Given a dataset, can we use Bayes’ Theorem to estimate how much we expect to learn from a set of features for a classification task? Introduction If you have ever been given a set of…
Ernst Ising’s Original Solution to His Model
How did Ernst Ising originally solve the “Ising model?” In 1920 Wilhelm Lenz proposed that ferromagnetism could be explained through the local interactions of spins in a material, and in1922 he gave this problem to…
Lollipop on an Inclined Plane
When I first started learning mechanics, I began with Fundamentals of Physics by Halliday, Resnick, and Walker. It was one of the canonical texts for introductory university physics, and it was pitched at students who…
The 2020 Election and The Probability of Electoral Mis-Alignment
In American politics, it is not common for a presidential candidate to win the Electoral College vote while losing the popular vote, but if it happens, one can be sure that there will be a…
Toy Model of Drag Forces
Can we compute the velocity-scaling behavior of drag forces using the simple model of an object moving through a gas cloud? When physicists discuss the “drag force” experienced by an object due to its interaction…
Three-Dice Problem in the Large N Limit
A few years ago, a roommate was going to various career fairs as a rep for his company, and (as one does) he spent some of the time away from his booth collecting swag from…
Superluminal Waves on a Train
Is faster than speed-of-light travel possible given the laws of relativity? One of the postulates of special relativity is that photons (and actually all massless particles) travel at the speed of light, and a corollary…
Renormalization Group of the Classical Pendulum
Does the simple mechanical system of the pendulum exhibit the properties inherent in the renormalization group? The renormalization group is a result from 20th-century physics, but its conceptual underpinnings are quite old. In certain manifestations,…
NYT Digits Puzzle – Generating Functions, Catalan Numbers, Complexity
(NOTE: As of August 18, 2023 the NYT Digits puzzle has been removed the the NYT website. A copy of the game has been reproduced on a new private site: https://engaging-data.com/digitsgame/) In the previous post,…
NYT Digits Puzzle – Incremental Programming and Recursion
(NOTE: As of August 18, 2023 the NYT Digits puzzle has been removed the the NYT website. A copy of the game has been reproduced on a new private site: https://engaging-data.com/digitsgame/) About a month ago,…