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Math & Algorithms

The most popular blog posts about math & algorithms on Hacker News. 95 posts.

2013
31

Bezier Curves and Picasso

Pablo Picasso Simplicity and the Artist Some of my favorite of Pablo Picasso’s works are his line drawings. He did a number of them about animals: an owl, a camel, a butterfly, etc. This piece called “Dog” is on my wall: Dachshund-Picasso-Sketch (Jump to interactive demo where we recreate “Dog” using the math in this…

34

Ethiopian Binary Math

Today, a witch doctor practices computer arithmetic. The University of Houston's College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them. The scene is a remote Ethiopian village in 1940. A Farmer offers his herd of 34 goats for sale…

35

The main trick in machine learning

I have been irritated that many recent introductions to machine learning/neural networks/whatever that fail to emphasise the most import trick in machine learning. Many internet resources don’t mention it, and even good textbooks often don’t drill it in to the reader the absolute criticality to success the trick is…

48

I hate the Pumping Lemma

I hate the Pumping Lemma for regular languages. It’s a complicated way to express an idea that is fundamentally very simple, and it isn’t even a very good way to prove that a language is not regula…

49

Exact numeric nth derivatives

Automatic differentiation is a well-studied technique for computing exact numeric derivatives. Dan Piponi has a great introduction on the subject , but to give you an overview, the idea is that you introduce an algebraic symbol such that but . Formulas involving are called dual numbers (e.g., , ) in much the same way…

50

The Fallacy of Cracking Contests (1998)

In this issue: The Fallacy of Cracking Contests How to Recognize Plaintext News The Doghouse: Iomega Zip Disks Counterpane Systems News Final Report from the Commerce Department Technical Advisory Committee on Key Recovery Comments From Readers About "CRYPTO-GRAM"

55

The keys to the keydom

Your security and privacy on the Internet (to the extent that such quaint notions still have meaning) depend on the difficulty of factoring certain large numbers. For example, take this 1,024-bit integer:

60

Probability Theory — A Primer

It is a wonder that we have yet to officially write about probability theory on this blog. Probability theory underlies a huge portion of artificial intelligence, machine learning, and statistics, and a number of our future posts will rely on the ideas and terminology we lay out in this post. Our first formal theory…