Published on: 2025-06-05 14:54:45
I’ve been long fascinated by the endless online debates about whether the infinite decimal expansion 0.9999… is exactly equal to 1. The canonical answer is yes. But there’s a considerable number of blogs that will try to convince you otherwise — and in the process, expose the sinister machinations of Big Math. What’s unique about this situation is that while it feels like bog-standard online crackpottery, it’s sort of running in reverse. The belief that 0.x must be less than 1.y makes perfect s
Keywords: 10 9999 frac infinite reals
Find related items on AmazonPublished on: 2025-06-20 12:59:25
Adventures in Symbolic Algebra with Model Context Protocol I spent last weekend playing with this new MCP protocol all the kids are talking about. And it's fun, but a bit early and rough around the edges. MCP, if you're not familiar, is Anthropic's answer to the question: "How do we get AI to actually DO things instead of just TALK about doing them?" It's a protocol that allows language models to call external tools, much like how your friend who claims to know everything actually calls their
Keywords: frac language llm mcp tool
Find related items on AmazonPublished on: 2025-06-25 22:04:14
A shower thought turned into a beautiful Collatz visualization I recently went on a nice long SCUBA diving trip with my wife and daughters. Lots of diving implies lots of showers, and lots of showers means lots of shower-thoughts! An especially interesting one I had turned into a nice way to visualize some aspects of the Collatz Conjecture. The Collatz Conjecture defines a very simple function on all positive integers as follows: If the number is even, divide it by 2 If the number is odd, mu
Keywords: bits collatz fractions plot thought
Find related items on AmazonPublished on: 2025-07-06 22:41:23
A few months ago I was working on an image classification problem with severe class imbalance - the positive class was much rarer than the negative class. As part of the model tuning phase, I wanted to explore the impact of class imbalance and try to mitigate it. A popular “off-the-shelf” solution to imbalance is weighting classes in inverse proportion to their frequency - which didn’t yield an improvement. This happened to me several times in the past, and other than basic intuition I couldn’t
Keywords: alpha beta frac left right
Find related items on AmazonPublished on: 2025-07-08 21:00:00
A galactic filament that stretches across 230 light-years in the Milky Way has suffered from a strange kink that has distorted its magnetic field, appearing as a fracture in a massive bone. New X-ray images captured by the Chandra Observatory may have finally helped astronomers diagnose its ailment, naming a fast-spinning neutron star as the culprit. The center of the galaxy is marked by enormous, bone-like structures threaded with parallel magnetic fields and swirling, high-energy particles. L
Keywords: bone fracture images pulsar radio
Find related items on AmazonPublished on: 2025-07-11 23:34:36
FractalU is a “school” for adults, taught from living rooms in New York City. We’ve run over 100 classes and taught thousands of students. Classes meet weekly and are held on evenings and weekends, since most of our students and teachers are working professionals. Here's a small sampling of our recent courses: We teach out of our homes, and keep the administrative burden low. That way, teachers can offer their classes at affordable rates. And adult students can make taking classes and learni
Keywords: class classes fractalu friends students
Find related items on AmazonPublished on: 2025-07-09 11:31:38
Using Coalton to Implement a Quantum Compiler Sep 6, 2022 By Elias Lawson-Fox, Aidan Nyquist, and Robert Smith Introduction: Coalton and the quilc compiler Quilc is a state-of-the-art optimizing compiler for quantum computers written in Common Lisp. It is capable of taking arbitrary quantum programs written in Quil, and compiling and optimizing them into code that conforms to the majority of quantum computing architectures that exist today. Quilc and its related tooling are around 50,000 li
Keywords: alg frac mathrm pi sqrt
Find related items on AmazonPublished on: 2025-07-09 16:31:38
Using Coalton to Implement a Quantum Compiler Sep 6, 2022 By Elias Lawson-Fox, Aidan Nyquist, and Robert Smith Introduction: Coalton and the quilc compiler Quilc is a state-of-the-art optimizing compiler for quantum computers written in Common Lisp. It is capable of taking arbitrary quantum programs written in Quil, and compiling and optimizing them into code that conforms to the majority of quantum computing architectures that exist today. Quilc and its related tooling are around 50,000 li
Keywords: alg frac mathrm pi sqrt
Find related items on AmazonPublished on: 2025-07-20 01:01:30
Given a function such as \(\tan x\), could you write \(\frac{d}{dx} \arctan x\) and \(\int \arctan x \; dx\), just from \(\tan x\), \(\frac{d}{dx} \tan x\) and \(\int \tan x \; dx\)? With some caveats, the inverse function theorem answers the former while the Legendre transformation answers the later. We’ll approach this with as much geometric intuition as possible, avoiding the dry application of formulas. Derivatives of inverse functions and the inverse function theorem Instead of approachin
Find related items on AmazonPublished on: 2025-08-12 01:24:41
⚠️ Warning: Contains flashing lights and colors which may affect those with photosensitive epilepsy. 🌱 This is an open-source project in active development. Introduction Bridging Fractals and Thought 💡 neurite.network unleashes a new dimension of digital interface... ...the fractal dimension. 🧩 Drawing from chaos theory and graph theory, Neurite unveils the hidden patterns and intricate connections that shape creative thinking. For over two years we've been iterating out a virtually limit
Keywords: ai click fractal neurite nodes
Find related items on AmazonPublished on: 2025-08-16 15:30:47
Differentiable Programming from Scratch Differentiable programming has become a hot research topic, and not only due to the popularity of machine learning frameworks like TensorFlow, PyTorch, and JAX. Many fields apart from machine learning are finding differentiable programming to be a useful tool for solving optimization problems. In computer graphics, differentiable rendering, differentiable physics, and neural representations are all gaining popularity. This article received an honorable m
Keywords: frac mathbf node partial prime
Find related items on AmazonPublished on: 2025-08-12 23:23:48
(Title image sourced from: Wikipedia - Trigonometry) Why I wanted to calculate the network latency between all my VPS nodes, and add the latency into the configuration file of Bird BGP daemon, so the network packets are forwarded through the lowest latency route. However, I have 17 nodes as of today, and I didn't want to manually run a ping command between each pair. So I came up with a solution: I can mark the latitudes and longitudes of the physical locations of my nodes, calculate the phys
Keywords: arctan cos frac function sin
Find related items on AmazonPublished on: 2025-08-17 18:26:00
Through a couple of different avenues I wandered, yet again, down a rabbit hole leading to the topic of this post. The first avenue was through my main focus on a particular machine learning topic that utilized some concepts from physics, which naturally led me to stochastic calculus. The second avenue was through some projects at work in the quantitative finance space, which is one of the main applications of stochastic calculus. Naively, I thought I could write a brief post on it that would sa
Keywords: equation frac partial process stochastic
Find related items on AmazonPublished on: 2025-08-19 05:26:00
Through a couple of different avenues I wandered, yet again, down a rabbit hole leading to the topic of this post. The first avenue was through my main focus on a particular machine learning topic that utilized some concepts from physics, which naturally led me to stochastic calculus. The second avenue was through some projects at work in the quantitative finance space, which is one of the main applications of stochastic calculus. Naively, I thought I could write a brief post on it that would sa
Keywords: equation frac partial process stochastic
Find related items on AmazonPublished on: 2025-08-22 09:54:51
Monte Carlo Crash Course Sampling In the previous chapter, we assumed that we can uniformly randomly sample our domain. However, it’s not obvious how to actually do so—in fact, how can a deterministic computer even generate random numbers? Pseudo-Random Numbers Fortunately, Monte Carlo methods don’t need truly random numbers. Instead, we can use a pseudo-random number generator (PRNG). A PRNG produces a deterministic stream of numbers that look uniformly random: By “look uniformly random,”
Keywords: f_ frac mathbf mathcal omega
Find related items on AmazonPublished on: 2025-08-31 17:29:29
Analytic Combinatorics -- A Worked Example 08 Apr 2025 - Tags: sage Another day, another blog post that starts with “I was on mse the other day…”. This time, someone asked an interesting question amounting to “how many unordered rooted ternary trees with $n$ nodes are there, up to isomorphism?”. I’m a sucker for these kinds of combinatorial problems, and after finding a generating function solution I wanted to push myself to get an asymptotic approximation using Flajolet–Sedgewick style analyt
Keywords: frac ldots left omega right
Find related items on AmazonPublished on: 2025-09-15 08:15:15
Quick intro LeetArxiv is Leetcode for implementing Arxiv papers . We help programmers transition into careers in computational research. You can also join our Reddit community here. Frontmatter for the 1931 paper ‘On Factoring Large Numbers’ by D.H. Lehmer and R.E. Powers *We provide a hand-written implementation that can be translated to different programming languages. 1.0 Introduction In 1931, at Stanford University, D.H Lehmer and R.E. Powers published a general integer factorization
Keywords: continued expansion fraction lehmer page
Find related items on AmazonPublished on: 2025-10-11 11:09:21
Statistical Formulas For Programmers By Evan Miller May 19, 2013 Being able to apply statistics is like having a secret superpower. Where most people see averages, you see confidence intervals. When someone says “7 is greater than 5”, you declare that they’re really the same. In a cacophony of noise, you hear a cry for help. Unfortunately, not enough programmers have this superpower. That’s a shame, because the application of statistics can almost always enhance the display and interpreta
Keywords: alpha confidence distribution frac test
Find related items on AmazonPublished on: 2025-10-23 11:10:55
Rotors: A practical introduction for 3D graphics 17 Apr 2023 When putting 3D graphics on a screen, we need a way to express rotations of the geometry we’re rendering. To avoid the problems that come with storing rotations as axes & angles, we could use quaternions. However quaternions require that we think in 4 distinct spatial dimensions, something humans are notoriously bad at. Thankfully there is an alternative that some argue is far more elegant and simpler to understand: Rotors. Rotors co
Find related items on AmazonPublished on: 2025-10-28 23:29:02
FlakeUI (v0.7-update) tags: user-interface, graph-visualization, zooming-elements-based, parent-children-orbiting, fractal-structure-inspired promotional material Would you like to bring a touch of adventurous spirit to your contents? Presenting your contents, FlakeUI does things a bit differently. As an original graph content navigating environment, it provides unusual experience in discovering information among your content selection. Possible applications are surely endless, and they are wa
Keywords: content contents dragging flakeui fractal
Find related items on AmazonPublished on: 2025-10-30 20:29:02
FlakeUI (v0.7-update) tags: user-interface, graph-visualization, zooming-elements-based, parent-children-orbiting, fractal-structure-inspired promotional material Would you like to bring a touch of adventurous spirit to your contents? Presenting your contents, FlakeUI does things a bit differently. As an original graph content navigating environment, it provides unusual experience in discovering information among your content selection. Possible applications are surely endless, and they are wa
Keywords: content contents dragging flakeui fractal
Find related items on AmazonPublished on: 2025-11-07 18:40:03
A beginner-friendly introduction to stochastic calculus, focusing on intuition and calculus-based derivations instead of heavy probability theory formalism. Introduction to Stochastic Calculus Introduction to Stochastic Calculus Notation and code for generating visuals are presented in the Appendix. 0. Introduction This document is a brief introduction to stochastic calculus. Like, an actual introduction. Not the textbook “introductions” which immediately blast you with graduate-level proba
Find related items on AmazonPublished on: 2025-11-06 06:25:51
February 22, 2025 at 14:53 Tags Math There's a cute math puzzle that can be interesting to folks on very different levels: Given exactly four instances of the digit 2 and some target natural number, use any mathematical operations to generate the target number with these 2s, using no other digits. Some examples can be done by elementary school kids: \[\begin{align*} 1&=\frac{2+2}{2+2}\\ 2&=\frac{2}{2}+\frac{2}{2}\\ 3&=2\cdot2-\frac{2}{2}\\ 4&=2+2+2-2\\ 5&=2\cdot 2 +\frac{2}{2}\\ 6&=2\cdot 2\
Keywords: align frac left log_ sqrt
Find related items on AmazonPublished on: 2025-11-05 05:51:22
Twitch has rolled out a number of changes to its violation enforcement system. The biggest change is that now infractions will disappear from an account “after a set amount of time.” This is great news for long-time creators, as minor violations stacked. This led to folks getting suspended as these smaller infractions piled up. The platform says that most minor infractions, like cheating in an online game, will expire after 90 days. More serious violations, like participating in hateful conduct
Keywords: infractions suspension time twitch violations
Find related items on AmazonGo K’awiil is a project by nerdhub.co that curates technology news from a variety of trusted sources. We built this site because, although news aggregation is incredibly useful, many platforms are cluttered with intrusive ads and heavy JavaScript that can make mobile browsing a hassle. By hand-selecting our favorite tech news outlets, we’ve created a cleaner, more mobile-friendly experience.
Your privacy is important to us. Go K’awiil does not use analytics tools such as Facebook Pixel or Google Analytics. The only tracking occurs through affiliate links to amazon.com, which are tagged with our Amazon affiliate code, helping us earn a small commission.
We are not currently offering ad space. However, if you’re interested in advertising with us, please get in touch at [email protected] and we’ll be happy to review your submission.