In his tower, the wizard Istar casts his fortieth fireball today while his apprentice diligently notes the exact qualities of each. On his workbench are piles of fireball spells yet untested, but Istar plans to catalogue them all. Only then can he begin to study what makes one fireball stronger than another.
While gathering herbs, Granny Annick thinks to herself: everyone says horseshoes are lucky, but how lucky are they? Now if I got ten people from the village to roll dice a few times, and gave them a coin for every number facing once with and once without a horseshoe, I'd only have to count the coins.
Sufficiently Analyzed Magic is a philosophy, whenever you find wizards, witches, sorcerers or mages who decide that lore and intuition is not enough: They want to understand how magic works and will do so through empirical evidence and experimentation. You have the beginnings of Sufficiently Analyzed Magic.
For a verse where Magic A Is Magic A, this is an inherently Justified Trope just as long as it makes sense for the culture: Empirical evidence and experimentation are the cornerstone of The Scientific Method, and there is no reason that it should be any less effective at discovering the details of a self-consistent series of rules just because it's called "magic" rather than "physics".
One of the many sides arguing over Un Equal Rites. Contrast with Magic Versus Science where this attitude belongs only to the scientists, and Flat Earth Atheist, where fans of "science" will loudly deny magic exists rather than accept empirical evidence. Not quite related to Magitek or Post-Modern Magik but may show up alongside either or cause them. Compare to Doing in the Wizard , Doing in the Scientist, and Sufficiently Advanced Aliens.
A subtrope of Fantastic Science. Compare and contrast The Spark of Genius. Can be a direct result of Rational Fic. For the sake of general cohesion, anything that more or less works thanks to magic but isn't actually called "magic" by anyone in the work falls under this trope. Compare Magic from Technology and Post-Modern Magik
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Magical Girl Lyrical Nanoha has got to have set a new standard in that its not just taken and sufficiently analyzed magic, but it's pretty much evolved to the point of understandable science. If Girl Genius is sufficiently analyzed magic in the Victorian Era, then Nanoha is its equivalent in the space age.
There's plenty of Magitek left over from Precursor civilizations lying around that isn't understood in the current era. It fits the trope since those civilizations simply had a better grasp of how the magic works. In space opera in general, precursor civilizations or alternate tech trees both can leave mind boggling advances in one aspect of technology while other aspects are actually lower or even unexplored. The artifacts of Ancient Belka and the like are the Magitek equivalent.
Most of the alchemists in Baccano! were content to discover the secret of alchemy. Szilard and Huey, on the other hand, decided to test everything related to it from, "exactly how fast do I heal from each individual injury?"note Regeneration is variable depending on both the severity of the injury and how many times it's been received before. The more times you've had your head blown off, the faster it reconstructs itself. to "can I combine human and dolphin DNA to create a viable homunculus?"note :Yes.
In Code Geass, this is how Lelouch takes to his Geass power after an awkward situation with Kallen where he first realizes it has limitations- namely, that it won't work on the same person more than once. Before making serious use of it again, he conducts several tests on random students to see what other limitations it has.
Though most people in Naruto don't bother with the details, there is clearly a pretty strong effort to understand the exact nature of chakra. Most of its basic workings can be found in textbooks.
Orochimaru in particular searches for the Naruto equivalent of the Theory of Everything, and believes current knowledge of chakra is barely scratching the surface.
Recent revelations about Sage of 6 paths myths seem to imply that Charaka is not of the Naruto world, but seems to come from somewhere else.
Much of the early part of Death Note consist of Light conducting tests with the Death Note to see what it's capable of — he takes it to such rigors that he's able to determine restrictions and abilities that even the death god it formerly belonged to didn't realize it had. Light's knowledge of these specific attributes is his key advantage in the mind games he plays with genius detective L.
In fact, the author of the work goes to great lengths to sufficiently analyse his magical object; there are a huge set of rules for the workings of the Death Note covering almost every possible eventuality.
It plays very well to Light's character, because someone as focused and meticulous as Light would make sure he knew every possibility and restriction of the Death Note. After all, what if there was a step in a master plan that failed at a crucial time because, say, the Death Note can't make someone do the impossible?
Nasuverse magic users tend to be very scholar-like, studying spells and the workings of mana and magical beings, experimenting to harness the sorceries, and passing their knowledge on to their descendants. This is actually an evolution that occurs within the series. It's noted in Kara no Kyoukai that originally, wizards believed that even explaining how their magic works to someone who doesn't know makes it less effective. In Melty Blood, Sion was originally cast out of her academy for daring to share research on her attempts to cure vampirism with other wizards outside of her academy. The events that occur within both series have apparently brought about a 180 turn, when it has become apparent to the wizards that they really need to know what the hell they're doing. In the manga, Sion is bemused how they completely ignore how she was ever banished in the first place.
In Fullmetal Alchemist, alchemy is studied exactly like a science. Alchemists do research like scientists, and those alchemists employed by the state are required to demonstrate the results of their research once a year in order to continue receiving funding (although the main characters do less research and more fighting with alchemy). They even discuss theories as to where the energy used in alchemy comes from (tectonic plate movement in the Manga/second Anime, souls of people from a parallel universe in the first anime).
An offhand remark of Ed's tells us that Alchemy began from cooking. Which is fitting, since preparation of food is about the most common chemistry people actively do.
Mahou Sensei Negima! treats magic in this manner as well. Spells, more often than not, work with the laws of physics rather than against them (those spells that do break physics are said to be the most advanced and difficult). Negi himself is described as conducting numerous tests and experiments when developing new spells and ways of stopping Magical Worlds from collapsing, and he even references scholarly articles in magical research at one point, in much the same way a modern-day physicist would reference another scientist's work.
Ghost Hunt is all over this trope. Featuring mystics, psychics, paranormal investigators and exorcists from various religions all working together at once, the show utilizes them and their techniques in a consistently logical fashion and they investigate paranormal activity in a similarly consistent action.
In fact, one of the premier psychics of that universe is on record stating that the only way that they can get respected by the scientific community as equals is if they research and document what they do with the same degree of rigor as people in accepted sciences.
In Bleach, the afterlife has an entire research division devoted to studying spiritual powers and coming up with technological applications for them.
Doctor Doom is a pro at this trope. Unlike his contemporary and rival, Reed Richards, Doom has a thorough understanding of not just earthly sciences, but magic as well. He's actually used this advantage on a number of occasions to one-up Reed (and most of the Marvel Universe at various points), although the inherent weaknesses of magic (usually, bartering/stealing the energy from a higher power) typically come to bite Doom in the backside.
Doom also blends magic and technology. For example, he use the sensors of his armor to copy the exact hand movements of spells when he sees them cast for the first time, and his gloves can automatically guide his hands through them. Thus allowing him to copy other wizards' spells far more quickly than it would normally take to master them.
Though there are limits to this. Copying the movement may not be enough without an understanding behind the magic or sufficient level of skill to handle the spell as Doom found out with a later attempt.
Hal Jordan in the early Silver Age run of his book did quite a bit of this to discover the exact limits and potential drawbacks of his Green Lantern Ring. And the tests themselves often kicked off the events of a story.
In Wild Cards, Water Lily was a subject of such tests.
In Dungeon Keeper Ami Ami's main advantage, other than her taking knowledge from her own world, is her scientific approach to magic and all the innovations she can make, especially with teams of research warlocks.
Harry Potter and the Methods of Rationality is all about this. Unlike other works which employ this trope, the protagonist runs into trouble when it turns out that unlike physics magic doesn't run on numbers and has its own equivalent to the Laws of Thermodynamics that's based entirely on what's fair.
Captain America: The First Avenger introduces us to the Tesseract Cube, the "Jewel of Odin's treasure room". Though most people who encounter it think of it as divine or mystical, the Red Skull merely thinks of it as highly advanced science which only his genius can fully unlock. When some other Nazi officers derisively refer to his inventions as magic, he even quotes a kind of proto-version of Clarke's Third Law (albeit a much more condescending version than Clarke would have used): "Great power has always baffled primitive men."
This is a plot point in the Thor movie. Jane Foster, rather than being a paramedic as in the original comics, is an astrophysicist. Thor, on the other hand, comes from Asgard, which seems to be a place of great magic... but as he points out to Jane, "Your ancestors called it magic... but you call it science. I come from a land where they are one and the same", which can be seen in the "tech" Asgard uses. The Destroyer is indistinguishable from any old super-science giant robot with a death ray, and if you took the operational end of the Rainbow Bridge and dropped it in a science-fiction movie, people wouldn't blink twice and simply consider it a teleporter or stargate.
In The Avengerssaid Destroyer is reverse-engineered into energy weapons and a Bifrost-like portal is built using real physics principles.
In Thor: The Dark World, a brief scene has Jane being scanned by a device called a "Soul Forge" and proceeding to stun the Asgardian healer present with a brief explanation about how it works and the scientific principles behind it. She then snarks at overly-grandiose names that Asgardians bestow upon their technology, whereas humans would call the device a "Quantum Field Generator", since that's what it does.
The Star Wars prequels did this with control over the Force. While the original trilogy implies that power in the magical Force is an abstract talent, the prequels reveal that control of the Force is determined by the presence of cellular organelles called Midichlorians. Thus, a Jedi's strength in the Force is a result of measurable, physical properties of his body. However, the Force itself still remains a mystical energy field rather than something that could be readily explained by science.
In Harry Potter, there are research departments in the Ministry of Magic, and the Half-Blood Prince's potions textbook is a prime example of a student improving and perfecting potions making through trial and error, study and observation, and Lord Voldemort delved further into the depths of dark magic than any wizard who came before him. Dumbledore's development of the uses of dragons' blood might also fall under this trope.
The Potterverse in general has an interesting perspective on this trope. Whilst magic is never described as being anything explicable by ordinary means, it is a force that seems to obey numerous immutable rules (although most of these, such as 'magic cannot revive the dead' appear to be moral rather than empirical.)
Heck, the fact that so many magical disciplines can be taught in a school at all is proof that they have been studied and recorded diligently over the centuries, and nearly all of what witches and wizards learn is simply how to duplicate the spells and potions that their forbears discovered.
Derk's forte in Dark Lord of Derkholm. He magically engineers plants and animals in his spare time, winding up with things like winged pigs, invisible cats, extraordinarily stupid cows and highly intelligent geese, and griffin children, who share the DNA of both him and his wife, along with whatever else he made them out of. (One is part house cat, while another is part actual lion, another has goose DNA, another uses actual eagle, etc.)
A Zig-Zagging Trope in Discworld: Magic changes its rules randomly in response to scientific study, still the Wizards in the High Energy Magic building have managed to start working out the laws governing how it changes. (Apparently it has something to do with "quantum".)
Goodie Whemper ("maysherestinpeace") was a "research witch" who live in Mad Stoat, Lancre. She investigated such things as exactly what species are eligible for the "Eye of Newt". One of her triumphs was discovering the exact breed of apple and type of knife to use in the old "predict your future husband's name with a thrown apple peel" if you wanted it to actually work; otherwise it would inevitably spell SCSSSC. Magrat inherited her cottage after her premature death during an experiment to find out how many bristles you could pull out of a broomstick midflight (not quite that many as it turns out).
Magrat followed in her footsteps, as did many of the witches who had lived in the cottage. In Lords and Ladies the advantage of this approach in other areas of witching is noted:
It's all very well a potion calling for Love-in-idleness, but which of the thirty-seven common plants called by that name in various parts of the continent was actually meant? The reason that Granny Weatherwax was a better witch than Magrat was that she knew that in witchcraft it didn't matter a damn which one it was, or even if it was a piece of grass. The reason that Magrat was a better doctor than Granny was that she thought it did.
The ritual that summons Death traditionally required a human sacrifice and lots of eldritch fires, but by the time the books start this has been refined to three bits of wood and four cubic centimetres of mouse blood. A later book introduced an even more refined version that just needed two bits of wood and an egg. "It has to be a fresh egg, though". It's even suggested that most magic can be pared down like this in a pinch, but is deliberately wrapped up in hard work, ceremony and mumbo-jumbo to keep people from trying it, for the same reason that we don't want hobbyists building nuclear bombs in their basements.
The Heralds of Valdemar series has a newly created school of magical theoreticians, who use geometry to work out what the effects of various bits of magic will be. There's some degree of conflict between them and the actual mages, who take a much more intuitive approach. As the Mage Storms series reaches its climax, it's conceded by even the most diehard "intuitionists" that the theoreticians have a point, and that their research works.
The Enchanted Forest Chronicles' Telemain did this. The implication being that this was the distinction between "magicians" and other magic-users (or, to put it another way, watch your ass, there's probably a few more like him lurking around Linderwall and the surrounding kingdoms).
The entire world of Randall Garrett's Lord Darcy stories is based on sufficiently analyzed magic.
In Rick Cook's Wiz Biz fantasy series, the trope standard Summon Everyman Hero spell finds a computer programmer, who proceeds to analyse magic and create a programming language for writing new magic spells. He doesn't understand magic himself, he just finds a few spells equivalent to basic assembler commands and combines them to make entire programming languages.
The world he lives in is explicitly one where most spells are nearly impossible to analyze because the more complex the spell is, the more it's changed by multiple random factors. He elegantly gets round this because his assembler spells are very very simple and therefore predictable.
The same "make spells using assembly language" idea is used in Gordon R Dickson's novel The Dragon Knight.
In Retribution Falls demonologists are basically scientists who build Magitek (more magic than tech) powered by demons, they're not particularly evil either.
In Charles Stross' The Laundry Series, magic is a science. Specifically, computer science. Alan Turing discovered how to use technology to contact other dimensions, most of which are full of not-very-nice creatures. It's very much a science, since why bother with all that drawing of sigils when you can just load up an app on your PDA that does the same thing?
The protagonist of L. E. Modesitt Jr's The Magic Engineer takes this approach to magic - he takes notes on the logic and mathematical principles by which magic works, and eventually understands the basis of the entire magical system and how the two forms of magic interact with the material world. He then uses this scientific understanding of magic to build Magitek steam-powered warships.
This is a major plot thread in A Star Shall Fall, the third Onyx Court book. It turns out that, while the mortal world operates according to the laws of physics and chemistry, the faerie world operates according to the laws of alchemy.
In The Dresden Files, Harry Dresden would spend his time on this, if he had a steady income and the world wasn't always in danger. Early in the series he repeatedly mentions a desire to just "research". The upgrades to his shield bracelet, force rings and summoning circle over the series read like Technology Porn, and he managed to add an anti-tamper mechanism to a magic shield that impressed even his mentor.
In general, Harry explores the mechanism of magic a lot, and lays out a fairly consistent system, even extrapolating new ways to do magic based on the rules. Can you use x to power your magic? If it has energy or inspires emotion. Things like fear, anger, love, wall sockets, thunderstorms, a kiss from Lara, etc.
Thomas, in his short story, describes his interaction with magic as much more mechanical, more akin to engineering. Make some calculations, perform a spell, get a result. He contrasts it to Harry's use of magic, which he describes as some absurdist science/art hybrid, where cheesy philosophy and Peter Parker actually matter to what Harry can do, where his belief that he can reshape the world actually lets him.
Waldo Butters is a medical examiner with absolutely zero magical talent. However, his analytical mindset and ability to remember random half-heard bits of information make him one of the best magical theorists on the planet. In a world where magic makes any technology go kablooie, he figures out a way to connect a spirit of intellect to the internet.
Lampshaded in Day Off when Harry is roleplaying with the Alphas and rails against the unrealistic spread of the magical fireball cast by Billy's wizard character.
In Cold Days, the magic used by Merlin to create the prison on Demonreach is so advanced that it seems like magic to a wizard.
By the same author, the fury-based magic of Codex Alera is so much a part of society that it has been meticulously analysed over the course of centuries, and as such the capabilities of different types are known very precisely. However, it becomes increasingly clear as Tavi's adventures continue that Alera's mindset has become extremely stagnant and complacent, and as such it has overlooked many possibilities for expanding its use of furycraft. For example, Tavi's greatest Crowning Moment Of Awesome in Cursor's Fury comes when he realises that the well-established use of aircrafting to bend light in a similar way to a telescope can be used on a much larger scale to focus sunlight into a death-ray.
David Weber's The War Gods series does this in the background. Basically it's a parallel universe, and there are different ways for humans to access energy fields resulting in the powers. The old Empire used the order of Wizards for things like construction as well as steel making.
While the The Wheel of Time's Aes Sedai can be fairly hidebound and set in what channeling can and can't do, individual research in the organization abounds. Systematic research is given a kickstart by the events of the story, and several main characters have their own areas of expertise; Egwene frequently spends nights testing the limits of Dreaming, Nynaeve's experiments with Healing lead to better healing methods and the ability to cure severing and even sai'din taint-madness, Elayne's work leads to her actually copying and creatingnew ter'angreal...
In Rivers of London DC Grant takes this approach to magic, learning exactly why magic causes electrical devices to short out and explode. This was started by the first Magician of London, Sir Isaac Newton, who codified virtually all the spells used.
Wizards in the backstory of the Her Majesty's Wizard series used to be like this, until they were all wiped out by sorcerers who just memorized pre-made spells from books written by Satan.
In Katherine Kurtz's Camber the Heretic, A Healer who is treating a Deryni with a head injury inadvertently turns off his patient's powers. Further testing shows that the technique also conceals the existence of those powers from other people (even down to physical reactions to a Deryni-specific drug), and turns up only one other Healer able to perform it. The protagonists devise a baptismal cult to turn off the powers of Deryni and send them into hiding in advance of a wave of persecution.
Fritz Leiber's Conjure Wife explores this trope, as a college professor discovers that witchcraft is an open secret among women (including his wife) and ends up analyzing magic himself.
Prof. A.Donda by Stanislaw Lem. The professor studied Svarnetics (as in Stochastic Verification of Automatized Rules of Negative Enchantment). He got in this due to a typo, but finding out the work is about providing a statistical framework for hexing is not a good enough reason to back off for a man versed in applied mathematics.
In Mistborn, allomancy- a magic system triggered by ingesting and "burning" various metals- was thoroughly explored by the Lord Ruler, who only allowed knowledge of ten basic metals to reach the general populace. As the series progresses, Vin uses her knowledge of allomancy's logical setup of powers to discover a handful of new metals with additional abilities. From the same series, it's revealed in the final book that the torture chambers of the Steel Inquisitors were actually laboratories for researching hemalurgy.
Lev Grossman's The Magicians and subsequent sequel play into this a lot. Magic is only doable by the most intelligent and obsessed people, as it requires memorizing enormous charts of data (moon position, weather), dozens of language (ancient and current), and the most elaborate hand gestures. Analysis is the main method of learning magic; only rare examples do magic spontaneously.
In Lord of Shadows, we very literally see that Sufficiently Analyzing Magic can give you Story Breaker Powers.
The Chronicles of Amber, considering how the Pattern is treated, also draws on this trope (although only a few family members seem to be in on how the magic works).
In Smoke and Shadows, Arra comes from an Alternate Universe where humans have developed magic to a greater extent than technology, but still combine it with the physical sciences and employ it in a scientific manner. Arra had little difficulty integrating magic with technology after she came to Tony's Earth. In particular she uses computers to assist with divination and performing the necessary mathematical calculations to create interdimensional gates. This is in stark contrast to magical practitioners from Tony's Earth, who tend towards a more traditional superstition-driven approach to magic.
There's an Asimov short story about a physicist who one day wakes up levitating above the bed. He spends the entire story trying to get funding and a research team to study the phenomenon, but despite being able to easily and repeatably demonstrate his ability to levitate, everyone still refuses to believe him. (Turning the story into an instance of "Everyone but me is a Flat Earth Atheist")
Uncle Andrew of The Chronicles of Narnia takes this approach to magic, doing experiments with guinea pigs to figure out how to reach Another Dimension. His experiments are finally successful in reaching the alternate worlds, but a really powerful sorceress like Jadis has nothing but disdain for people who use his approach. In an earlier book in the series Eustace, too, is against such a concept, when he decides that even repeating a bunch of magical formulas is going about it more analytically than what would be proper, and he should just "ask Aslan to take him to Narnia.
Max Barry's Lexicon is about the application of neuroscience to improve what was once bardic magic resulting in More Than Mind Control
In New Arcana, the Order of Neomages has research facilities and an entire research council. Since the world also has relatively developed science, it makes sense that people would apply scientific method to magic.
In Circle of Magic, magic, especially academic magic, works like this. You can earn credentials, go to university. In one book there's a microbiology lab with sterile protocols where they investigate a Mystical Plague, another where Niklaren spends most of his time at a conference on the various seeing magics of the world, and in yet another one mage describes the scientific principle of reproducibility. The reason it's not brought up as much is that the main characters have ambient magic, which is largely unexplored.
Lyndon Hardy's "Master of the Five Magics" series starts out with five kinds of magic whose rules have been studied and formalised to such a degree that each kind of magic uses different terms to indicate its ultimate law(s) - the Principles of thaumaturgy, the Doctrine of alchemy, the Maxim of magic, the Rule of sorcery, and the Laws of wizardry. The antagonist in the second book is attempting to conquer the world by mastering the meta-laws that govern which rules are dominant at any given time, then disconnecting them and bringing in new ways to perform these various arts that his troops have figured out but the established orders are unable to use - essentially trying to win by having analysed magic more than the other guys.
A Mage's Power: Dengel Tymh is a name known all over the world. This is because the world runs on magitek and he is the one who who codified magic as a practical science instead of a mystical art. His Introduction to Magecraft has been a best seller for over a thousand years.
Subversion: Moenghus attempts to exploit Sufficiently Analyzed Magic but ends up subverting it when he blinds himself as a necessary first step in learning the Psukhe, the magic of the Cishaurim, only to discover that the Psukhe relies almost entirely on intuition, emotion and passion—things the hyper-analytical Dunyain are practically incapable of, which means not only is he still powerless, he's also blind. Of course, since he isDunyain, even losing his eyesight really just Brought Him Down To Badass.
Played straight: Kellhus learns the Gnosis, a school of magic more dependant on language and possibly mathematics, and promptly becomes even more godlike than he already was. Granted, the Gnosis is already regarded as being very powerful In-Universe, but Kellhus takes it Up ToFourteen.
Live Action TV
The Wild Wild West, Dr. Miguelito Loveless discovered a way to enter an alternative dimension, the world inside a painting.
Myths & Religion
Thomas Aquinas essentially did this to Catholicism — he dismissed The Bible as a source of data, and approached the subject of God from the perspective of an Aristotelian empiricist. This "natural theology" has been popular among Catholic theologians ever since, and his version of the cosmological argument is considered by many people (both believers and atheists) to be the strongest argument for the existence of some sort of Creator.
Ars Magica is largely about this trope. One of the main reasons why each player controls a troupe of several characters is so that they can still go out and have adventures while their Magus is locked in the lab for months at a time, researching new rites or secrets of Forms and Techniques.
In Dungeons & Dragons, this is what separates Wizards from other spellcasters. To a greater extent, this is separates Archmages and practicers of metamagic from other spellcasters. To a much, much greater extent, this is what separates Artificers from all other practitioners of magic.
The Net Wizard's Handbook categorized fantasy settings by "Controllability of magic". The highest state was "Magic is a Science", i.e. no fundamental differences between teaching engineers how to work with electrical forces and teaching wizards how to work with magical forces.
Eberron is pretty much based on this. Magic has literally been commercialized and Magitek is widespread. Traveling on a magic-powered passenger train or sending a message to someone via a magical equivalent of a telegraph is seen as perfectly normal by most people.
The way magic works inExalted fits in perfectly with this philosophy, and the most powerful users of magic in the First Age (who, incidentally, are called sorcerer-engineers) had a decidedly empirical approach to their craft... to the extent that they harnessed the power of faith, magic, and technology to create the factory-cathedrals, the greatest workshops ever created in any universe. That's right, they actually analyzed the relationship between gods and their worshippers and used it to power Magitek assembly lines.
Comes up in several GURPS books dealing with magic, notably in Magic and Thaumatology.
Nephilim refers to magical techniques (e.g. Sorcery, Summoning, Alchemy, Necromancy) as "occult sciences" and states that the human understanding of "magic" is simply a silly superstition.
In the New World of Darkness there's usually one splat per gameline whose mission is to analyze their particular brand of magic. Due to balance issues, this never really gives them much of an advantage.
The Ordo Dracul in Vampire: The Requiem. Their ethos is, "Okay, we're cursed to avoid sunlight, given an inhuman hunger for blood, have a ravaging beast in the back of our heads, and are capable of superhuman feats. The question is, why? And just what else can we accomplish?"
The Null Mysteriis in Hunter: The Vigil are an organization of scientists who want to study the supernatural. They haven't had much success so far due to that pesky Masquerade but their attitude fits this trope perfectly. Their actual competence varies hugely Depending on the Writer; sometimes they're skilled scientists who're actually making progress and other times flat earth atheists who ignore obvious supernatural phenomena.
Necromancers in Geist The Sin Eaters, the sample character actually is a former university academic.
In Changeling: The Lost, this is the official hat of the Autumn Court- however, because most "magic" is simple contract law, it's fairly easy.
The fan game Genius The Transgression breaks the mould here: all the splats, especially the Scholastics, follow this ethos. Ironically, mad science consists almost entirely of non-repeatable phenomena making it much harder to study than most of the magic and powers from other gamelines.
The Cryptics from Demon The Fallen seek nothing less than to reverse-engineer Creation. Yes, the World of Darkness was made by God. And these demons try to analyze how She did it.
Demon: The Descent is made of this - the demons of the title are supernatural quantum intelligences who've been kicked out of the service of an entity known as the God-Machine that operates the world through occult Infrastructure and strange machinations. But what really makes it this trope is those machinations get results - what looks like strange, formless ritual to outsiders is actually a means-tested way of generating supernatural resources, as perceived through the eyes of a fractured god-like intelligence.
Hermetic mages in Shadowrun take this approach as opposed to the more intuitive "magic as art/religion" approach of shamans.
Vampire: The Masquerade: Dr. Netchurch is analysing the effects of all sorts of supernatural effects for science. However, while he can explain in detail the interactions between human faith and the forces maintaining the integrity of undead flesh, he dismisses thaumaturgy out of hand as unscientific.
The Armagus/Ars Magus of BlazBlue is this, a type of magic which relies on ambient seithr and scientific principles, is fairly simple to learn, and can be used to create Magitek. It was developed so that more people would be capable of fighting the Black Beast, which was impervious to mundane attacks. "Real" magic remains mysterious and extremely powerful.
Similar in Guilty Gear where the science behind the technology that produced the Gears was so fantastic is was called magic. But in the OVA and some dialog in the game it is stated as a form of man-made science and not magic but still different from "old school" science as we know it (but it's the old science that keep Zepp the flying nation in the air).
The Endless Space and Endless Legend games have Dust, nano-machines that can, among other things, grant sentience to other machines, give god-like powers to living beings and bend the laws of reality itself.
In Final Fantasy VII, the Shinra seemed to be using Aeris and her mother before her to study the magic of the ancients, although the story didn't go into much detail on this point.
Shinra also produces materia, so it's probably safe to assume they know a fair amount about regular magic as well.
The "magic" used by the characters in Final Fantasy VIII is more of a pseudo-magic created after analyzing the sorceress' magic. Of note: after a semi-sorceress' Mental Time Travel powers are analyzed, scientists are able to replicate them with the "Ellone Junction Machine."
In Final Fantasy XII, Dr. Cid spends years studying the God-made Nethicite in order to create artificial duplicates. Not only does he succeed, he improves upon his man-made Nethicite (which is just as magical as the other kind) and makes it more efficient.
In Final Fantasy XIII, the forces of Cocoon have created Manadrives capable of emulating the magic of the L'cie.
Shaping in Geneforge plays this trope to a T. New creations are traditionally made through experimentation, making one new creature after another with one slight modification each time and recording the results. The first game is about you being stranded on an island where you discover an abandoned research facility that had discovered DNA, and subsequently magical genetic engineering. The series as a whole delivers the message that the process of gaining knowledge gives you the wisdom to use that knowledge, and that simply being given power will lead to abuse.
The D'ni of the Myst Verse took this approach to their Writing and associated crafts.
In Tales of Symphonia, there are hints of this going on in Tethe'alla, particularly if you listen to the NPC discussions in Sybak University. The Elemental Research Laboratory is also tasked with studying SummonSpirits. The end result of this process can be seen in the Desian bases and later on the highly-advanced city of Welgaia, where the Magitek looks better suited to Space Opera.
Raine Sage also comments in some Z-skits that she feels dissatisfied using magic without fully comprehending how it works on a scientific level and wishes to study it further.
In World of Warcraft, magic is often treated as a science, to the point that three mage girls in Stormwind wander about the Mage District of Stormwind, talking about "the Surian theory" and "frequency shifts." Turns out they're apparently making a Love Potion.
Theorycrafting: players will spend hours debating, testing, experimenting, number crunching and quantifying every bit of information about their character stats. There are websites and tools devotes to running millions of simulations to squeeze that bit more damage out of a fight. Mages who do this especially run full force into this trope.
In Tides Of War, Kalecgos uses an arcane ball with a distinct recurring pattern to show Jaina Proudmoore what magic is made of. The realization stuns her.
This is basically how the Asura from Guild Wars 2 operate; they look at magic as just another field of science, and apply it accordingly. They have concepts such as Golemancy (robots/Mini-Mecha that basically use magic for the battery/OS), the Greater Magical Field Theory (conservation of mass/energy as applied to magic), and so forth.
Apparently this is how magic works in Touhou, according to All There in the Manual.Perfect Memento in Strict Sense's article of Marisa details her research on magic. It involves gathering magic mushrooms, doing various stuff on them, and recording whether they result in magical reactions or not. Those mushrooms also act as fuels to Marisa's magic attacks. Additionally, according to Patchouli, there is no fundamental difference between magic and science.
In The Elder Scrolls, there are various academic institutions dedicated to the study of magic, such as the Arcane University in the Imperial City, or the College of Winterhold in Skyrim, or the secretive Psijic Order. The Dwemer, a now extinct race given the misnomer "dwarves", excelled in this, having gone so far as to figure out a way to extract knowings from an ElderScroll without the reader suffering the usual detrimentaleffects of reading one directly. They also found applications for the sundered heart of Lorkhan, the god who devised existence (which may have accidentally or intentionally led to their vanishing from existence).
The Nasuverse is known for its incredibly complex rules of magic. Let's start with the fact that magecraft is very different from Magic, and then leave it at that.
Mori of The Dragon Doctors is a "magical scientist," someone whose basic job description is analyzing forms of magic and using appropriate forms of treatment for magical ailments.
Tedd of El Goonish Shive is attempting to treat magic just like any other area of the (mad) sciences — physics, chemistry, robotics, etc. So far, we've seen him trying empirical testing of transformation spells, running numbers instead of hoping that things "just work", and so forth. It's heavily, heavily implied that "Lord Tedd" resulted in one timeline when he forgot the value of friendship in lieu of obsessing over magic-turned-science — and thus, power — to the exclusion of all else.
Although Tedd is still studying it scientifically, magic in EGS has since been revealed not to be exactly Magic A. See the example under that trope for more info.
Erfworld: Sizemore notes that Parson Gotti takes this approach to learning how Erfworld and its gamelike mechanics work. Notable because those who wield magic in the world are typically content to solve their quandaries about how stuff works with heated philosophy and self-serving hearsay. It's likely that there are very few Erfworlders who really know the rules of their world.
It seems as if most Erfworlders are born (or "popped") with an innate understanding of the most basic rules of the world and the skills they need to practice their specialties, and this inherent knowledge tends to discourage further questioning ("Why ask questions when you already know most of the answers that matter?"). But Parson is ignorant of even the most basic aspects of Erfworld - and in asking those questions, he's also asking the sort of questions that lead to discoveries and tactics no one else in the world ever dreamed of.
This is what makes him The Dreaded or an Eldritch Abomination in the eyes of his enemies.For example he managed to change the type of a hex by linking a Croakamander and a Dirtamancer (Necromancer and Geomancer) to revive a dormant volcano. Something only the Titans could do.
Named during the "Cinderella" non-canon arc of Girl Genius. After using her Steam Punk tech-knowledge to repair the Good Fairy's magic wand, Agatha shouts "'Any sufficiently analyzed magic is indistinguishable from science!'"
Zeetha the Fairy Godmother: What's with the quotation marks? Who said that?
Vaarsuvius of The Order of the Stick points out "any sufficiently advanced — and repeatable — magic is indistinguishable from technology."
It's not prominent, but in Tales of the Questor, this is clearly the Racconan attitude to magic Lux Phyiscs. Word of God says that their willingness to collaborate and share knowledge is why Racconan wizards are so advanced.
Erik's attitude towards magic in Roommates is: "Magic is not incomprehensible. There are patterns; catalysts and reactions." He might have a point because, despite not having any actual magical abilities, even succeeds in playing magical advisor in one of the arcs.
Deucalion Chronicles is practically built on this trope; almost all technology present in the CU is magic-based.
Church of Red vs. Blue prefers to believe that his being a ghost is this, as opposed to Wash's must more mundane theory that Church is the Alpha AI.
The SCP Foundation recovers and studies anomalous objects in the world, many of them being the origin of folktales and urban legends around the world, and some of which have been directly responsible for some of our more recent innovations.
Tales of MU has a variation of this. While some magic "just works", such as divine healing, much of the mechanics of magic are explained, in excruciating detail. For example: enchantment works somewhat differently for each caster, but the methods of figuring out those variations is highly formalized. Though if you poke too hard at how the universe works, it will poke back.
Saga Of Soul's protagonist is a Magical Girl who, once she obtains her powers, immediately sets out to analyze and experiment with them. She even uses her magic to explore other scientific branches, such as creating unbihexium for physicists to study.
In "Boast Busters", Twilight Sparkle is seen experimenting to find out what magic, exactly, she is capable of.
In "Feeling Pinkie Keen", she spends the entire episode trying to debunk Pinkie Pie's claim of having a psychic "Pinkie Sense". When Pinkie points out that Twilight herself can do magic, she claims that her talent is a science, instead of something random like Pinkie's. Magic happens to be a natural trait of unicorn ponies like Twilight, and her friend Rarity demonstrates similar abilities.
In 'Bridle Gossip', Twilight again describes how rational, scientific magic differs from curses and mumbo-jumbo the others claim are coming from a stranger in the woods.
It's implied the reason Twilight is able to mimic most spells merely by seeing them in action is because of this. Because she's intelligent enough to analyze exactly what's going on to make the spell work, she's able to mimic it. She's even capable of casting inherent spells like Rarity's gem-finder and Celestia's dark magic simply by watching and analyzing it as it's cast.
Doctor Doom in Iron Man: Armored Adventures is similar to the comics incarnation that he appears to possess both advanced science and magical powers from his armor, much to Tony Stark's bewilderment as this version of him has only encountered technological threats until he met Doom. However, after further examining the armor Tony concludes that Doom is using extremely next-generation tech to manipulate quantum fields or some such Techno Babble, similar to the series Macguffins he and the Mandarin are searching for. Doom even summons an entity (or at least its arm) from another dimension to attack Iron Man and says that primitive people would have called it a demon, meaning that the "magic is advanced science and vice-versa" line in the Thor film may apply to Armored Adventures.
While nobody has been shown seriously studying and testing things in Avatar: The Last Airbender, the arts of bending the elements have been shown to work like this and several characters have been shown figuring out how to take bending principles to their logical conclusion: Iroh learned how to redirect lightning by applying waterbending's energy-flow principles to a firebender's ability to manipulate electricity. Toph recognized that while earthbending can't apply to metal, metal still carries earthen impurities that allow it to be bent. And Katara realized that her own sweat could be waterbent, shortly before meeting someone who figured out how, in rare circumstances, that could also apply to bodily fluids that are still inside the body. This also carries into The Legend of Korra, where Amon can rob a person of their bending ability by combining bloodbending (the aforementioned waterbending of bodily fluids) with known techniques to block bending by hitting pressure points to disrupt a person's energy flow.
Princess Bubblegum vehemently denies the existence of magic, and attributes all its properties to specifically applied scientific principles. This gets her in hot water with the very large wizard community.
In Rick and Morty, Rick devises a method in which he can scan cursed items from a spooky antiques store, figure out what each curse is, and starts a business removing them for people.
Rick: Hey Morty, quick question: does evil exist, and if so, can one detect and measure it? Trick question, Morty, the answer is yes, you just have to be a genius.
Many of the earliest scientists in Real Life started out trying to find God/gods/magic.
Sir Isaac Newton, co-inventor of calculus, describer of universal gravitation and the three laws of motion, among other accomplishments, for one tried to make gold with alchemy and count the exact date of the Judgement Day. It's often said he's the last alchemist rather than the first scientist.
Imhotep, the first known doctor (as well as the inventor of columns to hold up buildings and numerous other things) was also a high priest.
Much of the modern science we take for granted nowadays grew out of the semi-mystical field of alchemy.
Astronomy grew from a sub-field of Astrology.
Here's an extended example:
A certain crystal has the properties of Ulf and Droge. Another crystal has properties of Le and Cet. You need, for an alchemical process, a crystal with the properties of Le and Ulf. You make use of a specially-prepared solvent to seperate the crystals into their component properties, and then because of the strong affinity between Le and Ulf, compared to between Ulf and Droge or Le and Cet, a new crystal forms that cannot be seperated by this solvent, so you pour off the liquid that now contains Droge and Cet, which is useless to you, and use the Le/Ulf crystal in your experiments.
Explanation: The first crystal is hyDROGEn sULFate (or sulfuric acid); the second one is LEad aCETate. The solvent is distilled water. When the two substances dissolve in the distilled water, they react to form hydrogen acetate (acetic acid) and lead sulfate. The lead sulfate precipitates out of the solution, while the acetic acid stays dissolved and gets poured off with the water.
Many nutrition, hygiene, and sanitation practices were enforced for mystical or religious reasons long before the scientific principles for why they are a good idea were well-understood. The ancients may not have known exactly why eating pork and shellfish tended to make you sick in the Time Before Refrigerators, but as a deterrent, "God doesn't want you to eat pork and shellfish and will curse you if you do!" works as well as anything else.