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The 8000th Busy Beaver number eludes ZF set theory (2016)
I’ve supervised a lot of great student projects in my nine years at MIT, but my inner nerdy teenager has never been as personally delighted by a project as it is right now. To…
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Using k-d trees to efficiently calculate nearest neighbors in 3D vector space
What would the world look like if there were only 16 colors? I use k-d trees to perform nearest neighbor search to find out.
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City street orientations around the world
This post is adapted from this research paper that you can read/cite for more info. It analyzes and visualizes 100 cities around the world.
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Gamifying propositional logic: QED, an interactive textbook
About six years ago on this blog, I started thinking about trying to make a web-based game based around high-school algebra, and ended up using Scratch to write a short but playable puzzle game in …
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“I-Cut-You-Choose” Cake-Cutting Protocol Inspires Solution to Gerrymandering
CMU researchers say getting political parties to equitably draw congressional district boundaries can be as easy as sharing cake.
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How to explain infinity to kids
From the highly eclectic blog of Mark Dominus
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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…
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Towards λ-calculus
lambdaway is built on a wiki engine, lambdatank, and a small Lisp dialect, lambdatalk.
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The Federalist Papers: Author Identification Through K-Means Clustering
Using K-means clustering on writing style to classify disputed Federalist Papers authorship.
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The secret life of NaN
The floating point standard defines a special value called Not-a-Number (NaN) which is used to represent, well, values that aren’t numbers. Double precision ...
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Algorithms tutorial series for beginners
As a developer, you have the power to change the world! You can write programs that enable new technologies. For instance, develop software to find an earlier diagnosis of diseases. But that’s not the only way. You might do it indirectly by creating projects that make people more productive and help them free up time…
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How AI Training Scales
Stay up to speed on the rapid advancement of AI technology and the benefits it offers to humanity.
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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…
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The path that the decimal number system took from India to medieval Europe
In every day life we all do our calculations, whether for the taxman, our purchases, paying the household bills or in some academic discipline, using the place value decimal number system. It consi…
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Making Sense of Super Smash Bros. Melee
Draft: v1.1 | Posted: 1/9/2018 | Updated: 1/29/2018 | confidence of success: 85% | estimated time to completion: 1/15/2018 | importance: High
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MIT mathematicians solve age-old spaghetti mystery
Researchers have long have puzzled over why it’s so hard to break a piece of dry spaghetti into only two pieces. A new MIT study follows up on the musings of physicist Richard Feynman, showing how and why it can be done.
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The algebra and calculus of algebraic data types
Just as algebra is fundamental to the whole of mathematics, algebraic data types (ADTs) are fundamental to many common functional programming languages. They’re the primitives upon which all of our richer data structures are built, including everything from sets, maps, and queues, to bloom filters and neural networks .
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Thoughts On Machine Learning Accuracy
This blog shares some brief thoughts on machine learning accuracy and bias. Let’s start with some comments about a recent ACLU blog in which they ran a facial recognition trial. Using Rekognition, the ACLU built a face database using 25,000 publicly available arrest photos and then performed facial similarity searches…
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Learning Concepts with Energy Functions
Stay up to speed on the rapid advancement of AI technology and the benefits it offers to humanity.
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Decision Tables
I really like decision tables but they’ve fallen out of common knowledge. Let’s fix that. A decision table is a means of concisely representing branching and conditional computations. In the most basic form, you have some columns that represent the “inputs” as booleans and some columns that represent outputs and…
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Advanced techniques to implement fast hash tables
Array and hash table are probably the most important data structures. Some programming languages such as Perl, Lua and Javascript, almost build the language core on top of the two data structures. …
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Mod and remainder are not the same
A remainder and a modulus look so very similar, but they are not the same thing and worse, are treated differently by different programming languages. Do you know how your language handles mod?
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Reinforcement Learning with Prediction-Based Rewards
Stay up to speed on the rapid advancement of AI technology and the benefits it offers to humanity.
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Kelly Criterion (2007)
It’s fairly clear when one should buy a particular stock. One should buy stock when it is undervalued. What I have always wondered about is how much stock one should buy. A few months ago I stumbled upon the answer which is given by the Kelly criterion . It says that one should invest an amount to maximize one’s…
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How long is that Bézier?
Blog of Raph Levien.
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Mathematician-M.D. claims to have solved the 110-year-old Lindelöf hypothesis
A completely new approach suggests the validity of the 110-year-old Lindelöf hypothesis, opening up the possibilities of new discoveries in quantum computing, number theory and cybersecurity
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