While Awesomeness by Analysis can be very cool, it's not an ability that translates well in visual mediums — at least not without some help. One straightforward way to make a character's calculations striking is to superimpose their internal math outside themselves, in an abstract (but visible) form.
This makes a certain amount of sense when analyzing physical geometry. Things however get more troubled once unrelated math equations also begin floating around, especially if the characters are inexplicably looking at them in 3D space.
While math formulas are the most common variation of this, there are many other options. Trajectories can be plotted, simulations can be run, puzzle pieces can be visually combined. What matters is that it is projected on top of reality so the "calculating" can be visually seen and felt in parallel with reality. These calculations are sometimes combined with other visuals, although they tend to stay within a shared aesthetic palette (generally resembling glowing blueprints or chalk drawings).
While this trope usually suggests intelligence, it can also show up in more mundane situations and even represent being unable to understand the calculations involved. When parodied, it may end with them having calculated something entirely useless. It also doesn't strictly need to represent human thoughts and works just as well surrounding a machine doing advanced computations. The involvement of holograms or math magic may also justify this trope's visibility.
This can often overlaps with Exposition Diagram, Sherlock Scan, and E = MC Hammer.
Supertrope to Augmented Reality and Matrix Raining Code.
Compare Rebus Bubble which uses thought bubbles for conceptual addition. Contrast The Big Board, for when the calculations are diegetically written down instead.
Named for the player stat in Disco Elysium, which itself is a pun on a real technique for solving calculus.
Examples
- Dr. STONE:
- The second season intro features Senku's mind pouring calculations outwards around his classroom while contemplating. It also features Chrome and Ren admiring the science equations that swirl around them.
- When Senku first meets Chrome, another scientist existing in post-apocalyptic Japan, he challenges Senku to a contest of mathematics. Chrome's crushing defeat by Senku is symbolized by equations falling from the sky and pinning him to the ground.
- JoJo's Bizarre Adventure: Diamond is Unbreakable: During the fight between Yoshikage Kira and Josuke, Kira is able to calculate the travel speed of his air bullets by visualizing the distance between him and his finger as a triangle to do an equation.
- 'Kaguya-sama: Love Is War'': In episode 1, Shirogane and Kaguya's internal machinations are represented as layers of math equations streaming behind them.
- When Emmet unlocks his Master Builder powers in The LEGO Movie, this is initially communicated by him seeing each LEGO part's element number, complete with transparent visualizations of the respective parts showing potential ways to connect them. He uses this to engineer a Humongous Mecha by attaching together various pieces of construction hardware with almost no delay.
- A Beautiful Mind, John Nash would often visualize numbers lighting up from his POV when he was cracking codes. Though this visual symbolism also doubled to represent his schizophrenia.
- The Hangover: When Alan begins card counting during a game of blackjack, advanced calculus manifests briefly to surround him.
- The Librarians 2014: Justified. Due to a malignant brain tumor, Cassandra, already an intelligent scientist and mathematician, developed synesthesia, linking all five of her senses to her memory. The hallucinations caused by this allow her to process information and solve complex equations at incredible speeds, which the show depicts in the form of glowing calculations and images. However, the fact that the tumor which jumpstarted the ability will one day kill her and can overwhelm her once triggered, causing Psychic Nosebleed, makes her use it only sparingly until she is able to get the tumor removed in "And the Eternal Question", which unexpectedly makes the ability even stronger.
- Sherlock: Sherlock accessing his Mind Palace is styled like visual calculus, although he rarely uses it to crunch numbers.
- Disco Elysium: Naturally, the "Visual Calculus" stat in the game has this property, and shows it off while Harry reconstructs the possible bullet trajectory that killed The Hanged Man.
- Safer-Sephiroth’s Supernova ability in Final Fantasy VII displays several calculations used in astrophysics at the start of the attack.
- Genshin Impact: Downplayed with Kavah, whose animations resemble 3D blueprints and measuring with a compass, but don't explicitly show equations.
- "Tales from the Borderlands employs this when Fiona is trained in Vault-hunting by Athena, and onward. During high-octane action scenes, Fiona will often pause time to plan out her moves, which are usually projected onto the scene as her performing stunts in slow-motion. What she chooses to do in a given moment will often change the kinds of actions and Quick Time Events you perform in that scene.
- Honkai: Star Rail:
- Dr.Ratio has visualized math equations during his idle animations, and it's also incorporated into all of his attacks during combat. May overlap with Formulaic Magic since he seems able to weaponize these visualizations.
- Ruan Mei's character trailer features her (as a child) envisioning chemical diagrams upon seeing a frozen monster during a research expedition.
- Marvel Puzzle Quest:
- Amadeus Cho's "See the Math of It" power has a launch animation of him looking thoughtful as math equations appear around his head.
- M.O.D.O.K.'s "Doomsday Plan" power has a launch animation that parodies the "Confused Math Lady" meme, with M.O.D.O.K. looking confused as math equations and a geometric model appear in the air.
- In the video ''Vedal Answers The Hard Question
", Neuro-Sama asks Vedal how much are sum of integers from 1 to 100. Cue Vedal contemplating with various irrelevant formulae flying around him.
- In Gunnerkrigg Court, Kat has a breakthrough on how to design a new type of robot in Chapter 29, after observing a baby pigeon flapping its wings; this breakthrough is symbolized by a diagram measuring its skeletal structure and angles of its arms.
- Paranatural: When Dimitri realizes what Max is up to toward the end of the hitball game, he gets a devious look and his head is surrounded with images representing intelligence and strategy: a chess board with arrows indicating potential moves, nonsense equations, neurons, and Sun Tzu giving a thumbs up.
- The "Confused Math Lady" meme is a combination of clips from a Brazilian telenovela Senhora Do Destino with various math equations/diagrams superimposed over it. This Memetic Mutation is partially responsible for the recent popularity of using Visual Calculus to represent confusion.
- Mr. Peabody & Sherman: Mr. Peabody being Awesomeness by Analysis frequently uses visualized diagrams and equations in 3D space, allowing him to formulate complex plans with mathematical precision.
- Skylanders Academy: In "Days of Future Crash", Dark Spyro formulates a simple plan of taking advantage of Eruptor being in an essay predicament to try and get closer to his goal. And he formulates it with numbers floating around him and applying mathematics when his plan doesn't involve numbers at all.
