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The Spark of Genius

 The Spark of Genius
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Sometimes known as "Super Science" or mad science, it looks like science, but on a fundamental level it works very differently to regular science (or engineering).
In most settings, science and engineering are skills that any intelligent person can learn, while magic is a supernatural ability restricted to certain gifted individuals. In other settings, "The Spark of Genius" is an innate talent belonging to a unique few, much like magic or superpowers in other settings.
One key difference between normal science and The Spark is that, in the former, a scientific experiment can (at least in theory) be reproduced by anyone, while the latter only works because the unique gifts of certain individuals make it happen. Similarly, a device or invention can (at least in theory) be built by anyone with adequate plans (or reverse-engineering ability) and means of manufacturing, while the latter can only be built by the one person who understands it.
In extreme cases, one without The Spark cannot do what a gifted scientist or engineer can; even if they built a copy from the original blueprints, it just wouldn't work for anyone without The Spark. Perhaps because those with The Spark are Reality Warpers who make their inventions possible. Naturally between non-reproducible results and the spark belonging to an elite few, this is entirely incompatible with the scientific method.
In other cases, a sufficiently Badass Normal scientist or engineer could match someone with the spark, in which case the contrast may be one of Technician Versus Performer or Hard Work Hardly Works. However, in works where this trope applies, sufficiently skilled scientists and engineers are often much rarer than people who have The Spark. While it doesn't automatically conflict with the scientific method, in many works, those with The Spark are Mad Scientists and don't often demonstrate scientific rigor. Their toys can be copied exactly, but underlying principles are hard to reuse — these people run on "either you get it or you don't", without stopping to back up their demonstrable results with a good theory, or unable to explain the ideas they use when they want.
Real Life works quite differently.
New discoveries and inventions are often made independently by multiple people. New frontiers don't stay locked until one particular individual (and them alone) comes along.
Many people have sparks of insight (inspiration), but the breakthroughs often come from years of dedicated work (perspiration) by people who crunch the numbers or run huge batteries of tests.
Once the breakthrough is made, other scientists can usually understand and reproduce the results quite quickly. If the results can't be replicated, it's more likely to be an experimental variable that wasn't properly controlled by the first scientist.
Once a new invention is made public, it's very hard to stop other people from making something very similar. This is why inventors (and their corporations) often resort to legal means of protection.
Any sort of invention using modern technology usually requires a team of people, sub-suppliers, drawings, plans and documentation. This means that a) it's unlikely a single person can do much on their own, and b) there will usually be ways to recreate their work even without them being around.
Common in Steampunk. In some settings often or always combined with Science-Related Memetic Disorder or other science madness. Often combined with No Plans, No Prototype, No Backup, so that kidnapping the scientist themselves is the only way to recreate their work or prevent anyone else from doing so. May justify Reed Richards Is Useless by providing a rationale for why fantastic technology can't be mass-produced.
Compare Fantastic Science, which inverts this trope by making magic work like science rather than the other way around. Also compare For Science!, Weird Science, and Emperor Scientist. The products of The Spark of Genius are frequently examples of Magic-Powered Pseudoscience.

Examples
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DBTropes
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Worm has Tinkers, whose creations work best for them. Simpler creations can be studied and recreated, but most Tinker tech can only be modified or maintained by the Tinker who made it. To an extent, their ability can work in various branches, but each Tinker's specialty is unique.
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In Black Panther: Wakanda Forever, everyone in the world wants to get hold of Vibranium, but apparently, only one person in the world can design and build a detector (a 19-year-old student, of course). Once the Vibranium prospectors have this device, do they look at the plans and reverse-engineer it? No, they send it out on a mission for it to get captured. The only way to make another one is then to kidnap the student. Apparently, there is no other scientist or engineer in the world who can make one, despite how much world governments want to.
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Riff of Sluggy Freelance is known for creating inventions that can wrap physics around his little finger with little to no assistance. They're next to impossible to reproduce because he often leaves steps out of his notes that he considers "no-brainers". As per this trope, said "no-brainers" involve entirely new interpretations of physics or delicate design details that can stump all but the most brilliant scientists or those intimately familiar with his thought processes. Unfortunately for the cast, Dr. Schlock happens to fit both categories.
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Alphas: The Gadgeteer Genius Skylar has this ability. Most of the machines she assembles are impossible to replicate or go way beyond currently understandable human science, including the incredibly advanced processor core for a device that can track any human in the world that she built for the NSA. She also designs custom technology that sells at a premium. Her ability is apparently genetic, as she passed on that ability to her daughter.
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Ah! My Goddess:
Skuld is a child Goddess whose magical powers are too weak and immature to be useful, and who refuses to be treated as a child, so she builds machines to take the place of her magic powers. She can create machines using whatever scrap metal is at hand, or pulling apart a TV or VCR, to build Ridiculously Human Robots. (Never mind the fact that her machines are assembled in minutes with only the tools that fit in her pockets have perfectly fitting parts, and discarded tin cans can somehow turn into a circuitboard for an Instant A.I.: Just Add Water!.) The machines she builds from common household materials also have reality-warping effects, such as the ability to almost-infinitely expand space. This is downplayed, however, in that she's stated to simply use more sophisticated technology than what's available on Earth, and normal humans can reproduce her machines without problem if shown blueprints.
The trope really comes into play in a chapter where a professor at the university where Keichi is a student has spent his entire career dedicated to making robots that can walk like a human, and then one of Skuld's inventions happens to walk right by. He then kidnaps the Robot Girl, but can't figure out how to duplicate her.
After about 265 chapters of this, Skuld is ultimately portrayed as unconsciously using magic the whole time.
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The Grimnoir Chronicles: Actives have a magical ability to create machines. Most can be duplicated by regular scientists, but some machines like Buckminister Fuller's Dymaxion Nullifiers can only be built by him. Thomas Edison even built a telephone that could talk to the dead which uses elements that were supposed to annihilate one another on contact.
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The Spark of Genius
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Paranoia: In the adventure The Yellow Clearance Black Box Blues, one of the scientists in R&D, Willis-G-EEP-4, has treasonous psionic mutations that cause his inventions to work well on the test bench but fail out in the field when he isn't around. (For the players, the rather treasonous Mechanical Intuition and the uber-Treasonous Machine Empathy mutations fill a similar role.)
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SCP Foundation: A person affected by SCP-2801 ("A Dress-Up Box") temporarily gained the ability to create an anomalous device. Afterwards, it was determined that the device was non-functional and should not have worked. The only reason it did was because of the anomalous power of its creator.
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The Spark of Genius
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In the Whateley Universe, devisors are the strong form (their "devises" can break the laws of physics outright, but may or may not work for others, and will definitely not be replicable), and gadgeteers (who work within normal physics and chemistry, but can patent and mass-produce their creations) are the weak form; the two talents may be combined in one person.
Interestingly, it's been noted that the 'weak' form of this power is far more dangerous. A devisor will be more personally dangerous, and may have a small number of minions with better tools; but a gadgeteer can field a full army in functional power armor.
Note that even with a devisor, it is easier to make something that mostly follows physical laws (e.g., a sonic stunner that only hits the target rather than everyone around it) than something which does so blatantly (such as a shrink ray). Such 'minor' devises are a lot more reliable, and more likely to work when used by someone other than the devisor. Also, if a devisor creates something that breaks physical law, but then a gadgeteer finds an equivalent based on the devise but which works within physical laws (the so-called 'Devise test'), the devisor may get to have part of the patent credit. Thus, devising is often a balance between 'do something simple and reliable, and maybe leads to something patentable' and 'screw it, let's turn this up to 11 and see what happens'.
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Discworld: Burgholt Stuttley Johnson has what might be called the "Spark of Incompetence": his creations frequently break the laws of physics in ways even Discworld magic doesn't, but he never intends them to, and they rarely do anything related to what he did intend. As Thud! puts it:
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The Spark of Genius
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Both Skin Horse and Narbonic run on this, since they share a universe. Mad Science is relatively common, but it's explicitly nonsense. In fact, it's a plot point in Narbonic that a nascent Mad Scientist could make an impossible device function. There are VERY rare people who can replicate Mad results through standard science, but it's so rare Dr Lee from Skin Horse is likely the only one in the world who can pull it off. Since her results can be replicated, and she doesn't come with the standard Mad Scientist hangup of Awesome, but Impractical, she is FAR more dangerous.
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Tony Stark has to be the patron saint of this trope. Not only can he create a miniaturised ARC reactor in a cave (from a box of scraps no less!), and situate a 5GW reactor in his chest cavity without cooking himself, but he can forge an entirely new element seemingly from his own badassery. This exchange from Iron Man sums it up well, and will make any engineers out there feel sorry for the poor Head Engineer character who is basically being asked to do magic. It's almost a lampshade at that point. "I can't bend the laws of physics because of plot reasons!" Even when others try and recreate the Iron Man suit, they make minimum progress, of course, they're not Tony Stark!
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A Miracle of Science has SRMD as the weak form — mad scientists' inventions go into general use.
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In Remnant: From the Ashes, the scientist Harsgaard is creating technology that's beyond the understanding of other brilliant scientists in the "Dreamers" project. It turns out that an Eldritch Abomination has been feeding him information that only he can decipher.
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Exalted: A Solar Exaltation works like this for those interested in pursuing things like Lore and Craft. The Solar ability to perform feats of technical prowess that are unmatchable by any other is largely represented mechanically by Charms that break the normal limits on crafting and allow them to manufacture impossible components (as well as a basic setting conceit that Solars can reach areas beyond anybody else).
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Mutants & Masterminds: In the Paragons setting, devices created by superintelligent Paragons are called "ACME" devices. They frequently bend or outright break the laws of physics, and cannot be reproduced by any means (unless the person trying to recreate it is also a Paragon with enhanced intelligence). Sometimes, the ACME device can't even be used by anyone other than the creator, providing additional support for the in-universe theory that paranormal abilities are partly psychological.
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Marvel Cinematic Universe:
Tony Stark has to be the patron saint of this trope. Not only can he create a miniaturised ARC reactor in a cave (from a box of scraps no less!), and situate a 5GW reactor in his chest cavity without cooking himself, but he can forge an entirely new element seemingly from his own badassery. This exchange from Iron Man sums it up well, and will make any engineers out there feel sorry for the poor Head Engineer character who is basically being asked to do magic. It's almost a lampshade at that point. "I can't bend the laws of physics because of plot reasons!" Even when others try and recreate the Iron Man suit, they make minimum progress, of course, they're not Tony Stark!
In Black Panther: Wakanda Forever, everyone in the world wants to get hold of Vibranium, but apparently, only one person in the world can design and build a detector (a 19-year-old student, of course). Once the Vibranium prospectors have this device, do they look at the plans and reverse-engineer it? No, they send it out on a mission for it to get captured. The only way to make another one is then to kidnap the student. Apparently, there is no other scientist or engineer in the world who can make one, despite how much world governments want to.
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The World of Darkness:
Genius: The Transgression: The basic premise of the game is that a Genius' creations are often things that scientific consensus says just shouldn't work, though Geniuses are very aware and very unhappy that they aren't really doing anything remotely like science. In an interesting twist, Geniuses are unsure which of the two forms of this trope apply to them. Some say they're breaking the laws of nature, others say what they're doing is scientifically possible (in the World of Darkness anyway) but the nature of their condition means they're unable to create publishable research. In fact, the devices created by Geniuses break down and stop working when a normal person touches them. Simple observation alone isn't enough to break them (known as Mulder's Lament). Furthermore, Geniuses who cannot deal with the fact that they are making miracles instead of doing science will become unmada — dangerously insane, delusional Geniuses who are convinced that the scientific explanations they invent for their miracles are in fact the way the world works, and the force of their belief is such that they can warp the laws of physics by their very proximity.
Mage: The Ascension: In the backstory and in the prequel Mage: The Sorcerer's Crusade, the entire Order of Reason runs on this. The Order later transformed into the Technocratic Union, which still uses technology enhanced by magic, but is trying to enforce a paradigm closer to real science — dreaming of a fundamentally democratic world where any mortal will be able to make miracles through technology. In the original version, this was portrayed as an evil goal, but later versions were a bit more open to Both Sides Have a Point. The trope is still played straight by the Sons of Ether, who split off from the Union in the early 20th century. Due to the metaphysics involved, they're all (mostly) replicable with training; while an "Extraordinary Citizen" can't perform as easily or intuitively as an Enlightened Scientist, these technomagical "Sorcerers" can learn to replicate most of these miraculous feats. This doesn't actually require any amount of cosmic understanding or enlightenment, and is implied to be entirely possible for anyone — though even most scientists don't get to that level.
Werewolf: The Apocalypse: Many in the Glass Walker tribe can make "scientific discoveries" at a whim, such as combining random household chemicals into a powerful explosive. This kind of "discovery" costs gnosis to make, and the effect cannot be reproduced later.
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In Fallout 4, the robot scientist Curie wants to become human because she feels that as a robot, she can never experience scientific inspiration or make advances, she's limited to calculations and running experiments designed by humans. She even drops the trope name itself, lamenting her lack of "the spark of genius". You can help her fix the problem.
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GURPS Supers:
Wild Cards: Characters with superpowers are called Aces. Ace gadgeteers often create devices that cannot be duplicated by any other inventor and will not work for anyone but the inventor.
Supertemps: Blacksmith discovered that his card-throwing weapon violated the laws of physics, and that he had been subconsciously using his superpower of magnetic control to make it work. He also realized that this was why his weapon hadn't worked properly during testing unless he was present.
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The world of Girl Genius is based on Science! and the "sparks" who create and operate it; the Spark is both an innate intuition for Science and a charisma that influences people to follow them. Really strong Sparks can warp the laws of physics to their will. Of course, there are drawbacks as innate to the Spark as genius. And a focused Spark tends to be prone to melodramatics and getting interesting as they do what they do. Ordinary mechanics and engineers can reproduce their blueprints, but struggle to understand or modify them.
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Werewolf: The Apocalypse: Many in the Glass Walker tribe can make "scientific discoveries" at a whim, such as combining random household chemicals into a powerful explosive. This kind of "discovery" costs gnosis to make, and the effect cannot be reproduced later.
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Please Don't Tell My Parents I'm a Supervillain: This is a relatively common superpower in the setting, and there are apparently three "tiers" of devices produced by Mad Science. Tier One devices do things that we can do just as well or better with conventional technology. Tier Two is better than regular tech, but still obeys the generally accepted laws of physics. Tier Three breaks them.
Penny's powers allow her to create all kinds of crazy shit, which she's not always aware of doing, and can't readily replicate. Most of them don't have any evident power sources and in one case (the zombie ragdolls) they seem to produce the matter needed to reproduce out of thin air.
Penny's ex-superhero father, Brainy Akk, is unique in that he can translate superscience into something resembling actual science — albeit insanely complicated science backed by headache-inducing levels of ultra-complex math. Unfortunately, his blind spot regarding magic means that he usually has to give up once someone starts mixing Magitek into their designs... as Bad Penny does with ease.
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The Quest of the Unaligned: Played with in several different ways. The fire magic of the aeshes can be used to power regular devices, but it also allows the creation of things that are impossible, like flying cars or anti-gravity. On the other hand, many magic items can also be run on mundane electricity.
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This appears to be how Professor Farnsworth's inventions work on Futurama, as lampshaded in the page quote. It's also lampshaded by Hermes in "Calculon 2.0", who points out the Professor's method to bring a robot Back from the Dead is basically magic (specifically a satanic ritual) with the word "science" inserted.
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Mage: The Ascension: In the backstory and in the prequel Mage: The Sorcerer's Crusade, the entire Order of Reason runs on this. The Order later transformed into the Technocratic Union, which still uses technology enhanced by magic, but is trying to enforce a paradigm closer to real science — dreaming of a fundamentally democratic world where any mortal will be able to make miracles through technology. In the original version, this was portrayed as an evil goal, but later versions were a bit more open to Both Sides Have a Point. The trope is still played straight by the Sons of Ether, who split off from the Union in the early 20th century. Due to the metaphysics involved, they're all (mostly) replicable with training; while an "Extraordinary Citizen" can't perform as easily or intuitively as an Enlightened Scientist, these technomagical "Sorcerers" can learn to replicate most of these miraculous feats. This doesn't actually require any amount of cosmic understanding or enlightenment, and is implied to be entirely possible for anyone — though even most scientists don't get to that level.
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The Dark Eye: The dwarves have developed their craftsmanship so far that some humans went insane trying to grasp it.
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Warhammer 40,000: Ork science explicitly works in this way. Only orks with the mad science gene (called 'Mekboyz') get the inspiration to go out and do mad science in the first place, and their works can never be identically reproduced by anyone. Including by the Mek who originally built the first device (orks find repetition boring). This is justified because ork science only works because orks thinks it should due to the background psychic field all orks subconsciously generate, and all orks know that only Mekboyz can do stuff like that anyway. Even the Mekboyz themselves do not know quite how they do what they do, the requite "know-wots" being an intuitive product of their Genetic Memory rather than education and logical thought.
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World Domination in Retrospect has Mix N'Max, whose concoctions have odd and impossible effects, but only function because he made them, like a carnivorous brain that attacks zombies.
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The Academy of Superheroes universe has this in the form of Violation Physics and supertech. It can only be created by Gadgeteer Geniuses and can only be used by people with some level of superpowers. If enough normaltech is incorporated into it, it becomes accessible to regular humans at decreased efficacy.
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Super Minion: Tinkers can create unique technology nobody can understand, and even the less impressive stuff they make tends to be completely incomprehensible to anyone who hasn't been innoculated with benedicci.
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Wild Cards: The various Gadgeteer Genius superheroes explicitly possess a superpower that allows them to create gadgets beyond the reach of ordinary science.
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Deadlands: A Mad Scientist is a strong version of this trope that believes it's a weak version. They get the mechanical insight for their inventions stolen from the future by evil spirits and it's most likely powered, made out of, or weaponizing the souls of the damned (a.k.a. ghost rock). They believe they've just made a better steam engine and don't understand why most of the scientific community can't just follow their plans to the future for science.
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In Quest for Glory, the local scientists are actually Boomerang Bigot wizards who use their technology to tell themselves that what they are doing isn't magic. The protagonist tries to argue that magic is actually a form of science, but they simply refuse to accept that magic even exists... even when he levitates and shows off with fireballs and other magic fireworks before their very eyes. It turns out that they do know that magic works, it's just that they consider it to be a crime against reality, so they just ignore him while he's showing off, and try to assassinate him later.
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Astro City: Roy Virgil, a.k.a. the Astro-Naut. He was so smart that he could copy the alien technologies he saw on his space adventures without the benefit of reverse-engineering them — just knowing what was possible was sufficient.
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Alterien: Oberon can conceive and design virtually any type of machine to perform nearly any sort of function he imagines. His designs always produce working devices. He can also determine how an existing machine works through psychometry.
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Genius: The Transgression: The basic premise of the game is that a Genius' creations are often things that scientific consensus says just shouldn't work, though Geniuses are very aware and very unhappy that they aren't really doing anything remotely like science. In an interesting twist, Geniuses are unsure which of the two forms of this trope apply to them. Some say they're breaking the laws of nature, others say what they're doing is scientifically possible (in the World of Darkness anyway) but the nature of their condition means they're unable to create publishable research. In fact, the devices created by Geniuses break down and stop working when a normal person touches them. Simple observation alone isn't enough to break them (known as Mulder's Lament). Furthermore, Geniuses who cannot deal with the fact that they are making miracles instead of doing science will become unmada — dangerously insane, delusional Geniuses who are convinced that the scientific explanations they invent for their miracles are in fact the way the world works, and the force of their belief is such that they can warp the laws of physics by their very proximity.
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In the GURPS adaptation of Girl Genius, the Spark advantage comes in levels from 0-5 and gadgets come in five levels based on complexity, with scientific realism never a factor. Whether non-Sparks are even capable of invention is up to GM fiat but if allowed they operate at a severe penalty to invent even the simplest gadgets.
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Dawn of a New Age: Oldport Blues: This is Ivy's superpower. She can create inventions that are far beyond what most are capable of, to a degree that's almost Reality Warping. What stops her from complete domination is that the spark only works in brief spurts — once she's finished her invention, she returns to her average intelligence and is unable to replicate the creation process.
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Gakuen Alice: Hotaru. The titular "Alice Academy" is a place for students with special powers, with each student having a unique "Alice". In Hotaru's case, she has an "Invention Alice", allowing her to build wondrous devices.
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Lady Bird: Inverted for Void Cowboy. His modified Tinker power lets him take any piece of Tinkertech, improve it, and create blueprints that will let mundane science reproduce it, but he cannot create original devices.
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The Chronicles of Professor Jack Baling: In the second episode, the reader learns that what Jack and those like him do can never be replicated by regular scientists, and often not even by other mad scientists.
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Jingle Jangle: A Christmas Journey: Jeronicus Jangle, his daughter Jessica and his granddaughter Journey. Their unparalleled genius with inventing is implied to be some sort of gift rather than just plain science; when working out equations for their inventions, they write the equations in the air and glowing light surrounds them. They also use fantastical terms such as the 'circumference of spectacular' and 'square root of impossible'. This is compared to Gustafson, who despite stealing Jangle's blueprints did not have this spark.
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The following is a list of statements referring to the current page from other pages.

 The Spark of Genius
processingCategory2
Make My Index Live!
 The Spark of Genius
processingCategory2
Tropes on Science and Unscience
 Galilei Donna / int_ce03051f
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The Spark of Genius
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The Spark of Genius
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The Spark of Genius
 Academy of Superheroes / int_ce03051f
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The Spark of Genius
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The Spark of Genius
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The Spark of Genius
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The Spark of Genius
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The Spark of Genius
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The Spark of Genius
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The Spark of Genius
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The Spark of Genius
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The Spark of Genius
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The Spark of Genius
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The Spark of Genius