In this post I will describe one small but important part of the theory of causal inference, a causal calculus developed by Pearl. This causal calculus is a set of three simple but powerful algebraic rules which can be used to make inferences about causal relationships. In particular, I’ll explain how the causal calculus can sometimes (but not always!) be used to infer causation from a set of data, even when a randomized controlled experiment is not possible. Also in the post, I’ll describe some of the limits of the causal calculus, and some of my own speculations and questions.

We study fifteen months of human mobility data for one and a half million individuals and find that human mobility traces are highly unique. In fact, in a dataset where the location of an individual is specified hourly, and with a spatial resolution equal to that given by the carrier's antennas, four spatio-temporal points are enough to uniquely identify 95% of the individuals. We coarsen the data spatially and temporally to find a formula for the uniqueness of human mobility traces given their resolution and the available outside information. This formula shows that the uniqueness of mobility traces decays approximately as the 1/10 power of their resolution. Hence, even coarse datasets provide little anonymity. These findings represent fundamental constraints to an individual's privacy and have important implications for the design of frameworks and institutions dedicated to protect the privacy of individuals.

MathJax is an open source JavaScript display engine for mathematics that works in all modern browsers. No more setup for readers. No more browser plugins. No more font installations… It just works.

If you are a small software company, you have got a much better chance of getting a decent sized chunk of a small market, than 1% of a huge market. As a general rule of thumb, I would say pick a market for which you have got a decent chance of getting in the top ten Google results for important search terms (power laws again). You can even do this by going after a small segment of a big market. e.g. a CRM solution aimed at companies that trade on EBay. Or perhaps a CRM solution aimed at companies that trade on EBay in the Spanish-speaking market. You can always broaden your focus if you are successful in a small market. Whatever you do, don’t stand in front of investors and pitch them the 1% fallacy. It makes you look an idiot. I should know, because I’ve done it.

Julia is a high-level, high-performance dynamic programming language for technical computing, with syntax that is familiar to users of other technical computing environments. It provides a sophisticated compiler, distributed parallel execution, numerical accuracy, and an extensive mathematical function library. The library, largely written in Julia itself, also integrates mature, best-of-breed C and Fortran libraries for linear algebra, random number generation, signal processing, and string processing. In addition, the Julia developer community is contributing a number of external packages through Julia’s built-in package manager at a rapid pace. Julia programs are organized around multiple dispatch; by defining functions and overloading them for different combinations of argument types, which can also be user-defined. For a more in-depth discussion of the rationale and advantages of Julia over other systems, see the following highlights or read the introduction in the online manual.

Do you like fiction and mathematics? Are you looking for a book or story that might be useful for the students in your math class? Are you interested in what our society thinks about mathematicians? Then you've come to the right place. This database lists over one thousand short stories, plays, novels, films, and comic books containing math or mathematicians.

PROBLEM: You are a web programmer. You have users. Your users rate stuff on your site. You want to put the highest-rated stuff at the top and lowest-rated at the bottom. You need some sort of "score" to sort by.

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CORRECT SOLUTION: Score = Lower bound of Wilson score confidence interval for a Bernoulli parameter.

The Gothenburg group has developed a psychological model of patterns as seen and selected by humans, and incorporated it in their IQ test solving programs. The result is a program that attacks abstract problems using approaches similar to those a very smart person would use.

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"Our programs are beating the conventional math programs because we are combining mathematics and psychology. Our method can potentially be used to identify patterns in any data with a psychological component, such as financial data. But it is not as good at finding patterns in more science-type data, such as weather data, since then the human psyche is not involved," says Strannegård.

I've noticed over the years that different numbers have their own "personalities". If you're a mathematician doing a calculation and you get the answer 248, it means something completely different than if you get 247 — because the number 248 shows up in all sorts of amazing places, while 247 is just dull. So when I was invited to give the Rankin Lectures in Glasgow, I thought it would be fun to explain this idea with some examples. I decided to give separate talks on three of my favorite numbers: 5, 8, and 24.

The first one should be quite easy for everyone. After that they get harder, but they're still meant to be expository and fun, Here you can see streaming videos of my talks — and also my slides, which have links to references that fill in the details.

Every educated person really ought to have a basic understanding of accounting. Just like maths, science, programming, music, literature, history, etc., it’s one of those things which helps you make sense of the world. Although dealing with money is not much fun, it’s an unavoidable part of life, so you might as well take a few minutes to understand it.

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Eventually I figured it out: basic accounting is just graph theory. The traditional ways of representing financial information hide that structure astonishingly well, but once I had figured out that it was just a graph, it suddenly all made sense.