Jeffrey Bryant
Paco Jain
Michael Trott

Hidden Figures: Modern Approaches to Orbit and Reentry Calculations

February 24, 2017
Jeffrey Bryant, Scientific Information Group
Paco Jain, Research Programmer, Wolfram|Alpha Scientific Content
Michael Trott, Chief Scientist

The movie Hidden Figures was released in theaters recently and has been getting good reviews. It also deals with an important time in US history, touching on a number of topics, including civil rights and the Space Race. The movie details the hidden story of Katherine Johnson and her coworkers (Dorothy Vaughan and Mary Jackson) at NASA during the Mercury missions and the United States’ early explorations into manned space flight. The movie focuses heavily on the dramatic civil rights struggle of African American women in NASA at the time, and these struggles are set against the number-crunching ability of Johnson and her coworkers. Computers were in their early days at this time, so Johnson and her team’s ability to perform complicated navigational orbital mechanics problems without the use of a computer provided an important sanity check against the early computer results.

Row[{Show[    Entity["Movie", "HiddenFigures::k39bj"][     EntityProperty["Movie", "Image"]], ImageSize -> 101], "  ",    Show[Entity["PopularCurve", "KatherineJohnsonCurve"][     EntityProperty["PopularCurve", "Image"]], Axes -> False,     Background -> LightBlue, ImageSize -> 120]}]


Posted in: History, Mathematics

Michael Trott

How Many Animals and Arp-imals Can One Find in a Random 3D Image?

February 23, 2017 — Michael Trott, Chief Scientist

And How Many Animals, Animal Heads, Human Faces, Aliens and Ghosts in Their 2D Projections?


In my recent Wolfram Community post, “How many animals can one find in a random image?,” I looked into the pareidolia phenomenon from the viewpoints of pixel clusters in random (2D) black-and-white images. Here are some of the shapes I found, extracted, rotated, smoothed and colored from the connected black pixel clusters of a single 800×800 image of randomly chosen, uncorrelated black-and-white pixels.



Michael Gammon

Analyzing and Translating an Alien Language: Arrival, Logograms and the Wolfram Language

January 31, 2017 — Michael Gammon, Communications Project Coordinator, Public Relations

Black and white logogram

If aliens actually visited Earth, world leaders would bring in a scientist to develop a process for understanding their language. So when director Denis Villeneuve began working on the science fiction movie Arrival, he and his team turned to real-life computer scientists Stephen and Christopher Wolfram to bring authentic science to the big screen. Christopher specifically was tasked with analyzing and writing code for a fictional nonlinear visual language. On January 31, he demonstrated the development process he went through in a livecoding event broadcast on


Jeremy Sykes

Meet the Authors of Hands-on Start to Wolfram Mathematica, Second Edition

January 24, 2017 — Jeremy Sykes, Publishing Assistant, Wolfram Media

Hands-on Start cover

Jeremy Sykes: To celebrate the release of Hands-on Start to Wolfram Mathematica and Programming with the Wolfram Language (HOS2), now in its second edition, I sat down with the authors. Working with Cliff, Kelvin and Michael as the book’s production manager has been an easy and engaging process. I’m thrilled to see the second edition in print, particularly now in its smaller, more conveniently sized format.


Jofre Espigule-Pons

Exploring a Boxing Legend’s Career with the Wolfram Language: Ali at 75

January 17, 2017 — Jofre Espigule-Pons, Consultant, Technical Communications and Strategy Group

Muhammad Ali (born Cassius Marcellus Clay Jr.; January 17, 1942–June 3, 2016) is considered one of the greatest heavyweight boxers in history, with a record of 56 wins and 5 losses. He remains the only three-time lineal heavyweight champion, so there’s no doubt why he is nicknamed “The Greatest.”

I used the Wolfram Language to create several visualizations to celebrate his work and gain some new insights into his life. Last June, I wrote a Wolfram Community post about Ali’s career. On what would have been The Greatest’s 75th birthday, I wanted to take a minute to explore the larger context of Ali’s career, from late-career boxing stats to poetry.

First, I created a PieChart showing Ali’s record:

bouts = <|"TKO" -> 21, "KO" -> 11, "UD" -> 18, "RTD" -> 5, "SD" -> 1,     "LUD" -> 2, "LSD" -> 2, "LRTD" -> 1|>; PieChart[bouts, ChartStyle -> 24,   ChartLabels ->    Placed[{Map[Style[#, Bold, FontSize -> 14] &, Values[bouts]],      Map[Style[#, FontFamily -> "Helvetica Neue", Bold,         FontSize -> 16] &, Keys[bouts]]}, {"RadialCenter",      "RadialCallout"}], PlotRange -> All,   SectorOrigin -> {Automatic, 1},  ChartLegends -> {"Technical Knockout", "Knockout",     "Unanimous Decision", "Retired", "Split-Decision",     "Lost - Unanimous Decision", "Lost - Split-Decision",     "Lost - Retired"},   PlotLabel ->    Style["Ali's Record", Bold, FontFamily -> "Helvetica Neue",     FontSize -> 22], ImageSize -> 410]
Ali's Record


Nick Lariviere

Automotive Reliability in the Wolfram Language

January 13, 2017 — Nick Lariviere, Kernel Developer, Core Mathematica Engineering

This post originally appeared on Wolfram Community, where the conversation about reliable cars continues. Be sure to check out that conversation and more—we can’t wait to see what you come up with!

For the past couple of years, I’ve been playing with, collecting and analyzing data from used car auctions in my free time with an automotive journalist named Steve Lang to try and get an idea of what the used car market looks like in terms of long-term vehicle reliability. I figured it was about time that I showed off some of the ways that the Wolfram Language has allowed us to parse through information on over one million vehicles (and counting).

Vehicle Class Quality Index Rating


John Moore

Recent Wolfram Technology Books

January 9, 2017 — John Moore, Marketing and Technical Content Team Lead

We’re always excited to see new books that explore new ways to use Wolfram technologies. Authors continue to find inventive ways to think with the Wolfram Language. A variety of new Wolfram technology books have been published over the past few months. We hope that you’ll find something on this list to support your new year’s resolution to upgrade your skills. (Update: also look for the newly released Chinese translation of Stephen Wolfram’s An Elementary Introduction to the Wolfram Language.)

Toolbox for Mathematica Programmers, Option Valuation under Stochastic Volatility II and CRC Standard Curves and Surfaces with Mathematica


Posted in: Books

John Moore

Our Readers’ Favorite Stories from 2016

January 3, 2017 — John Moore, Marketing and Technical Content Team Lead

Story image collage

It’s been a busy year here at the Wolfram Blog. We’ve written about ways to avoid the UK’s most unhygienic foods, exciting new developments in mathematics and even how you can become a better Pokémon GO player. Here are some of our most popular stories from the year.


Kathryn Cramer

Gardening à la Gardner

December 28, 2016 — Kathryn Cramer, Technical Communications and Strategy Group

When looking through the posts on Wolfram Community, the last thing I expected was to find exciting gardening ideas.

The general idea of Ed Pegg’s tribute post honoring Martin Gardner, “Extreme Orchards for Gardner,” is to find patterns for planting trees in configurations with constraints like “25 trees to get 18 lines, each having 5 trees.” Most of the configurations look like ridiculous ideas of how to plant actual trees. For example:

One of Pegg's orchard plans


Eric Weisstein
Ian Ford

The Semantic Representation of Pure Mathematics

December 22, 2016
Eric Weisstein, Senior Researcher, Wolfram|Alpha Scientific Content
Ian Ford, Pure Math Developer, Wolfram|Alpha Scientific Content

Graph of relationships between spaces


Building on thirty years of research, development and use throughout the world, Mathematica and the Wolfram Language continue to be both designed for the long term and extremely successful in doing computational mathematics. The nearly 6,000 symbols built into the Wolfram Language as of 2016 allow a huge variety of computational objects to be represented and manipulated—from special functions to graphics to geometric regions. In addition, the Wolfram Knowledgebase and its associated entity framework allow hundreds of concrete “things” (e.g. people, cities, foods and planets) to be expressed, manipulated and computed with.

Despite a rapidly and ever-increasing number of domains known to the Wolfram Language, many knowledge domains still await computational representation. In his blog “Computational Knowledge and the Future of Pure Mathematics,” Stephen Wolfram presented a grand vision for the representation of abstract mathematics, known variously as the Computable Archive of Mathematics or Mathematics Heritage Project (MHP). The eventual goal of this project is no less than to render all of the approximately 100 million pages of peer-reviewed research mathematics published over the last several centuries into a computer-readable form.

In today’s blog, we give a glimpse into the future of that vision based on two projects involving the semantic representation of abstract mathematics. By way of further background and motivation for this work, we first briefly discuss an international workshop dedicated to the semantic representation of mathematical knowledge, which took place earlier this year. Next, we present our work on representing the abstract mathematical concepts of function spaces and topological spaces. Finally, we showcase some experimental work on representing the concepts and theorems of general topology in the Wolfram Language.