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Adam Savage's One Day Builds: Rhombic Dodecahedron with Matt Parker!

In this special One Day Build filmed earlier this year, mathematician Matt Parker (StandUpMaths) visits the cave to build a rhombic dodecahedron with Adam! Be prepared for lots of fun geometry discussion as Adam and Matt try to make abstract math concepts tangible with a physical build. They also take this construction a few steps further by lining the inside of the polyhedron with mirrors and LED strips for an infinty mirrored effect!

Numberphile - Still Untitled: The Adam Savage Project - 11/5/19
We have a special guest this week: Brady Haran, creator of the YouTube channel Numberphile! We welcome Brady to the cave and talk about the origin of Numberphile--along with Brady's other channels--his video making process, and some of his favorite Numerphile episodes.
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Adam Savage and Vsauce's Michael Stevens Build a Kendama!

Adam is joined by Vsauce's Michael Stevens for a special One Day Build in the cave. Michael has recently taken up playing the Kendama, a Japanese cup and ball toy, and Adam helps make one from scratch that helps optimize his play. This build engrosses both into topics of machining, knot tying, and geometric conundrums.

Algorithm Turns Any Object into a Rubik's Cube

Columbia University's Timothy Sun and Changxi Zheng presented this research paper and video illustrating a computational method to turn any 3D model into a Rubik's Cube-style puzzle. Presented at this year's SIGGRAPH, the software analyzes any user-supplied 3D model and inserts the proper twisty joints into the design, which can then be 3D printed into an interlocking puzzle. (h/t Gizmodo)

In Brief: How JPEG Image Compression Works

Your smartphone's camera sensor and lens are the primary factors contributing to how your photos look, but your camera app's JPEG compression algorithm is also an important factor. Not all lossy compression settings are the same, and YouTube channel Computerphile has a new series explaining JPEG compression. The latest video features image analyst Mike Pound, who explains the Discrete Cosine Transform function that is the key behind JPEG. It's a really interesting watch that's not too difficult to follow along! (h/t Petapixel)

In Brief: ILM's John Knoll on the Death Star and Star Wars Physics

A week ago, attendees at Star Wars Celebration got the first glimpse of the first Star Wars Anthology film, named Rogue One. Director Gareth Edwards revealed that the film would be about the theft of the Death Star plans before the events of Episode IV, and showed a short teaser clip created by ILM specifically for the announcement. The clip, which has yet to be officially released by Lucasfilm (but for which bootleg copies were immediately uploaded to YouTube), showed the massive Death Star looming over the horizon of a forested planet. AICN writer and professional astronomer used screencaps of that footage to calculate the physics of that shot to assess it's "realism", and was subsequently contacted by effects legend John Knoll to walked through ILM's thinking behind that shot. Knoll's explanation is wonderfully geeky, and shows how much thought effects artists and engineers put into their work, beyond just the "wow" factor. It's the very best of sci-fi apologetics, from the behind-the-scenes technicians closest to canon. (h/t Gary Whitta)

In Brief: Optimal Search Strategy for Finding Waldo

Remember those Where's Waldo books? (They even made a TV show about them.) Slate ran a story back in 2013 showing you the location of Waldo in all seven books in the series, but the interesting part of that story was that the authors claimed to have devised the best search strategy for finding the character. AI researcher and data visualization geek Randy Olson took Slate's data one step further, putting Waldo's locations through a genetic algorithm to devise an optimal search path. Of course, you and I know that the point of those books was never really to find Waldo. It was to admire the art of illustrator Martin Handford. Handford, like cross-section artist Stephen Biesty, worked in a uniquely dense visual style that I most associate with 90s' children's books. They were the Quentin Blake for millennials. (h/t Laughingsquid)

What Makes a Coin Toss Random?

Numberphile interviews Stanford professor Persi Diaconis about the factors that make a coin toss seemingly completely random, and how he and his colleagues determined what factors most affect the outcome. And some of you may already know this, but theoretical analysis of the physics of coin flipping shows that the odds aren't actually exactly 50-50. There's an ever-so-slight bias toward the side that was facing up during the toss.

Pixar Explains the Math Behind Smooth Character Rendering

Ready to give your brain a little workout? See if you can follow along in this Numberphile video as Tony DeRose of Pixar Research explains some of the mathematics behind the rendering and animation of characters in modern CG films. It went over my head at around the five-minute mark, but the gist is that the use of certain math principles and algorithms let rendering programs subdivide vertices in geometry for smooth curves and surfaces. Computer scientists know this as the Catmull-Clark algorithm.

Show and Tell: The Curta Calculator

Inventern champ Sean Charlesworth joins us in the Tested office this week to share one of his prized possessions: a Curta mechanical calculator. Designed in the 1940s before electronic calculators, this hand-cranked device was considered the the most precise pocket calculator available, and was used by rally car drivers and aviators.

In Brief: Predicting Someone's Age By Their Name

In the new Planet of the Apes movie, Keri Russell's character briefly talks about how she had a young daughter who died of the simian flu virus. As the character was telling the story, my friend--who had not seen the film--leaned over to me and said "I bet her daughter's name was Sarah." And indeed, just a second later, that's what was uttered on screen. This prediction led to a discussion post-screening about why Sarah was such a suitable (and predictable) name to evoke the image of a child never seen in the film. Why is Sarah evocative of a young child and not a name like Bessie or Helen? Earlier this year, Nate Silver's FiveThirtyEight did a statistical analysis of the popularity of names, based on public data from Social Security Administration. We've seen websites and apps that show how popular names are over time, but Silver's team went a step further to calculate the median ages for every common and uncommon name, for both male and female names. Of all living Sarah's, for example, the median age is 26. While if you were to meet a Helen in person, it's more likely that she's older, given that the median age for Helen's still alive is 73. And the names with the youngest median age? For girls, it's Ava, and for boys, it's Liam. Jayden comes in at a close second. Thanks, Will and Jada.

In Brief: How to Win at Rock Paper Scissors

MIT Technology Review has details about a recent study carried out at the Zhejiang University in China on rock-paper-scissors strategy. Conventional thinking was that the best strategy for not losing in the long run was to choose your play at random--as defined by the Nash equilibrium mixed strategies solution of game theory. But the research done with 360 students at the university indicated that play choices were conditional and patterns emerged. Specifically, winners of one round tend to stick with the same action, while losers switch to the next action in a sequence (in the order of rock, paper, scissors). The researchers are preparing future studies to determine whether this type of conditional response is a basic decision-making mechanism or a byproduct of fundamental neural mechanism. Gambit play was not taken into consideration.

"The Infinite Hotel, a thought experiment created by German mathematician David Hilbert, is a hotel with an infinite number of rooms. Easy to comprehend, right? Wrong. What if it's completely booked but one person wants to check in? What about 40? Or an infinitely full bus of people?" A fun thought experiment to visualize the concept of infinity. Your brain starts to hurt at the two-and-a-half-minute mark. The full TED-Ed lesson is here.

Celebrating Benoît Mandelbrot, The Father of Fractals

A poignant interview with the late Benoît Mandelbrot, in which the legendary mathematician talks about the beauty in which a simple formula can create a universe of complexity. "IBM celebrates the life of Benoit B. Mandelbrot, IBM Fellow Emeritus and Fractal Pioneer. In this final interview shot by filmmaker Erol Morris, Mandelbrot shares his love for mathematics and how it led him to his wondrous discovery of fractals. His work lives on today in many innovations in science, design, telecommunications, medicine, renewable energy, film special effects, video game graphics, and more." Learn more about Mandelbrot here, and watch the 2010 TED talk he gave on fractals here.

Movies by the Numbers: Why the 1960s were the Most Creative Decade

Any a film critic or movie buff for the golden age of film, and you'll probably get an answer that includes the 1960s and 1970s. The 1940s and 1950s gave us incredible performances and scripts from the Hollywood studio system, but the later decades gave rise to an incredible array of filmmakers like Jean-Luc Godard, Stanley Kubrick, and Francis Ford Coppola, who pushed forward the cinematography and psychology of movies.

Turns out there are actually numbers to back up the wisdom of movie fanatics. Wired picked up on a study that analyzed IMDB tags to determine how creative movies have been decade-by-decade. Granted, novelty--especially novelty as defined by tags on IMDB--isn't going to be the most universally accurate measurement of film quality. But the numbers show that more new concepts and creative films came from the industry in the 1960s.

Image credit: Warner Bros. Pictures

The study's authors used "crowdsourced keywords from the Internet Movie Database as a window into the contents of films, and prescribe[d] novelty scores for each film based on occurrence probabilities of individual keywords and keyword-pairs." The study focused on keywords used as tags on IMDB, which describe specific story elements and locations, genres, and other movie trends.

So how does novelty, and by association creativity, come into play? Analyzing those keyword tags. "We devise[d] a method to assign a novelty score to each film on the basis of the keywords associated with it and the keywords appearing in all films that were released prior to it," the study explains. They collected data from the years 1929 through 1998, then ran everything through some equations to deduce novelty. Sure enough:

Ultimate Tic-Tac-Toe is Mind Bending

Ultimate Tic-tac-toe is a game math nerd Ben Orlin recently discovered at a mathematician's picnic. The game is played with one giant tic-tac-toe grid, with each of the nine squares filled with another smaller tic-tac-toe game board. The rules are a little more sophisticated than regular tic-tac-toe, though. The object is to win the big board by winning the right combinations of small boards, but each turn takes place in a different small board, which is determined by where your opponent last played. So players have to play a meta game of strategically placing X's and O's in the small boards to direct where their opponent will get to play next. Orlin says that when he plays it, strategies surface where players make intentionally bad moves in the small boards to avoid sending the other player into a good places in the larger grid. Yo dawg, it's tc-tac-toe Inception. (h/t Boingboing, Kottke, Andy Baio)

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POV: Solving Three Rubik's Cubes While Juggling

Stanford student (and World Cube Association member) Ravi Fernando uploaded this video of his famous rubix's cube juggling feat from a first-person perspective. The cubes are solved at the 1:38, 4:15, and 5:55 marks. There's even a near drop!

The Origin of the Plus and Minus Symbols

If math is the only universal language, as the saying goes, then it's a language more or less like any other. And approaching it like a language makes us think about elements of mathematics that we normally take for granted. For example: When and how did the symbols for addition and subtraction come from? Astrophysicist Mario Livio was curious and decided to find out the answers for himself, and the resulting blog post is an interesting mathematics history lesson.

Though mathematics has been around for more than two thousand years--famous mathematician Pythagoras lived in the 6th century BC--Livio traced the + sign back to the 1300s.

"There is little doubt that our + sign has its roots in one of the forms of the word 'et,' meaning 'and' in Latin," writes Livio. "The first person who may have used the + sign as an abbreviation for et was the astronomer Nicole d’Oresme (author of The Book of the Sky and the World) at the middle of the fourteenth century. A manuscript from 1417 also has the + symbol (although the downward stroke is not quite vertical) as a descendent of one of the forms of et."

The - sign, meanwhile, hasn't been around as long--Livio writes that it first appeared in 1481 in a German algebra manuscript. Neither the + or - symbol appeared in English writing on math until 1551. And, like any other language, the writing of mathematics has evolved over the years. Livio notes a few examples of how the symbols have changed into the forms we now know:

Mirror Master: Mathematician Cures the Driver-Side Blindspot

Mirrors are old. Thousands of years old. They don't exactly seem like the trickiest bit of technology to invent--once you've spotted your reflection in a shiny piece of stone or metal, you're going to figure it out pretty quickly. And once glassmaking came around, well, the leap to glass mirrors seems only natural. The silvered-glass mirrors that we know and love today are relatively young, comparatively--they were invented in the early 1800s. Since then, inventors have discovered convex glass can provide a wider field of view of the world, and glass surfaces with both concave and convex segments (aka carnival mirrors) can create crazy distorted reflections of reality.

The work of mathematics professor R. Andrew Hicks may represent the most significant evolution in mirror technology since...well, glass. Hicks has been using math for years to design mirrors that reflect light in just the right ways--they're essentially finely-tuned versions of the carnival mirrors that make everything look all wacky--and has come up with some impressive reflective surfaces.

For example, he's developed a curved mirror that reflects the world without reversing its image. It's one smooth piece of glass, not a pair of mirrors connected at a 90-degree angle like a traditional non-reversing mirror. As you'd expect from a mathematics professor, algorithms made it all possible--Hicks worked out equations to represent the kind of reflection he wanted to create, then used those to develop the coordinates for thousands of tilted points on the mirror's surface.

Hicks has invented and patented a driver-side mirror for cars that eliminates blind spots.

When those coordinates are fed to a machine and ground away with a diamond, they can create all sorts of mirror variations--another example, which Hicks calls the vampire mirror, doesn't even create a true mirror image. If you look into the mirror and wave your left hand around, it'll look like you're actually moving you right.

More importantly, Hicks has invented and patented a driver-side mirror for cars that eliminates blind spots. Here's how it works.