June 2, 2016 — Michael Trott, Chief Scientist
In a recent blog, Stephen Wolfram discusses the idea of what he calls “gravitational crystals.” These are infinite arrays of gravitational bodies in periodic motion. Two animations of mesmerizing movements of points were given as examples of what gravitational crystals could look like, but no explicit orbit calculations were given.
In this blog, I will carefully calculate explicit numerical examples of gravitational crystal movements. The “really” in the title should be interpreted as a high-precision, numerical solution to an idealized model problem. It should not be interpreted as “real world.” No retardation, special or general relativistic effects, stability against perturbation, tidal effects, or so on are taken into account in the following calculations. More precisely, we will consider the simplest case of a gravitational crystal: two gravitationally interacting, rigid, periodic 2D planar arrays embedded in 3D (meaning a 1/distance2 force law) of masses that can move translationally with respect to each other (no rotations between the two lattices). Each infinite array can be considered a crystal, so we are looking at what could be called the two-crystal problem (parallel to, and at the same time in distinction to, the classical gravitational two-body problem).
May 19, 2016 — Michael Trott, Chief Scientist
Some thoughts for World Metrology Day 2016
Please allow me to introduce myself
I’m a man of precision and science
I’ve been around for a long, long time
Stole many a man’s pound and toise
And I was around when Louis XVI
Had his moment of doubt and pain
Made damn sure that metric rules
Through platinum standards made forever
Pleased to meet you
Hope you guess my name
Introduction and about me
In case you can’t guess: I am Jean-Charles de Borda, sailor, mathematician, scientist, and member of the Académie des Sciences, born on May 4, 1733, in Dax, France. Two weeks ago would have been my 283rd birthday. This is me:
Nearly two hundred years after Friedrich Bessel introduced his eponymous functions, expressions for their derivatives with respect to parameters, valid over the double complex plane, have been found.
In this blog we will show and briefly discuss some formerly unknown derivatives of special functions (primarily Bessel and related functions), and explore the history and current status of differentiation by parameters of hypergeometric and other functions. One of the main formulas found (more details below) is a closed form for the first derivative of one of the most popular special functions, the Bessel function J:
April 21, 2016 — Jofre Espigule-Pons, Consultant, Technical Communications and Strategy Group
Putting some color in Shakespeare’s tragedies with the Wolfram Language
After four hundred years, Shakespeare’s works are still highly present in our culture. He mastered the English language as never before, and he deeply understood the emotions of the human mind.
Have you ever explored Shakespeare’s texts from the perspective of a data scientist? Wolfram technologies can provide you with new insights into the semantics and statistical analysis of Shakespeare’s plays and the social networks of their characters.
William Shakespeare (April 26, 1564 (baptized)–April 23, 1616) is considered by many to be the greatest writer of the English language. He wrote 154 sonnets, 38 plays (divided into three main groups: comedy, history, and tragedy), and 4 long narrative poems.
April 15, 2016 — Eila Stiegler, Quality Analysis Manager, Wolfram|Alpha Quality Analysis
It’s four months into the new year. Spring is here. Well, so they say. And if the temperatures do not convince you, the influx of the number of runners on our roads definitely should. I have always loved running. Despite the fact that during each mile I complain about various combinations of the weather, the mileage, and my general state of mind, I met up with 37,000 other runners for the Chicago Marathon on October 11, 2015. As it turns out, this single event makes for a great example to explore what the Wolfram Language can do with larger datasets. The data we are using below is available on the Chicago Marathon results website.
This marathon is one of the six Abbott World Marathon Majors: the Tokyo, Boston, Virgin Money London, BMW Berlin, Bank of America Chicago, and TCS New York City marathons. If you are looking for things to add to your bucket list, I believe these are great candidates. Given the international appeal, let’s have a look at the runners’ nationalities and their travel paths. Our GeoGraphics functionality easily enables us to do so. Clearly many people traveled very far to participate:
April 7, 2016 — Wolfram Blog Team
Authors that choose to incorporate Wolfram technologies into their books are practitioners in a variety of STEM fields. Their work is an invaluable resource of information about the application of Mathematica, the Wolfram Language, and other Wolfram technologies for hobbyists, STEM professionals, and students.
March 31, 2016 — Devendra Kapadia, Mathematica Algorithm R&D
Picture of Green’s Windmill by Kev747 at the English language Wikipedia.
In 1828, an English corn miller named George Green published a paper in which he developed mathematical methods for solving problems in electricity and magnetism. Green had received very little formal education, yet his paper introduced several profound concepts that are now taught in courses on advanced calculus, physics, and engineering. My aim in writing this post is to give a brief biography of this great genius and provide an introduction to GreenFunction, which implements one of his pioneering ideas in Version 10.4 of the Wolfram Language.
March 25, 2016 — Wolfram Blog Team
Mark your calendars now for the 2016 Wolfram Technology Conference! Join us October 18–21 at Wolfram headquarters in Champaign, Illinois, where we’ll be getting things off to an exciting start with a keynote address by Wolfram founder and CEO Stephen Wolfram on Tuesday, October 18 at 5pm.
Our conference gives developers and colleagues a rare opportunity for face-to-face discussion of the latest developments and features for cloud computing, interactive deployment, mobile devices, and more. Arrive early for pre-conference training opportunities, and come ready to participate in hands-on workshops, nonstop networking opportunities, and the Wolfram Language One-Liner Competition, just to name a few activities.
We are also looking for users to share their own stories and interests! Submit your presentation proposal by July 15 for full consideration. Last year’s lineup included everything from political data science to winning hackathon solutions to programming in the Wolfram Cloud… and literally almost everything in between. Review a sampling of the 2015 talks below, or visit our website for more.
Commanding the Wolfram Cloud—Todd Gayley
February 26, 2016 — Emily Suess, Technical Writer, Technical Communications and Strategy Group
Kip Thorne, physicist, New York Times bestselling author, and professor emeritus at Caltech, ignited fans’ passion for science through his work on the movie Interstellar. The sci-fi adventure won the 2015 Academy Award for Best Visual Effects, and the first cuts of some of those stunning visuals were created with Mathematica and the Wolfram Language.
“Mathematica was my way of testing whether or not I had the equations right,” says Thorne, whose computational approach to producing images led to publication in the American Journal of Physics and Classical and Quantum Gravity.
February 25, 2016 — Adriana Rose, Business Development, Partnerships
For the last few days, we’ve been discussing Wolfram Programming Lab and how it is a tool for those teachers looking to incorporate coding into their computational classrooms. Today is the last day of the series, and I’m going to talk about the experiences I’ve had with Programming Lab. What I’ve seen from numerous workshops is that adopting a computational thinking approach increases engagement and supports creativity in the classroom. Having an engaged classroom is paramount; otherwise, teachers risk students falling into a dangerous spiral of disinterest that prevents them from learning and is likely to cause classroom management problems. Programming Lab gives teachers the ammunition to fight boredom and create exciting lesson plans.
My colleague Ishwarya and I have been visiting elementary, middle, and high schools for the past couple of years to teach workshops of various lengths. It’s been such a help to have the Wolfram Language in the cloud. Without downloading any software, students are able to go to a website and start programming immediately. I usually start off my workshops with the Getting Started and Draw a Sphere Explorations. Here are some of the kids that I’ve worked with in the past year or so: