Finding the median in a list seems like a trivial problem, but doing so in linear time turns out to be tricky. In this post I’m going to walk through one of my favorite algorithms, the median-of-medians approach to find the median of a list in deterministic linear time. Although proving that this algorithm runs in…
Tired of equations and matrices? Ready to learn the easy way? This post explains the Kalman Filter simply with pictures and examples!
I recently learned an interesting fact about Fibonacci numbers while watching a random number theory video on YouTube. Fibonacci numbers can be used to approximately convert from miles to kilometers and back. Here is how. Take two consecutive Fibonacci numbers, for example 5 and 8. And you're done converting. No...
A guide on how to generate sudokus of any difficulty.
If an expert can't understand your explanation, you've dumbed it down too much!
Math from Three to Seven: The Story of a Mathematical Circle for Preschoolers, Alexander Zvonkin (Moscow Center for Continuing Mathematical Education, 2007).
I wrote a little book about entropy; here’s the current draft: • What is Entropy? If you see typos and other mistakes, or have trouble understanding things, please let me know! An altern…
Sweep-and-prune is my go-to algorithm when I want to quickly implement collision detection for a game. I think it’s an awesome and elegant algorithm, so I wrote a post about it.
The man who gave us the solution to the Entscheidungsproblem
Rasmus Kyng has written the near-perfect algorithm. It computes the maximum transport flow at minimum cost for any kind of network – be it rail, road or electricity – at a speed that is, mathematically speaking, impossible to beat.
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.
I spent 2022 learning to draw and was blindsided by the rise of AI art There is lots to say about this, whether it has been or will be a good thing for artists and society in the long run. I hope to write about it in another post. models like Stable Diffusion. Suddenly, the computer was a better artist than I could…
A traditional subjective Bayesian will assume a data generating distribution (aka a likelihood when viewed as a function of the parameters). Then, conditional on this assumption, they encode their prior beliefs as a prior distribution over parameters. After this, they turn the crank on posterior inference and don’t…
This is basically a compilation of the lecture notes I wrote when teaching 36-401, Modern Regression, in fall 2015 . I offer it here on the chance that it might be of interest to those learning, or teaching, linear regression. There's no shortage of resources on that, but I have tried to present the subject as though…
Pavel has found a new 3-state 4-symbol Busy Beaver champion which can compute an “Ackermann-level” function and halts with exactly
Avi Wigderson is the recipient of the 2023 ACM A.M. Turing Award for foundational contributions to the theory of computation, including reshaping our understanding of the role of randomness in computation, and for decades of intellectual leadership in theoretical computer science.
Physics likes optimization! Subject to its boundary conditions, the time evolution of a physical system is a critical point for a quantity called an action. This point of view sets the stage for Noether's principle , a remarkable correspondence between continuous invariances of the action and conservation laws of the…
A visual, interactive guide to what bloom filters are, when you would use them, and how they work.
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I recently implemented a small program to visualize the inner workings of a scheme that compresses floating point timeseries by XORing subsequent values. The resulting visualizations are quite neat…
If you’ve done any 3D programming, you’ve likely encountered the zoo of techniques and representations used when working with 3D rotations. Some of them are better than others, depending on the situation.
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 …
On the one hand they are easy to explain, they are just numbers that have no factors other than one and themselves, but on the other hand they contain endless complexity. They show up in numerous places, ranging from mathematical concepts and conjectures to interesting looking visualizations and cryptography…
Pathfinding applied to the software solution domain
Update (April 19): Yilei Chen announced the discovery of a bug in the algorithm, which he does not know how to fix. This was independently discovered by Hongxun Wu and Thomas Vidick. At present, th…
If you overheard the phrase "1 in a million chance" in someone else's casual conversation, what might they be talking about?
