Madoka Magica and Science: Difference between revisions

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[[File:Madoka Starry Sky.jpg|thumb|Madoka amongst the stars.]]
This page is dedicated to the scientific analysis of the series. This page is a placeholder for the following articles:
This page is dedicated to the scientific references within the series.


==Astronomy==
;[[Astronomy]]
Anonymous observes that nearly all the [[witch]]es and [[familiar]]s have names corresponding to [[wikipedia:celestial objects|celestial objects]] within the [[wikipedia:solar system|solar system]]:
:Witches and Familiars as asteroids, Kyubey as an alien, ...
;[[Population dynamics]]
:"Magical Girls are born from wishes. Witches are born from curses" ([[Kyubey]], [[Episode 2]]). Let us see how both populations evolve over time, and whether or not the Earth has a chance of surviving against witches in the end.
;[[Thermodynamics|Thermodynamics and Entropy]]
:Kyubey's speech about Entropy in [[Episode 9]] led to an uproar among fans for its inaccuracy. Let us see why.


{|class="wikitable" style="line-height: 1.6em; width: 100%;"
[[Category:Science| ]]
! style="text-align: center; background: #efefef; width: 20%;"|Name
! style="text-align: center; background: #efefef; width: 30%;"|Celestial object
! style="text-align: center; background: #efefef; width: 50%;"|Description
|-
![[Gertrud]]
|    710 Gertrud
|a minor planet orbiting the sun
|-
!Anthony
|    272 Antonia
|an asteroid
|-
!Adelbert
|    719 Albert
|An asteroid
|-
![[Suleika]]
|    563 Suleika
|a minor planet orbiting the sun
|-
!Ulla
|    375 Ursula
|a large main-belt asteroid
|-
![[Charlotte]]
|Charles
|    a lunar crater
|-
!Pyotr
|    2720 Pyotr Pervyj
|a main-belt asteroid
|-
![[Elly]]
|    2650 Elinor
|an asteroid
|-
!Daniyyel
|    Daniell
|a lunar crater
|-
!Jennifer
|    6249 Jennifer
|an asteroid
|-
![[Albertine]]
|    1290 Albertine
|an asteroid
|-
!Anja
|    265 Anna
|an asteroid
|-
![[Gisela]]
|    352 Gisela
|an asteroid
|-
!Dora
|    668 Dora
|a main-belt asteroid
|-
![[Elsa Maria]]
|    182 Elsa <br />    170 Maria
|both asteroids
|-
!Sebastian
|    1482 Sebastiana
|an asteroid
|-
![[Uhrmann]]
|    possibly Hermann or 10239 Hermann
|a lunar crater/a main belt asteroid.
|-
!Bartels
|    17823 Bartels
|a main-belt asteroid
|-
![[Oktavia]]
|    598 Octavia
|an asteroid
|-
!Holger
|    9266 Holger
|a main-belt asteroid
|-
![[speculah:Walpurgis Night|Walpurgis]]
|    256 Walpurga
|an asteroid
|-
![[Isadel]]
|    210 Isabella
|a main-belt asteroid
|-
![[Patricia]]
|    436 Patricia
|a main-belt asteroid
|-
![[Roberta]]
|    335 Roberta
|a large main-belt asteroid
|-
![[Kriemhild Gretchen]]
|    242 Kriemhild
|a main-belt asteroid.
|}
 
==Biology and the Food Chain==
[[file:Population model.png|thumb|Graphical representation of population model used.]]
 
<blockquote>''"You know about the food chain, right? I'm sure you learned about it in school.  The witches eat the weak humans.  And we eat those witches.  That's the way stuff works, right?"'' <br />-'''[[Kyouko]]''' in [[Episode 5]]</blockquote>
 
Both the [[magical girl]] and [[witch]] populations draw their numbers from the general human population.  For this population model we assume that both are in a vast minority in comparison to the overall human population, and the loses that result from magical activities contribute insignificant changes to it.
 
===Population Modeling===
The magical girl population ['''M(t)'''] increases by the number of new girls QB contracted ['''C'''], and decreases by the rate of them dying ['''D'''] or becoming ['''B'''] witches.  The Witch population ['''W(t)'''] increase by the number of matured  [[familiar]]s ['''F'''] per witch as well as the rate of magic girls that became witch, but decreases when magic girls hunt and kill ['''K'''] them.  These premises can be summarized as following:
 
*ΔM(t)= C - D * M(t) - B *M(t) = C - (D + B) * M(t)
*ΔW(t)= B * M(t) + F * W(t) - K * M(t) = F * W(t) + (B - K) * M(t)
::''Where '''D, B, F, K''' are values between [0,1], while '''C, M(t), and W(t)''' are whole numbers.''
 
===Population at Equilibrium===
If both populations are in equilibrium, then there is no changes to both the witch and magical girl population ['''ΔM(t)''' = 0 & '''ΔW(t)''' = 0].  It follows that the number of magic girls contracted need to balance the number that died or become witch in the same period ['''C = (D + B) M(t)''']; and the number of witches matured from minions balances out numbers contributed by magic girls ['''N * W(t) = (K - B) M(t)'''].
 
'''Observations''':
*Every dead magic girl is one that did not become a witch.  For [[Kyuubey]], whose goal is to harvest energy from the magic girl-to-witch transformation, every death meant time wasted contracting the girl.  It makes sense for him to design a system where most Witches are weaker than Magic Girls in order to reduce magic girl casualty rate. ['''B > D''']
*If magic girls are stronger than witches, it follows that the typical Magic Girl will kill multiple Witches before becoming one ['''K - B''' > 0].  Because of this, there's a need for an alternative source for creating witches.  This explains why while Kyuubey cares only of the energy from Magic Girl-Witches transformation, the supplementary system of witch growth from familiars exist.
*At equilibrium, the magic girl population is equal to '''C / (D + B)'''.
*At equilibrium, the witch population is '''(B - K) M(t)'''.  If the Magic Girl population is also in equilibrium, then the witch population is '''C*(B - K)/(D + B)'''.
 
===General Solution===
[[File:Matlab witches-MG population 2.png|thumb|One possible scenario for changes in magical girls and witches over time]]
The general solution for the witch and magic girl populations are:
*[[File:Closed form for M(t).png]]
*[[File:Closed form for W(t).png]]
for some constant α and β. If we assume witches and magic girls are introduced by QB's civilization, thus initial population of both at the system's introduction were zero ['''M(0)=0 W(0)=0'''].  W(t) and M(t) becomes:
*[[File:Closed form of M(t) at M(0)=0.png]]
*[[File:Closed form of W(t) at W(0)=0.png]]
 
'''Observations''':
*The magic girl population will always reach equilibrium at '''C / (D + B),'''  regardless of initial number of magical girls or actual values of '''C, D, or B'''.  This restrain by Kyuubey's ability to contract new girls may explain why there seems to be so few magical girls around.
*Even when a significant number of magic girl is introduced initially, their numbers will eventually whithered down to sustainable population level of '''C/ (D + B)'''.  This is a natural consequence of limited linear growth rate and independent of environmental or crowding stresses.
*In contrast, the witch population never reach equilibrium.  The number of witches will fluctuate minutely at the initial period, but inevitably the minion growth ['''e^Nt'''] will outpace all other variables, and the population will explode into exponential growth.  The growth may be capped due to human depopulation from witch activities, but at this point the initial premises of the model breaks down.
*Due to the above, any planet with this magic girl and witch system in place is inevitably doomed to extinction.  It is not possible to save the human population, with exception of exterminating all witches and magic girls.  This may explain why Kyuubey simply abandoned Earth rather than attempt sustainable farming of the planet.
[[Category:Articles]]
[[Category:Fanmade analysis]]
[[Category:Science]]
 
== Thermodynamics and Entropy ==
[[File:QB loves entropy.jpg|thumb|[[Kyuubey]] loves Entropy too!]]
[http://youtube.com/watch?v=TbRSd2THTUQ This BBC special] is an excellent refresher course on Entropy.
 
Assume Incubators are trying to sustain the entire universe using the misery of little girls. According to data gathered by the Wilkinson Microwave Anisotrophy Probe (WMAP), energy density of the universe comes down to roughly 9.9 x 10^-30 g/cm3, or 0,889767627 joules/km^3. The expansion rate of the universe, again as determined by WMAP observations is roughly 71.9 (km/s)/Mpc, ignoring other studies. The minimum radius of the universe, as determined by cosmic microwave background radiation data, is 12 gigaparsecs. Consequently, the universe gains at least 862800 kilometers of radius per second, which comes down to a volume gain of 1.48656647 × 10^54 kilometers cubed per second.
 
Thus, in order to maintain the energy density of the universe (admittedly, though, there are better ways to preserve life) 1.32269872 × 10^54 joules is required every second. Let us use high estimates and say that there is one magical girl for every 1,000 people. As of now, there are roughly 6,9 billion living people, so there are 6,900,000 magical girls across the world. Assume that every magical girl defeats a witch every two days, and hands over her Grief Seed to an Incubator for its energy to be collected. This comes down to roughly 40 witches being defeated every second. Therefore, if the energy density of the universe is to be maintained, every Grief Seed needs to have an energy output of at least 3.31249766 × 10^52 joules. What can you do with this sort of energy?
 
:'''A'''. Supply the Earth’s energy needs for roughly 8,6 octillion years, a timespan 6,2802117 × 10^17 times the current age of the universe.
 
:'''B'''. Create 3,68565071 × 10^35 kilograms of any matter (except cheese.) This comes down to about 184027 sun-sized stars, 61 billion Earth-sized planets or a single supermassive black hole with a radius of 547298,036 kilometers, roughly 1,4 times the distance between Earth and the Moon.
 
:'''C'''. In a single year, enough energy is collected to create roughly 10 galaxies the size of our Milky Way.
 
:'''D'''. Create a single explosion a few hundred thousand times stronger than any gamma ray burst we’ve observed so far. This would end most, if not all life (at least carbon-based life as we know it) pretty much everywhere from Earth to Andromeda galaxy.”
 
Personally, the only reason I can muster for this bizzare turn is that the writers want to change the setting. In the previous episodes, QB has become a bit too obviously antagonistic, making him a villain of sorts. But this development changes things, making QB not a villain but an act of god. Something outside human power. So the objective here becomes not “winning,” but rather “surviving”

Latest revision as of 03:55, 4 July 2011

This page is dedicated to the scientific analysis of the series. This page is a placeholder for the following articles:

Astronomy
Witches and Familiars as asteroids, Kyubey as an alien, ...
Population dynamics
"Magical Girls are born from wishes. Witches are born from curses" (Kyubey, Episode 2). Let us see how both populations evolve over time, and whether or not the Earth has a chance of surviving against witches in the end.
Thermodynamics and Entropy
Kyubey's speech about Entropy in Episode 9 led to an uproar among fans for its inaccuracy. Let us see why.
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