1981
Hilbert Transform
Concise summary of the Hilbert transform: mathematics, effects on signals, and applications in telecommunications.
Top posts
Every blog post that took off on Hacker News, ranked by the votes of its best submission. 2,851 posts.
1982
Generalizations of Fourier analysis (2021)
When I first learned about Fourier series and integrals, I hated it because it seemed like a collection of many ad-hoc definitions, formally related but very different.
1983
The Vector Space of the Polish Parliament in Pictures
In fact, only of the lower house, the Sejm. During its current term, 460 deputies voted 5545 times since the 8th of November 2011. The Sejm website publishes the individual results of the votes as …
1984
1985
Things I would like to see in a computer algebra system
If I were to design a computer algebra system (CAS) from scratch today, I would try to achieve the following goals. Several ideas have already been implemented in one system or another, but certainly not all at once. Some ideas could be adopted by existing CASes; others would require fundamentally different designs or…
1986
My God, It’s Full of Dots
Please click or tap in the gray square below. It will fill with a jolly tableau of colored disks—first big blue ones, then somewhat smaller purple ones, and eventually lots of tiny red dots.
1987
Towards deep symbolic reinforcement learning
Towards deep symbolic reinforcement learning Garnelo et al, 2016 Every now and then I read a paper that makes a really strong connection with me, one where I can’t stop thinking about the imp…
1988
1989
1990
TLA+ in Practice and Theory, Part 3: The Temporal Logic of Actions
TLA, the Temporal Logic of Actions is the core of TLA+. It is a temporal logic that minimizes the use of temporal reasoning in favor of more ordinary mathematics. It is a general mathematical framework for describing and reasoning about algorithms and systems.
1991
Effort – a possibly new algorithm for LLM Inference
A possibly new algorithm for LLM Inference. Adjust smoothly - and in real time - how many calculations you'd like to do during inference.
1992
Calculating a record-breaking 31.4T digits of Pi with GCP
Pi in the sky: Calculating a record-breaking 31.4 trillion digits of Archimedes’ constant on Google Cloud
1993
I disagree with Turing and Kahneman regarding statistical evidence (2014)
It’s funny. I’m the statistician, but I’m more skeptical about statistics, compared to these renowned scientists.
1994
Why the Dow is a useless market index
The Dow Jones Industrial Average (or 'the Dow', ^DJI, DJIA), is a stock market index created back in 1896 by Charles Dow, a journalist. The goal of the index is provide a view of the stock market's health. The Dow is an index of just 30 (arbitrarily chosen) stocks, weighted by the stock prices of its component…
1995
1996
1997
Why category theory matters in programming
Divide and conquer has been a core strategy in software engineering. We decompose our systems into smaller modules with focused, simple…
1998
1999
Tofolli gates are all you need
Any Boolean function can be computed with Tofolli gates, and Tofolli gates are reversible, and so any Boolean function can be computed reversibly.
2000
Dividing a Square into 7 Similar Rectangles
This is a continuation of my post Dividing a square into similar rectangles, in which I discussed this puzzle: if you partition a square into n similar rectangles, what proportions can these rectan…
2001
A Graphical Introduction to Lattices
Here is my (extended) family tree: Everyone in the tree shares at least one common ancestor and at least one common descendant. This ...
2002
2003
Crafting formulas: Lambdas all the way down
We build complex mathematical formulas bottom-up using pure lambda calculus. Includes instructions of how to translate Taylor series and other approximations to lambda terms.
2004
Oded Wins the Knuth Prize
Just announced $latex {\dots}&fg=000000$ Oded Goldreich is one of the top researchers in cryptography, randomness, and complexity theory. Today Ken and I wish to thank the Knuth Prize Committee…
2005
Understanding Convolutions (2014)
neural networks , convolutional neural networks , convolution , math , probability
2006
A step by step backpropagation example (2015)
Background Backpropagation is a common method for training a neural network. There is no shortage of papers online that attempt to explain how backpropagation works, but few that include an example…
2007
Commit Graph Drawing Algorithms
This article is one chapter of my master thesis entitled “Design and implementation of a graphical user interface for git”. It describes the algorithm I designed to draw the commit graph in my own prototype git client called gitamine. I have adapted the content so that it fits better with this blog. Drawing graphs is…
2008
Hotelling’s Game, or Why Gas Stations Have Competitors Nearby
There are hundreds of gas stations around San Francisco in the California Bay area. One might think that gas stations would spread out to serve local neighborhoods. But this idea is contradicted by a common observation. Whenever you visit a gas station, there is almost always another in the vicinity, often just across…
2009
The Coin Flip: A Fundamentally Unfair Proposition? (2009)
Douglas G. Steigerwald joined the faculty of the Department of Economics at the University of California, Santa Barbara after completing an M.A. in Statistics and a Ph.D. in Economics at the University of California, Berkeley. His research and teaching focus on frontier econometric methods at the intersection of…
2010
Echo Chess: The Quest for Solvability
Chess puzzles, but you are what you eat.