Most schools teach number systems the same way. First they teach natural numbers (or “counting numbers”), then integers, rationals, reals, and complex numbers, in that order. Rationals are countable and reals are not, but that’s okay. Once you start taking roots, you need a number system more powerful than a countable…
A blog by Sam Greydanus
I found the creator of Rainbow Table's paper, aimed at cryptanalysts, was pretty inaccessible considering the simplicity and elegance of Rainbow Tables, so this is an overview of it for a layman.
If you make $10 profit each time you sell a product, what cost per conversion should you aim for? Answering this question isn't easy, but it can teach us a…
A few weeks ago I wrote about Kuhn’s theory of paradigm shifts and how it relates to Bayesian inference. In this post I want to back up a little bit and explain what Bayesian inference is, and eventually rediscover the idea of a paradigm shift just from understanding how Bayesian inference works.
How can a theorem prover use the convention that 1/0=0 and still be consistent?
Parts 1 and 2 are found here and here
It is thought that the wheel was invented more than five thousand years ago, yet modern machine learning tools were only developed in the past few decade...
Research in Scientific Computing in Undergraduate Education2020117 points30 commentsMath & Algorithms details
DARPA challenges The Defense Advanced Research Projects Agency (DARPA) has issued 23 mathematical challenges. DARPA says the solution of any one of these challenges would have the effect of “…
Sketches of an interactive arithmetic for programming by Glen Chiacchieri.
Notes on Interval Tree Clocks
If you click on this picture, you’ll see a zoomable image of the Milky Way with 84 million stars: But stars contribute only a tiny fraction of the total entropy in the observable Universe. If…
by Carles Gelada and Jacob Buckman WARNING: This is an old version of this blogpost, and if you are a Bayesian, it might make you angry. Click here for an updated post with the same content. Context: About a month ago Carles asserted on Twitter that Bayesian Neural Networks make...
The map is not the territory reminds us that our mental models of the world are not the same as the world itself. It cautions against confusing our abstractions and representations with the complex, ever-shifting reality they aim to describe.
Decision tables are easy, simple, and powerful. You can teach them in five minutes and write one in half that time. You can look at a table and understand what it’s saying, see if it matches your problem, and check for design flaws. So it’s kinda weird that there’s basically nothing about them online. I wrote an…
For latency, anyway. A common architecture pattern is the “task queue”: tasks enter an ordered queue, workers pop tasks and process them. This pattern is used everywhere from distributed systems to thread pools. It applies just as well to human systems, like waiting in line at a supermarket or a bank. Task queues are…
I am an economist at the Federal Trade Commission with a very basic statistics question, one that I have put to several fairly high-powered econometricians, and to which no one has had a satisfying answer.
Several years ago, I developed a public lecture on the cosmic distance ladder in astronomy from a historical perspective (and emphasising the role of mathematics in building the ladder). I previous…
Every philosophy has holes, and it is the responsibility of proponents of a philosophy to point out these problems. Here are a few holes in Bayesian data analysis: (1) the usual rules of conditional probability fail in the quantum realm, (2) flat or weak priors lead to terrible inferences about things we care about…
With this year’s International Conference on Machine Learning (ICML) being over, it is time to have another instalment of this series. Similar to last year’s post , I shall cover several papers that caught my attention because of their use of topological concepts—however, unlike last year, I shall not restrict the…
Patrick Honner tweeted a few days ago: My 7 yo pointed out that our 300 piece puzzle actually contains 18 x 18 = 324 pieces and I just don’t know what to believe anymore. — Patrick Honner (@M…
Lately, I’ve been playing around with inventing a visual writing system for lambda calculus.
Using graph theory and Ryanair route data to find cheap multi-city flight loops through Europe.
This is our most recent work, started and led by Aleksey Charapko . (This is a joint post with him.) You can get the paper at arxiv.org . Th...
Pathfinding is one of these topics that usualy baffles game developers. The A* algorithm in particular is poorly understood, and the general belief seems to be that it’s arcane magic.
