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PFP: A Probabilistic Functional Programming Library for Haskell (2006)

A Probabilistic Functional Programming Library for Haskell Version: June 2006 Distributions can represent events, such as the roll of a die or the flip of a coin. For example, or example, the outcome of a die roll can be expressed as follows. die :: Dist Int die = uniform [1..6] die > die 1 16.7% 2 16.7% 3 16.7% 4 16.7% 5 16.7% 6 16.7% uniform uniform succOrId x = uniform [x, x+1] choose succOrId x = choose 0.5 x (x+1) droll = die >>= succOrId droll = do d <- die succOrId d To use t

The sisters “paradox” – counter-intuitive probability

It seems simple, but it isn't There are a couple of famous counter-intuitive problems in probability theory and the sisters "paradox" is one of them. I'll tell you the problem, let you guess the solution, and then give you some of the background. Here's the problem: a family has two children. You're told that at least one of them is a girl. What's the probability both are girls? (International Film Service / American Releasing Co., Public domain, via Wikimedia Commons) Assume that the pr

Uncertain<T>

You know what’s wrong with people? They’re too sure of themselves. Better to be wrong and own it than be right with caveats. Hard to build a personal brand out of nuance these days. People are attracted to confidence — however misplaced. But can you blame them? (People, that is) Working in software, the most annoying part of reaching Senior level is having to say “it depends” all the time. Much more fun getting to say “let’s ship it and iterate” as Staff or “that won’t scale” as a Principal.

The sisters "paradox" – counter-intuitive probability

It seems simple, but it isn't There are a couple of famous counter-intuitive problems in probability theory and the sisters "paradox" is one of them. I'll tell you the problem, let you guess the solution, and then give you some of the background. Here's the problem: a family has two children. You're told that at least one of them is a girl. What's the probability both are girls? (International Film Service / American Releasing Co., Public domain, via Wikimedia Commons) Assume that the pr

Important machine learning equations

Motivation Machine learning (ML) is a powerful field driven by mathematics. Whether you’re building models, optimizing algorithms, or simply trying to understand how ML works under the hood, mastering the core equations is essential. This blog post is designed to be your go-to resource, covering the most critical and “mind-breaking” ML equations—enough to grasp most of the core math behind ML. Each section includes theoretical insights, the equations themselves, and practical implementations in

The Most Important Machine Learning Equations: A Comprehensive Guide

Motivation Machine learning (ML) is a powerful field driven by mathematics. Whether you’re building models, optimizing algorithms, or simply trying to understand how ML works under the hood, mastering the core equations is essential. This blog post is designed to be your go-to resource, covering the most critical and “mind-breaking” ML equations—enough to grasp most of the core math behind ML. Each section includes theoretical insights, the equations themselves, and practical implementations in

AGI is an engineering problem, not a model training problem

Published: Aug 13, 2025 | at 11:00 AM We’ve reached an inflection point in AI development. The scaling laws that once promised ever-more-capable models are showing diminishing returns. GPT-5, Claude, and Gemini represent remarkable achievements, but they’re hitting asymptotes that brute-force scaling can’t solve. The path to artificial general intelligence isn’t through training ever-larger language models—it’s through building engineered systems that combine models, memory, context, and determ

Backpropagating through a maze with candle and WASM

Loading WASM module... Width: Height: Wall Density: Learning Rate: Max Steps: Generate & Optimize This demo uses gradient descent to solve a discrete maze. Try playing with the hyperparameters to see how they affect the optimization process! No neural network involved: logits are directly optimized, from a random initialization, for each maze. This runs entirely on your local device, thanks to candle and Rust's support for WebAssembly. You can disconnect from the Internet after loading this

What I learned gathering nootropic ratings (2022)

Credit: Ultra Heaven In this post, I analyze nootropics ratings I gathered through a recommender system. Jump directly to What I learned if you don’t like caveats and methodology. The effectiveness of a nootropic varies a lot from one person to another (your mileage will vary). This is why I built a nootropic recommendation system Enter ratings on nootropics you’ve tried, and it will spit out nootropics liked by people with similar rating patterns. This was initially based on the 2016 SlateSta

What I learned gathering nootropic ratings

Credit: Ultra Heaven In this post, I analyze nootropics ratings I gathered through a recommender system. Jump directly to What I learned if you don’t like caveats and methodology. The effectiveness of a nootropic varies a lot from one person to another (your mileage will vary). This is why I built a nootropic recommendation system Enter ratings on nootropics you’ve tried, and it will spit out nootropics liked by people with similar rating patterns. This was initially based on the 2016 SlateSta

Trump Says “Very Wealthy People” Are Ready to Buy TikTok

Just weeks after extending the deadline for its sale for a third time, President Donald Trump announced Sunday that he has found a buyer for TikTok’s U.S. operations. The popular social media app has been under intense pressure due to a law passed in 2024 that requires its Chinese parent company, ByteDance, to sell the platform or face a nationwide ban. The legislation stems from bipartisan concern in Washington that the Chinese government could access the data of American users or use the app

Trump says he’s found a buyer for TikTok

In Brief A group of “very wealthy people” is set to buy short-form video app TikTok, according to President Donald Trump. “We have a buyer for TikTok, by the way,” Trump said in a Fox News interview on Sunday morning. “I think I’ll need probably China’s approval. I think President Xi [Jinping] will probably do it.” Trump declined to share more details about the buyers, saying only that he would reveal their identities in two weeks (apparently his favorite unit of time). Trump has repeatedly

New IQ research shows why smarter people make better decisions

This article has been reviewed according to Science X's editorial process and policies . Editors have highlighted the following attributes while ensuring the content's credibility: Credit: Pixabay/CC0 Public Domain A new study from the University of Bath's School of Management has found that individuals with a higher IQ make more realistic predictions, which supports better decision-making and can lead to improved life outcomes. The research, published in the Journal of Personality and Social

The probability of a hash collision (2022)

The probability of a hash collision Tags: probability A hash function takes arbitrarily complex input - a word, a website, an image, a human being - and maps it to a single number. This is useful for various computer science stuffs, such as data storage and cryptography. For example, let's say you want to store a book in one of N N N boxes. If you put the book in a random box, it's quite likely that you'll forget which box you picked, especially as N N N gets bigger. What you can do instead i

The Probability of a Hash Collision

The probability of a hash collision Tags: probability A hash function takes arbitrarily complex input - a word, a website, an image, a human being - and maps it to a single number. This is useful for various computer science stuffs, such as data storage and cryptography. For example, let's say you want to store a book in one of N N N boxes. If you put the book in a random box, it's quite likely that you'll forget which box you picked, especially as N N N gets bigger. What you can do instead i

Proba-3's first artificial solar eclipse

Enabling & Support Proba-3’s first artificial solar eclipse 16/06/2025 24672 views 108 likes Today, the European Space Agency’s Proba-3 mission unveils its first images of the Sun’s outer atmosphere – the solar corona. The mission’s two satellites, able to fly as a single spacecraft thanks to a suite of onboard positioning technologies, have succeeded in creating their first ‘artificial total solar eclipse’ in orbit. The resulting coronal images demonstrate the potential of formation flying tec

Why This Recent Total Solar Eclipse Was the First of Its Kind

The Sun’s outer atmosphere—the corona—only reveals itself during total solar eclipses, which happen about every 18 months on Earth, and are only visible along a narrow path. These events offer scientists a rare opportunity to observe the Sun’s violent surface—but now, they won’t have to wait on the cosmos to do so. On Monday, June 16, the European Space Agency (ESA) announced that its Proba-3 mission created the world’s first artificial total solar eclipse. The mission’s two satellites, the O