View source for 10^−43

'''10<sup>-43</sup>''' ({{Runes|10}}^{{Runes|−43}}) is a [[witch]] from the mobile game [[Puella Magi Madoka Magica Side Story: Magia Record|Magia Record]]. Its existence was only known through its [[familiar]]s, the Echos, until the witch itself was revealed in the first chapter of Arc 2.5.

In the anime for Magia Record, a large Familiar with a green hue was seen within 10<sup>-43</sup>'s barrier. Upon its defeat, the barrier disappeared. This is most likely the final form of the familiars as they grow through the different stages.

As a magical girl, her wish was "Give me a fertile paradise for our family's prosperity."

==Witch==
{{Card
|name          = 10<sup>-43</sup>
|runes         = 10 −43
|image         = File:10^−43WitchCard.png
|japanese_desc = 象徴の魔女　その性質は『啓示』
現代に至る悠久の時代すべてに干渉しながら自身の繁栄を極めようとしている魔女。
魔法少女の宿命を覆すシステムに干渉して世界を覆う被膜を取り込んだことにより、魔女の体は大地に広がる１つの都市となり、結界は地球を包むほど広大になった。
過去と未来へ自身を波及させ、どの時代にも自分という個しかいない状況を作るまであと１歩となった魔女は、最後に∞の力を取り込もうとしているが、自分では身動きが取れないため、己の分体に頼るしかなくなっている。
|english_desc  = A witch who attempts to bring herself to the pinnacle of prosperity, while interfering with every era in the dizzyingly-long line of history leading to the present day.
By interfering with the system that overturns the fate of Puella Magi and absorbing its world-covering membrane, the witch’s body has become a single massive city that spreads across the land, and her Labyrinth is vast enough to engulf the whole Earth.
She is now only one step away from suffusing herself through the past and future, making herself into the only individual that exists in any era. The last step is to absorb the power of infinity into herself, but because she can no longer move around on her own, she’s forced to rely on her own offshoots.
|type          = Symbol Witch
|nature        = Revelation
|episodes      = [[Puella Magi Madoka Magica Side Story: Magia Record]]
}}

{{Card
|name          = 10<sup>−1</sup>
|runes         = 10 −1
|image         = File:1021.png
|japanese_desc = 象徴の魔女　その性質は『啓示』
抗えない使命を帯びているかのように、ひたすら繁殖を続ける魔女。意識を持たないので、出自や年齢はわからず、何をしたいのかも考えたことがない。ただ、自分を増やしたいという空疎な行動原理に従って、今まで増やしてきた自分の分身と連携しながら更なる分裂を続けている。しかし、繁殖以外の意思がないので、いくら数を増やしても、見つかると簡単に潰されてしまう。ゆえに魔女にとっての栄華はほど遠い。
|english_desc  = A witch who simply continues to proliferate herself, as if charged with an inexorable duty. Because she has no consciousness, her place of origin and age are unknown, and she has never thought about what she wants to do. She simply obeys the hollow behavioural instinct to proliferate, working together with all of her previous offshoots to replicate herself ever further. But because she has no intent beyond proliferation, she’s easily stamped out when discovered, no matter how many of her there are. Thus, prosperity for this witch is still a long ways off.
|type          = Symbol Witch
|nature        = Revelation
|episodes      = [[Puella Magi Madoka Magica Side Story: Magia Record]]
}}
 
{{Card
|name          = 10<sup>−3</sup>
|runes         = 10 −3
|image         = File:10^−3WitchCard.png
|japanese_desc = 象徴の魔女　その性質は『啓示』
抗えない使命を帯びているかのように、ひたすら繁殖を続ける魔女が成長した姿。
硬質な羽を増やして空を舞う力を手に入れつつ、3つの時代を見渡せる能力も身に付けたが、増えることだけが行動原理なのは成長前から変わっていない。
無意識にリスクを排除するようになり、他の自分に危機を知らせるような行動をとるようになったものの、成長していない魔女には、その意図を汲み取ることができないので、なんの意味もなしていない。
|english_desc  = A more mature form of a witch who simply continues to proliferate herself, as if charged with an inexorable duty.
She has grown rigid wings and become able to dance through the sky, as well as gained the ability to watch over 3 eras. But much like her immature state, her only behavioural instinct is to proliferate herself.
She now unconsciously attempts to eliminate risks, and sometimes behaves as if to warn her other selves of danger, but the immature versions of the witch can’t grasp her intent, so there’s no point to it at all.
|type          = Symbol Witch
|nature        = Revelation
|episodes      = [[Puella Magi Madoka Magica Side Story: Magia Record]]
}}
{{Card
|name          = 10<sup>−5</sup>
|runes         = 10 −5
|image         = File:10^−5WitchCard.png
|japanese_desc = 象徴の魔女　その性質は『啓示』
抗えない使命を帯びているかのように、ひたすら繁殖を続ける魔女が成長した姿。
他の時代に生きる自分に危機を知らせても意味がないことに気づいた魔女は、ようやく状況を理解すると、地に足をつけながら5つの時代を見渡すようになった。
誘導することを覚えた魔女は、5つの時代を見渡しながら他の自分が成長できる可能性を見出すと、危機を知らせるのではなく一瞬だけ体の自由を奪い、向かわせたい方へ促すようになっている。
|english_desc  = A more mature form of a witch who simply continues to proliferate herself, as if charged with an inexorable duty.
Once she realized that it was pointless to announce danger to the versions of herself in other eras, the witch finally comprehended her situation, and became able to watch over 5 eras with her foot planted firmly on the ground.
She has now learned how to properly guide others. When she sees a potential moment of growth for one of her other selves in one of those 5 eras, instead of alerting them to danger, she steals control of their body for just a moment and urges them in the direction she wants them to go.
|type          = Symbol Witch
|nature        = Revelation
|episodes      = [[Puella Magi Madoka Magica Side Story: Magia Record]]
}}
{{Card
|name          = 10<sup>−7</sup>
|runes         = 10 −7
|image         = File:10^−7WitchCard.png
|japanese_desc = 象徴の魔女　その性質は『啓示』
抗えない使命を帯びているかのように、ひたすら繁殖を続ける魔女が成長した姿。 繁殖のために親である魔女を最上にするため、自分を食らわせることにしたこの魔女 は、自身が最上の食事となるために、他の魔女を誘導して自らが食らい続けてきた。 成長を果たした魔女は黄金の羽で浮遊し、7つの時代を見渡せるようになったばかりか、陰陽の概念を中和させたクセのない最上の一品となった。高らかなラッパの音色は、 自分を生み落としてくれた親の魔女に向けられている。
|english_desc  = A more mature form of a witch who simply continues to proliferate herself, as if charged with an inexorable duty.
In order to raise her parent witch to supremacy for the sake of proliferation, this witch has decided to feed herself to her parent.
In order to make herself into the supreme meal, she has manipulated and consumed many other witches herself.
The now-mature witch floats upon golden wings, can watch over 7 eras, and has even balanced out her essences of yin and yang to become a perfect dish with no peculiar or outstanding flavors.
The lofty sound of her trumpet is directed towards the parent witch who gave her the gift of life.

|type          = Symbol Witch
|nature        = Revelation
|episodes      = [[Puella Magi Madoka Magica Side Story: Magia Record]]
}}

== Minions ==
{{Card
|name          = Echo
|runes         = ECHO
|image         = File:Card_Echo.png
|japanese_desc = 
人間から奪った生命力に応じ成長する姿を変えると言われる象徴の魔女の手下達の中で、イス憑きと呼ばれる種類他魔女の手下に比べごく僅かな愉力を元に樣々な姿へと何段階も成長する。繁殖そのものを目的としており、ある程度成長した者は魔女にならずとも自身で新しい手下を産み落とすことが出来る。椅子を形どり、その利便性と完成されたフォルムを噛みしめて成長している模様。
|english_desc  = Minions of the witch of symbols. Their role is to proliferate.
These Familiars of the Symbol Witch are called Haunting Chairs. They grow and transform by absorbing vital energy from humans. Compared to other Familiars they can change shape with a small amount of vital energy. Their primary goal is reproduction. Once they have grown enough, they can produce other Familiars, despite not being Witches. They grow, thoroughly enjoying the convenience and completeness of their forms.
|type          = Symbol witch's minion I-IV
|task          = Proliferate
|episodes      = [[Puella Magi Madoka Magica Side Story: Magia Record|Magia Record]], [[Magia Record Episode 6: I'll Do Anything|MagiReco Episode 6]],[[Puella Magi Madoka Magica Magia Exedra|Magia Exedra]]
}}
{{Card
|name          = Echo
|runes         = ECHO
|image         = File:Echo II Card.png
|japanese_desc = 
人間から奪った生命力に応じ成長する姿を変えると言われる象徴の魔女の手下達の中で、ヒト憑きと呼ばれる種類他魔女の手下に比べごく僅かな愉力を元に樣々な姿へと何段階も成長する。繁殖そのものを目的としており、ある程度成長した者は魔女にならずとも自身で新しい手下を産み落とすことが出来、1匹見かけたら30匹は存在すると恐れられる。見つけたら増える前に必ず駆除しよう。
|english_desc  = Minions of the witch of symbols. Their role is to proliferate. 
The witch of symbols has many minions, said to grow and change shape in accordance with the life force they steal from humans. This type is known as the Hominid Dweller.
They grow and evolve through many different stages, using only a fraction of the life force that other witches’ minions would use. Their goal is simply to proliferate. Those that grow to a certain stage can give birth to their own minions in turn, even without becoming a full-fledged witch.
If you find 1, there’s bound to be 30 more where it came from, so you’d better exterminate them before they multiply even further.
|type          = Symbol witch's minion II-IV
|task          = Proliferate
|episodes      = [[Puella Magi Madoka Magica Side Story: Magia Record|Magia Record]], [[Magia Record Episode 7: I Want to Go Home with You|MagiReco Episode 7]]
}}
{{Card
|name          = Echo
|runes         = ECHO
|image         = 
|japanese_desc = 
人間から奪った生命力に応じ成長する姿を変えると言われる象徴の魔女の手下達の中で、トリ憑きと呼ばれる種類他魔女の手下に比べごく僅かな愉力を元に樣々な姿へと何段階も成長する。繁殖そのものを目的としており、ある程度成長した者は魔女にならずとも自身で新しい手下を産み落とすことが出来る。鳥を形どり、なんでも突き回しながら脳髄を揺らし、人類にはたどり着けない境地で成長している模様。
|english_desc  = Minions of the witch of symbols. Their role is to proliferate.
The witch of symbols has many minions, said to grow and change shape in accordance with the life force they steal from humans. This type is known as the Bird Dweller.
They grow and evolve through many different stages, using only a fraction of the life force that other witches’ minions would use. Their goal is simply to proliferate. Those that grow to a certain stage can give birth to their own minions in turn, even without becoming a full-fledged witch.
They assume the shape of a bird, and poke around at just about everything while vibrating their brains– a unique world of development that humanity could hardly hope to reach.
|type          = Symbol witch's minion II
|task          = Proliferate
|episodes      = [[Puella Magi Madoka Magica Side Story: Magia Record|Magia Record]],
}}


==Observations==

Fitting with her wish as a magical girl, her familiars and labyrinth have heavy femininity, fertility, and infertility symbolism - her familiars grow from egg-shaped to being in cribs, then sitting in chairs (fertility), before finally becoming feminine humanoids with empty holes in their stomachs (infertility). In the anime, the presumed final form of the familiars is humanoid figure standing on all fours, with an open hole where its head would be. Furthermore, the witch's labyrinth features mannequins with pink brooches and rings (femininity); pink crystal pillars around which the rings sit and eggs rolling through the sky and across the ground (fertility); and dead, barren trees (infertility); with the entrance to her labyrinth and her witch kiss both being keyholes (femininity and fertility).

Her name is 10<sup>−43</sup>, with the third [[Runes|rune]] corresponding to the [[Wikipedia:Caret|caret character (^)]] and the fourth rune representing the negative (−) symbol, which was first introduced with this witch. This makes her name the first name in the series that consists entirely out of numerals and punctuation marks. 10 to the power of −43 would result in the number 0.0000000000000000000000000000000000000000001. In the [[Wikipedia: Planck units |Planck Units]], 10<sup>−43</sup> is the minimum used in this scale, and thus, she could also be a reference to the [[Wikipedia: Planck_units#In_cosmology|Planck epoch]] (the first moments of the universe, by "10<sup>−43</sup>"s) and to the [[Wikipedia: Planck Units#Planck time|Planck time]]. Finally, 10<sup>−43</sup> also could be a reference the infinitesimal, an infinitely small number approaching but not quite reaching zero. As it is in some sense the opposite of infinity (which represents the infinitely large), this would make it an antithesis to [[Infinite Iroha]].

In all her previous forms, 10<sup>−43</sup> had planets, halos and trumpets that were increasing each time she got stronger. In her 10<sup>−1</sup> form, her head is the planet [[Wikipedia:Mars|Mars]] (identifiable by the presence of the [[Wikipedia:Valles Marineris|Valles Marineris]] canyon), named for the Roman god of war and consort of Venus, goddess of love and sexuality. In this form, she has two halos (the rhombus/diamond above her head and the disc behind her), what appears to be a wing on her left side, and a large trumpet she wields in her hand. Her body resembles a block of marble with parts of it carved out as if to create a statue or piece of art.

In her 10<sup>−3</sup> form, her head is the planet [[Wikipedia: Jupiter|Jupiter]], named for the Roman god of thunder and king of Olympus. Mars, alongside the planet [[Wikipedia: Mercury|Mercury]], is now part of her body. Now she has six halos (three rhombus/diamond above her head and three discs behind her), three large trumpets merged together and three wings, but has lost one of her hands. In addition, her body now resembles a triangular plate made of marble.

In her 10<sup>−5</sup> form, her head is the planet [[Wikipedia: Saturn|Saturn]], named for the Roman god of time and agriculture, father of Jupiter. Jupiter, alongside Mars, Mercury and the planet [[Wikipedia: Venus|Venus]], are now part of her body. Now she has ten halos (five rhombus/diamond above her head and five discs behind her), five large trumpets merged together and five wings, that turned from white to blue. Her body now resembles a diamond or irregular octahedron made of marble.

In her 10<sup>−7</sup> form, her head consists of both the [[Wikipedia: Sun|sun]] and [[Wikipedia: Moon|moon]] fused into a Yin-Yang form. Saturn, Jupiter, Venus, Mercury and Mars are all part of her body. Now she has fourteen halos (seven rhombus/diamond above her head and seven discs behind her), seven large trumpets merged together, and seven wings, that turned from blue to gold. She also regained her second arm. Her body are three circles that resemble the [[Wikipedia: Solar System|solar system]], made of marble. This solar system-like form is still present in her final form, atop of her body.

All of the forms she assumed before her final form made her resemble an Abrahamic angel, and her increasing amount of trumpets could be a reference to the [[Wikipedia: Seven Trumpets|Seven Trumpets of Apocalypse]]. Her wish also evokes similar themes, and there are similar religious themes in her barrier, suggesting she could have once been a character out of Abrahamic mythology, such as Eve or Sarah (Abraham's wife). 10<sup>−43</sup> also seems to be based on the [[Wikipedia: Tower of Babel|tower of Babel]], since in this form she is a gigantic golden statue a top of a large tower with many stairs.

An [[Wikipedia:Echo|echo]] is the identical reflection of a sound off a surface, thus referencing that the Familiars are offshoots of the Witch that share her single-minded desire to reproduce into copies of her and each other. In Greek mythology, [[Wikipedia:Echo (mythology)|Echo]] was a nymph (a nature spirit) who was cursed for talking so much so as to only be able to repeat what others said. She later fell in love with a man named Narcissus, who spurned her love and was thus himself cursed to fall in love with his reflection so intensely that he ultimately wasted away and died from not leaving his own sight. Eventually Echo faded until all that was left was her repeating voice.

Her multiple different forms seem to represent the theory of evolution, as both the witch and its familiars are described as evolving and changing. [[:File:Symbol 01.png|10<sup>−43</sup>'s original form]], seen as a silhouette, is much more simple than her final form.

==Trivia==
*The Witch was seen in [[Magia Record Story Puella Historia The Ikusamiko of Kamihama Arc|Puella Historia The Ikusamiko of Kamihama Arc]] during the Warring States Period. This could mean that the witch is around 500 years old.
**[[:File:Witch_178.PNG|Two of]] [[:File:Witch_177.PNG|the new]] Echo variants introduced in Arc 2.5 reuse [[:File:Episode_7_Familiar_Battle_1.png|designs]] [[:File:Episode_7_Familiar_Battle_2.png|seen in]] [[Magia Record Episode 7: I Want to Go Home with You|Episode 7]] of the game's anime adaptation. There, they were released from inside one of [[Alina Gray|Alina Gray's]] weapon containment cubes and had presumably been modified by her artistic endeavors and efforts to make them stronger.
*She is the first witch to have a name entirely made of mathematical symbols and numbers.

==Gallery==
===Official Art===
<gallery>
File:Echo I - Magireco Archive.jpg|Echos from the Magia Archive
File:Echo II-IV - Magireco Archive.jpg
</gallery>
=== Magia Record===
====Sprites====
<gallery>
File:Enemy 6208 l.png| 10<sup>−43</sup>, The Symbol Witch
File:Enemy 6221 l.png|Witch sprite (10<sup>−1</sup>)
File:Enemy 6223 l.png|Witch sprite (10<sup>−3</sup>)
File:Enemy 6225 l.png|Witch sprite (10<sup>−5</sup>)
File:Enemy 6227 l.png|Witch sprite (10<sup>−7</sup>)
File:6201 10-43 emblem.png|Witch's Kiss
File:Enemy 7201 l.png|Echo I sprite
File:Enemy 7202 l.png|Echo II (Haunting Chairs) sprite
File:Enemy 7203 l.png|Echo III (Haunting Chairs) sprite
File:Enemy 7204 l.png|Echo IV (Haunting Chairs) sprite
File:Enemy 7205 l.png|Echo II (Hominid Dweller) sprite
File:Enemy 7206 l.png|Echo III (Hominid Dweller) sprite
File:Enemy 7207 l.png|Echo IV (Hominid Dweller) sprite
File:Enemy 7208 l.png|Echo II (Bird Dweller) sprite
</gallery>

====Biography Cards====
<gallery>
File:10-243 bio.PNG|10<sup>−43</sup> Witch bio
File:Witch_181.PNG|10<sup>−1</sup> Witch bio
File:Witch 2nd vio.png|10<sup>−3</sup> bio
File:Witch 3rd bio.png|10<sup>−5</sup> bio
File:Witch_186.png|10<sup>−7</sup> bio
File:Screenshot_2017-09-07-01-32-23.png|Echo I bio
File:Screenshot_2017-09-07-01-32-28.png|Echo II (Haunting Chairs) bio
File:Screenshot_2017-09-07-01-32-34.png|Echo III (Haunting Chairs) bio
File:Screenshot_2017-09-07-01-32-39.png|Echo IV (Haunting Chairs) bio
File:Witch_177.PNG|Echo II (Hominid Dweller) bio
File:Witch_178.PNG|Echo III (Hominid Dweller) bio
File:Witch_179.PNG|Echo IV (Hominid Dweller) bio
File:Witch_180.PNG|Echo II (Bird Dweller) bio
File:Memoria 1014 c.png|Memoria card
</gallery>

====Screenshots====
<gallery>
File:Symbol Witch 2nd.png
File:Symbol Witch 2nd name.PNG
File:Symbol Witch battle.PNG
File:Symbol2 side attack.PNG
File:Symbol2 vertical attack.PNG
File:Symbol Witch deferted.PNG|10<sup>−3</sup> defeated
File:Witch 3rd single attack 1.png|10<sup>−5</sup> attack 01
File:Witch 3rd single attack 2.png|10<sup>−5</sup> attack 02
File:Witch 3rd attack.png|10<sup>−5</sup> attack
File:Witch 3rd blast.png|10<sup>−5</sup> blast
File:witch 3rd side attack.png|10<sup>−5</sup> side attack
File:witch 3rd vertical attack.png|10<sup>−5</sup> vertical attack
File:Witch 4th side attack 1.PNG|10<sup>−7</sup> side attack
File:Witch 4th side attack 2.PNG
File:Witch 4th vertical attack 1.png|10<sup>−7</sup> vertical attack
File:Witch 4th vertical attack 2.PNG
File:Witch 4th deferted.PNG|10<sup>−7</sup> defeated
File:10-243 Battle.PNG
File:Symbol magia 1.PNG|10<sup>−43</sup> magia
File:Symbol magia 2.PNG
File:Symbol vertical attack.PNG|10<sup>−43</sup> vertical attack
File:10-243 side attack 1.PNG|10<sup>−43</sup> side attack
File:10-243 side attack 2.PNG
File:Symbol 01.png
File:Symbol 02.png
File:Symbol 03.png
File:Symbol 04.png
File:Symbol 05.png
File:Symbol 06.png
File:Symbol 07.png
File:80901 monument7 move.jpg
File:51198 map.jpg
File:51198 witch beam1.jpg
File:Memoria 1933.jpg
</gallery>

====Barrier====
<gallery>
File:Symbol Witch's Barrier 1.jpg
File:Symbol witch barrier.jpg
</gallery>

===Anime===
<gallery>
File:Episode 6 Symbol Witch 1.png|Echos and their barrier from [[Magia Record Episode 6: I'll Do Anything|Episode 6]]
File:Episode 6 Symbol Witch 2.png
File:Episode 6 Symbol Witch 3.png
File:Episode 6 Symbol Witch 4.png|{{Runes|WE HAVE THE RIGHT TO BREED}} (We have the right to breed)
File:Episode 6 Symbol Witch 5.png
File:Episode 6 Symbol Witch 6.png
File:Episode 6 Symbol Witch 7.png
File:Episode 6 Symbol Witch 8.png
File:Episode 6 Symbol Witch 9.png
File:Episode 6 Symbol Witch 10.png
File:Episode 6 Symbol Witch 18.png
File:Episode 6 Symbol Witch 20.png
File:Episode 6 Symbol Witch 21.png
File:Episode 6 Symbol Witch 22.png
File:Episode 6 Symbol Witch 23.png
File:Episode 6 Symbol Witch 24.png
File:Episode 6 Symbol Witch 25.png
File:Episode 6 Symbol Witch 26.png
File:Episode 6 Symbol Witch 27.png
File:Episode 6 Symbol Witch 28.png
File:Episode 7 Alina's Barrier 9.png|Echos and their barrier from [[Magia Record Episode 7: I Want to Go Home with You|Episode 7]]
File:Episode 7 Alina's Barrier 11.png
File:Episode 7 Alina's Barrier 12.png
File:Episode 7 Alina's Barrier 13.png
File:Episode 7 Familiar Battle 1.png
File:Episode 7 Familiar Battle 2.png
File:Episode 7 Familiar Battle 5.png
File:Episode 7 Familiar Battle 6.png
File:Episode 7 Familiar Battle 25.png
File:Episode 7 Kyoko Rescue 7.png
File:Episode_7_Kyoko_Rescue_22.png
File:Episode 7 Kyoko Rescue 24.png
</gallery>

==External Links==
* [https://www.youtube.com/watch?v=-SOBYROa7jA Recording of 10<sup>−1</sup>'s battle animations]
* [https://www.youtube.com/watch?v=ujFmx-N6rwY Recording of 10<sup>−3</sup>'s battle animations]
* [https://www.youtube.com/watch?v=mc0S7yH8gTY Recording of 10<sup>−5</sup>'s battle animations]
* [https://www.youtube.com/watch?v=HmXC115DoT0 Recording of 10<sup>−7</sup>'s battle animations]
* [https://www.youtube.com/watch?v=OB657WqS6iQ Recording of 10<sup>−43</sup>'s battle animations]


==Memoria Cards==
{{Magia Record Memoria Header}}
{{File:Memoria 1014 c.png}}
{{File:Memoria 1933 c.png}}
{{File:Memoria 1936 c.png}}
{{Magia Record Memoria Footer}}

== See Also==
*[[Puella Magi Madoka Magica Side Story: Magia Record]]
[[Category:Witches]]