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Formula for the Unformulable

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A standard equation in Anti-Grinch Arithmetic.

Science and mathematics are awesome. Lots of concepts we know from nature and real life can be described and explained with lovely equations and elegant formulas. Think about those gorgeously complex representations of organic chemistry... No wonder some characters get certain ideas and start thinking that everything can be explained with complex calculations or that everything can be reduced to a refined formula.

This trope is an attempt to use numeric concepts to calculate the uncalculable — things like love or happiness or who-did-it and how-to-get-laid. A character tries to solve a non-scientific problem with science and mathematics and tries to find a formula for it.

They write the formula or equation (usually on a big chalkboard or whiteboard as it is most visually appealing, but a piece of paper will do just as well) and they use not-so-symbolic representations, or they try to count items that cannot be counted together to solve the mystery of the concept they try to grasp. The more mathematical operations they use, the better — think square numbers and third powers, square roots and cube roots, multiplications and fractions, trigonometric functions, integrals... you name it. Sometimes somebody particularly bold might write an academic paper or a whole book in this style.

To count as an example, the formula (or at least part of it) must be seen or read out loud. Can involve the use of an Exposition Diagram to display the proof. But depend on the fact that viewers will be often teased with an Unreveal Angle and won't see the full solution in all its glory.

Related tropes

  • 20% More Awesome: Hilarious statistics for something which is incapable of being measured.
  • Applied Mathematics: Essentially logic expressed in pictograms and mathematics. Both this trope and Applied Mathematics run solidly on Rule of Funny.
  • E = MC Hammer: Nonsensical equations; plain old gibberish resembling math.
  • Measuring the Marigolds: A character tries to reduce the concept of something they enjoy into an abstract equation or precise scientific explanation, but the work implies that thus the concept loses its charm.
  • Rebus Bubble: Symbolic representation of a character's mind (whereas in this trope, the character literally writes their ideas on the board or a piece of paper).
  • Thing-O-Meter: A device that measures a less-plausibly-measurable concept, like "fun" or "badass."

EXAMPLES = (Work ÷ Author + Trope + mathematics × science) ÷ tropers' effort

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  • In one commercial for Max, a man suggests a romantic night with his wife...and produces a ridiculously complex formula for deciding what they should watch, only for her to simply suggest that they watch Max.

    Anime & Manga 
  • In Is This A Zombie?, there is this board. The objective was to explain how galaxies rotate... uh, probably. There are some pictures of singing kitties, flowers and fish in the formula, mixed with numbers and some mathematical operations like square root.
  • The old man in Paranoia Agent spends the entire series working on a massive, impossibly complex equation. After Maniwa goes crazy and the old man is incapacitated, he takes up work on the equation. The last shot of the series is Maniwa finally completing the equation and gasping. What the equation represents is never stated, though a popular fan theory is that the Lil' Slugger scenario is a Vicious Cycle.
  • Bastion Misawa of Yu-Gi-Oh! GX applies complex math to Duel Monsters strategies, to the point that he writes equations on his dorm walls and his cards.

    Comic Books 
  • The Anti-Life Equation is a MacGuffin in the DC Comics universe, normally sought out by Darkseid. What, exactly, it is varies Depending on the Writer, but it's generally a mathematical formula for complete mind-control. Somehow. The Anti-Life Equation essentially "proves" that life is meaningless. It is the counterpart to the Life Equation, which is the proof that life has meaning.
  • In Transmetropolitan, one of the short stories is about a apartment block that was suddenly consumed by an immense flashfire that consumed everything and everyone within... except for a single room, known to be occupied by an eccentric old man. Within was a mathematical formula for a perfect society, with equations for happiness, dignity and freedom. The old man had spent his entire life working on it, and was on the verge of solving the equation... but Spider theorised that a simple error in the maths had ended up causing the fire and the deaths of thousands of innocent people just as he reached his final conclusions. The old man was never seen again.
  • Meet Dkrtzy RRR, the Green Lantern of space sector 188. It is a sentient mathematical equation representing willpower itself... somehow.

    Films — Animation 
  • In The Nightmare Before Christmas, Jack tries to find a formula/equation for Christmas when he tries to figure out the meaning of this intriguing holiday. It's quite elaborate and it includes a snowman multiplied by bracket that has chestnuts divided by open fire, the whole thing is divided by a bell multiplied by 12th root of December 25th plus Sandy Claws. And some sugar plum visions and egg nog and holly and ice or snow should be there as well. See it here.

    Films — Live-Action 
  • In Mazany Filip (parody of film noir hardboiled detective stories), the great detective from the title writes a formula when he tries to figure out who the murderer is. He covers a really huge blackboard. He makes a tiny mistake: It is not Vilma, but Velma.

  • In The Bridge of San Luis Rey, Brother Juniper tries various calculations, using quantities supposedly expressing people's spiritual traits, to show that a good and just God could allow those people to die in a bridge collapse.
  • Mollusk from Emperor Mollusk versus The Sinister Brain keeps a pie-chart quantifying "just how vast and indifferent the universe is."

    Live-Action TV 
  • In the 30 Rock episode "Khonani", Jack tries to decide between his two Love Interests by following his HEART. HEART being an acronym for Hard Equations and Rational Thinking. It doesn't work.
  • On The Big Bang Theory episode "The Friendship Algorithm", Sheldon tries to make a formula for making friends. He draws a diagram of it on a whiteboard and follows it while calling Barry on the phone. When he gets caught in an infinite loop, Howard rushes in and adds an escape to the diagram to help Sheldon get unstuck.
  • In the Community episode Competitive Wine Tasting, Abed attends a media studies class on series Who's the Boss? taught by Professor Peter Sheffield. He asks the class a rhetorical question "Who was the boss?" and Abed in all seriousness tells him it was Angela, amusing Sheffield who retorts that it isn't that simple. Abed insists and is then offered to teach the next class. He conclusively proves that Angela was in fact the boss. His formula covers an enormous board, and viewers get to see he used some organic chemistry in his calculations.
  • In How I Met Your Mother, Barney writes a formula on a huge whiteboard when he tries to figure out how to make his friend/crush Robin sleep with him again. The formula includes the right amount of nostalgia and booze. The solution is to get her to Ted's wedding, Ted being her ex-boyfriend and great friend.


  • In Proof by David Auburn, Catherine reads through her father's notebooks and discovers in them signs of his impending senility.
    "Let X equal the quantity of all quantities of X. Let X equal the cold. It is cold in December. The months of cold equal November through February. There are four months of cold, and four of heat, leaving four months of indeterminate temperature. In February it snows. In March the Lake is a lake of ice. In September the students come back and the bookstores are full. Let X equal the month of full bookstores. The number of books approaches infinity as the number of months of cold approaches four. I will never be as cold now as I will in the future. The future of cold is infinite. The future of heat is the future of cold. The bookstores are infinite and so are never full except in September..."

  • In Questionable Content, Hannelore's father asks Martin how happy she is on Earth and then hands him a giant book which will apparently show him how to calculate this. It is not shown if it works since Martin couldn't understand it.
  • In the xkcd cartoon "Useless", the author has tried to calculate the square root, cosine, derivative, and various increasingly complex mathematical operations on a love heart, and concluded that "My normal approach is useless here."

    Web Original 
  • SCP Foundation:
    • SCP-1313 is an otherwise ordinary math equation that evaluates to one live female grizzly bear, which will materialize near or in the person that solved it and likely proceed to maul them. Notably, SCP-1313's results can be used in other equations, meaning that it is possible to take the square root of a grizzly bear (which is apparently a prime number).
      Footnotes: Research into the possible military applications of irrational, exponential, and imaginary grizzly bears is currently being undertaken by a joint team from the Foundation's mathematical and zoological departments.
    • SCP-4656 is a process by which someone formulates non-existent connections between unrelated data sets, eventually presenting them as an axiomatic proof. SCP-4656-2 refers to the formulae, which can involve "raising 'meals that remind you of home' to exponential powers, multiplying imaginary numbers by 'the color black', and taking the square root of 'Former Vice President Joe Biden'." The entry insists that "these connections do not actually exist" because the non-existent connections being depicted as logically true can result in a Cosmic Retcon or a Reality-Breaking Paradox.

    Web Videos 
  • Unraveled: In "Scientifically calculating the game of the year", Brian attempts to objectively calculate which game was the best of 2018, despite this obviously being a largely subjective criteria. Brian realizes his mistake when his formula outputs Fortnite as the winner due to its massive popularity completely obliterating all the other criteria the formula attempted to account for.

    Western Animation 
  • In Numb Chucks, Buford uses a board and equations to come up with the perfect insulting nickname for the Chucks, which he actually series on "Numbsickles".
  • Rick and Morty: Rick has worked out a mathematical proof that both Morty and Summer are "pieces of shit" and is all too pleased to wheel out the whiteboard to show off his work. He probably could have waited until they had escaped from the reality destroying void first, though.
    • Rick and his alternate universe selves appear to have a knack for quantifying the seemingly unquantifiable, from evil to even Rick-ness itself.
  • The Simpsons: When Homer gets a brain upgrade, he mathematically proves the non-existence of God while working out a plan for a flat tax. Even his hyper-religious neighbor Ned can't find any errors in it.
  • South Park:
    • In the episode "Cash for Gold", Cartman writes an equation on a whiteboard. It looks roughly like the following (all numbers appear as subscripts; so does the last lowercase p):
      gcfs2 - puc2j2 + cb(sn)/d1Op = GOLD
      Mathematical genius: it's the Formula for Gold. "Guys with 'Cash for Gold' signs gets you people's unwanted crappy jewelry, which, when added to a cable-based shopping network, divided by demented old people, equals gold."
    • In the episode "Fishsticks", Kanye West tries to figure out the pun based joke of the title.
      "Alright, now what do we know about fishsticks? [adds more words to the board] They're breaded, they're fried, they're frozen. Then under me we have rapper, genius. And gay fish are homosexual. They swim. [begins connecting words] Is it because breaded has something to do with genius? Which swims?"

    Real Life