot like Jupyter Notebooks . Notebooks are a community standard for communicating and performing interactive computing. They are a document that blends computations, outputs, explanatory text, mathematics, images, and rich media representations of objects. It allows you to interleave blocks of text (in…

Solving the daily calendar puzzle

About a month ago I was watching a YouTube video where YouTuber Drew Gooden was struggling with a “weird” puzzle: This is what the puzzle looks like: It has 10 pieces that can be flipped/rotated and placed on a calendar. They claim there is a solution for each day/month/weekday combination. In the YouTube video Drew is struggling and says: The problem is, I’ll never be able to prove that But… what…

All The Music: the Megamix

Or a clickbait title: How I became the world’s most prolific DJ, using code. This week I stumbled across a cool project: All The Music . Damien Riehl (programmer/copyright attorney) and Noah Rubin (programmer) decided to generate all possible songs with the basic 8 major notes (C4,D4,E4,F4,G4,A4,B4 and C5) with length 12. All these songs have been ‘freely’ released under the ‘Creative Commons’…

Roadtrip to Ludolph van Ceulen

Today is March 14th (3/14), otherwise known as Pi Day! Calculating Pi To celebrate Pi Day people often try to come up with cool and interesting ways to calculate π, or to celebrate the number in weird ways. Here is a great example by the excellent Matt Parker (from Stand-up Maths): He’s using the “Isaac Newton”-way to calculate π by hand. This method was discovered by Isaac Newton and German…

From Wordle to Nerdle

About two months ago I wrote a blogpost about what strategies you could use to solve Wordle in the most efficient way. In the end I wrote a program that looks ahead a single guess and finds the word that gives you the most information. The main hype around Wordle (and all of the clones), seems to have settled down now… but I still play some of them. Nerdle One clone I really enjoyed playing the…

An algorithm for Wordle

If you’ve used Twitter during the begining of 2022 you’ll almost certainly have seen people posting tweets like this: Wordle 202 3/6 ⬜⬜⬜⬜🟨 🟨⬜⬜⬜⬜ 🟩🟩🟩🟩🟩 This is the result of playing the latest viral game “Wordle”. The concept is very easy, you have to guess a 5-letter word each day. For each guess you get the basic “Mastermind” reply, green for the correct character, yellow if it’s in the…

Divide by three using shift and add

Today I stumbled across this excellent short video bij Mathologer: This simple proof shows that 1/3 is the same as: 1/4 + 1/4^2 + 1/4^3 + 1/4^N… As a programmer I wanted to try and program this. Dividing by multiples of two (like 4^3) is extremely easy in binary, we just shift a number to the right. So if you have some integer X and we want to divide by 4, we do X >> 2 , if we want to divide by…

Hex grid in single integer

AZsPCs: AP Math Al Zimmermann hosts awesome Programming Contests every once in a while. They usually run for a long time (multiple months) and it allows mathematicians and programmers to compete in optimization problems. Usually the search space is very large and optimal solutions aren’t found for large N-values. This time the contest was called “AP Math” and the goal was: Given a hexagonal grid…