Math Behind Movies
I love a good action-packed movie with fight scenes and special effects that transport and encompass me through the magic of cinematography. I particularly enjoy movies that keep me on the edge of my chair consumed by emotions that parallel those of the protagonist. The original Doctor Strange is my favorite.
What many may not realize is that behind the visual effects is math. That is right. The best movies - the ones that evoke heart-wrenching emotions: fear, suspense, excitement - leverage mathematics to create scenes which keep the viewer teetering happily between realism and improbability. But what exactly goes into the production of such films that exhilarate, unite, and inspire people across the world?
Let’s take Marvel films as an example. In the 1980s, superhero movies were under-funded with minimal fan bases. Superhero stories were a written genre (comic books) that relied on an individual’s imagination to come alive. Marvel rebuilt this superhero society into a shared experience by bringing it to life on the big screen. Yes, today Marvel hires popular actors and pithy writers to develop characters within dramatic storylines, but Marvel has done so much more. Marvel launched profitable superhero franchises through their investment in groundbreaking CGI accompanied with mind-blowing stunts; stunts that make the viewer believe in the near-impossible.
Try recalling your first-time watching Doctor Strange; just what made it so special? To many, including me, the moment that left your mouth agape was when the world began to morph around itself and Doctor Strange. This swirling reality was based on math, specifically the Mandelbrot set. The Mandelbrot set is a geometric, never-ending pattern that marks a certain set of points in the complex plane (Ornes). The illusions of bending buildings are actually ‘bent’ into fractal patterns - the Madelbrot. “On Doctor Strange, the Mandelbrot is one of the first effects we tried to nail,” said, Computer Graphics Supervisor, Alexis Wajsbrot. “And it was the last we delivered.” This world, only imaginable through the wonders of CGI, was “aimed at discovery and exploration, giving the user infinite space to discover the beauty of mathematics.” Wajsbrot went on to emphasize the importance of math in the creation of his vision. He said, “a good visual-effects artist needs to be open-minded and curious about the world he lives in. And there are so many interesting things in fractals.” Imagine how fractals could be utilized as CGI continues to advance.
Beyond CGI, math is imperative in most any stunt. For instance, a rigged car accident, similar to that of Stephen Strange, which acted as a turning point in his life’s trajectory: one that eventually led him to become the marvelous Doctor Strange. But what actually goes into such stunts? Simply put, math. Mathematics is an essential foundation, especially regarding car stunts. You have to meticulously and perfectly calculate time, speeds, angles, and braking distance (Mathspig). Typically “To ensure that the stuntman lands [correctly] we analyze the uncertainty in his trajectory and extract the landing point uncertainty. We go on to construct a numerical simulation of the impact and motion…” explains mathematicians Jeffrey Giansiracusa, Ernie Esser, and Simon Pai (Giansiracusa).
Math is also vital in stunt rigging. Stunt rigging is the control of wires, ropes and machinery used for visual effects (Stefankski). An example of stunt rigging is when Doctor Strange flies with the help of the Cloak of Levitation . Rather than use CGI, which would not yield such realistic results, the actor, Benedict Cumberbatch, utilized stunt rigging to artfully create the illusion of flying. Getting these stunts right involves heaps of calculations to work out where to rig ropes and with what force to pull on each (Lindenberg). Having said this, I’d argue, they are worth the effort seeing as how believable superpowers are, the foundation of successful Marvel franchises.
Marvel became the powerhouse leader in the superhero genre because of their investment and commitment to using math. It is math that allowed Marvel to make such advancements in both CGi and stunts. It is the application of math that gave their movies the wow-factor that previous superhero movies lacked. Math is the foundation for an entire superhero category, and it is now considered essential in all other genres that use stunts or CGI. All in all, no matter where you look you can find mathematics.
Sources:
The official site for Marvel movies, characters, comics, TV. Marvel Entertainment. (n.d.). Retrieved April 23, 2023, from https://www.marvel.com/
Giansiracusa, Jeffrey, et al. “Cardboard Comfortable When It Comes to Crashing - University of Washington.” Washington University Math, 16 Apr. 2003, https://sites.math.washington.edu/~morrow/mcm/uw24.pdf.
Lindenberg, Jenna. “The Secret Science behind Movie Stunts.” CSIROscope, 26 July 2018, https://blog.csiro.au/the-secret-science-behind-movie-stunts/.
Mathspig. “Movie Stunt Math: Rolling a Car.” Mathspig Blog, 29 Oct. 2018, https://mathspig.wordpress.com/2018/10/29/1-movie-stunt-math-rolling-a-car/.
Ornes, Stephen. “How Math Makes Movies like Doctor Strange so Otherworldly.” Science News Explores, 25 Feb. 2020, https://www.snexplores.org/article/math-movies-doctor-strange-otherworldly.
Stefankski, Marcel, and Simon Van Lammeren. “Stunt Rigging & Wireworks.” Actionpact Stunts - Stunts for Film & Television, https://www.actionpact.nl/services/stunt-rigging/#:~:text=Stunt%20rigging%20is%20an%20essential,provide%20for%20custom%2Dmade%20solutions.
