The latest blog posts to take off on Hacker News. 2,851 posts.
Ever wondered how the ^.?$|^(..+?)\1+$ regular expression can tell you if a number is not prime? In this blog post you'll learn how and why it works. Code examples in Java, JavaScript, Python and Perl are provided.
I have long struggled with understanding what probability-generating functions are and how to intuit them. There were two pieces of the puzzle missing for me, and we’ll go through both in this article.
My currently understanding of types
Goodhart's Law is useless. It tells you about a phenomenon, but it doesn't tell you how to solve it. We look at how organisations actually prevent Goodhart's Law, and illustrate this with Amazon's Weekly Business Review as an example.
Runescape has been a game near and dear to my heart since I was a child. Though I do not actively play anymore, it still functions as an interesting programming project substrate. Most recently, I created a bot that automatically executes trades on the Grand Exchange in order to conduct market making via common…
Now let’s talk about one more seemingly unrelated topic just so we can “surprise” ourselves when we realize it’s category theory. By the way, in this chapter there will be another surprise in addition to that, so don’t fall asleep.
The graph of daylight over the course of a year looks like a sine wave, but is it?
Ben Recht got my attention with a tweet about his blog post "The Higgs discovery did not take place.” I’m generally a fan of Ben’s writing, but I think he’s off base on a number of issues, and I’ll explain why. [Updated Oct 23rd, 2024] Ben's …
Building an intuition for the mathematics behind the "TLA" in "TLA+"
Intro to HM
Tog’s Paradox (also known as The Complexity Paradox or Tog’s ComplexityParadox) is an observation that products aiming to simplify a task for users tend toinspire new, more complex tasks. It’s one ...
From the highly eclectic blog of Mark Dominus
The **Gaussian distribution**, or **normal distribution** is a key subject in statistics, machine learning, physics, and pretty much any other field that deals with data and probability.
Here is a cheap way to obtain a set of standard weights, for measuring weights up to about 100 gram, to an accuracy of about 0.5 gram : Use the coins of the currency of your country. Thus one can make use of the fact that these coins are fabricated in mass production, and because of that have not only a constant shape…
I’m a professional mathematician. That means somebody pays me to do math. I’m also a recreational mathematician. That means you might have to pay me to get me to stop. Wearing my recreational mathe…
What is Damas-Hindley-Milner?
Representation Alignment for Generation: Training Diffusion Transformers Is Easier Than You Think
Our geometric intuition developed in our three-dimensional world often fails us in higher dimensions. Many properties of even simple objects, such as higher dimensional analogs of cubes and spheres, are very counterintuitive. Below we discuss just a few of these properties in an attempt to convey some of the weirdness…
This is Bob. And I’d like to know the best way for us to code a bunch of models in JAX to use to evaluate parallel algorithms including normalizing flows. I’m going to dump out my current thinking, but I’m really hoping to get feedback from experts on the best way to do this without starting a flame war in the…
Important new study from Apple
What happens if we start from this configuration and take a single step of the game? Here is a snapshot of the next generation:
The Black–Scholes formula is the crown jewel of quantitative finance. The formula gives the fair price of a European-style option, and its success can ultimately be measured by its impact on option markets. Before the formula’s publication in 1973 (Black & Scholes, 1973; Merton, 1973) , option markets were relatively…
They seem harmless enough, 52 thin slices of laminated cardboard with colorful designs printed on their sides. Yet, as another illustration of the mantra that complexity begins from the most simple systems, the number of variations that these 52 cards can produce is virtually endless. The richness of most playing card…
What follows is an unusual story of perseverance. We start with a conjecture and after some plot twists end up discussing the meaning of truth. While the title is a spoiler, you might not be able t…
We recently made a Polylog video about a nonstandard way of understanding the P vs NP problem. As usual, our goal was to present an underrated idea in a broadly understandable way, while being slig…
Math from Three to Seven: The Story of a Mathematical Circle for Preschoolers, Alexander Zvonkin (Moscow Center for Continuing Mathematical Education, 2007).
A wintertime climate change solution
This blog is intended to be a place to share ideas and results that are too weird, incomplete, or off-topic to turn into an academic paper, but that I think may be important. Let me know what you think! Contact links to the left.
