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Algorithmic Solution to My Insomnia
I’ve struggled with insomnia for all of my adult life. It began in college and has waxed and waned in severity ever since, correlating with stress levels…
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Your yearly dose of is-the-universe-a-simulation
Yesterday Ryan Mandelbaum, at Gizmodo, posted a decidedly tongue-in-cheek piece about whether or not the universe is a computer simulation. (The piece was filed under the category “LOL.…
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Why isn't everything normally distributed?
Heights are normally distributed because height is determined by many factors. But why are other things with many inputs not normally distributed?
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Communicating Advanced Mathematics to Kids
I’ve often thought that we could do a lot better job of explaining “advanced” mathematics concepts in simple language for the benefit of a wider audience. As a student, I never liked being told, “We’ll explain that to you next year.” As a teacher, I’ve always wanted be able to give real answers to students’…
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A Pragmatic Introduction to Signal Processing
A retirement project created and maintained by Tom O'Haver , Professor Emeritus , Department of Chemistry and Biochemistry
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Designing a Tree Diff Algorithm Using Dynamic Programming and A*
During my internship at Jane Street 1 , one of my projects was a config editing tool that at first sounded straightforward but culminated in me designing a custom tree diffing algorithm using dynamic programming, relentlessly optimizing it and then transforming it into an A* accelerated path finding algorithm. This…
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Understanding the math behind 0x5f3759df and the fast inverse square root (2012)
This post is about the magic constant 0x5f3759df and an extremely neat hack, fast inverse square root, which is where the constant comes from.
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Why is the Quintic Unsolvable?
In this article, I hope to convince you that the quintic equation is unsolvable, in the sense that I can’t write down the solution to the equation \[ ax^5 + bx^4 + cx^3 + dx^2 + ex + f = 0 \] using only addition, subtraction, multiplication, division, raising to an integer power, and taking an integer root. In fact, I…
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Kalman filters and functional programming
A paper on Kalman filtering and functional folds that I alluded to previously has been split into several papers and posted online.
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Designing state machines
Explore exciting job opportunities at Getaround. Join our international team revolutionizing carsharing and sustainable transportation. Apply today!
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Clojure Linear Algebra Refresher: Eigenvalues and Eigenvectors
I stumble upon eigenvectors and eigenvalues regularly when reading about machine learning topics. They seem to be important. They are not introduced in those...
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Matrices from a geometric perspective
Graphics is all about geometry. In particular, there are points that have a certain color, and the pattern of colors gives you a certain picture. You can change the way the points are distributed by applying certain transformations like translation (movement), rotation and scaling. While most people familiar with the…
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LaTeX Math in MS Office
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Writing a Faster Sorting Algorithm
These days it’s a pretty bold claim if you say that you invented a sorting algorithm that’s 30% faster than state of the art. Unfortunately I have to make a far bolder claim: I wrote a …
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How many floating-point numbers are in the interval [0,1]?
Most commodity processors support single-precision IEEE 754 floating-point numbers. Though they are ubiquitous, they are often misunderstood. One of my readers left a comment suggesting that picking an integer in [0,232) at random and dividing it by 232, was equivalent to picking a number at random in [0,1). I am not…
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Game Theory Reveals the Future of Deep Learning
If you’ve been following my articles up to now, you’ll begin to perceive, what’s apparent to many advanced practitioners of Deep Learning…
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Graph Isomorphism update: quasipolynomial claim restored
On January 4 I announced that Harald Helfgott pointed out an error in the analysis of my Graph Isomorphism test. The error invalidated my previous claim of quasipolynomial efficiency. The text of the announcement is appended below.
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The Minsky circle algorithm
Consider the following pseudocode: x <- 32; y <- 0; while(true){ x <- x – floor((1/8) * y); y <- y + floor((1/8) * x); plotPointAt(x, y); } x and y are always integers. This draws…
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Visualizing the Math Behind Logistic Regression and Newton's Method
The Laziest Programmer - Because someone else has already solved your problem.