My new office space suffers from a shortage of photons, so I’ve been wiring up light fixtures. As I was snaking 14-gauge cable through the ceiling cavity, I began to wonder: Why is it called 14-gauge? I know that the gauge specifies the size of the copper conductors, but how exactly? The number can’t be a simple…
L19 = 208168199381979984699478633344862770286522453884530548425639456820927419612738015378525648451698519643907259916015628128546089888314427129715319317557736620397247064840935
;; Done Twice as a "Dojo" at Villiers Park on Thursday 19th March 2015 ;; To groups of about 15 ultra-clever teenagers who were thi...
Big O notation is a great tool. It allows one to quickly make smart choices among various data structures and algorithms. But sometimes a casualBig O analy...
Around 2006, my friend Dan Christensen created a fascinating picture of all the roots of all polynomials of degree ≤ 5 with integer coefficients ranging from -4 to 4:
I was out for drinks with Josh Long and some other friends from work, when he found out I "speak math." He had come across this …
Posts and writings by Datanice
Mathematics, applications of mathematics to life in general, and my life as a mathematician.
Apparently MTA (the company running the NYC subway) has a real-time API. My fascination for the subway takes autistic proportions and so obviously I had to analyze some of the data.
A space efficient UTF-8 binary-to-text encoding
Although the mathematics involved with neural networking is not a trivial matter, a user can rather easily gain at least an operational understanding of their structure and function.
How Stephen Wolfram helped with the theory of interstellar travel, communication with aliens and questions from the actors in “Arrival”, the movie.
Graph theory is my favourite topic in mathematics and computing science and in this blog post I’ll introduce an algebra of graphs that I’ve been working on for a while. The algebra has become my go-to tool for manipulating graphs and I hope you will find it useful too.
Benedikt Bitterli's Portfolio
In the post on matrices in Codea I mentionned that an affine transformation (things like rotation, scaling, translation) ℝ 3 → ℝ 3 could be specified by giving four vectors. In this post I want to examine that a little more closely for the special case of a rotation. That is to say: how can I encode a rotation in ℝ 3…
Some time ago I gave a talk in which I showed that something unexpected happened with a deck of playing cards. I had some volunteers try it, and while they did so I talked about just how many orderings there are for 52 cards. I computed (an approximation to) $52!$ (52 factorial) by hand. It's not so hard - you just…
Note: the following is a record of some whimsical mathematical thoughts and computations I had after doing some grading. It is likely that the sort of problems discussed here are in fact well studi…
This is part 11 of Categories for Programmers. Previously: Natural Transformations. See the Table of Contents. Introduction to Part II In the first part of the book I argued that both category theo…
I have a simple fast Fourier transform implementation on the page Free small FFT in multiple languages , whose asymptotic time complexity is the optimal Θ( n log n ). I wanted to know how much additional speed-up could be obtained by reorganizing memory access patterns and using SIMD vector arithmetic instructions…
Everyone should read Leo Breiman's 2001 article, Statistical Modeling: The Two Cultures . (Summary: Traditional statisticians start with a distribution. They try to identify the parameters of the distribution from data that were actually generated from it. Applied statisticians start with data. They have no idea where…
graph theory, music theory
Today I will present how to implement in Python a simple yet effective algorithm for proceduraly generating 2D landscapes. It is called Midpoint Displacement (or Diamond-square algorithm,…
Update! I tested more hash functions in a follow-up post. See More Hash Function Tests .
Detecting (and correcting) errors in digital signals.
