TLA, the Temporal Logic of Actions is the core of TLA+. It is a temporal logic that minimizes the use of temporal reasoning in favor of more ordinary mathematics. It is a general mathematical framework for describing and reasoning about algorithms and systems.
The Dow Jones Industrial Average (or 'the Dow', ^DJI, DJIA), is a stock market index created back in 1896 by Charles Dow, a journalist. The goal of the index is provide a view of the stock market's health. The Dow is an index of just 30 (arbitrarily chosen) stocks, weighted by the stock prices of its component…
Just announced $latex {\dots}&fg=000000$ Oded Goldreich is one of the top researchers in cryptography, randomness, and complexity theory. Today Ken and I wish to thank the Knuth Prize Committee…
Douglas G. Steigerwald joined the faculty of the Department of Economics at the University of California, Santa Barbara after completing an M.A. in Statistics and a Ph.D. in Economics at the University of California, Berkeley. His research and teaching focus on frontier econometric methods at the intersection of…
The abacus counting device dates back thousands of years but has, in the past century, been replaced by calculators and computers. But studies show that abacus
For today’s post, I’ve drawn material not just from one paper, but from five! The subject matter is ‘word2vec’ – the work of Mikolov et al. at Google on efficient vect…
Edit 12/19/2017: added a new subsection on analyzing Chutes & Ladders as an Absorbing Markov Chain.
The following tweet has been making the rounds on social media: Notice that since the Democrats won overall, it would be impossible for Republicans to win all seven districts, no matter how the map…
Out there in the wider world—OK, OK, among Luboš Motl, and a few others who comment on this blog—there appears to be a widespread opinion that P≠NP is just “a fashionable dogma of…
In this post I describe the Asynchronous Computability Theorem, which uses tools from Algebraic Topology to show whether a task is solvable…
Printer Friendly: The whole text in one file , all 164,000 words, convenient for printing. (The printed length will vary, depending to your browser settings. For me it’s 401 pages.)
Heap's algorithm for constructing all permutations is efficient and simple but not easy to understand. This article explains Heap's algorithm by example.
The recommended scrypt parameters in the Go docs were recently brought up for discussion given they haven’t changed since 2009.
TLA+ is a formal specification and verification language intended to help engineers specify, design and reason about complex, real-life algorithms and software or hardware systems. We explore its motivation, application and principles of design.
In the two months since I last blogged, the US has continued its descent into madness. Yet even while so many certainties have proven ephemeral as the morning dew—the US’…
Today's article is a short one. Not because Singular Value Decomposition (SVD) is not important, but because it is so ubiquitous that we'll touch it in other...
Floating-point math puts a big overhead on a computer that doesn't have a floating-point coprocessor; but we really do need floating-point for all but the simplest operations— or do we?? Can we really do things like trig, log, and square-root functions without floating point?
When discussing the validity of the Axiom of Choice, the most common argument for not taking it as gospel is the Banach-Tarski paradox. Yet, this never particularly bothered me. The argument …
Edward Tufte’s The Visual Display of Quantitative Information (1998, 2nd edition 2001) is a classic book, arguably his best, and certainly a key text in the field of information graphics (whi…
In software, we generate random numbers by calling a function called a "random number generator". Such functions have hidden states, so that repeated calls to the function generate new numbers that appear random. If you know this state, you can predict all future outcomes of the random number generators. O'Neill, a…
In this post I'm going to explore how a mathematical concept can be redefined in progressively more computer-oriented terms, all the way from high level languages down to machine code, ready for direct execution by a computer. To that end, I'm going to define the same logic in several different but related formats:
Sieve of Eratosthenes animation Source: Wikipedia[0] One of the things we need to do when finding Perrin Pseudo-Primes is to recognise prime numbers so we can see if the numbers predicted by the Perrin test to be prime, are. So we need to generate primes. For small primes (for some definition of "small") this can be…
Let’s say you are trying to find the distance between two points in 2D, but that these points are in a universe that “wraps around” like old video games – leaving the screen…
Humans don’t start their thinking from scratch every second. As you read this essay, you understand each word based on your understanding of previous words. You don’t throw everything away and start thinking from scratch again. Your thoughts have persistence.
