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Magic Is Mental

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A trope that is nearly omnipresent when magic is involved: Magic is a product of the mind, not the body. Magic requires study and concentration to use. The best mages are smart, wise, perceptive, and all-around great minds. It's even in the word "Wizard", which used to mean "Philosopher" and came from the word "Wise". The word magic itself descends from magos/magi, meaning "one of the members of the learned and priestly class", AKA a Gentleman and a Scholar from Ancient Persia. It's not accidental wordplay that forces you to learn basic spelling before you can study spellcasting.
As such, this trope has many, many consequences: In an ensemble group, those with magics will tend to be the smartest. They are the most well-learned, those who have studied and are the wisest. They will be The Smart Guy.
In games with stats, magic is often related to a "mental" attribute if it's not its own, segregated attribute. Popular choices are intelligence/smarts/logic, willpower/wisdom/spirit, or charisma/personality.note These being the three mental-oriented attributes in Dungeons & Dragons' six-attribute system is probably not a coincidence. Different types of magic may require different attributes, with Hermetic Magic favoring the first, and divine magic favoring the second.
This trope is why we have Squishy Wizard — magic requires a strong mind, not a strong body, and this is the handwave often used. One Sub-Trope is Concentration-Bound Magic, where magic lasts only so long as the wielder is exerting continuous focus and effort.
Often, Asian works follow the trope less rigorously, with magic being shown as a product of both mind and body. Thus seeing characters study, train, and combine magic with martial arts is not rare.
Note even in some works where magic is mental, there is "backlash", which damages the mage's body. At a low level, it causes exhaustion; at a high level, it causes death.
Related to Enlightenment Superpowers. Psychic Powers may be the modern equivalent, and consider Magic or Psychic? when the two are paired in the same work. Since one of the applications of magic is launching projectile attacks, this trope often leads to Smart People Shoot. Magic A Is Magic A is when magic works consistently enough that it can be studied empirically, making it even more well-suited to intelligent wielders.
See also Ritual Magic, which may involve a lot of memorization and concentration. Not to be confused with (but might coexist with) Power Born of Madness. Compare Emotional Powers.

Examples
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Wizardry: Spellcasters depend on either intelligence, senses, or piety.
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Very much in effect with sorcery, the primary magic-system in Belgariad, which is also called "the Will and the Word" for a reason — the sorcerer needs to will something to happen, then use a spoken word (what word isn't important, as long as the sorcerer can see some connection between it and the effect they want) to actually make it happen. Of course, if you try to do something too far removed from reality, expect the natural forces involved to slap you down rather painfully.
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In A Certain Magical Index, espers rely on extremely complex mental equations to use their abilities, and as a result, they possess Super-Intelligence as a Required Secondary Power. Accelerator, the world's strongest esper, has a brain superior to the world's fastest supercomputers and becomes significantly weaker after suffering brain damage. It's even possible for certain espers to boost their powers by linking their minds together to spread out the work.
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Dark Souls: Sorcery is a scholarly pursuit studied and taught in prestigious schools, and is affected by the Intelligence stat, while divine Miracles are affected by the Faith stat. Pyromancy, seen as a primitive and unsavoury magic, gets no benefit from stats (and is a Minmaxer's Delight because of it). By the second game, pyromancy has since lost this stigma and is now studied as a respected school of magic, and can now benefit from either Intelligence or Faith. There's also the introduction of Hexes, dark magic that requires levelling Intelligence and Faith equally.
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In the Lyrical Nanoha franchise, magic requires an understanding of advanced mathematics to use. Part of the reason Fate and Nanoha are so talented at magic is that they're both math prodigies.
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Shin Megami Tensei games play with this. In the original Megami Tensei I and II, magic offense, defense and MP were all determined by the Intellect stat, though with Shin Megami Tensei Intellect was split into two stats — Intelligence, which increased the effectiveness of status ailment inducing/instant-kill magic such as Marin Karin and greatly increased MP, and Magic, which corresponded more to a character's sixth sense and made offensive magic more efficient. Later games abandoned Intelligence, though the Magic stat still has some correlation with the character's mind.
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The Dresden Files magic stems from life and emotions, but concentration and willpower are what allow one to use magic to achieve anything.
Also an interesting case in that an individual body can affect magic ability as much as a mind does.
The arguably best example is the Archive — superlative spell-casting ability (thanks to being the hereditary repository of all written human knowledge) in the body of a child when Harry meets her for the first time. In her next appearance, even when effectively crippled, she goes toe to toe with a dozen Fallen Angels and is winning handily before it turns out that they were cheating and using gas that would affect her far quicker than them, thanks to a lack of body mass.
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 The Dresden Files
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In Discworld, wizard-magic is based on knowledge (the three known wizarding universities are the Disc's centres of pure learning, compared with the vocational schools run by the guilds), and witch-magic is based on force of personality. (In D&D terms, Intelligence and Charisma.) The Disc's etymology for wizard is "wys-ars" ("one who, at the bottom, is very wise").
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Golden Sun has this in the form of psynergy, short for psychic energy. However, the Squishy Wizard aspect is entirely relative: Two party members are of the Magic Knight persuasion, and the other two have slightly less HP and attack power, but magical ability is tied to elemental affinity so there isn't really a single magic-only character. It gets spelled out in the kung fu dojo where the master explains that the practitioners use chi (the power of the body), but the Adepts use ki (the power of the mind).
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In most Savage Worlds setting, magic is related to the spirit attribute. If not, it's smarts. But always one of those two.
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In Necroscope, in order to gain the power to time travel and teleport, Harry Keogh, and his heirs, has first to be able to calculate the infinite length of a Moebius strip in finite terms. When he is stripped of his ability to do math, he loses that ability. He has other innate abilities, and most psi users' abilities are inborn, but this one has to be learned and expressed mathematically.
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Critical Role: Tal'Dorei Campaign Setting: Some of the features allow characters to break the rules of spellcasting are described as being the result of intense study, meditation, and focus.
The Dual-Focused feature comes as a result of strenuous mental exercises and allows a spellcaster to focus on two different incantations at once.
Flash Recall allows spellcasters to violate the normal rules of Vancian Magic by using their keen memory to prepare a spell in an instant rather than having to spend hours right after waking up preparing a whole list of spells.
The Spelldriver feature allows a character to cast a spell of 2nd level or lower as a bonus action and still cast any level of spell as an action due to "intense focus, training, and dedication," even though such a thing is impossible in the base rules of Dungeons and Dragons.
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 Critical Role: Tal'Dorei Campaign Setting (Tabletop Game)
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Throughout the series (prior to Skyrim doing away with Attributes), the "Schools of Magic" are tied to "mental" attributes (Intelligence, Willpower, and Personality). Additionally, your maximum Magicka is determined by your Intelligence (with multipliers applied based on your race and birthsign), while your Magicka regen rate is determined by your Willpower.
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 The Elder Scrolls V: Skyrim (Video Game)
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Dragon Age: Origins: Willpower determines mana. Interesting subversion in that Cunning, the stat that models the character's raw intellectual capacity, social acumen, cleverness and perceptiveness, does not aid magic in any way.
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Pathfinder averts this for the Scarred Witch Doctor (a Witch archetype exclusive to Orcs) and the Kineticist (an occult Bender), both of which use Constitution as casting stat, with the Kineticist also using Dexterity for secondary effects.
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 Pathfinder (Tabletop Game)
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In Dungeons & Dragons, wizards used their intelligence as the stat governing their magic. Clerics used wisdom. In later editions, some classes used charisma. Generally, "Learned" arcane magic was tied to intelligence, divine and natural magic to wisdom, and inborn magic to charisma.
4th edition both inverts the trope and plays it straight. Wizards and sorcerers use Intelligence and Charisma respectively, but a sorcerer's secondary attributes key off his Strength and Dexterity, while some Wizard builds use Dexterity or Constitution as opposed to Wisdom or Charisma. Warlocks can use Charisma or Constitution as their primary stat, and Battleminds (psychic warriors) use Constitution.
Pathfinder averts this for the Scarred Witch Doctor (a Witch archetype exclusive to Orcs) and the Kineticist (an occult Bender), both of which use Constitution as casting stat, with the Kineticist also using Dexterity for secondary effects.
D&D 5th Edition Plays this trope in different ways for different classes:
Wizards, Cleric, Druids and Sorcerer still play it straight.
Bards, having been reclassified as full casters, but who still cast off their charisma stat, play it straight as well, but in a different manner.
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Divinity: Original Sin and Original Sin II: The magic skill lines (Elemental Powers plus Witchcraft/ Necromancy), Magic Wands, and Staffs are tied to the user's Intelligence attribute. Damage scales with Intelligence, and, in the first game, higher Intelligence reduces Attack Failure Chance and cooldown time.
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Avatar: The Last Airbender: Bending is partially mental, which is shown by how the various benders meditate to improve their abilities. Unlike other examples, bending is also partly physical, since the bending arts require intense physical movements. However, some Master benders are able to perform elaborate acts with minor amounts of bodily movement. King Bumi is able to bend large amounts of rock with just his head, even when his body is bound by metal. Combustion Man, Yakone, and Amon are uniquely capable of bending just by thinking, something referred to as "psychic bending." It is a very rare skill.
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In The Traitor Son Cycle, sorcerers craft their spells in their mind palaces, so a sharp mind, a good memory and an ability to focus quickly are all required to be any good at magic.
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 The Traitor Son Cycle
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Doctor Strange (2016) plays with this: while the sorcerers of Kamar-Taj are encouraged to undergo physical training, seemingly in order to subvert Squishy Wizard, it is emphasized that casting spells has no physical requirements. Strange believes that he can't do it because his hands are damaged — but then he's shown someone who can cast spells without having a hand at all. The first magic user that Strange encounters actually had spinal damage and was a quadriplegic. He uses magic as a patch to his nervous system, allowing him to function as a normal human being.
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The Dragon Prince: Very much the case for Dark Magic, where learning spells and rituals are practically an academic pursuit. Primal Magic, however, is decidedly less so, where a great deal of spirituality is required to connect to a Primal Source, and magic itself is a product of both mind and body (dancing, arm/hand movements, breathing, etc).
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Ogre Battle: Intelligence determines a magic attack's damage.
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The Elder Scrolls
Throughout the series (prior to Skyrim doing away with Attributes), the "Schools of Magic" are tied to "mental" attributes (Intelligence, Willpower, and Personality). Additionally, your maximum Magicka is determined by your Intelligence (with multipliers applied based on your race and birthsign), while your Magicka regen rate is determined by your Willpower.
In each of the games, the Mages Guild (or local equivalent) essentially doubles as the guild for scholars as well. In Skyrim, it is even called a college.
The notion of Soul Gems also feeds into this. With very few exceptions (usually related to divine magic), all of the enchanted objects in the setting are powered by living souls whose energy is trapped in physical gems. The implication, of course, is that objects need the power of a mind in order to have magical ability.
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Schooled in Magic: The formation of a spell is regularly compared with the writing of computer code, only in the mind alone. Great mental discipline is required to do anything worthwhile with magic and a lack of discipline would be deadly.
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Final Fantasy: In Final Fantasy II, Final Fantasy III, Final Fantasy IV, and Final Fantasy XI, intelligence dictates black magic damage while mind/spirit dictates white magic. In most other games of the series, Magic Power is its own stat or intelligence governs all types of magic.
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In Magic: The Gathering in-role your cards are your spells, and you draw them from your library. Many cards that affect cards in your hand and library (drawing, discarding, searching, etc.) represent things happening to the mind or knowledge, and a few other cards represent things happening to cards in your graveyard (your discard pile) as affecting memories. In terms of flavour, the colours of magic are largely defined by one's mindset and belief system, but ultimately magic is just a tool usable by pretty much everyone (i.e. Jace Beleren, a Blue spellcaster, has made use of both White and Black spells), so averted aside from spells associated with the mind.
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Deliberately and consistently averted. In both Mage: The Ascension and the later Mage: The Awakening, both a character's raw magical power and their capability with different sorts of magic were based on traits (Arete and Gnosis, respectively, for power and Spheres or Arcana for ability) completely separate from the mundane ones (including intelligence and the like). That means that mechanically speaking, nothing is preventing you from making a wizard who's anything from a borderline mental retard to a world-class genius — and nothing is preventing the former from being a far greater wizard than the latter. Rotes (highly specific magical effects with a higher chance of working, as opposed to the more commonly used "improvised" magic) are always based on a mundane skill and attribute in addition to a magical one, but those could just as easily be Stamina and Streetwise as Intelligence and Science.
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Wanda Maximoff takes it further in Doctor Strange in the Multiverse of Madness. Discovering that she is The Scarlet Witch, she's capable of complex spellcasting spontaneously through sheer force of will, after her abilities previously appeared to be telepathy and telekinesis. Though capable of highly advanced spellcasting with actual reference material, she's also only capable of achieving such power when thoroughly traumatized, and as such is highly vulnerable to corruption by sinister sources of mystical knowledge.
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In Shadowrun, Magic is its own attribute, but only the mental attributes (Willpower, Intuition, and Charisma) can be used to resist drain, the strain of using magic. Thus having higher attributes allows one to cast more spells.
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My Little Pony: Friendship Is Magic: Unicorn magic is shown to work this way due to mage-in-training Twilight Sparkle being The Smart Girl among the Mane Six. In "Feeling Pinkie Keen", Twilight mentions while practicing with Spike that spell-casting requires complete focus and concentration. It's shown again in "Magic Duel", where Twilight is trained by Zecora to better her magic, and her stray thoughts of Trixie cause her magic to fail.
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Child of the Storm has magic primarily derived from The Dresden Files and Harry Potter, and while physical training is recommended, isn't necessary. If you're in better shape, you tend to have more stamina and more capacity for handling power (plus, being able to handle yourself in close combat can be a crucial advantage), yes, but most magic is about mental focus and studying to control it. The better you understand magic, the more you can do with less power: as Harry Dresden points out, he's in roughly the same weight class as Doctor Strange for raw power. However, Strange's vast knowledge and experience mean that he knows exactly how to apply it for maximum effect. For instance, both of them can summon lightning bolts, but it takes far less energy to split an atom and while Dresden can't split an atom, Strange definitely can.
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Post-Secret Wars (2015), the Marvel Universe has had a number of previously purely scientist heroes dabbling in magic in the present or possible futures. A time-displaced Beast from the past and an alternate-future Iron Man both became sorcerers, the latter becoming Sorcerer Supreme. In one event starring Doctor Strange and other Sorcerers Supreme, Isaac Newton is recruited along with other wizards for a magic crisis.
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The Dresden Files: The three key magic skills — for characters who have the appropriate powers to begin with — are Lore (knowing what you're doing), Conviction (literally the strength of your beliefs), and Discipline (staying focussed). Physical traits don't enter the picture, although it's also worth noting that nothing prevents a wizard from being hopelessly ignorant in the fields of mundane higher knowledge (covered by the Scholarship skill).
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Mother: The amount of PP is determined by IQ, and attacks that disrupt the opponent's senses render them unable to use PSI.
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Lufia: Intelligence determines spellcasting power.
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Diablo III uses Wisdom as the attribute governing mana and magic damage.
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This is how (human) magic works in Rivers of London books. You have to learn the mental forms in order to do magic, and practice visualising the concepts or it doesn't work. To make things harder, thanks to Isaac Newton, all the names of the forms are in Latin. And the forms have to stack in order to work. To throw a fireball, you have to learn how to visualise the fire, then how to visualise it moving, then have to visualise how to make it track a target... And after that, your brain trickles out your ears (if you've done it wrong).
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In Quest for Glory, Intelligence affects your ability to cast spells and your mana if you are a Magic User.
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Two spells introduced in Harry Potter and the Prisoner of Azkaban require the caster to think certain things;
Riddikulus (used to fight boggarts that turn into your worst fear) requires the caster to think of something funny happening to what they're afraid of.
Expecto Patronum needs you to focus on a happy memory in order to beat the happiness eating Dementors.
Magic in general is treated as a school topic. It's something you study, read, do written homework about. There's the implication of some element of physical skill (Wand flicks, and potions in particular may require a steady hand and good timing) and thus practice involved, but in general, magic as taught at Hogwarts is more akin to a combination of theoretical and lab courses like chemistry than say, physical education (of course, you still need magical ability from birth, as Petunia found out).
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Played straight in the fanmade Genius: The Transgression, though: while the raw power of your Mad Science and your various capabilities within the field are determined by independent traits (Inspiration and Axioms), the actual process of creating Wonders always depends upon a mental attribute (intelligence if you're working methodically in a lab, wits if you're kitbashing on the spot), so a stupid Mad Scientist wouldn't last long. To prevent this, each Mad Scientist actually gets a bonus to either attribute during character creation — making sure that there wouldn't be, by default, any stupid ones, that they'd be smarter than the average person on average, and that they would be far more likely to be literal geniuses rather than just Mad ones.
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Ultima: One's spellcasting depends on either intelligence or wisdom.
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In GURPS, "Magery" (the advantage that allows you to be a mage) is a mental advantage, which means that it stems from your mind rather than from your body (so it stays with you if you switch bodies with someone, etc.)
Also, the default magic system has spells being skills based on the IQ attribute.
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Ra: Using magic requires more than just saying the words of the spell, you have to think your way through them as well. This is likened to performing advanced mental arithmetic. Part of a mage's daily routine is meditation for this reason.
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In the Imager Portfolio series by L. E. Modesitt, Imagers use their 'magic' completely with their minds, by seeing/imagining them in their heads, but they have to have a complete mental picture and understanding of its elemental and chemical make up or they can do things like blow themselves up by mixing chemicals which react explosively with each other. They also can image in their sleep as they dream, so they have to sleep in protected, lead-shielded rooms, alone, even if they are married (or they could accidentally kill their spouses).
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In The Bartimaeus Trilogy, almost all magic involves harnessing spirits, all varieties of which require different methods to summon, contain, and control, and information about which is recorded in books in numerous dead languages (partially because the information is old, partially to stop commoners from learning about it). As such being a magician involves fluency in multiple languages, memorizing an exhaustive list of symbols and being able to reproduce them perfectly and with correct placement, as well as remembering huge amounts of trivia as to the idiosyncrasies of various subspecies. Children are given an extensive intelligence test to determine whether they have the capacity to become a magician.
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Ars Magica: Zig-zagged. The Intelligence stat boosts magical laboratory projects like Item Crafting and creating spells, representing the scholarly nature of magical practice in the setting. However, active spellcasting (either instantaneous or Ritual Magic) is boosted by Stamina instead, since it's a physical effort and can inflict Fatigue levels if the spell is at the limit of the mage's capabilities.
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One Fantastic Four story introduced heroes from the Bad Future of Old Man Logan. One of them was Bruce Banner's son, in permanent Hulk form but also raised on science by Reed Richards. When his gamma mutation is neutralized, it's apparent that it was also a mental handicap, and he suddenly becomes intelligent enough to decipher and cast spells from an ancient grimoire no one else could.
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The following is a list of statements referring to the current page from other pages.

 Magic Is Mental
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Magic and Powers
 Kaleidoscope (Fanfic) / int_da176edb
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Magic Is Mental
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Magic Is Mental
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Magic Is Mental
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Magic Is Mental
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Magic Is Mental
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Magic Is Mental
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Magic Is Mental
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Magic Is Mental
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Magic Is Mental
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Magic Is Mental
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Magic Is Mental
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Magic Is Mental