The popularity of Twitter has really exploded in the past few months. The service poses a simple question: “What are you doing?” Users respond in 140 characters or less. The 140-character limit comes from the 160-character limit of SMS messages, minus a few characters for things like the user’s screen name. Twitter could probably best be described as “micro-blogging.” It’s kind of a cross between blogging and instant messaging.

People use Twitter for all kinds of reasons, everything from staying in touch with friends to receiving announcements and support from companies with a presence on Twitter. Here are a few examples:
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Mathematica has long been used by university-level faculty and researchers for work in math, physics, engineering, and many other fields. Good at everything from creating class documents and lab assignments to analyzing and visualizing data collected during experiments, Mathematica has become the software of choice for millions of academic researchers, faculty, and students because it is an all-in-one system that combines powerful computing and visualization capabilities with sophisticated documentation and presentation tools.

But in my years of working with universities as Wolfram Research’s Academic Program Manager, I’ve come to realize that many students who will become future high school teachers aren’t using Mathematica in their math and science education classes. Why is that? Some have told me that they heard somewhere along the line that Mathematica was too difficult to learn and use. Others had assumed that it was too powerful for their needs, or not completely applicable to the subjects they would be teaching. But those that do take a closer look at Mathematica are usually amazed by what they see.
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The “Droste effect” is when images recursively include themselves. The name comes from Droste brand cocoa powder, which was sold in 1904 in a box that showed a nurse carrying the same box which, in turn, showed the nurse carrying the box, and so on. The simplest form is to use a scale and transform on an image to place an exact copy within it, and then repeat. Take a look at this Demonstration using the original Droste box artwork. But much more interesting results can be achieved when you get complex analysis involved. M.C. Escher was the first to popularize applying conformal mapping to images, but with computers we can easily apply the same ideas to photographs, to get results like this:

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The idea struck me as I was toweling off after a swim: what would happen if I crossed the Mercedes-Benz and Grignani logos from my February 2009 blog post, Exploring Logo Designs with Mathematica? Hybrid vigor is a well-known phenomenon responsible for increased yields in corn, and metaphorically, for the economic and cultural flourishing of civilizations that engage in foreign trade. Would the progeny of Benz and Grignani show similar effects?

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I’m a GPS addict. I have a handheld GPS, a computer GPS, a GPS phone, two GPS watches, two GPS cameras, and maybe some others. Wherever I go, chances are pretty good I have at least one GPS with me. Anytime I run/bike/hike/walk/ski I keep a record of where I went using GPS. Now that I have all this data I want to make use of it in a meaningful way. Mathematica is a fantastic tool to analyze all my geographic data.

Here’s an example from a recent trail run I did at a nearby park. The data is stored in a GPX (GPS exchange format) file, which is a specific type of XML. We can bring the data into Mathematica using Import.
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Each release of Mathematica brings with it powerful new tools that can be applied to an ever-widening range of fields, so it’s no surprise that a great many faculty members at all levels choose Mathematica as the tool around which to base their curricula. My first introduction to the software came during my undergraduate education when I took a differential equations course. As my professor went through the syllabus and explained what topics we would cover that semester, she also mentioned that we would be using Mathematica and showed some examples of what it could do.

Having never used mathematical technology more sophisticated than a graphing calculator, I did admittedly have a bit of a rocky start with the language and syntax. I remember my professor spending a lecture period going over the basics of how to enter input and perform computations, but I decided to dismiss all that advice and just figure it out myself—which seemed to be a good idea at the time. I probably should have paid closer attention to my professor’s tutorial, because I soon became frustrated at what seemed like a very rigid language. As I investigated further—mostly by looking at all the examples in the documentation—I quickly realized that by learning a few simple rules one could effectively harness the program and produce powerful results. Ultimately it was Mathematica’s consistent language design that got me excited about learning more.
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Recent versions of Mathematica introduced useful data functions related to linguistics. In Version 7, Mathematica’s integrated string manipulation and visualization functions provide a powerful platform for computational linguistics. Both DictionaryLookup and WordData give programmatic access to curated data that’s ready for computation.

DictionaryLookup has been extended to cover more languages, while WordData has information on word meaning, structure, and usage, as well as cognitive and grammatical relationships between words. Let’s look at a range of examples, starting with some interesting and amusing word facts.

DictionaryLookup currently contains word lists for 27 different languages:

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Recently, I was in Puerto Rico giving Mathematica talks to faculty and students within the University of Puerto Rico and Inter American University of Puerto Rico system. First off, I loved the islands and the weather. Second, the people were enthusiastic, understanding of my broken Spanish, and wonderful people with whom to interact and discuss Mathematica integration.

On my flight home, I realized that it would be good to document a little bit of my experience talking with educators about integrating Mathematica into courses and how Mathematica 7 has completely changed my perspective (and uniformly, their perspective) as well.

I’ve now been at Wolfram Research almost 12 years. My experiences at the company have been quite varied. I have traversed the country in the MathMobile (see below) showing lots of people at schools, companies, and government labs how to start using Mathematica; I have sat at a desk in technical support answering questions from longtime users on how to do (and fix) pretty detailed programming; I have worked in public relations to convey to the press why Mathematica is such an important topic for them to cover.
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