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Analyzing Your Email with Mathematica

In Stephen Wolfram's recent blog post about personal analytics, he showed a number of plots generated by analyzing his archive of personal data. One of the most common pieces of feedback we received was that people wanted to know how they could perform the same kind of analysis on their own data. So in this blog post I'm going to show you how to analyze your email the same way Stephen Wolfram did. Naturally, we did all the data cleaning and analysis for Stephen's data in Mathematica, so we'll be using Mathematica for everything here as well. All the code can be downloaded here. Let's start with that really cool diurnal plot Stephen did of his outgoing email. This plot shows the date and time each email was sent, with years running along the x axis and times of day on the y axis:
Paul-Jean Letourneau, Lead Computational Biology Developer, Algorithms R&D
Computation & Analysis

Making of the “Facts of the Moment” Plaque for the David Cameron Visit

Several people have asked me to write about the virtual plaque that we made for the official opening of the Wolfram Research Europe office by UK Prime Minister David Cameron. The concept that came out of the short brainstorming meeting was to have a button on an iPad that would trigger a video on our display board, leading to an image showing facts about the world at the moment of revelation. This is the story of how we made it happen.
Jon McLoone, Director, Technical Communication & Strategy
Computation & Analysis

Happy 10*9*8+7+6-5+4*321 !

I was amazed to see this tweet from our friends at the Museum of Mathematics:

10*9*8+7+6-5+4*321Happy New Year!

— Museum of Math (@MoMath1) January 3, 2012 A quick check with Mathematica verified that, yes indeed, 10*9*8+7+6-5+4*321 = 2012. Wow! How in the world did anyone discover that rare factoid? And how long will it be until another year arrives that can be similarly expressed? That's the sort of question that's so easy to answer with Mathematica that I couldn't not have a look. It turns out that what seemed to me like a rare jewel is as common as dirt. In fact, there is only one year in the next 100 that can't be expressed by interspersing +, -, *, /, or nothing between the numbers in order from 10 to 1! In subsequent correspondence with George Hart, the museum's Chief of Content, he told me that he learned the idea from Hans Havermann, who wrote about it in a blog post last year. I've discovered what he had up his sleeve: abundant computing.
Christopher Carlson, Senior User Interface Developer, User Interfaces
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The Longest Word Ladder Puzzle Ever

UPDATE: The solution to the puzzle and more comments from Jon have been added at the bottom of the post. On the long flight to the recent Wolfram Technology Conference, I ended up on the puzzle page of a newspaper. My attention was drawn to a word ladder puzzle, where you must fill in a sequence of words from clues, but each word differs from the previous by only a single letter. Here, for example, is a simple puzzle already solved:
best from a position of superiority or authority
bast strong woody fibers obtained especially from the phloem of from various plants
bash a vigorous blow
bath a vessel containing liquid in which something is immersed (as to process it or to maintain it at a constant temperature or to lubricate it)
math a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement
I wasn't going to do a blog entry on this, as it is a very similar task to my "Exploring Synonym Chains" post that I wrote some time ago, but that changed with a chance conversation at the (excellent) Technology Conference. Proving that one never stops learning, Charles Pooh, one of our graph theory developers, pointed out to me that my synonyms item could have been done much better. I had broken one of the very rules that I wrote about in my "10 Tips for Fast Mathematica Code" entry—"Use built-in functions." I had effectively re-implemented the built-in Mathematica commands GraphPeriphery and GraphDiameter. So, armed with these two new functions, let's find the longest word ladder puzzle that can be made using Mathematica's English dictionary.
Jon McLoone, Director, Technical Communication & Strategy
Computation & Analysis

11/11/11 11:11:11—The Right Time to Look at a Number

World War I officially ended in 1918 at the 11th hour of the 11th day of the 11th month. Remembrance Day is observed in Commonwealth countries to recall the end of the war and to remember the members of the armed forces who gave their lives for the cause. This year we observe Remembrance Day on 11/11/11. Beyond the somberness of this memorial day, those of us who are mathematically inclined consider the surprising ways we can combine 1s to achieve beautiful results. Some of these combinations involve rather unpleasant calculations, so we'll let Mathematica do the heavy lifting while we marvel at the results! Today I'll share 11 interesting places in which 1 appears. Let's jump in. 1. Can anything of interest come from combining the humble digit 1 with the square root and plus symbol? As the demonstration below suggests, given the right nesting, you get an infinite series that converges to φ = 1.61803..., the golden ratio.
Sol Lederman, Technical Communications Specialist, Technical Communication & Strategy Group
Computation & Analysis

Industrial Pumpkin Carving with Mathematica

The art of pumpkin carving is hard to master, yet once a year parents in many countries are asked to perform this traditional and messy form of art. It's time for a change in this old tradition. In fact, our colleague Jon McLoone already made a significant advance in pumpkin carving, mainly using implicit functions and RegionPlot3D. This year, I decided to make a contribution of my own that is more interactive and easier to use, with Mathematica or Mathematica Home Edition, of course. Let's start with a list. These are the things you need for traditional pumpkin carving. A nice looking pumpkin Carving tools of your choice: from a spoon and knife (if you are a true professional) to an industrial 36,000 rpm power rotary tool (seriously, I know someone who uses one) A bunch of candles to be placed inside the pumpkin A pattern for the carving on paper For industrial Mathematica pumpkin carving, you need these tools. B-spline curve, surface, and function Color processing functions Morphological image processing functions ParametricPlot3D with Texture A pattern for the carving as a bitmap Intrigued? Let us begin.
Yu-Sung Chang, Technical Communication & Strategy Group
Computation & Analysis

From Pi to Puzzles

Neil Bickford calculated the first 458 million terms for the continued fraction of pi, breaking the previous record of 180 million. He used Mathematica to develop his code and verify his results—which he posted shortly after he turned 13.

Bickford, who broke the record last fall, said creating the early version of the pi continued-fraction generator was “the best thing I’ve ever used Mathematica for.”

Elizabeth Shack, Technical Marketing Project Manager, Project Management
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How I Made Wine Glasses from Sunflowers

Eons ago, plants worked out the secret of arranging equal-size seeds in an ever-expanding pattern around a central point so that regardless of the size of the arrangement, the seeds pack evenly. The sunflower is a well-known example of such a "spiral phyllotaxis" pattern: It's really magical that this works at all, since the spatial relationship of each seed to its neighbors is unique, changing constantly as the pattern expands outwardly—unlike, say, the cells in a honeycomb, which are all equivalent. I wondered if the same magic could be applied to surfaces that are not flat, like spheres, toruses, or wine glasses. It's an interesting question from an aesthetic point of view, but also a practical one: the answer has applications in space exploration and modern architecture.
Christopher Carlson, Senior User Interface Developer, User Interfaces
Computation & Analysis

Celebrating the Fourth of July with Mathematica Fireworks

What could be a better way to celebrate the Fourth of July than beautiful fireworks in the dark sky? And what could be a better way to create fireworks on your screen than using Mathematica? There are a few different ways to create firework "effects" on computers, but it would be a shame if we chose to use just graphical effects with Mathematica. Yes, we are going for the full-scale particle simulation. Here is the synopsis. We create a firework simulation. With a mouse click, we seed a number of particles on the screen. Each particle has a different initial velocity, and it will follow the projectile motion. The particles spend a limited time on the screen, in which their opacity will diminish gradually. There will be a few customizable effects—colors and trails.
Yu-Sung Chang, Technical Communication & Strategy Group
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