The latest blog posts to take off on Hacker News. 163 posts.
For several years I have been designing and implementing a functional teaching language especially for use in the context of a Discrete Mathematics course. The idea is for students to be exposed to…
Today I'd like to share some math connecting ideas from information theory, algebra, and topology. It's all in a new paper I've recently uploaded to the arXiv (https://arxiv.org/abs/2107.09581), which describes a correspondence between Shannon entropy and functions on topological simplices that obey a version of the…
EDIT: I never expected this post to garner so much interest. Just to be clear, using the constant is a very bad idea in almost every situation I can think of. Even instructions like RCPSS should only be used by people who are convinced that the tradeoffs are worth it (or don’t have any other choice). Subtracting from…
One of the easiest ways to start a (friendly) fight in a group of mathematicians is to bring up the axiom of choice. I'll explain what it is, why it's so controversial, and hopefully shed some light on how we choose axiomatic systems and what that means for the math we do.
Mathematician: That depends on what you mean by “universe.” Here’s a framing: A circle of radius R centered at a point P is the set of all points in the plane with distance R fro…
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This post explores some concepts behind Gaussian processes, such as stochastic processes and the kernel function. We will build up deeper understanding of Gaussian process regression by implementing them from scratch using Python and NumPy.
What the research is: The Ribbon filter is a new data structure that is more space-efficient than the popular Bloom filters that are widely used for optimizing data retrieval. One of the ways that …
Andrew Gelman, a statistics professor at Columbia, and Aki Vehtari, a computer science professor at Finland’s Aalto University, recently published a list of the most important statistical ideas in the last 50 years. Here, they break it down in easy-to-understand terms.
If you aren’t used to staring at math, Poisson’s equation looks a little intimidating:
In tackling machine learning (and computer science in general) we face some deep philosophical questions. Questions like, “What does it mean to learn?” and, “Can a computer learn?” and, “How do you define simplicity?” and, “Why does Occam’s Razor work? (Why do simple hypotheses do well at modelling reality?)” In a…
papad Hard to believe Sanjeev Arora and his coauthors consider it “a basic tool [that should be] taught to all algorithms students together with divide-and-conquer, dynamic programming, and random sampling.” Christos Papadimitriou calls it “so hard to believe that it has been discovered five times and forgotten.” It…
Here are the slides of my talk “The dawn of formalized mathematics” from the 8th European Congress of Mathematics , which is taking place online and in Protorož, Slovenia, from June 20 to 26, 2021:
Locality-sensitive hashing (LSH) is a set of techniques that dramatically speed up search-for-neighbors or near-duplication detection on data. These techniques can be used, for example, to filter out duplicates of scraped web pages at an impressive speed, or to perform near-constant-time lookups of nearby points from…
You can construct the Rule 110 cellular automaton in JPEG XL.
Deep neural networks have long been considered too complex to understand from first principles — but new research does just that, presenting a theoretical framework for DNNs.
Recently I was doing some work decoding the new Galileo High Accuracy Service data. In short, this new service will allow Galileo (“European GPS”) users to achieve decimeter-level accuracy, which is nice. This “HAS” data is transmitted highly redundantly by making good use of Reed-Solomon encoding. To work with this…
Physicists have proved that a subatomic particle can switch into its antiparticle alter-ego and back again, in a new discovery revealed today. An extraordinarily precise measurement made by Oxford researchers using the LHCb experiment at CERN has provided the first evidence that charm mesons can change into their…
When it comes to accuracy, how you add a series of arbitrary values together, and average them still matters.
So, you’ve probably heard of the Kelly Criterion in the context of gambling or maybe also in the context of investing. When gamblers talk about the Kelly Criterion they are often referring to the idea of sizing your bets, which is the very intuitive idea that if you bet too much of a percentage of your total wealth…
Implementing strict three point perspective is ridiculous. You’ll never need it. Let’s do it anyway.
I my previous blog post, I documented how one might proceed to compute the number of digits of an integer quickly. E.g., given the integer 999, you want 3 but given the integer 1000, you want 4. It is effectively the integer logarithm in base 10. On computers, you can quickly compute the integer logarithm … Continue…
Learn the theory behind how to perform sensor and camera calibration.
OK, since no one is posting, you get to endure another Monopoly post! After our recent attempt to play the shortest actual game of Monopoly on record, we started to wonder about what the shortest T…
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Fallacies are fake or deceptive arguments, "junk cognition," that is, arguments that seem irrefutable but prove nothing. Fallacies often seem superficially sound and they far too often retain immense persuasive power even after being clearly exposed as false. Like epidemics, fallacies sometimes "burn through" entire…
