1411
Using spaced repetition systems to see through a piece of mathematics
By Michael Nielsen, January 2019
New
The latest blog posts to take off on Hacker News. 2,391 posts.
1412
Using Fourier Transforms to Multiply Numbers
The purpose of this article is to show you step-by-step examples of how to use the Fourier transform algorithm to multiply two numbers. The primary advantage of using fourier transforms to multiply numbers is that you can use the asymptotically much faster 'Fast Fourier Transform algorithm', to achieve better…
1413
“The Book of Why” by Pearl and Mackenzie
Judea Pearl and Dana Mackenzie sent me a copy of their new book, “The book of why: The new science of cause and effect.”
1414
Warning Signs in Experimental Design and Interpretation (2007)
When an experimental study states "The group with treatment X had significantly less disease ( p = 1%)", many people interpret this statement as being equivalent to "there is a 99% chance that if I do treatment X it will prevent disease." This essay explains why these statements are not equivalent. For such an…
1415
9999999999999999.0 – 9999999999999998.0
Note that some of the wrong answers can be fixed with various workarounds. For example Common–Lisp gives the correct answer for:
1416
Towards a Better Pythagorean Cup
There was an article on Hacker News the other day by David Richeson entitled Make Your Own Pythagorean Cup . A Pythagorean cup is a cup with a built-in siphon. Supposedly invented by Pythagoras, the cup functions just like an ordinary cup as long as it is only filled to a certain level. If anyone gets greedy and tries…
1417
Gaussian Processes Are Not So Fancy
Gaussian Processes have a mystique related to the dense probabilistic terminology that's already evident in their name. But Gaussian Processes are just models, and they're much more like k-nearest neighbors and linear regression than may at first be apparent.
1418
Measuring the size of the Earth by watching a shadow on a wall
Recently I've been discussing the details of measuring the size of the Earth by watching a shadow descending a wall at sunrise, or ascending at sunset. The sums are easy enough if you do it at either Equinox, and at the Equator, and you can read about it here:
1419
A sane introduction to maximum likelihood estimation and maximum a posteriori
It is frustrating to learn about principles such as maximum likelihood estimation (MLE), maximum a posteriori (MAP) and Bayesian inference in general. The main reason behind this difficulty, in my opinion, is that many tutorials assume previous knowledge, use implicit or inconsistent notation, or are even addressing a…
1420
A Visual Exploration of Gaussian Processes
Consulting software engineer and research scientist. I build visualization systems for complex data and machine learning models.
1421
Pathfinding for Tower Defense
In a Tower Defense game, there are many enemies that are all headed to the same place. In many Tower Defense games, there is a predetermined path, or a small number of paths. In some, such as the classic Desktop Tower Defense [1] , you can place towers anywhere, and they act as obstacles that affect the paths taken by…
1422
How long is that Bézier?
Blog of Raph Levien.
1423
Connected Components – The one Graph Algorithm you need to know
Graphs provide us with a very useful data structure.
1424
Deciphering the postcard-sized raytracer
"He's done it again!" was my first thought as I looked at the back of a postcard sized Pixar flier [1] which was covered in code. In the lower right corner, the blob of statements and expressions had been signed by none other than Andrew Kensler. For those who are not familiar with him, Andrew is the programmer who…
1425
The Wavefunction Collapse Algorithm Explained
The Wavefunction Collapse Algorithm teaches your computer how to riff. The algorithm takes in an archetypical input, and produces procedurally-generated outputs that look like it.
1426
Why are amplitudes complex?
[By prior agreement, this post will be cross-posted on Microsoft’s Q# blog, even though it has nothing to do with the Q# programming language. It does, however, contain many examples th…
1427
Advent of Code Python Solutions, Explained
I first participated in Advent of Code (AoC) in 2017. My co-workers at Formlabs introduced it to me. This year (2018), quite a lot of Formlabs folks are taking part and we have a nice private leaderboard going. I'm having a lot of fun with it. I've been staying up until midnight to work on the problems as soon as…
1428
Neural Networks as Ordinary Differential Equations
Recently I found a paper being presented at NeurIPS this year, entitled Neural Ordinary Differential Equations, written by Ricky Chen, Yulia Rubanova, Jesse Bettencourt, and David Duvenaud from the University of Toronto. The core idea is that certain types of neural networks are analogous to a discretized differential…
1429
Machine Learning Trick of the Day: Instrumental Thinking
· Read in · 1499 words · All posts in series · [dropcap]This[/dropcap] trick is unlike the others we’ve conjured. It will not reveal a clever manipulation of a probability or an integral or a…
1430
1431
Secrets of smooth Béziers
I haven’t posted here much lately, and I admit, it’s because I’ve gotten sidetracked thinking about curves again. I did my PhD thesis on curves, so spent years thinking about them, then put that on hold for a while, aside from some work in crunching font file sizes down.
1432
Hamiltonian Monte Carlo explained
Understanding an effective way of sampling from complex distributions with 3d-demonstrations
1433
Algebras we love
If you work with anything that can be modeled mathematically, you most likely know that many things you work on can be expressed with algebras. However, if you are not a graduate of a computer science course or similar you might not know how ubiquitous they are and how often you rely on some of them. (And I don’t mean…
1434
A Programmer's Introduction to Mathematics
For the last four years I’ve been working on a book for programmers who want to learn mathematics. It’s finally done, and you can buy it today. The website for the book is pimbook.org, which has purchase links—paperback and ebook—and a preview of the first pages. You can see more snippets later in the book on the…
1435
The deepest problem with deep learning
Some reflections on an accidental Twitterstorm, the future of AI and deep learning, and what happens when you confuse a schoolbus with a…
1436
How to design co-programs
I recently attended the Matthias Felleisen Half-Time Show, a symposium held in Boston on 3rd November in celebration of Matthias’s 60th birthday. I was honoured to be able to give a talk ther…
1437
Math and Analogies
Here's a talk on "Math And Analogies" I did for the Center on Contemporary Art (CoCA) in Seattle. What's this? Well, it's a number. Probably written down a…
1438
Ryanair, Hamiltonian Cycles, and using graph theory to find cheap flights
Using graph theory and Ryanair route data to find cheap multi-city flight loops through Europe.
1439
Fast, Constant-Time Sphere Indexing
Map any 3D point on or above a triangle-subdivided sphere to a triangle index in constant time, without recursion, table lookups or complicated branching logic.
1440
Shamir’s Secret Sharing Scheme
Consider a scenario in which you are tasked with managing the security of a bank's vault. The vault is considered impenetrable without a key, which you are g...