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* EXISTENCE ITSELF. Face it. What do ''you'' understand about life, the universe and everything that isn't fundamentally this trope?
* Dreams. The ones that make sense are perhaps the least common.
** In fact, the original Surrealist movement used dreams as its main inspiration. Given our tendency to refer to weird things as "surreal" nowadays, one could argue that dreams are the origin of MindScrew art.
** While there's certainly theories, there's still no known definite explanation as to how they occur.
* The theory of UsefulNotes/{{relativity}}. What’s your understanding of space and time? Location, distance, speed are all unambiguous, time is the same for everyone, etc? It's wrong. Space (and time too, possibly) just doesn't work that way. And that's just Special Relativity. Its big brother General Relativity is a lot more mind-screwing than that.
* Time even more so than space. Is it a real, tangible force that flows in four or more directions in four or more dimensions? Or is it just an existential explanation for gradual change which sates our need to catalog events and arrange everything into patterns? (Or alternately - [[Series/DoctorWho from a non-linear, non-subjective viewpoint - is it more like]] [[TimeyWimeyBall a big ball of wibbly-wobbly, timey-wimey]]... ''[[BuffySpeak stuff]]''?) The debate has raged for hundreds of years. Not helping is the fact that sometimes physics doesn't need to take time into account. Neither is the fact that, according to some simulations, time might be slowing down. Or maybe not--how would we know?
** For that matter, anything related to time travel theories. To further the point, look at the TemporalParadox and TimeyWimeyBall tropes. Read those and tell me you are not confused.
* Black holes. Read UsefulNotes/BlackHoles and you’ll (not) understand why.
* UsefulNotes/RichardFeynman once quipped, "Anyone who claims to understand quantum mechanics has not been paying attention." To give ''one'' example: small particles behave like waves. When a light wave goes through two slits right next to each other, it creates an interference pattern of light and dark bars. Doing the same with lots of electrons yields the same results, with light bars meaning more electrons hit there and dark bars meaning less. Doing the same with one electron at a time and adding the results together yields the ''exact same'' result. Translation: the electron goes through ''both slits'' and ''interferes with itself''. Observing the electron as it goes through gives a pattern of just two bars, as if the electron behaves solely like a particle, meaning simply ''observing the experiment'' changes the results.
* Given what we said above, it seems that any theory that reconciles general relativity with quantum mechanics would necessarily be a MindScrew itself.
* Negative Numbers (numbers less than zero) can be this to children first getting introduced to them ("how the heck can I have fewer than zero apples?"), and they tend to give the same reaction when introduced to Imaginary Numbers (numbers multiplied by ''i'', the square root of -1) later on in life.
** Abstract algebra, topology, and anything in UsefulNotes/{{mathematics}} that isn't immediately usable in some engineering/economics field (and those aren't completely exempt). Forget everything that you claim to know about such "trivial" things as addition, multiplication, division, space (space, as in 3D space), etc. Remember that some of the trippier aspects of quantum-mechanics are just special cases in mathematics.
*** Mathematically, Quantum Theory is quite simple, really. It's in trying to make sense of it that things get ugly.
*** One of the weirder things to come out of topology and set theory is a mathematical structure called the "[[http://en.wikipedia.org/wiki/Long_line_%28topology%29 long line]]". It's like the usual real line, but ''much longer''. Yes, it's longer than a line of infinite length. (Making sense of what that means requires some set theory.) So much longer, in fact, that even an infinite sequence of steps can only cover a tiny portion of it.
*** Almost any mathematical concept taken to a high-enough level qualifies, right up to the concept of ''numbers''. Much of this has to do with the weirdness inherent in set theory (everything is a set; an element in a set, which is a type of subset; a subset of a set, which can itself be considered a set; or a relation on a set) and infinities (yes, plural--there are different sizes. See below).
** For spatial mathematics, consider this: The 'right-hand' 3-dimensional Vector direction of Y is counter-clockwise from X, which is clockwise from Z, which is counter-clockwise from Y. What this means is that Left is -1, Right is + 1, Down is -1, Up is + 1... and Backward is + 1, Forward is -1. Somehow, this makes the math work ''right''.
* Anything about 4-dimensional objects (or worse, more). Take the three spacial (..."axises"?) of our 3D universe: up/down, left/right, and forward/backward. All of them are at ninety degrees to one another. a 4D universe would have all of those as well, plus an additional one ''simultaneously at ninety degrees to all of them as well.'' If you take a bunch of 2D squares and fold them up, you get a cube. If you take a bunch of 3D cubes and fold ''those'' ..."up", you get a [[http://commons.wikimedia.org/wiki/File:8-cell-simple.gif tesseract]].[[note]]No, not [[Film/{{Thor}} that one]]. Think more ''Literature/AWrinkleInTime'', only not quite.[[/note]] [[MindScrewdriver Most experts assume that beings from a purely 2-dimensional universe would find 3D space just as mind-screwey]].
* Fractals. Taken from the right perspective, it's impossible to tell a tiny sliver of melting ice from a glacier hundreds of square miles in size. Many natural features exhibit self-similarity across mind-boggling scales.
* e[[superscript:iπ]]--an irrational, transcendental number raised to the power of the product of another transcendental number and an ''imaginary'' number--equals ''[[ShockingSwerve what now]]''?
** [[spoiler:-1]].
** Leading to Euler's identity (aka Euler's equation), widely considered to be an example of deep [[http://en.wikipedia.org/wiki/Mathematical_beauty mathematical beauty]]: e[[superscript:iπ]] + 1 = 0.
* Speaking of [[http://en.wikipedia.org/wiki/E_(mathematical_constant) e]], it has so many nice properties in so many seemingly unrelated areas that it seems to be a key component '''OF MATH ITSELF'''. Think about it.
** [[http://en.wikipedia.org/wiki/List_of_topics_related_to_%CF%80 Same with]] π.
* [[http://en.wikipedia.org/wiki/Imaginary_number Imaginary numbers]]. A product of sheer impossibility created by the simple action of taking the square root of a negative number.
** Electrical engineers use them to model the behavior of Alternating Current (AC) circuits because they actually ''do'' correctly describe how these circuits behave!
** Not only applicable in electrical engineering, but fluid dynamics and aerodynamics too. Well defined two-dimensional fluid flows can be complete solved using a [[http://en.wikipedia.org/wiki/Schwarz%E2%80%93Christoffel_mapping series of transformations involving imaginary numbers.]]
* The Riemann Zeta function. Initially defined as a series, its continuation gives us gems such as the apparent sum 1+2+3+4+5+6+... = -1/12. Add in imaginary numbers and an interesting connection with prime numbers (numbers that are only divisible by 1 and themselves, and with a seemingly random distribution) and you get an object so weird it's still not fully understood. No wonder the Riemann hypothesis (roughly, whether some of the points where the Zeta function equals zero are all located on a single line that crosses the real numbers, with consequences on the distribution of prime numbers) is considered one of the most difficult problems in mathematics.
* [[http://en.wikipedia.org/wiki/Negative_temperature Negative temperature]]. No, not negative Celsius or Fahrenheit, that would make too much sense. It is a truly negative temperature in ''[[BeyondTheImpossible Kelvin]]''. It is the temperature of something so "cold" it is hotter than anything with a positive temperature so when they come into contact heat will flow from the system with negative temperature to the one with positive temperature. In other words, temperature seen as a dial that has been turned past the 0-point and ended up at the other "end point".
* Biggest Mind Screw in UsefulNotes/{{Mathematics}} or a faulty proof?
-->[[UsefulNotes/FermatsLastTheorem "It is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second into two like powers. I have discovered a truly marvellous proof of this, which this margin is too narrow to contain."]]
** i.e., for "x[[superscript:n]] + y[[superscript:n]] = z[[superscript:n]] you can only find integer values for x, y and z that will produce a valid equation where n <= 2.
** Considering that it was never mentioned by Fermat again and that the eventual solution was 150 pages of extremely complex math involving mathematical concepts that didn't exist during Fermat's time (i.e. before ''basic calculus''), it's almost certain that Fermat discovered his proof was wrong and never mentioned that fact, or [[{{Troll}} had no proof at all]], but we may never know. Some have suggested that his theorem was a practical joke to frustrate fellow mathematicians: It's true, they just couldn't ''prove'' it. It is now the mathematical equivalent of the TheGreatPoliticsMessUp: Some Sci-Fi shows say that Fermat's Theorem has still never been solved (''Series/StarTrekTheNextGeneration'', for example, made a reference to it saying that it wasn't solved), when it fact it finally has.
* The [[http://en.wikipedia.org/wiki/Banach-Tarski_theorem Banach-Tarski theorem]] states that any ball can be divided into pieces and reassembled into two balls the same size as the original. ''Webcomic/IrregularWebcomic'' offers an [[http://www.irregularwebcomic.net/2339.html explanation]] in (almost) layman's terms as to how this is possible. [[spoiler:It isn't. It only works with mathematical abstractions, not actual objects.]]
* Gödel's Incompleteness Theorems. The first one shows that any consistent axiomatic system sophisticated enough to encompass elementary arithmetic contains statements that are true but cannot be proved in the system. Even more mind-screwtastic is Tarski's Indefinability Theorem, which states that the set of true statements in an axiomatic system is a non-namable set. Just think about it: it states that ''truth is indefinable in an axiomatic system''.
* If you thought ''Film/TheMatrix'' was mind-boggling, and you Did The Research, you already should be familiarized with Monsieur Jean Baudrillard. If don't, and you don't want to know that we live in a increasingly complex fake reality over-imposed onto reality by the media apparatus and the exchange system which we gladly buy in a daily basis, you better keep it that way. A brief reflexion on his school of thought:
** Simulacrum is not what covers the truth.
** Is truth the one which covers the fact that there is no truth.
** Simulacrum is true.
*** You may find it amusing at first, the scary part comes when you start nodding and saying "[[OhCrap Uh oh, it's starting to make sense]]".
* The Zen Koan is to make you achieve enlightenment by Mind Screws.
** What did your face look like before your parents were born?
** Two hands clap and there is a sound. What is the sound of one hand?
*** Don't know, ask [[VideoGame/StarCraft Rory Swann]].
*** [[WesternAnimation/TheSimpsons Bart Simpson]] figured that one out--[[FridgeBrilliance he just slapped his fingers against his palm]].
*** [[Literature/{{Discworld}} It's "cl". The other hand makes the "ap"]].
*** [[http://buttersafe.com/2007/08/09/consulting-the-master/ This apparently]].
** "What is Buddha?" Dongshan said, "Three pounds of flax."
** Mu
* Complexity Theory (aka Ramsey Theory), which is at least as old as Chaos Theory and is the counterpart to it; it states that, given enough data, it is impossible for there '''not''' to be some kind of pattern to them. (Which doesn't signify that said pattern ''means'' anything...)
* [[http://en.wikipedia.org/wiki/Boltzmann_brain Boltzmann brain]]. A BrainInAJar-like, self-aware entity that, [[TimeAbyss given enough time]], would appear from nothing, complete with false memories and totally oblivious to the fact it's in the middle of the most absolute nowhere.
** And there's some evidence that this is more likely than the world as we know it being real.
* The concept of solipsism: Everything and everyone around you exists only so long as you do, potentially for as long as you do. You are the lynch-pin of the universe.
* Ever think about parallel universes? Most would have completely different sets of physical laws, assuming "laws" are a viable concept; or even if "concepts" have the capability to exist. Or if existence in itself is warped beyond human comprehension. And the worst thing of all, is that all these crazy, otherworldly, incomprehensible laws all makes sense within that universe, it all conforms to that universe's rules or "laws". Just thinking about it makes your head hurt.
** It's even worse. See the "infinite" entry below.
* Infinity and eternity will make your head hurt. [[UpToEleven Especially the fact that some infinities are larger than others]].
** If you consider possibilities such as our universe being infinite and/or an infinite number of [[AlternateUniverse other universes existing]], is even more brain-hurting, as ''everything would happen an infinite number of times''. Solutions to the paradoxes brought by them range from assuming time will end someday to [[YouCannotGraspTheTrueForm our inability to compute infinite probabilities]].
* LSD's effects. Completely subjective to the individual and utterly incomprehensible to someone who has never taken it.
* [[TrueArtIsIncomprehensible True Art]].
* PostModernism ''loves'' this.
* Many Website/ChuckNorrisFacts and [[RussianReversal Soviet Russia jokes]] count as this. Just ''how'' does a car drive a human?
* The [[http://www.maydaymystery.org/mayday/ May Day Mystery]], an uncategorizable and indescribable series of bizarre documents, possibly the coded annals of a conspiracy. Sure, it could all just be an (insanely) elaborate hoax, but WhatDoYouMeanItsNotSymbolic? If you squint and turn your head it kind of looks like an AlternateRealityGame.
* [[http://www.buzzfeed.com/mjs538/60-completely-unusable-stock-photos This collection of stock photos]]. While most are simply funny or inappropriate, some make absolutely no sense, like the one showing a man with a pineapple for a head.
* The now-infamous [[http://en.wikipedia.org/wiki/The_dress_(viral_phenomenon) dress]]. Depending on how your brain processes color, it may appear to be either white and gold or blue and black--and good luck convincing someone who sees it the other way. (The real colors, apparently, are blue and black.)
** And now more and more people who TakeAThirdOption have appeared, claiming that the dress is blue and dark gold.
** The [[https://en.wikipedia.org/wiki/Yanny_or_Laurel "Yanny vs. Laurel" auditory illusion]] is a similar (and similarly [[MemeticMutation memetic]]) phenomenon, though for the ears this time rather than the eyes.
* Research on [[https://en.wikipedia.org/wiki/Dual_consciousness_(neuroscience) dual consciousness]]. It is not even known whether it really exists, and how to define it.
* Wiki/TVTropes:
** At least half the entries in WildMassGuessing.
** The ThirdPersonPerson page. How many of the RealLife entries are posted by the person they speak of?
* ''Webcomic/{{Homestuck}}'''s [[StealthPun ~ATH]] coding language is a parody of programming in general, and esoteric languages in the specific.
** Any [[http://en.wikipedia.org/wiki/Esoteric_programming_language esoteric programming language]] will qualify as a MindScrew. For bonus points, there's one named "brainfuck."
* There's a joke that goes, "On a foggy morning, two people encountered each other on opposite ends of a long bridge. On one end, Alice stood, peering over the bridge and wondering if the person across was Bob or not. On the other side, Bob stood, believing the person across the bridge to be Alice but not being sure of it. Then the two people crossed simultaneously, met in the middle, and discovered to their surprise that it was neither of them."
* Paradoxes are a great way to way to screw with your mind and make you question everything. Spend some time reading the [[https://en.wikipedia.org/wiki/List_of_paradoxes List of paradoxes]] on Wiki/TheOtherWiki. Here are some examples.
** Raven paradox: (or Hempel's Ravens): Observing a green apple increases the likelihood of all ravens being black.
** Ant on a rubber rope: An ant crawling on a rubber rope can reach the end even when the rope stretches much faster than the ant can crawl.
** Potato paradox: If you let potatoes consisting of 99% water dry so that they are 98% water, they lose 50% of their weight.
** Hilbert's paradox of the Grand Hotel: If a hotel with infinitely many rooms is full, it can still take in more guests.
** Moore's paradox: "It's raining, but I don't believe that it is."
** There are many statements that are paradoxical but true, such as "The only constant is change" or "you're unique, just like everyone else."
* As ''Film/{{Inception}} ''points out, a dream never really has a beginning, we always find ourselves in the middle of it. Knowing that, ask yourself, do you remember your life beginning, or did you just find yourself in the middle of it?
* Division by zero, of course. It's such a strange concept it can't even be done with ''imaginary numbers''.
* Graham's number is so incomprehensible that there doesn't exist enough writing material known to man to fully write it down! If you tried to fully comprehend it, your ''head would explode into a black hole''. And even ''that's'' small compared to TREE(3). And even '''that's''' small compared to SSCG(3)! And of course that's small compared to infinity.
* Irish politician Boyle Roche once missed a meeting of Parliament, and gave the excuse that [[InsaneTrollLogic "Mr. Speaker, it is impossible I could have been in two places at once, unless I were a bird."]] What the hell?
* The Fosbury Flop, which has been the standard technique for competitive high jumpers since it was created by Dick Fosbury in the late 1960s, is full of this trope:
** For starters, just watching it can induce mental confusion—it involves turning around at the takeoff point and going backwards over the bar.
** Even more mind-boggling: The jumper's center of gravity passes ''under the bar'' even on a successful jump!
* [[https://en.wikipedia.org/wiki/Thomson%27s_lamp Thompson's Lamp]]. Basically, imagine a lamp set on a timer for two minutes, after a minute the lamp turns on, after half that time (30 seconds) it turn off again, after 15 seconds it turns on again and so on, halving the time ad infinitum. The question being: would the lamp be on or off at the end? Neither answer seems to make sense, as both imply there would be an "end" to infinity.
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* EXISTENCE ITSELF. Face it. What do ''you'' understand about life, the universe and everything that isn't fundamentally this trope?
* Dreams. The ones that make sense are perhaps the least common.
** In fact, the original Surrealist movement used dreams as its main inspiration. Given our tendency to refer to weird things as "surreal" nowadays, one could argue that dreams are the origin of MindScrew art.
** While there's certainly theories, there's still no known definite explanation as to how they occur.
* The theory of UsefulNotes/{{relativity}}. What’s your understanding of space and time? Location, distance, speed are all unambiguous, time is the same for everyone, etc? It's wrong. Space (and time too, possibly) just doesn't work that way. And that's just Special Relativity. Its big brother General Relativity is a lot more mind-screwing than that.
* Time even more so than space. Is it a real, tangible force that flows in four or more directions in four or more dimensions? Or is it just an existential explanation for gradual change which sates our need to catalog events and arrange everything into patterns? (Or alternately - [[Series/DoctorWho from a non-linear, non-subjective viewpoint - is it more like]] [[TimeyWimeyBall a big ball of wibbly-wobbly, timey-wimey]]... ''[[BuffySpeak stuff]]''?) The debate has raged for hundreds of years. Not helping is the fact that sometimes physics doesn't need to take time into account. Neither is the fact that, according to some simulations, time might be slowing down. Or maybe not--how would we know?
** For that matter, anything related to time travel theories. To further the point, look at the TemporalParadox and TimeyWimeyBall tropes. Read those and tell me you are not confused.
* Black holes. Read UsefulNotes/BlackHoles and you’ll (not) understand why.
* UsefulNotes/RichardFeynman once quipped, "Anyone who claims to understand quantum mechanics has not been paying attention." To give ''one'' example: small particles behave like waves. When a light wave goes through two slits right next to each other, it creates an interference pattern of light and dark bars. Doing the same with lots of electrons yields the same results, with light bars meaning more electrons hit there and dark bars meaning less. Doing the same with one electron at a time and adding the results together yields the ''exact same'' result. Translation: the electron goes through ''both slits'' and ''interferes with itself''. Observing the electron as it goes through gives a pattern of just two bars, as if the electron behaves solely like a particle, meaning simply ''observing the experiment'' changes the results.
* Given what we said above, it seems that any theory that reconciles general relativity with quantum mechanics would necessarily be a MindScrew itself.
* Negative Numbers (numbers less than zero) can be this to children first getting introduced to them ("how the heck can I have fewer than zero apples?"), and they tend to give the same reaction when introduced to Imaginary Numbers (numbers multiplied by ''i'', the square root of -1) later on in life.
** Abstract algebra, topology, and anything in UsefulNotes/{{mathematics}} that isn't immediately usable in some engineering/economics field (and those aren't completely exempt). Forget everything that you claim to know about such "trivial" things as addition, multiplication, division, space (space, as in 3D space), etc. Remember that some of the trippier aspects of quantum-mechanics are just special cases in mathematics.
*** Mathematically, Quantum Theory is quite simple, really. It's in trying to make sense of it that things get ugly.
*** One of the weirder things to come out of topology and set theory is a mathematical structure called the "[[http://en.wikipedia.org/wiki/Long_line_%28topology%29 long line]]". It's like the usual real line, but ''much longer''. Yes, it's longer than a line of infinite length. (Making sense of what that means requires some set theory.) So much longer, in fact, that even an infinite sequence of steps can only cover a tiny portion of it.
*** Almost any mathematical concept taken to a high-enough level qualifies, right up to the concept of ''numbers''. Much of this has to do with the weirdness inherent in set theory (everything is a set; an element in a set, which is a type of subset; a subset of a set, which can itself be considered a set; or a relation on a set) and infinities (yes, plural--there are different sizes. See below).
** For spatial mathematics, consider this: The 'right-hand' 3-dimensional Vector direction of Y is counter-clockwise from X, which is clockwise from Z, which is counter-clockwise from Y. What this means is that Left is -1, Right is + 1, Down is -1, Up is + 1... and Backward is + 1, Forward is -1. Somehow, this makes the math work ''right''.
* Anything about 4-dimensional objects (or worse, more). Take the three spacial (..."axises"?) of our 3D universe: up/down, left/right, and forward/backward. All of them are at ninety degrees to one another. a 4D universe would have all of those as well, plus an additional one ''simultaneously at ninety degrees to all of them as well.'' If you take a bunch of 2D squares and fold them up, you get a cube. If you take a bunch of 3D cubes and fold ''those'' ..."up", you get a [[http://commons.wikimedia.org/wiki/File:8-cell-simple.gif tesseract]].[[note]]No, not [[Film/{{Thor}} that one]]. Think more ''Literature/AWrinkleInTime'', only not quite.[[/note]] [[MindScrewdriver Most experts assume that beings from a purely 2-dimensional universe would find 3D space just as mind-screwey]].
* Fractals. Taken from the right perspective, it's impossible to tell a tiny sliver of melting ice from a glacier hundreds of square miles in size. Many natural features exhibit self-similarity across mind-boggling scales.
* e[[superscript:iπ]]--an irrational, transcendental number raised to the power of the product of another transcendental number and an ''imaginary'' number--equals ''[[ShockingSwerve what now]]''?
** [[spoiler:-1]].
** Leading to Euler's identity (aka Euler's equation), widely considered to be an example of deep [[http://en.wikipedia.org/wiki/Mathematical_beauty mathematical beauty]]: e[[superscript:iπ]] + 1 = 0.
* Speaking of [[http://en.wikipedia.org/wiki/E_(mathematical_constant) e]], it has so many nice properties in so many seemingly unrelated areas that it seems to be a key component '''OF MATH ITSELF'''. Think about it.
** [[http://en.wikipedia.org/wiki/List_of_topics_related_to_%CF%80 Same with]] π.
* [[http://en.wikipedia.org/wiki/Imaginary_number Imaginary numbers]]. A product of sheer impossibility created by the simple action of taking the square root of a negative number.
** Electrical engineers use them to model the behavior of Alternating Current (AC) circuits because they actually ''do'' correctly describe how these circuits behave!
** Not only applicable in electrical engineering, but fluid dynamics and aerodynamics too. Well defined two-dimensional fluid flows can be complete solved using a [[http://en.wikipedia.org/wiki/Schwarz%E2%80%93Christoffel_mapping series of transformations involving imaginary numbers.]]
* The Riemann Zeta function. Initially defined as a series, its continuation gives us gems such as the apparent sum 1+2+3+4+5+6+... = -1/12. Add in imaginary numbers and an interesting connection with prime numbers (numbers that are only divisible by 1 and themselves, and with a seemingly random distribution) and you get an object so weird it's still not fully understood. No wonder the Riemann hypothesis (roughly, whether some of the points where the Zeta function equals zero are all located on a single line that crosses the real numbers, with consequences on the distribution of prime numbers) is considered one of the most difficult problems in mathematics.
* [[http://en.wikipedia.org/wiki/Negative_temperature Negative temperature]]. No, not negative Celsius or Fahrenheit, that would make too much sense. It is a truly negative temperature in ''[[BeyondTheImpossible Kelvin]]''. It is the temperature of something so "cold" it is hotter than anything with a positive temperature so when they come into contact heat will flow from the system with negative temperature to the one with positive temperature. In other words, temperature seen as a dial that has been turned past the 0-point and ended up at the other "end point".
* Biggest Mind Screw in UsefulNotes/{{Mathematics}} or a faulty proof?
-->[[UsefulNotes/FermatsLastTheorem "It is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second into two like powers. I have discovered a truly marvellous proof of this, which this margin is too narrow to contain."]]
** i.e., for "x[[superscript:n]] + y[[superscript:n]] = z[[superscript:n]] you can only find integer values for x, y and z that will produce a valid equation where n <= 2.
** Considering that it was never mentioned by Fermat again and that the eventual solution was 150 pages of extremely complex math involving mathematical concepts that didn't exist during Fermat's time (i.e. before ''basic calculus''), it's almost certain that Fermat discovered his proof was wrong and never mentioned that fact, or [[{{Troll}} had no proof at all]], but we may never know. Some have suggested that his theorem was a practical joke to frustrate fellow mathematicians: It's true, they just couldn't ''prove'' it. It is now the mathematical equivalent of the TheGreatPoliticsMessUp: Some Sci-Fi shows say that Fermat's Theorem has still never been solved (''Series/StarTrekTheNextGeneration'', for example, made a reference to it saying that it wasn't solved), when it fact it finally has.
* The [[http://en.wikipedia.org/wiki/Banach-Tarski_theorem Banach-Tarski theorem]] states that any ball can be divided into pieces and reassembled into two balls the same size as the original. ''Webcomic/IrregularWebcomic'' offers an [[http://www.irregularwebcomic.net/2339.html explanation]] in (almost) layman's terms as to how this is possible. [[spoiler:It isn't. It only works with mathematical abstractions, not actual objects.]]
* Gödel's Incompleteness Theorems. The first one shows that any consistent axiomatic system sophisticated enough to encompass elementary arithmetic contains statements that are true but cannot be proved in the system. Even more mind-screwtastic is Tarski's Indefinability Theorem, which states that the set of true statements in an axiomatic system is a non-namable set. Just think about it: it states that ''truth is indefinable in an axiomatic system''.
* If you thought ''Film/TheMatrix'' was mind-boggling, and you Did The Research, you already should be familiarized with Monsieur Jean Baudrillard. If don't, and you don't want to know that we live in a increasingly complex fake reality over-imposed onto reality by the media apparatus and the exchange system which we gladly buy in a daily basis, you better keep it that way. A brief reflexion on his school of thought:
** Simulacrum is not what covers the truth.
** Is truth the one which covers the fact that there is no truth.
** Simulacrum is true.
*** You may find it amusing at first, the scary part comes when you start nodding and saying "[[OhCrap Uh oh, it's starting to make sense]]".
* The Zen Koan is to make you achieve enlightenment by Mind Screws.
** What did your face look like before your parents were born?
** Two hands clap and there is a sound. What is the sound of one hand?
*** Don't know, ask [[VideoGame/StarCraft Rory Swann]].
*** [[WesternAnimation/TheSimpsons Bart Simpson]] figured that one out--[[FridgeBrilliance he just slapped his fingers against his palm]].
*** [[Literature/{{Discworld}} It's "cl". The other hand makes the "ap"]].
*** [[http://buttersafe.com/2007/08/09/consulting-the-master/ This apparently]].
** "What is Buddha?" Dongshan said, "Three pounds of flax."
** Mu
* Complexity Theory (aka Ramsey Theory), which is at least as old as Chaos Theory and is the counterpart to it; it states that, given enough data, it is impossible for there '''not''' to be some kind of pattern to them. (Which doesn't signify that said pattern ''means'' anything...)
* [[http://en.wikipedia.org/wiki/Boltzmann_brain Boltzmann brain]]. A BrainInAJar-like, self-aware entity that, [[TimeAbyss given enough time]], would appear from nothing, complete with false memories and totally oblivious to the fact it's in the middle of the most absolute nowhere.
** And there's some evidence that this is more likely than the world as we know it being real.
* The concept of solipsism: Everything and everyone around you exists only so long as you do, potentially for as long as you do. You are the lynch-pin of the universe.
* Ever think about parallel universes? Most would have completely different sets of physical laws, assuming "laws" are a viable concept; or even if "concepts" have the capability to exist. Or if existence in itself is warped beyond human comprehension. And the worst thing of all, is that all these crazy, otherworldly, incomprehensible laws all makes sense within that universe, it all conforms to that universe's rules or "laws". Just thinking about it makes your head hurt.
** It's even worse. See the "infinite" entry below.
* Infinity and eternity will make your head hurt. [[UpToEleven Especially the fact that some infinities are larger than others]].
** If you consider possibilities such as our universe being infinite and/or an infinite number of [[AlternateUniverse other universes existing]], is even more brain-hurting, as ''everything would happen an infinite number of times''. Solutions to the paradoxes brought by them range from assuming time will end someday to [[YouCannotGraspTheTrueForm our inability to compute infinite probabilities]].
* LSD's effects. Completely subjective to the individual and utterly incomprehensible to someone who has never taken it.
* [[TrueArtIsIncomprehensible True Art]].
* PostModernism ''loves'' this.
* Many Website/ChuckNorrisFacts and [[RussianReversal Soviet Russia jokes]] count as this. Just ''how'' does a car drive a human?
* The [[http://www.maydaymystery.org/mayday/ May Day Mystery]], an uncategorizable and indescribable series of bizarre documents, possibly the coded annals of a conspiracy. Sure, it could all just be an (insanely) elaborate hoax, but WhatDoYouMeanItsNotSymbolic? If you squint and turn your head it kind of looks like an AlternateRealityGame.
* [[http://www.buzzfeed.com/mjs538/60-completely-unusable-stock-photos This collection of stock photos]]. While most are simply funny or inappropriate, some make absolutely no sense, like the one showing a man with a pineapple for a head.
* The now-infamous [[http://en.wikipedia.org/wiki/The_dress_(viral_phenomenon) dress]]. Depending on how your brain processes color, it may appear to be either white and gold or blue and black--and good luck convincing someone who sees it the other way. (The real colors, apparently, are blue and black.)
** And now more and more people who TakeAThirdOption have appeared, claiming that the dress is blue and dark gold.
** The [[https://en.wikipedia.org/wiki/Yanny_or_Laurel "Yanny vs. Laurel" auditory illusion]] is a similar (and similarly [[MemeticMutation memetic]]) phenomenon, though for the ears this time rather than the eyes.
* Research on [[https://en.wikipedia.org/wiki/Dual_consciousness_(neuroscience) dual consciousness]]. It is not even known whether it really exists, and how to define it.
* Wiki/TVTropes:
** At least half the entries in WildMassGuessing.
** The ThirdPersonPerson page. How many of the RealLife entries are posted by the person they speak of?
* ''Webcomic/{{Homestuck}}'''s [[StealthPun ~ATH]] coding language is a parody of programming in general, and esoteric languages in the specific.
** Any [[http://en.wikipedia.org/wiki/Esoteric_programming_language esoteric programming language]] will qualify as a MindScrew. For bonus points, there's one named "brainfuck."
* There's a joke that goes, "On a foggy morning, two people encountered each other on opposite ends of a long bridge. On one end, Alice stood, peering over the bridge and wondering if the person across was Bob or not. On the other side, Bob stood, believing the person across the bridge to be Alice but not being sure of it. Then the two people crossed simultaneously, met in the middle, and discovered to their surprise that it was neither of them."
* Paradoxes are a great way to way to screw with your mind and make you question everything. Spend some time reading the [[https://en.wikipedia.org/wiki/List_of_paradoxes List of paradoxes]] on Wiki/TheOtherWiki. Here are some examples.
** Raven paradox: (or Hempel's Ravens): Observing a green apple increases the likelihood of all ravens being black.
** Ant on a rubber rope: An ant crawling on a rubber rope can reach the end even when the rope stretches much faster than the ant can crawl.
** Potato paradox: If you let potatoes consisting of 99% water dry so that they are 98% water, they lose 50% of their weight.
** Hilbert's paradox of the Grand Hotel: If a hotel with infinitely many rooms is full, it can still take in more guests.
** Moore's paradox: "It's raining, but I don't believe that it is."
** There are many statements that are paradoxical but true, such as "The only constant is change" or "you're unique, just like everyone else."
* As ''Film/{{Inception}} ''points out, a dream never really has a beginning, we always find ourselves in the middle of it. Knowing that, ask yourself, do you remember your life beginning, or did you just find yourself in the middle of it?
* Division by zero, of course. It's such a strange concept it can't even be done with ''imaginary numbers''.
* Graham's number is so incomprehensible that there doesn't exist enough writing material known to man to fully write it down! If you tried to fully comprehend it, your ''head would explode into a black hole''. And even ''that's'' small compared to TREE(3). And even '''that's''' small compared to SSCG(3)! And of course that's small compared to infinity.
* Irish politician Boyle Roche once missed a meeting of Parliament, and gave the excuse that [[InsaneTrollLogic "Mr. Speaker, it is impossible I could have been in two places at once, unless I were a bird."]] What the hell?
* The Fosbury Flop, which has been the standard technique for competitive high jumpers since it was created by Dick Fosbury in the late 1960s, is full of this trope:
** For starters, just watching it can induce mental confusion—it involves turning around at the takeoff point and going backwards over the bar.
** Even more mind-boggling: The jumper's center of gravity passes ''under the bar'' even on a successful jump!
* [[https://en.wikipedia.org/wiki/Thomson%27s_lamp Thompson's Lamp]]. Basically, imagine a lamp set on a timer for two minutes, after a minute the lamp turns on, after half that time (30 seconds) it turn off again, after 15 seconds it turns on again and so on, halving the time ad infinitum. The question being: would the lamp be on or off at the end? Neither answer seems to make sense, as both imply there would be an "end" to infinity.
----
[[redirect:MindScrew]]
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* Speaking of [[http://en.wikipedia.org/wiki/E_(mathematical_constant) e]], it has so many nice properties in so many seemingly unrelated areas that it seems to be an key component '''OF MATH ITSELF'''. Think about it.

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* Speaking of [[http://en.wikipedia.org/wiki/E_(mathematical_constant) e]], it has so many nice properties in so many seemingly unrelated areas that it seems to be an a key component '''OF MATH ITSELF'''. Think about it.
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i is the square root of -1, not 0


* Negative Numbers (numbers less than zero) can be this to children first getting introduced to them ("how the heck can I have fewer than zero apples?"), and they tend to give the same reaction when introduced to Imaginary Numbers (numbers multiplied by ''i'', the square root of zero) later on in life.

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* Negative Numbers (numbers less than zero) can be this to children first getting introduced to them ("how the heck can I have fewer than zero apples?"), and they tend to give the same reaction when introduced to Imaginary Numbers (numbers multiplied by ''i'', the square root of zero) -1) later on in life.
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double oops


* Anything about 4-dimensional objects (or worse, more). Take the three spacial (..."axises"?) of our 3D universe: up/down, left/right, and forward/backward. All of them are at ninety degrees to one another. a 4D universe would have all of those as well, plus an additionalone ''simultaneously at ninety degrees to all of them as well.'' If you take a bunch of 2D squares and fold them up, you get a cube. If you take a bunch of 3D cubes and fold ''those'' ..."up", you get a [[http://commons.wikimedia.org/wiki/File:8-cell-simple.gif tesseract]].[[note]]No, not [[Film/{{Thor}} that one]]. Think more ''Literature/AWrinkleInTime'', only not quite.[[/note]] [[MindScrewdriver Most experts assume that beings from a purely 2-dimensional universe would find 3D space just as mind-screwey]].

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* Anything about 4-dimensional objects (or worse, more). Take the three spacial (..."axises"?) of our 3D universe: up/down, left/right, and forward/backward. All of them are at ninety degrees to one another. a 4D universe would have all of those as well, plus an additionalone additional one ''simultaneously at ninety degrees to all of them as well.'' If you take a bunch of 2D squares and fold them up, you get a cube. If you take a bunch of 3D cubes and fold ''those'' ..."up", you get a [[http://commons.wikimedia.org/wiki/File:8-cell-simple.gif tesseract]].[[note]]No, not [[Film/{{Thor}} that one]]. Think more ''Literature/AWrinkleInTime'', only not quite.[[/note]] [[MindScrewdriver Most experts assume that beings from a purely 2-dimensional universe would find 3D space just as mind-screwey]].
Is there an issue? Send a MessageReason:
oops


* Anything about 4-dimensional objects (or worse, more). Take the three spacial (..."axises"?) of out 3D universe: up/down, left/right, and forward/backward. All of them are at ninety degrees to one another. a 4D universe would have all of those as well, plus an additionalone ''simultaneously at ninety degrees to all of them as well.'' If you take a bunch of 2D squares and fold them up, you get a cube. If you take a bunch of 3D cubes and fold ''those'' ..."up", you get a [[http://commons.wikimedia.org/wiki/File:8-cell-simple.gif tesseract]].[[note]]No, not [[Film/{{Thor}} that one]]. Think more ''Literature/AWrinkleInTime'', only not quite.[[/note]] [[MindScrewdriver Most experts assume that beings from a purely 2-dimensional universe would find 3D space just as mind-screwey]].

to:

* Anything about 4-dimensional objects (or worse, more). Take the three spacial (..."axises"?) of out our 3D universe: up/down, left/right, and forward/backward. All of them are at ninety degrees to one another. a 4D universe would have all of those as well, plus an additionalone ''simultaneously at ninety degrees to all of them as well.'' If you take a bunch of 2D squares and fold them up, you get a cube. If you take a bunch of 3D cubes and fold ''those'' ..."up", you get a [[http://commons.wikimedia.org/wiki/File:8-cell-simple.gif tesseract]].[[note]]No, not [[Film/{{Thor}} that one]]. Think more ''Literature/AWrinkleInTime'', only not quite.[[/note]] [[MindScrewdriver Most experts assume that beings from a purely 2-dimensional universe would find 3D space just as mind-screwey]].

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* Abstract algebra, topology, and anything in UsefulNotes/{{mathematics}} that isn't immediately usable in some engineering/economics field (and those aren't completely exempt). Forget everything that you claim to know about such "trivial" things as addition, multiplication, division, space (space, as in 3D space), etc. Remember that some of the trippier aspects of quantum-mechanics are just special cases in mathematics.
** Mathematically, Quantum Theory is quite simple, really. It's in trying to make sense of it that things get ugly.
** One of the weirder things to come out of topology and set theory is a mathematical structure called the "[[http://en.wikipedia.org/wiki/Long_line_%28topology%29 long line]]". It's like the usual real line, but ''much longer''. Yes, it's longer than a line of infinite length. (Making sense of what that means requires some set theory.) So much longer, in fact, that even an infinite sequence of steps can only cover a tiny portion of it.
** Almost any mathematical concept taken to a high-enough level qualifies, right up to the concept of ''numbers''. Much of this has to do with the weirdness inherent in set theory (everything is a set; an element in a set, which is a type of subset; a subset of a set, which can itself be considered a set; or a relation on a set) and infinities (yes, plural--there are different sizes. See below).
* For spatial mathematics, consider this: The 'right-hand' 3-dimensional Vector direction of Y is counter-clockwise from X, which is clockwise from Z, which is counter-clockwise from Y. What this means is that Left is -1, Right is + 1, Down is -1, Up is + 1... and Backward is + 1, Forward is -1. Somehow, this makes the math work ''right''.
* Anything about 4-dimensional objects (or worse, more). If you take a bunch of 2D squares and fold them up, you get a cube. If you take a bunch of 3D cubes and fold ''those'' up, you get a [[http://commons.wikimedia.org/wiki/File:8-cell-simple.gif tesseract]].[[note]]No, not [[Film/{{Thor}} that one]]. Think more ''Literature/AWrinkleInTime'', only not quite.[[/note]]

to:

* Negative Numbers (numbers less than zero) can be this to children first getting introduced to them ("how the heck can I have fewer than zero apples?"), and they tend to give the same reaction when introduced to Imaginary Numbers (numbers multiplied by ''i'', the square root of zero) later on in life.
**
Abstract algebra, topology, and anything in UsefulNotes/{{mathematics}} that isn't immediately usable in some engineering/economics field (and those aren't completely exempt). Forget everything that you claim to know about such "trivial" things as addition, multiplication, division, space (space, as in 3D space), etc. Remember that some of the trippier aspects of quantum-mechanics are just special cases in mathematics.
** *** Mathematically, Quantum Theory is quite simple, really. It's in trying to make sense of it that things get ugly.
** *** One of the weirder things to come out of topology and set theory is a mathematical structure called the "[[http://en.wikipedia.org/wiki/Long_line_%28topology%29 long line]]". It's like the usual real line, but ''much longer''. Yes, it's longer than a line of infinite length. (Making sense of what that means requires some set theory.) So much longer, in fact, that even an infinite sequence of steps can only cover a tiny portion of it.
** *** Almost any mathematical concept taken to a high-enough level qualifies, right up to the concept of ''numbers''. Much of this has to do with the weirdness inherent in set theory (everything is a set; an element in a set, which is a type of subset; a subset of a set, which can itself be considered a set; or a relation on a set) and infinities (yes, plural--there are different sizes. See below).
* ** For spatial mathematics, consider this: The 'right-hand' 3-dimensional Vector direction of Y is counter-clockwise from X, which is clockwise from Z, which is counter-clockwise from Y. What this means is that Left is -1, Right is + 1, Down is -1, Up is + 1... and Backward is + 1, Forward is -1. Somehow, this makes the math work ''right''.
* Anything about 4-dimensional objects (or worse, more). Take the three spacial (..."axises"?) of out 3D universe: up/down, left/right, and forward/backward. All of them are at ninety degrees to one another. a 4D universe would have all of those as well, plus an additionalone ''simultaneously at ninety degrees to all of them as well.'' If you take a bunch of 2D squares and fold them up, you get a cube. If you take a bunch of 3D cubes and fold ''those'' up, ''those'' ..."up", you get a [[http://commons.wikimedia.org/wiki/File:8-cell-simple.gif tesseract]].[[note]]No, not [[Film/{{Thor}} that one]]. Think more ''Literature/AWrinkleInTime'', only not quite.[[/note]][[/note]] [[MindScrewdriver Most experts assume that beings from a purely 2-dimensional universe would find 3D space just as mind-screwey]].
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* UsefulNotes/RichardFeynman once quipped, "If you think you understand quantum mechanics--you don't understand quantum mechanics." To give ''one'' example: small particles behave like waves. When a light wave goes through two slits right next to each other, it creates an interference pattern of light and dark bars. Doing the same with lots of electrons yields the same results, with light bars meaning more electrons hit there and dark bars meaning less. Doing the same with one electron at a time and adding the results together yields the ''exact same'' result. Translation: the electron goes through ''both slits'' and ''interferes with itself''. Observing the electron as it goes through gives a pattern of just two bars, as if the electron behaves solely like a particle, meaning simply ''observing the experiment'' changes the results.

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* UsefulNotes/RichardFeynman once quipped, "If you think you "Anyone who claims to understand quantum mechanics--you don't understand quantum mechanics.mechanics has not been paying attention." To give ''one'' example: small particles behave like waves. When a light wave goes through two slits right next to each other, it creates an interference pattern of light and dark bars. Doing the same with lots of electrons yields the same results, with light bars meaning more electrons hit there and dark bars meaning less. Doing the same with one electron at a time and adding the results together yields the ''exact same'' result. Translation: the electron goes through ''both slits'' and ''interferes with itself''. Observing the electron as it goes through gives a pattern of just two bars, as if the electron behaves solely like a particle, meaning simply ''observing the experiment'' changes the results.
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* The Riemann Zeta function. Initially defined as a series, its continuation gives us gems such as the apparent sum 1+2+3+4+5+6+... = -1/12. Add in imaginary numbers and an interesting relation involving prime numbers (numbers that are only divisible by 1 and themselves, and with a seemingly random distribution) and you get an object so weird it's still not fully understood. No wonder the Riemann hypothesis (roughly, whether some of the points where the Zeta function equals zero are all located on a single line that crosses the real numbers, with consequences on the distribution of prime numbers) is considered one of the most difficult problems in mathematics.

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* The Riemann Zeta function. Initially defined as a series, its continuation gives us gems such as the apparent sum 1+2+3+4+5+6+... = -1/12. Add in imaginary numbers and an interesting relation involving connection with prime numbers (numbers that are only divisible by 1 and themselves, and with a seemingly random distribution) and you get an object so weird it's still not fully understood. No wonder the Riemann hypothesis (roughly, whether some of the points where the Zeta function equals zero are all located on a single line that crosses the real numbers, with consequences on the distribution of prime numbers) is considered one of the most difficult problems in mathematics.
Is there an issue? Send a MessageReason:
None


* The Riemann Zeta function. Initially defined as a series, its continuation gives us gems such as the apparent sum 1+2+3+4+5+6+... = -1/12. Add in imaginary numbers and an interesting relation involving prime numbers (numbers that are only divisible by 1 and themselves, and with a seemingly random distribution) and you get an object so weird it's still not perfectly understood. No wonder the Riemann hypothesis (roughly, whether some of the points where the Zeta function equals zero are all located on a single line that crosses the real numbers, with consequences on the distribution of prime numbers) is considered one of the most difficult problems in mathematics.

to:

* The Riemann Zeta function. Initially defined as a series, its continuation gives us gems such as the apparent sum 1+2+3+4+5+6+... = -1/12. Add in imaginary numbers and an interesting relation involving prime numbers (numbers that are only divisible by 1 and themselves, and with a seemingly random distribution) and you get an object so weird it's still not perfectly fully understood. No wonder the Riemann hypothesis (roughly, whether some of the points where the Zeta function equals zero are all located on a single line that crosses the real numbers, with consequences on the distribution of prime numbers) is considered one of the most difficult problems in mathematics.
Is there an issue? Send a MessageReason:
None


* The Riemann Zeta function. Initially defined as a series, its continuation gives us gems such as the apparent sum 1+2+3+4+5+6+... = -1/12. Add in imaginary numbers and an interesting relation involving prime numbers (numbers that are only divisible by 1 and themselves, and with a seemingly random distribution) and you get an object so weird it's still not perfectly understood. No wonder the Riemann hypothesis (roughly, whether some of the points where the Zeta function equals zero are all located on a single line that crosses the real numbers, with consequences over the distribution of prime numbers) is considered one of the most difficult problems in mathematics.

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* The Riemann Zeta function. Initially defined as a series, its continuation gives us gems such as the apparent sum 1+2+3+4+5+6+... = -1/12. Add in imaginary numbers and an interesting relation involving prime numbers (numbers that are only divisible by 1 and themselves, and with a seemingly random distribution) and you get an object so weird it's still not perfectly understood. No wonder the Riemann hypothesis (roughly, whether some of the points where the Zeta function equals zero are all located on a single line that crosses the real numbers, with consequences over on the distribution of prime numbers) is considered one of the most difficult problems in mathematics.
Is there an issue? Send a MessageReason:
None

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* The Riemann Zeta function. Initially defined as a series, its continuation gives us gems such as the apparent sum 1+2+3+4+5+6+... = -1/12. Add in imaginary numbers and an interesting relation involving prime numbers (numbers that are only divisible by 1 and themselves, and with a seemingly random distribution) and you get an object so weird it's still not perfectly understood. No wonder the Riemann hypothesis (roughly, whether some of the points where the Zeta function equals zero are all located on a single line that crosses the real numbers, with consequences over the distribution of prime numbers) is considered one of the most difficult problems in mathematics.
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None

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* [[https://en.wikipedia.org/wiki/Thomson%27s_lamp Thompson's Lamp]]. Basically, imagine a lamp set on a timer for two minutes, after a minute the lamp turns on, after half that time (30 seconds) it turn off again, after 15 seconds it turns on again and so on, halving the time ad infinitum. The question being: would the lamp be on or off at the end? Neither answer seems to make sense, as both imply there would be an "end" to infinity.
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** There are many statements that are paradoxical but true, such as "The only constant is change" or "you're unique, just like everyone else."

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Another real-life example: The Fosbury Flop.



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* The Fosbury Flop, which has been the standard technique for competitive high jumpers since it was created by Dick Fosbury in the late 1960s, is full of this trope:
** For starters, just watching it can induce mental confusion—it involves turning around at the takeoff point and going backwards over the bar.
** Even more mind-boggling: The jumper's center of gravity passes ''under the bar'' even on a successful jump!

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